C-SURE CROSS SECTIONS FOR UNRESOLVED

RESONANCES FROM ENDFIB

G.L. Singer and R.A. Grimesey

nerojet nuclear Company1 4

NATIONAL REACTOR TESTING STATION

DATE PUBLISHED-MAY 1972

Idaho Falls, ldaho - 83401

PREPARED FOR THE

U. S. ATOMIC ENERGY COMMISSION IDAHO O P E R A T I O N S OFFICE U N D E R C O N T R A C T AT(10-11-1375

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER

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L E G A L N O T I C E

T h i s r e p o r t was p r e p a r e d a s a n a c c o u n t ~ f work sponsored by t h e U n i t e d S t a t e s Government . N e i t h e r the U n i t e d S t a t e s n o r t h e U n i t e d S t a t e s A t o m i c Energy Commission, n o r any o f t h e i r emp loyees , n o r any o f t h e i r c o n t r a c t o r s , s u b c o n t r a c t o r s , o r t h e i r employees, makes any w a r r a n t y , e x p r e s s o r i m p l i e d , o r assumes any l e g a l l i a b i l i t y o r r e s p o n s r b ~ l i t y f o r t h e a c c u r a c y , c o m p l e t e - ness o r u s e f u l n e s s o f any i n f o r m a t i o n , a p p a r a t u s , p r o d u c t o r p r o c e s s d i s - c l o s e d , o r r e p r e s e n t s t h a t i t s use w o u l d n o t i n f r i n g e p r i v a t e l y owned r i g h t s .

Mathematics and Computers TID-4500

C -SURE

CROSS SECTIONS FOR UNRESOLVED R E S ~ C E S FROM ENDF /B

G . L . S i n g e r and R. A . G r i m e s e y

AEROJET NUCLEAR COMPANY

Date Published - May 1972

PREPARED FOR THE U. S. ATOMIC ENERGY COMMISSION IDAHO OPERATIONS OFFICE

UNDER CONTRACT NO. AT(10-1)-1375

ABSTRACT

The C-SURE code c a l c u l a t e s unresolved c a p t u r e , f i s s i o n , and compound

e l a s t i c s c a t t e r i n g c r o s s s e c t i o n s from ENDF/B d a t a a t ene rg i e s s p e c i f i e d

by input . These c a l c u l a t i o n s inc lude Doppler broadening t o provide tem-

p e r a t u r e dependent d a t a , so t h a t se l f - sh ie ld ing can au toma t i ca l ly be

accounted f o r i n t h e unresolved resonance c a l c u l a t i o n .

The program inc ludes t h e fol lowing f e a t u r e s : miniminn card i n p u t ,

a n ENDF'/B update f a c i l i t y , and t h e op t ion of a s e p a r a t e p r i n t o u t of t h e

s-wave and p-wave unresolved resonance con t r ibu t ions .

CONTENTS

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . i i I . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . 1

I1 . UNRESOLVED RESONANCE CALCULATIONS . . . . . . . . . . . . 2

. . . . . . . . . . . . . . . . 1 D I S C U S S I O N OF EQUATIONS 2

2 . D E F I N I T I O N O F TERMS . . . . . . . . . . . . . . . . . 1 2

. . . . . . . . . . . . I11 . SMOOTH CROSS SECTION CALCULATIONS 1 6

I V . INPUT INSTRUCTIONS . . . . . . . . . . . . . . . . . . . . 1 7

. . . . . . . . . . . . . . . . . . . . . 1 TYPES O F INPUT 1 7

2 . PROGRAMCONTROLDATA . . . . . . . . . . . . . . . . . . 1 7

. . . . . . . . . . . . . . . . . . . . . 3 . E N D F I B DATA 24

3.1 C o m p l e t e E N D F I B D a t a . . . . . . . . . . . . . . 24 3.2 E N D F I B C h a n g e D a t a . . . . . . . . . . . . . . . 24

. . . . . . . . . . . . . . . . . . . . . . . V PROGRAM OUTPUT 2 5

1 . PRINTED OUTPUT . . . . . . . . . . . . . . . . . . . . 25

. . . . . . . . . . . . . . . . . 2 . PUNCHED CARDOUTPUT 2 5

3 . ERRORMESSAGES . . . . . . . . . . . . . . . . . . . . 2 5

V I . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . 2 7

APPENDIX A -- INTEGRATIONS OVER THE CHI-SQUARED D I S T R I B U T I O N S . . 2 8

. . . . . . . . . . . . . . . . APPENDIX B -- INPUT/OUTPUT U N I T S 32

. . . . . . . . . . . . . APPENDIX C -- SUBROUTINE D E S C R I P T I O N S 33

.. . . . . . . . . . . . . . . . . . . . . APPENDIX D FLOW CHART 3 6

. . . . . . . . . . . . . . . . .. APPENDIX E SAMPLE PROBLEM S E T 37

TABLES

. . . . . . . . . . . . . . . . . . I C a r d X n p u t Ins t ruc t ions 18

. . . . . . . . . . . . . . . . . . . . . . . A.1 . V a l u e s o f p i 3 1

. . . . . . . . . . . . . . . . . . . . . . A.11 . V a l u e s of 31

iii

The C-SURE code c a l c u l a t e s Doppler broadened r a p t u r e , f i s s i o n , and

compound e l a s t i c s c a t t e r i n g c ross sec t ions a t an a r b i t r a r y s e t of energy

po in t s f o r t h e unresolved resonance range. The smooth background c r o s s

s e c t i o n s may be ca lcu la t ed o u t s i d e t h e unresolved resonance range a s w e l l

a s i n t h e unresolved range. The code w i l l read input e i t h e r from an

ENDFIB t ape o r from cards based on t h e ENDF/B format.

Shielded c ross sec t ions may be ca lcu la t ed wi th in t h e framework of

t h e Narrow Resonance Approximation w i t h l i t t l e a d d i t i o n a l computation

time required r e l a t i v e t o i n f i n i t e l y d i l u t e c ross sec t ions .

A d e r i v a t i o n of t h e equations used by t h e code is included along

wi th s u i t a b l e references and d iscuss ion .

Options o r f e a t u r e s of t h e C-SURE code include:

1. I n i t i a l d e f a u l t va lues and, f o r stacked runs , s to rage of previous

input va lues reduce t o a minimum t h e number of va lues requi red a s

input .

2 . The program can genera te t h e mesh a t which c ross sec t ions a r e evalu-

a ted or t h e user may input h i s own mesh.

3 . ENDFIB input is from e i t h e r t ape o r cards.

4 . The ENDFIB d a t a from a d a t a t ape may be punched i n t h e format requi red

f o r C-SURE card input .

5. Indiv idual cards of t h e i n i t i a l ENDFIB d a t a may be replaced i n sub-

sequent runs of a s e r i e s .

6 . A s i n g l e i so tope of an ENDFIB m a t e r i a l may be se l ec ted f o r processing.

7. Smooth s c a t t e r i n g , ' capture , and f i s s i o n c r o s s sec t ions may be calcu-

l a t e d beyond t h e unresolved resonance range.

8. The p r i n t o u t s of t h e s-wave and p-wave unresolved resonance con t r i -

but ions may be separa te .

11. UNRESOLVED RESONANCE CALCULATIONS

1. DISCUSSION OF EQUATIONS

C-SURE c a l c u l a t e s unresolved c a p t u r e , f i s s i o n , and compound e l a s t i c -

s c a t t e r i n g c r o s s s e c t i o n s from ENDFIB d a t a L b 1 a t ene rg i e s s p e c i f i e d by

input . These c a l c u l a t i o n s inc lude Doppler broadening t o provide tempera-

t u r e dependent d a t a , so t h a t s e l f - sh i e ld ing can au toma t i ca l ly be accounted

f o r i n t h e unresolved resonance c a l c u l a t i o n .

I n t h e fol lowing s e c t i o n , key d e f i n i t i o n s w i l l b e suppl ied and a

complete list of d e f i n i t i o n s w i l l be provided i n t h e fol lowing s e c t i o n .

The ENDFIB d a t a f o r t h e unresolved range con ta in a complete s e t of

average o r t abu la t ed resonance parameters f o r each R-state and J - s t a t e .

Energy dependent average parameters < D > < r > ' , <I' > , < r > R , J ' n R,J Y R,J f R,J '

and < r > a r e s p e c i f i e d f o r each o r b i t a l angular momentum s t a t e R of t h e R , J

neu t ron and each t o t a l angular momentum s t a t e J of t h e compound nucleus .

I n a d d i t i o n , t h e number of degrees of freedom, p f o r t h e s t a t i s t i c a l R , J '

chi-squared d i s t r i b u t i o n of each average p a r t i a l width < r k > i n t h e R J

unresolved range i s spec i f i ed . The average l e v e l spacing < D) is energy R, J

dependent, bu t is assumed cons tan t a s f a r a s s t a t i s t i c a l f l u c t u a t i o n s a r e

concerned-. The unresolved equat ions i n C-SURE permit R = 0, 1, 2, f o r s,

p, and d wave neut rons , r e s p e c t i v e l y , . a n d up t o f o u r J s t a t e s f o r p and

d wave neut rons (only two J s t a t e s are p o s s i b l e f o r s wave neut rons cor-

responding t o t h e two p o s s i b l e s p i n o r i e n t a t i o n s of t h e i n c i d e n t neut rons) .

The equat ions from which C-SURE c a l c u l a t e s t h e pointwise unresolved

resonance c r o s s s e c t i o n s a r e based upon f i n i t e range reso lved resonance

i n t e g r a l s i n t h e narrow resonance (NR) approximation f o r a mixture of 151

~ - i so topes .

I n t h e f i n a l form of t h i s equat ion , t h e denominator permi ts t h e

e f f e c t s of f i r s t o rde r ove r l ap of resonances i n t h e (R,J) sequences of a

g iven i so tope . I (E) i n t h e numerator i s t h e cap tu re , f i s s i o n , o r r

compound e l a s t j c s c a t t e r i n g c r o s s s e c t i o n of t h e p a r t i c u l a r sequence (R,J)

of t h e i so tope being considered. The average parameters given i n t h e

ENDFIB l i b r a r y a r e sub jec t t o s t a t i s t i c a l f l u c t u a t i o n i n t h e unresolved

range i n each sequence (R,J) according t o chi-squared d i s t r i b u t i o n s where

t h e p r o b a b i l i t y of a p a r t i c u l a r va lue of t h e v a r i a b l e r i s g iven by

where n is t h e number of degrees of freedom i n t h e chi-squared d i s t r i b u -

t i o n , r* (t) i s t h e normalized gamma o r f a c t o r i a l func t ion (not a l e v e l

width) , and d,J

The < r > a r e t h e average p a r t i a l widths g iven i n t h e ENDF/B l i b r a r y R , J

f o r t h e unresolved range and rR y J i s a va lue i n t h e chi-squared X

s t a t i s t i c a l d i s t r i b u t i o n .

A t i n f i n i t e d i l u t i o n , a n asymtot ic 1 i E . f l u x i s assumed and Equation

(1) f o r t h e c a p t u r e , f i s s i o n , and compound e l a s t i c c r o s s s e c t i o n s a t an

energy (E) y i e l d s , 181

NLS NJS, 2n

<u,(E)> = k2 -'x R=O J < D > R . , ~ ~ o s ~ $ R

NLS NJSR g~ '

= iS xzD>R , Jc0s2+ R=O J

NLS NJSR 2IT2 r (E) Q (E) -2% (E) r (E) s in2$

k2 + - C C < D > ~ R=O J

(5) where NLS is t h e number o f . i n c i d e n t n e u t r o n ' o r b i t a l angular momentum

s t a t e s R and NJSR is t h e number of compound nuc'leus open decay channels ,

each wi th t o t a l angular momentum J , f o r a g iven R s t a t e . For each open

decay channel ,

3

where I is t h e ground s t a t e s p i n of t h e t a r g e t nucleus.

The < ) i n Equations ( 3 ) , (4) , and (5) imply s u i t a b l e f l u c t u a t i o n

averages of t h e p a r t i a l widths rx f o r t h e s i n g l e l e v e l resonance formulas

over t h e chi-squared s t a t i s t i c a l d i s t r i b u t i o n s given by Equation ( 2 ) .

Equations ( 3 ) , (4 ) , and (5) a r e only v a l i d a t i n f i n i t e d i l u t i o n f o r

t h e n a t u r a l l i n e shape of t h e Bre i t Wigner s i n g l e l e v e l resonance formula.

To inc lude t h e e f f e c t s of Doppler broadening and f i n i t e s e l f s h i e l d i n g

where t h e f i r s t o rde r e f f e c t s of resonance ove r l ap between d i f f e r e n t

sequences of a m a t e r i a l a r e p re sen t , a more s o p h i s t i c a t e d approximation

is requi red . The gene ra l f e a t u r e s of t h i s approximation can be obtained

from t h e so-cal led two sequence approximation f o r a s i n g l e i so tope . 151

The two sequences r e f e r r e d t o h e r e could be considered t o be t h e two s p i n

s t a t e s f o r s-wave neutrons of t he ' i so tope . Consider ZT(E) i n t h e numera-

t o r and denominator of Equation ( I ) ,

where z1 and C 2 a r e t h e resonant c r o s s s e c t i o n s f o r t h e f i r s t and t h e r r

second sequences, r e s p e c t i v e l y , and each inc ludes a sum over a l l reson-

ances i n t h e sequence. The i n d i v i d u a l sequences a r e t r e a t e d a t t h i s

p o i n t a s i f t h e resonances were resolved.

The e f f e c t s of o t h e r sequences and o t h e r i so topes a r e present i n

t h e two sequence approximation only t o t h e ex t en t t hey a r e present i n

C t h e t o t a l s c a t t e r i n g c r o s s s e c t i o n i n t h e v i c i n i t y of t h e resonances P

under cons idera t ion . I n t h e approximations which fo l low, t h e assumptions

i n genera l a r e based on t h e v a l i d i t y of t h e NR approximation i n t h e un-

resolved range and t h e f a c t t h a t C > C: + C 2 which is t h e usua l case . P r

I n t h e event t h a t t h e s e cond i t i ons a r e not p r e s e n t , i t imp l i e s t h a t

h igher order terms i n t h e expansions a r e not n e g l i g i b l e and t h a t t h e . ,

r e s u l t a n t s i n g l e sequence equat ions do not adequate ly r ep re sen t resonance

over lap e f f e c t s . Higher o rde r terms have been der ived and appl ied under

t h e s e condi t ions i n f a s t r e a c t o r c a l c u l a t i o n s ; [51 however, t h e s e

extens ions of t h e theory a r e beyond t h e scope of t h e present d i scuss ion

and r e q u i r e a more cumbersome development.

The numerator f o r t h e resolved c a p t u r e c r o s s s e c t i o n of t h e f i r s t

sequence is expanded i n t h e fol lowing way t o c l a r i f y t h e f i r s t o rde r

e f f e c t s of resonance over lap between t h e two sequences.

I n ob ta in ing Equation (9) from Equation (8), t h e narrow resonance

assumption was employed i n t h e l a s t s t e p t o e l i m i n a t e a l l bu t t h e i ' t h

resonance i n t h e denominators of t h e two sequences. The resonances of

each sequence a r e assumed t o be spaced f a r enough a p a r t so t h a t a s t h e

i ' t h resonance i n t h e numerator i s encountered, on ly t h e e f f e c t s of t h a t

same resonance a r e encountered i n t h e denom.inator. The term i n t h e

bracke t of Equation (9) i s a smal l c o r r e c t i o n term f o r t h e over lap of t h e

second sequence resonances on t h e f i r s t sequence.

The denominator i s expanded i n a s l i g h t l y d i f f e r e n t fash ion .

where t h e narrow resonance assumption was aga in employed i n t h e l a s t s t e p .

The average e f f e c t i v e c r o s s s e c t i o n f o r t h e f i r s t sequence resonances is

then Equation (9) d iv ided by Equation (11).

The parentheses i n t h e numerator con ta in t h e f i r s t o rde r e f f e c t s of

resonance over lap of second sequence resonances on t h e f i r s t sequence.

The parentheses i n t h e denominator c o n t a i n t h e f i r s t o rde r e f f e c t s of t h e

mutual over lap of t h e two sequences. We w i l l now demonstrate t h a t t h e

f i r s t o rde r over lap e f f e c t of second sequence resonances on t h e f i r s t

sequence approximately cance l s between t h e numerator' and denominator of

Equation (12). I f t h e numerator of Equation (12) i s expanded we o b t a i n ,

The second i n t e g r a l i s t h e i n t e g r a l of t h e product of t h e terms of t h e

two sequences. Since t h e two sequences a r e independent, t h e r e l a t i v e

p o s i t i o n s of i nd iv idua l resonances i n t h e two sequences a r e randomly

d i s t r i b u t e d . I f t h e narrow resonance assumption i s v a l i d a t a l l , i t can

be demonstrated t h a t t h i s random supe rpos i t i on of t h e two sequences w 5 l l

r e s u l t i n only an occas iona l coincidence between ind iv idua l resonances

i n t h e two sequences. When t h i s i s t r u e , t h e c o n t r i b u t i o n from t h e I

second sequence t o t h e i n t e g r a l over one resonance i n t h e f i r s t sequence

w i l l be approximately 1 / C a cons tan t f o r t h e i n t e g r a t i o n , and t h e i n - P'

t e g r a l of t h e product may be rep laced by t h e product of s e p a r a t e i n t e g r a l s

over t h e two sequences t o f i r s t o rder . Conversely, tirst sequence reson-

ances a r e only occas iona l ly i n . co inc idence wi th second sequence resonances

a n d . t h e same is t r u e f o r t h e i n t e g r a l s of t h e second sequence. The

numerator of Equation (12) may then be w r i t t e n a s

where t h e 1 /E dependence of t h e in tegrand has been f ac to red o u t s i d e t h e

integrand a s 1 / ( E -El) , a slowly vary ing f a c t o r i n t h e in tegrand r e l a t i v e 2

t o t h e resonances i n t h e two sequences.

The same approximation i s appl ied t o t h e over lap terms i n t h e de-

nominator of Equation (12) and Equation (12) becomes

The v a l i d i t y of t h i s approximat5on depends on t h e v a l i d i t y of t h e

narrow resonance assumption and t h e l e v e l d e n s i t y of t h e two sequences.

I f t h e resonances a r e t r u l y narrow so t h a t t h e resonances i n each se-

,quence approach a l i n e s p e c t r a t hen t h e product i n t e g r a l w i l l y i e l d

r e s u l t s very c l o s e t o t h e i n t e g r a l of t h e s e p a r a t e sequences. I n g e n e r a l ,

t h e higher t h e energy, t h e more v a l i d i s t h e narrow resonance approxima-

t i o n . The v a l i d i t y of t h e NR approximation depends on t h e p r o b a b i l i t y

of a neutron s c a t t e r i n g a c r o s s t h e resonance i n a s i n g l e c o l l i s i o n . The

s i n g l e c o l l i s i o n s c a t t e r i n g i n t e r v a l i s g iven by E(1-a) and hence v a r i e s

a s E. The width of t h e resonances v a r i e s a s r0 6 a 6. By t h i s s imple n

comparison i t i s seen t h a t a s energy i n c r e a s e s , t h e width of t h e s i n g l e

c o l l i s i o n i n t e r v a l w i l l even tua l ly over take t h e resonance widths making

t h e NR approximation v a l i d even though it may. no t be v a l i d i n t h e reso lved

resonance range. ~.

The bracke t i n t h e numerator con ta ins t h e e f f e c t s of f i r s t o rde r

ove r l ap of second sequence resonances on t h e f i r s t sequence. Th i s term

is - a l so present i n t h e denominator a s a f a c t o r of t h e f i r s t sequence

i n t e g r a l . I f we d i v i d e t h e numerator and denominator of Equation (13)

by t h e bracke t i n t h e numerator and r e a r r a n g e . t h e terms i n t h e denomina-

t o r we o b t a i n

c1 +C r P

1 i

<9> = (14)

I f t h e narrow resonance assumption i s v a l i d , t h e second bracke t i n

t h e denominator w i l l be approximately 1.0. This second bracke t i n t h e

denominator i s s i g n i f i c a n t when t h e r e is s t rong ove r l ap between t h e two

sequences. Experimental evidence i n d i c a t e s t h a t only i n t h e c a s e o f ex-

treme Doppler broadening i n mixtures of f i s s i l e i s o t o p e s where t h e l e v e l

d e n s i t y is high does t h e t h i r d term become very s i g n i f i c a n t . Self over-

l a p e f f e c t s i.n t h e numerator of Equation (14) a s w e l l a s second o rde r

ove r l ap e f f e c t s between d i f f e r e n t sequences have not been included i n t h e

numerator of Equation (14). The i n c l u s i o n of t h e s e e f f e c t s r e q u i r e a more

s o p h i s t i c a t e d development t han we a r e desc r ib ing here . [ 51

Neglect of the . second bracke t i n ' the denominator of Equation (14)

y i e l d s an equat ion i d e n t i c a l t o one f o r a s i n g l e sequence expansion us ing

t h e narrow resonance assumption.

This equat ion i s c a l l e d t h e S ing le Sequence Approximation. It i s

widely used f o r t h e c a l c u l a t i o n of unresolved resonance c r o s s s e c t i o n s

' fo r f a s t r e a c t o r s . [ 3 1 equa t ion (15) is t h e one t h e unresolved equat ions

of C-SURE and PHROG a r e .based upon. It is t h e equiva len t of t h e e f f e c t i v e

resonance i n t e g r a l f o r t h e s i n g l e sequence approximation wi th a cor rec-

t i o n i n t h e denominator f o r f l u x pe r tuba t ion ac ros s t h e resonances. The

e f f e c t of o t h e r sequences and a d d i t i o n a l m a t e r i a l s is included only i n

s o f a r a s t hey a r e p re sen t i n C i n t h e Narrow Resonance Assumption. P

I f Equation (15) i s d iv ided through by Nay t h e atom d e n s i t y of t h e

absorber , and t h e Doppler broadened s i n g l e l e v e l resonance formula sub-

s t i t u t e d f o r t h e c r o s s s e c t i o n s neglec t ing i n t e r f e r e n c e s c a t t e r , Equa-

t i o n (15) becomes

where t h e sum over (R,J) i nc luaes t h e c o n t r i b u t i o n t o t h e cap tu re c r o s s

s e c t i o n from a l l neut rons R and a l l s p i n s t a t e s J f o r a g iven R. a is P

now t h e s c a t t e r i n g c r o s s s e c t i o n per absorber atom. The i n t e r v a l E2-El

about E is small enough t h a t 1 / E can be f a c t o r e d ou t of t h e denominator

y e t l a r g e enough t o i nc lude many narrow resonances. I f t h e resonances

a r e t r u l y narrow t h e i n t e g r a t i o n limits can b e extended from zero t o

i n f i n i t y s i n c e t h e resonance c r o s s s e c t i o n i s only l a r g e a t t h e midpoint

energy E between E2 and El. The i n t e r v a l E2-El i s equal t o t h e number

of resonances Ni t imes t h e average l e v e l spacing <D> f o r a g iven R,J

sequence (R,J). The sum over t h e resonances i then becomes, i n t h e

l i m i t , a f l u c t u a t i o n i n t e g r a l over t h e s t a t i s t i c a l chi-square d i s t r i b u -

t i o n s f o r each spec i e s .

where P ( r ) is g iven by Equation (2) and n

10

J(0,B) i s a func t ion of t h e p a r t i a l width f l u c t u a t i o n i n t e g r a l s through

t h e dependence .of 0 and B on t h e p a r t i a l widths. The compound e l a s t i c

c r o s s s e c t i o n i s g iven by

where i t is r equ i r ed t h a t x g p = 2R+1 and p i s t h e number of J R,J . R Y J J

degrees of freedom f o r t h e neutron width of a p a r t i c u l a r J s t a t e co r r e s -

ponding ' to t h e number of open decay channels f o r t h e compound nucleus

wi th t o t a l angular momentum J formed wi th neut rons of angular momentum R .

For f i s s i o n a b l e . i so topes , s t a t i s t i c a l f l u c t u a t i o n s a r e p r e s e n t . f o r ::

both t h e f i s s i o n width and t h e neutron width and t h e equat ions become [ 3 1

I f i n f i n i t e l y d i l u t e c r o s s s e c t i o n s a r e reques ted , t h e denominator

i n each of t h e above equat ions is e f f e c t i v e l y s e t equal t o 1.0 and t h e

numerator i s evaluated a t a = l o 7 . I n t h i s ca se , t h e numerator of P

Equations (20) , (21) , and (22) y i e l d s a r e s u l t i d e n t i c a l t o Equations ( 3 ) ,

( 4 ) , and ( 5 ) f o r f i s s i o n a b l e i so topes . For o the r va lues of 8 and B ,

J (8 ,B) is i n t e r p o l a t e d from t a b l e s and both t h e numerator and denominator

a r e evaluated.

Equations (17) , (19) , (20) , (21) , and (22) w i l l y i e l d pointwise

unresolved resonance c r o s s s e c t i o n s a t e i t h e r i n f i n i t e d i l u t i o n o r f i n i t e

d i l u t i o n w i t h temperature dependence. The energy mesh can be inpu t t o

t h e code and is completely a r b i t r a r y . The input parameters f o r t h e un-

reso lved range of a g iven m a t e r i a l may be e i t h e r read d i r e c t l y o f f a n

ENDFIB t ape from F i l e 2 and F i l e 3 o r input by ca rds when f i t t i n g c r o s s

s e c t i o n s t o experimental d a t a . When F i l e 3 d a t a a r e p re sen t a s w e l l a s

F i l e 2 d a t a , background c ros s s e c t i o n s a r e ca l cu la t ed over t h e same energy

mesh and added t o t h e compound c r o s s s e c t i o n s a t each energy poin t .

2. DEFINITION OF TERMS

A complete l i s t i n g of a l l t h e v a r i a b l e s used i n t h e above equat ions

w i l l now be g iven

i s t h e summation over a l l J and R-states of a g iven i so tope

R , J

< D > ~ , is t h e average l e v e l spacing f o r each E , J s t a t e of t h e compound nucleus

<r (E) J

i s t h e average t o t a l width a t E f o r t h e s p i n s t a t e R , J

<ry (E) >L, i s t h e average r a d i a t i o n width a t E

< r f ( ~ ) > , , i s t h e average f i s s i o n width a t energy E

< r x ( ~ ) > , y J i s a p a r t i a l width permit ted i n t h e ENDFIB f i l e f o r a l l o the r extraneous open decay channels , eg, d i s c r e t e l e v e l i n e l a s t i c e x c i t a t i o n (<Tx> i s not p r e s e n t l y processed by C-SURE) R Y J

<yo > is t h e average reduced neut ron width n

R Y J

LI i s t h e number of degrees of freedom i n t h e neut ron width ' y J d i s t r i b u t i o n

V (E) i s t h e p e n e t r a b i l i t y of t h e t a r g e t nucleus f o r i n c i d e n t ' neutrons of ;ngular momentum

where

a, t h e opaque nucleus channel r a d i u s , e q u a l s 10.123 A: + .08]

@ L i s t h e phase s h i f t and

@ 2 = 6 - tan-' (3?;2 - ) where P" = kRa

and where

R i s t h e noncompound ( p o t e n t i a l ) s c a t t e r i n g l e n g t h of t h e a absorber ( i n u n i t s of 10'12cm.) a s given i n F i l e 2 of ENDFIB.

The parameters <I' Y (E)>Ry J , < rf (E)>%, J , < f : ( ~ ) > ~ , J , and <6>&, a r e

e i t h e r a cons t an t va lue f o r a given R , J s t a t e o r , i f t abu la t ed d a t a

v a l u e s a r e given, a r e determined a t each energy by i n t e r p o l a t i o n .

The f l u c t u a t i o n i n t e g r a l s i n ~ ~ u a t i o n s (20) - (22) can be represented

where f ( x ) r e p r e s e n t s t h e argument of t h e in tegrands .

Equation (23) r e p r e s e n t s i n t e g r a t i o n over t h e chi-squared d i s t r i b u -

t i o n s used t o t a k e i n t o account f l u c t u a t i o n s of t h e f i s s i o n and neut ron

width, r e s p e c t i v e l y .

P ) is t h e chi-squared d i s t r i b u t i o n f o r t h e neutron width.

P ( s ) i s t h e chi-squared d i s t r i b u t i o n f o r t h e f i s s i o n width. k

r is t h e r a t i o of neutron width a t E t o mean neut ron ,wid th a t E.

s is t h e r a t i o of f i s s i o n width a t E t o mean f i s s i o n wid th a t E.

i s t h e r e l a t i v e probabi l i , ty of absorp t ion . For s u f f i c i e n t l y l a r g e va lues IT

of . B , t h e approximation, J(8,B) = , i s used. 2 m .

$ (8 ,x ) i s t h e symetr ic Doppler l ine-shape func t ion .

wher e

a is t h e e f f e c t i v e s c a t t e r i n g c r o s s s e c t i o n per absorber '

atpm i n t h e NR approximation

- !Lo i s t h e r a d i u s o r t h i ckness of t h e absorber lump

C is t h e Dancoff p i n shadowing f a c t o r

a is t h e sum of t h e s c a t t e r i n g c r o s s s e c t i o n s per absorber m atom f o r a l l moderators i n t h e absorber lump

N is t h e lump absorber atom d e n s i t y a

gJ i s t h e s t a t i s t i c a l weight f o r J s t a t e l e v e l s

J i s t h e t o t a l angular momentum quantum number of t h e compound nucleus

.I i s t h e ground s t a t e s p i n of t h e t a r g e t nucleus

A. is t h e atomic mass r a t i o

111. SMOOTH CROSS SECTION CALCULATIONS

The smooth c r o s s s e c t i o n s a r e det.ennined by i n t e r p o l a t i o n using t h e

v a l u e s from ENDF/B, F i l e 3 . The i n t e r p o l a t i o n scheme used is determined

from t h i s f i l e .

Caution should be used a t t h e unresolved range l i m i t s , a s t h e smooth

v a l u e s a r e u s u a l l y d iscont inuous a t t h e s e po in t s . When reading i n t h e

i n p u t mesh, t h e r e f o r e , t h e va lues f o r unresolved range l i m i t s should be

a l t e r e d s l i g h t l y t o make s u r e t h e va lues a r e j u s t i n s i d e t h e unresolved

range. When t h e program gene ra t e s t h e mesh, t h i s i s done au tomat ica l ly .

I V . INPUT INSTRUCTIONS

1. TYPES OF INPUT

There a r e two types of i npu t d a t a , program c o n t r o l d a t a and ENDFIB

da ta . When ENDFIB d a t a a r e i n p u t on ca rds , t h e ca rds fo l low t h e program

c o n t r o l d a t a f o r a g iven run. For s tacked runs , t h i s impl ies c o n t r o l

d a t a and ENDFIB d a t a fo l low each o t h e r a l t e r n a t e l y .

2. PROGRAM CONTROL DATA

The program c o n t r o l d a t a c o n s i s t of one o r more t i t l e ca rds , one

i n t e g e r d a t a ca rd , one f l o a t i n g p o i n t ' d a t a ca rd , and an o p t i o n a l s e r i e s

of mesh c a r d s f o r each run of a s e r i e s . I f so s p e c i f i e d on t h e i n t e g e r

ca rd , ENDFIB d a t a ca rds may fo l low t h e previous da t a .

The program i s designed t o r e q u i r e t h e use r t o provide a minimum of

i npu t d a t a . A s e t of i n i t i a l d e f a u l t va lues i s suppl ied so t h a t t h e u s e r

may, f o r most u s e s , l e a v e most of t h e d a t a blank f o r t h e i n i t i a l run.

For a s e r i e s of runs , t h e v a r i a b l e va lues from t h e previous run a r e used

a s t h e d e f a u l t va lues , except f o r two cases s p e c i f i e d i n Table I. Th i s

' s i m p l i f i e s t h e running of a s e r i e s of t h e same type of problems; however,

i f t h e v a l u e of a v a r i a b l e from t h e previous run i s not d e s i r e d t h e use r .

must be s u r e t b r e s e t t h i s va lue . I f a v a r i a b l e i s not t o be used a t

a l l , s e t t h e v a r i a b l e t o "-1" f o r i n t e g e r v a r i a b l e s o r t o "-1.0" f o r

f l o a t i n g po in t v a r i a b l e s .

Table I g ives a d e s c r i p t i o n of t h e program c o n t r o l d a t a ca rds . Of

a l l t h e v a r i a b l e s on t h e i n t e g e r and f l o a t i n g po in t d a t a ca rd , t h e only

v a r i a b l e abso lu t e ly r e q u i r i n g a n inpu t v a l u e on t h e i n i t i a l run i s t h e

v a r i a b l e "MATNO". Other normally used v a r i a b l e s a r e denoted by an

a s t e r i s k . The r equ i r ed ca rds a r e denoted by a double a s t e r i s k . Where

t h e input d e s c r i p t i o n i s involved, a concise s ta tement of purpose pre-

cedes t h e d e s c r i p t i o n of t h e u s e of t h e v a r i a b l e .

TABLE I

CARD INPUT INSTRUCTIONS

**Card 1: Format (20A4, T80,Al) (To run a s e r i e s of m a t e r i a l s , r e p e a t t h i s card .)

Var iab le . Columns Desc r ip t ion

RUNTL(1) 1-4

RUNTL(2) 5-8 T i t l e card t o be p r in t ed as a heading f o r each page of ou tput .

RUNTL (20) 77-80

ASTQ 80 I f ASTQ is a n a s t e r i s k , t h e fol lowing ca rd i s expected t o be a t i t l e card (or t h e type descr ibed below a s Card 1 ' ) .

Card 1' (op t iona l s e r i e s ) : Format (19A4 ,A3 ,A1) (Present on ly i f column 80 of t h e preceding card was a n as te r i sk . ' )

Var iab le Columns Desc r ip t ion

REPRT(2) 5-8

T i t l e card t o be p r in t ed wi th t h e i n i t i a l i npu t l i s t i n g only .

REPRT (20) 7 7 - 7 9 ' ~

ASTQ 80 . I f ASTQ i s a n a s t e r i s k , t h e fol lowing card is expected t o be a t i t l e card of this same t y p e .

Note: The above impl ies t h a t t i t l e . c a r d s a r e continued t o be read i n u n t i l t h e r e i s not an a s t e r i s k i n Column 80 of t h e l a s t t i t l e card .

**Card 2: Format (1215) ( In t ege r Data Card)

I n i t i a l Defau l t

Va r i ab l e Columns Desc r ip t i on Value

*MATNO 1-5 . ENDFIB m a t e r i a l number. (0)

, I f MATNO is l e f t b lank , o r set equa l t o z e r o , on runs o t h e r than t h e i n i t i a l r un of s tacked r u n s , t h e ENDFIB d a t a f o r t h e previous run (or t h i s d a t a mod- i f i e d by u s e of NDFBCH and ENDFIB d a t a change ca rds ) w i l l be reused f o r t h i s run. I n t h i s c a s e , t h e fo l lowing inpu t v a r i a b l e s must no t be changed : IDTAP, ISONLY, NDFB. The u s e of t h e ENDFIB d a t a of t h e previous run i s superseded i f IREW=l, i n which c a s e t h e d a t a w i l l be re read and any v a r i a b l e may be used. I n s tacked r u n s , t h e MATNO's must be i n t h e same o rde r a s on t h e ENDFIB t a p e (nondecreasing o rde r ) o r e l s e IREW (rewind) must be used.

* IDTAP 6-10 ENDFIB t a p e number. (-1)

I f IDTAP i s used , the t a p e number w i l l be checked, and t h e t i t l e - o f t h e t a p e w i l l be p r i n t e d a t t h e t o p of each page of ou tpu t .

INUMSH 11-15 . The inpu t u n i t f o r t h e mesh. (5)

This v a r i a b l e i s a p p l i c a b l e on ly i f MESHRD # -1, i e , on ly i f t h e mesh is read i n .

IPTIME 16-20 Purpose: t ime informat ion p r i n t o u t . (-1)

I f IPTIME = 1, then t h e t ime e lapsed from t h e previous 'time p r i n t o u t and t h e cumulat ive. ' t ime w i l l be p r i n t e d a t f r e - quent i n t e r v a l s .

IPTPLG 21-25 Purpose: mesh de te rmina t ion -- s imp le s t (50) t ype -

I f IPTPLG i s used , t h e program w i l l c r e a t e t h e mesh a t which t h e c r o s s s e c t i o n s a r e eva lua ted . IPTPLG i s t h e number of p o i n t s per. u n i t l e t h a r g y f o r t h e mesh. Thus, c r o s s s e c t i o n s a r e eva lua ted a t a l e t h a r g y spacing of I/IPTPLG between t h e lower and upper unresolved range l i m i t s . Th i s v a r i - a b l e is a p p l i c a b l e o n l y , i f MESHRD = -1,

I n i t i a l Defaul t

Var iab le Columns Descr ip t ion Value

I SKCFP 26-30 Purpose: skipping c r o s s s e c t i o n types . (-1

I f ISKCFP = -1 a l l types of r e a c t i o n s present a r e processed. I f ISKCFP i s d i v i s i b l e by 2, cap tu re c r o s s s e c t i o n s w i l l be skipped. I f ISKCFP i s d i v i s i b l e by 3 , f i s s i o n c r o s s s e c t i o n s w i l l be skipped. I f ISKCFP is d i v i s i b l e by 5, s c a t t e r i n g w i l l be skipped. Example: set ISKCFP = 1 5 t o do cap tu re only.

ISONLY 31-35 . Purpose: s e l e c t i n g a s i n g l e i s o t o p e (-1) from a m a t e r i a l .

I f f o r a n EM)F/B m a t e r i a l conta in ing more than one i so tope , i t is des i r ed t o process only t h e N'th i so tope , s e t .

ISONLY equal t o N. ISONLY can b e used- t o s k i p t h e unresolved c a l c u l a t i o n s and do only t h e smooth by s e t t i n g ISONLY = -2.

LETHM 36-40 Purpose> mesh determinat ion. (-1)

I f LETHM = -1, t h e mesh read i n should be i n u n i t s of energy i n ascending order . I f LETHM = +1, t h e mesh read i n should be i n u n i t s of l e t h a r g y i n descending o rde r .

MESHRD 41-45 Purpose: f o r reading i n t h e mesh.

I f MESHRD = -1, do no t read any mesh ca rds , bu t u s e t h e IPTPLG o p t i on

I f MESHRD = +1, f o r problem 1 of s tacked r u n s , read t h e mesh ca rds ( s ee card 4 ) ; f o r problem

N , N > 1, of s tacked runs , then u s e t h e mesh of t h e musL r e c e n t prev ious run read i n w i th MESHRD 2 1.

I f MESHRD = 2, read t h e mesh f o r t h i s problem ( see ca rd 4 ) .

Also, f o r 1 and 2, t h e mesh generated is l i s t e d i f not prev ious ly l i s t e d .

I f MESHRD = 3, do as f o r 1 except do no t l i s t t h e mesh generated.

I f MESHRD = 4 , do a s f o r 2 except do no t l i s t t h e mesh generated.

I f t h e mesh read i n extends beyond t h e , unresolved range l i m i t s , t h e v a r i a b l e s ELORED and EHIRED must a l s o be used t o extend t h e range.

2 0

I n i t i a l D e f a u l t

V a r i a b l e Columns D e s c r i p t i o n Value

NDFB 46-50 I n p u t u n i t f o r t h e ENDFIB d a t a . (9)

I f NDFB = 5, see c a r d 5 .

NDFBCH 51-55 Purpose: a l l o w s changes i n ENDFIB (-1) c a r d d a t a .

I f NDFBCH = N , t h e n N ENDFIB change c a r d s a r e expected i n s t e a d of a complete s e t of ENDFIB d a t a c a r d s . See c a r d 5. NDFB must e q u a l 5 i f NDFBCH is used.

NDFPUN 56-60 Purpose: punches ENDFIB c a r d d a t a . (-1)

I f NDFPUN i s p o s i t i v e , t h e ' u n r e s o l v e d and smooth c a p t u r e and f i s s i o n d a t a decks a r e punched from t h e ENDFIB l i b r a r y i n t h e p roper fo rmat f o r u s e a s i n p u t t o C-SURE.

I f t h i s v a r i a b l e is u s e d , NDFB must n o t e q u a l 5 , NDFBCH must e q u a l -1, and MATNO must n o t e q u a l z e r o and must n o t b e e q u a l t o MATNO f o r t h e p r e v i o u s r u n , u n l e s s t h e t a p e i s rewound, i e , IREW = 1. NDFPUN i s n o t saved b u t must ' be r e a d ' i n each t i m e punching i s d e s i r e d .

IREW 61-65 Purpose: t o rewind ENDFIB t a p e . (-1

I f IREW = 1, t h e . t a p e f o r t h i s r u n i s rewound. To avo id t h e u s e r a c c i d e n t l y rewinding t h e t a p e on a l l subsequent r u n s , t h i s v a l u e i s n o t saved b u t must be r e a d i n each t i m e rewinding i s d e s i r e d .

**Card 3: Format (6E11.0). ( F l o a t i n g P o i n t Da ta Card)

I n i t i a l D e f a u l t

V a r i a b l e Columns D e s c r i p t i o n Value

MTABN 1-11 Purpose: change t h e abundance weight- (-1 • ) i n g o f a n i s o t o p e .

S e t t h e v a l u e of t h e abundance f o r t h e i s o t o p e be ing p rocessed . t o ALTABN. The u s e o f ALTABN r e q u i r e s t h e u s e of ISONLY. (The main u s e of ALTABN is t o change t h e abundance weigh t t o 1 . .O when o n l y o n e i s o t o p e of a material i s be ing p r o c e s s e d . )

I n i t i a l Defaul t

Var iab le Columns Desc r ip t ion Value

*SIGP 12-22 The v a l u e of SIGP inpu t should equal ( lo7 1

where , om is t h e sum over a l i moderators of t h e s c a t t e r i n g c r o s s s e c t i o n s per absorber atom.

Na i s t h e lump absorber atom d e n s i t y - R i s t h e r a d i u s o r t h i ckness of t h e agsorber lump

C i s t h e Dancoff c o r r e c t i o n f a c t o r .

SMFAC 23-33 I£ SMTAC i s used , t hen a l l smooth c r o s s (1.0) s e c t i o n s a r e mu l t ip l i ed by SMFAC be fo re being p r in t ed . The main use of t h i s v a r i a b l e i s t o a l low weighting of t h e smooth c r o s s s e c t i o n s when only 1 i s o t o p e . of a n ENDFIB m a t e r i a l is processed.

SMFAC may be used only i f ISONLY i s used.

*TKELVN 34-44 The temperature i n degrees Kelvin (10-O)

ELORED Purpose: Energy Range Determinat ion

(10-20) EHIRED 45-55 56-66 1 ( 2 x 1 0 ~ )

ELORED and EHIRED a r e used a s t h e lower and upper energy range l i m i t s i n eV,for determining t h e e n e r g i e s . a t which t h e c r o s s s e c t i o n s a r e evaluated. These input va lues a r e over r idden by t h e code when they would r e s u l t i n zero v a l u e s f o r a l l c r o s s s e c t i o n s a t t h e beginning and end of t h e range they would determine. ELORED i s over r idden by t h e minimum of t h e lowest energy i n t h e smooth f i l e a t which cap tu re , f i s s i o n , o r s c a t t e r i n g i s given and t h e lower energy l i m i t of t h e unresolved resonance range. EHIRED i s over r idden by corresponding maximum va lues . However, i f ELORED o r EHIRED i s s e t equal t o -2.0, t h e rang,e l i m i t used w i l l be t h e corresponding unresolved resonance.energy range l i m i t .

card 4 (op t iona l s e r i e s ) : Format (6E11.0,712) (Energy Mesh Cards)

Var iab le Columns Descr ip t ion

EA(1) - 1-11 7. EA (2) 12-22

Energy po in t s a t which c r o s s s e c t i o n s a r e t o be evaluated.

w ( 6 ) 55-66

IA(1) 67-68 The number of p o i n t s t o be i n s e r t e d , equa l ly spaced i n energy, between t h e above energy va lues . I f 2 5 I 5 6 and i f IA(1) = N , t hen N mesh po in t s a r e i n s e r t e d between t h e energy p o i n t s given

1A(6) 77-78 above, EA(1-1) and EA ( I ) . For IA(1) = N , N mesh, p o i n t s a r e i n s e r t e d between EA(6) on t h e previous card and EA(1) on t h e c u r r e n t card.

I A (7 79-80 This va lue must be zero f o r a l l mesh ca rds except t h e l a s t . On t h e l a s t mesh ca rd , i f t h e l a s t va lue f o r a mesh po in t is g iven i n EA(I), then IA(7) must equal I , i e , IA(7) i n d i c a t e s which f i e l d i s t h e l a s t f i . e l d t o be read on t h e l a s t mesh card .

Note: To make changing t h e mesh e a s i e r , a l l zero va lues i n . e n e r g y , a f t e r t h e f i r s t mesh poin t on card 1, columns 1-11, a r e ignored. The mesh generated must no t exceed 1000 po in t s .

Card 5 (op t iona l s e r i e s ) : . Format (See Chapter I V Y Sec t ion 3,)

' I f ENDFIB d a t a c a r d s o r change ca rds a r e used, a s they must be when NDFB = 5, then i n s e r t them here . See Chapter I V Y Sec t ion 3 , f o r a d e s c r i p t i o n of t h e ca rds requi red .

3. ENDFIB DATA

3.1 Complete ENDFIB Data.

For ENDFIB d a t a read from t ape , t h e d a t a format used by C-SURE must

conform t o t h e requirements descr ibed i n r e f e rence [ 6 ] .

For ENDFIB d a t a read from ca rds , t h e d a t a format used by C-SURE i s

s l i g h t l y modified t o e l imina te some super f luous d a t a as fol lows. The

d a t a f o r F i l e 1 a r e rep laced by a s i n g l e t i t l e card (format: 20A4). The

F i l e 2 d a t a a r e t h e same except t h a t t h e subsec t ion f o r t h e resolved

resonance range is omit ted. F i l e 3 i s i d e n t i c a l i n both c a s e s , bu t only

r e a c t i o n types 2 ( e l a s t i c s c a t t e r i n g ) , 18 ( f i s s i o n ) , and 102 (capture)

a r e allowed. E i t h e r F i l e 2 o r F i l e 3 may be omit ted. No o t h e r f i l e s

may.be p re sen t . The end of t h e ENDFIB card d a t a %s recognized when an

ENDFIB t ape end r e c o r d ' i s encountered. This card must con ta in a "-1" i n

columns 69 and 70, a blank i n column 71, and a "0" i n column 72. .

3.2 ENDFIB Change Data

Whenever ENDFIB has been read i n on c a r d s dur ing an e a r l i e r run of

a s e r i e s of r u n s , i n d i v i d u a l ca rds of t h e s e d a t a may b e rep laced by u s e

of t h e input v a r i a b l e NDFBCH ( a l s o s e e Table I , Card 2 ) . The format of

t h e s e ENDFIB change ca rds i s i d e n t i c a l t o t h a t of t h e c a r d s they r ep lace .

There a r e s e v e r a l requirements when using ENDFIB d a t a change cards .

Some previous run of t h e s tacked runs and t h e p re sen t run must have t h e

input v a r i a b l e NDFB = 5. Each ENDFIB d a t a change c a r d , placed consecu-

t i v e l y i n t he p o s i t i o n ind ica t ed a s Card 5 i n Table I , w i l l r e p l a c e t h e

f i r s t ENDFIB card from t h e previous run which has a n i d e n t i c a l sequence

number i n columns 77-80. The new ca rds t o r e p l a c e o ld d a t a from t h e

e a r l i e r run of t h e s tacked runs must be i n t h e same r e l a t i v e sequence

a s t h e e a r l i e r da t a .

V . PROGRAM OUTPUT.

1. PRINTED OUTPUT

The p r i n c i p l e output c o n s i s t s of t h e fol lowing c r o s s s e c t i o n s f o r

s c a t t e r i n g , cap tu re , and f i s s i o n : t o t a l (smooth p lus resonance) , r e -

sonance c o n t r i b u t i o n , smooth c o n t r i b u t i o n , s-wave resonance c o n t r i b u t i o n ,

and p-wave resonance con t r ibu t ion . Less output than l i s t e d above may be

produced i f some of t h e above a r e not app l i cab le . I f f i s s i o n d a t a a r e

p re sen t , s-wave and p-wave resonance c o n t r i b u t i o n s w i l l be p r in t ed f o r

a maximum of 600 energy va lues per run. S c a t t e r i n g c r o s s s e c t i o n s w i l l

be p r in t ed f o r a maximum of 500 energy va lues per run.

Each page of output i s headed by a t i t l e l i n e which inc ludes t h e

program name, t h e d a t e of t h e l a s t r e v i s i o n , t h e d a t e of t h e run , and t h e

page number. The fol lowing l i n e c o n s i s t s of a t i t l e t o t h e run , which

i s generated a combination of d a t a from both t h e ENDFIB l i b r a r y and card

inpu t . The t h i r d l i n e p r in t ed may c o n s i s t of t h e t a p e t i t l e and t h e

ENDFIB m a t e r i a l number.

The inpu t c a r d s a r e l i s t e d a s they a r e read and aga in a f t e r d e f a u l t

va lues have been appl ied . I f t h e mesh is i n p u t , t h e expansion i s l i s t e d .

I f card inpu t i s used f o r ENDFIB d a t a , it i s l i s t e d .

The program checks t h e input and p r i n t s app ropr i a t e e r r o r messages.

2 . PUNCHED CARD OUTPUT

I f . t h e input v a r i a b l e NDFPUN i s s e t p o s i t i v e , t h e unresolved and'

smooth c a p t u r e and f i s s i o n d a t a decks a r e punched from t h e E:JDF/B l i b r a r y

i n t h e proper format f o r l a t e r u s e a s input t o C-SURE. See Chapter I V Y

Sect ion 3 , f o r a d e s c r i p t i o n of t h e s e cards .

3 . ERROR MESSAGES

The program checks t h e input and may inform t h e use r t h a t he has

made an e r r o r . A l i s t of e r r o r s tops w i l l be found i n Appendix C ,

Subtrau;tine Dencni@an?l, by subroutine' t hen by e r r o r number.

I f t h e cause of t h e e r r o r i s not apparent in 'p roblems involving

s tacked runs , t h e use r may have f o r g o t t e n t o r e s e t one of h i s v a r i a b l e s

f o r t h e new run . For example, t h e use r may encounter an e r r o r message

s t a t i n g t h a t t h e d a t a on h i s f l o a t i n g po in t d a t a card a r e n o t meaningful

and g i v e a number 935 wi th t h e e r r o r message. Ins tead of becoming unduly

d i s tu rbed s i n c e h i s i npu t card was a p e r f e c t l y v a l i d s e t o f zeroes , he

should check t h e previous run f o r va lues on t h e corresponding card which

may need t o b e r e s e t us ing a "-1". (See Chapter I V , Sec t ion 2.) He may

f i n d i n t h i s example, t h a t he has r e s e t ISONLY t o -1 from 2 , s ay , bu t

has not r e s e t ALTABN o r SMFAC, s i m i l a r l y .

V I . REFERENCES

.H. C . Honeck, ENDFIB -- S p e c i f i c a t i o n s f o r a n Evaluated Nuclear Data F i l e f o r Reac to r A p p l i c a t i o n s , BNL-50066 (T-467) ENDF 102 (May 1966) .

D. E. Kusner, R. A. Dannels , and S. Kellman, ETOG-1, A FORTRAN I V Program t o P r o c e s s Data from t h e ENDF/B F i l e t o t h e MUFT, GAMY and ANISN Formats , WCAP-3845-1, ENDF 144 (December 1969) .

B. J . ~ o ~ ~ e . 1 , A. L. Rago, .and D . M. O'Shea, M C ~ , A ~ b d e t o C a l c u l a t e Mul t ig roup Cross S e c t i o n s , ANL-7318 (June 1967) .

H. M. Sumner, ERIC 2 , A FORTRAN Program t o C a l c u l a t e Resonance In- t e p r a l s and from Them E f f e c t i v e Cap ture and F i s s i o n Cross -Sec t ions , AEEW-R-323. ( A p r i l 1964) .

. .

R. B. Nicholson and E. A. F i s c h e r , "The Doppler E f f e c t i n F a s t Re- a c t o r s , " Advances i n Nuclear S c i e n c e and Technology, Vol. &, New York: Academic P r e s s , I n c . (1968) pp. kk0-19.2.

M. K. Drake, Da ta Formats and Procedures f o r t h e ENDF Neutron Cross S e c t i o n L i b r a r y , BNL 50274, ENDF 102, Vol. I (October 1970) .

R. L. C u r t i s , G. L. S i n g e r , F . J . Wheeler, and R. A. Grimesey, PHROG--A FORTRAN I V Program t o Genera te F a s t Neutron S p e c t r a and Average Mul t ig roup C o n s t a n t s , IN-1435 ( A p r i l 1971).

G. I. B e l l and S. G l a s s t o n e , Nuclear Reac to r Theory, New York: Van Nostrand Reinhold P u b l i s h i n g Co. (1970).

APPENDIX A

INTEGRATIONS OVER THE CHI-SQUARED DISTRIBUTIONS

The i n t e g r a t i o n s over t h e chi-squared d i s t r i b u t i o n s ind ica t ed i n

Equations (17) through (22) a r e a c t u a l l y performed us ing t h e fo l lowing

approximations. For f i s s i l e i so topes ,

For n o n f i s s i l e i so topes t h e r e a r e no f i s s i o n widths involved so t h a t

Equation (A-1) becomes

These equat ions and cons t an t s g ive a 10-point i n t e g r a t i o n wi th one

o r two degrees of freedom f o r t h e neutron wid th d i s t r i b u t i o n s and a

5-point i n t e g r a t i o n wi th one t o four degrees of freedom f o r t h e f i s s i o n

width d i s t r i b u t i o n . A j u s t i f i c a t i o n f o r t h e approximation of t h e form

of Equation (A-2) i s given below. The j u s t i c a t i o n f o r t h e double i n t e -

g r a l approximation above i s s i m i l a r . The pi and p!, a r e cons t an t s whose 1

va lues a r e g iven i n Tables '1 and 2 and which were determined a s fo l lows -

and a s described. i n Appendix A of MC 2[31 and i n t h e ERIC-2 code. [41

Values of z a r e determined such t h a t i

where P i s t h e chi-squared d i s t r i b u t i o n of o r d e r - a . N i s s e t t o 1 0 f o r n t h e neutron-width d i s t r i b u t i o n s which may be of o rde r 1 o r 2 and s e t t o

5 f o r t h e f i ss ion-width d i s t r i b u t i o n s which may be of o rde r 1, 2 , 3 , o r 4 .

= 0 and zN = W . N-1 p o i n t z a r e involved, bes ides t h e p o i n t s z i 0

. .

Within each i n t e r v a l (zi z ) average va lues f o r x , represented

by pis a r e determined using

Figure 1 shows t h e s e choices of t h e . z i and pi.

Fig . 1 Choice of z i and p i f o r approximation of S ( f ( x ) ) by 5 po in t i n t e g r a t i o n .

Now,

so t h a t , by t h e t r apezo ida l r u l e , t h e fol lowing approximation holds.

Using Equation (A-3)

' Thus,

The J (0,B) t a b l e s used by C-SURE t o approximate t h e va lues g iven

by Equation (17) were t e s t e d us ing t h e QUICKW sub rou t ine of M C ~ , The

t a b l e look-up and i n t e r p o l a t i o n method was found t o be above fou r t imes

f a s t e r than t h e QUICKW method and only s l i g h t l y l e s s accu ra t e . Frequent ly

t h e u s e o'f t h e t a b l e i s not necessary. For va lues of B s u f f i c i e n t l y

l a r g e , t h e formula f o r J (8, B) f o r t h e i n f i n i t e d i l u t e c a s e ,

J(-,B) = . r r / 2 6 ? m - , is use&.

[ 31 TABLE A-I .

VALUES OF pi

Used f o r I n t e g r a t i o n of Neutron-width D i s t r i b u t i o n s with One o r Two Degrees of rei id om

TABLE A-11 [31

Degrees of Freedom, n

Index, i 1 2

1 0.00525430 0.0517550

.2 0.0371740 0.163089

3 0.103133 0.288398

4 0.207850 0.431720

5 0.359875 0.599144

VALUES OF p f ,

Degrees of reedo om, n

Index, i 1 2

6 0.574320 0.800477

7 0.879486 1.05263

8 1.33502 1.39297

9 2.10558 1.91582

1 0 4.39230 3.30400

Used f a r I n t e g r a t i o n of Fission-width D i s t r i b u t i o n s wi th one', Two, Three, o r our Degrees of Freedom

L

Degrees of Freedom, k

Index, i' '1 2 3 4

1 0.0212093 0.107400 0.189269 0.254966

2 0.155477 0.360070 0.476304 0.549072

3 0.467072 0.699863 0.793185 0.82565

4 1.10710 ' 1.22312 1.2357 6 1.23075

5 3 ; 24914 2.60955 2.30575 2..12265

APPENDIX B

INPUT/OUTPUT UNITS

For t r an u n i t s 5', 6 , and 7 a r e ' u s e d f o r card i n p u t , p r in t ed ou tpu t ,

and punched ou tpu t , r e s p e c t i v e l y . The d e f a u l t va lue f o r t h e ENDFIB

l i b r a r y is u n i t 9. Un i t s 55 and 56 a r e s c r a t c h u n i t s which a r e needed

only i f t h e opt ion t o change ind iv idua l ca rds of p rev ious ly read i n card

d a t a a r e used. I n t h i s ca se , t hese u n i t s a l t e r n a t e s t o r i n g t h e o r i g i n a l

and t h e a l t e r e d ENDFIB d a t a . Unit 1 i s used temporar i ly t o s t o r e ENDFIB

d a t a which a r e t o be punched and is no t needed i f NDFPUN = -1 f o r a l l

runs.

APPENDIX C

SUBROUTINE DESCRIPTIONS

This appendix con ta ins a b r i e f d e s c r i p t i o n of t h e C-SURE subrout ines*

i n t h e o rde r they appear i n t h e code. Also included i s a l i s t of c a l l s

t o o t h e r subrout ines and a l i s t of numbered e r r o r s tops .

MAIN Main c a l l i n g r o u t i n e of C-SURE.

Calls:. I N I N , NDFB5, PAGE, PAGI, RESU, TMAT, F F 1 , TMF2, TMF3, TIM, TPOS, TRID, ZERO.

ARMESH . Generates t h e mesh.

Ca l l s : PAGE

BLOCK DATA Contain J(f3,B) t a b l e s f o r Doppler broadening and sh i e ld ing .

CONT . Reads ENDFIB CONT record.

CPOS Reads ENDFIB card d a t a t o determine proper f i l e and sec t ion .

EC HNG Changes ind iv idua l ENDFIB d a t a ca rds prev ious ly s to red .

Ca l l s : PAGE

EDUMP Clears b u f f e r s and o b t a i n s dump when c e r t a i n e r r o r s occur.

ERR Error r o u t i n e

Calls: EDUMP

FJCJTB I n t e r p o l a t e s i n J (0,B). f o r Doppler broadening

HOLL Reads ENDFIB HOLL record

Ca l l s : CONT, LIST

I N I N Card input r o u t i n e

C a l l s : ARMESH, I N I N T R , LSTMSH, ERR, PAGE

Error s tops : 920; Input no t allowed: MATNO = 0 on f i r s t run o r MATNO < 0.

925; Input not allowed: ISONLY < -2 o r ISONLY' > 10.

*Most of t h e t a p e handling subrout ines were taken e s s e n t i a l l y i n t a c t from ETOG-l(2); s e v e r a l o t h e r subrout ines have r o o t s i n t h i s code. :2

930; Input not allowed: TKELVN is negat ive .

I N I N T R

LIST

LSTMSH .

LRF 2

PAGE

PAGI

PENTRA

RESU

RWENDF

SMCHK

935; Input not allowed: ISONLY = -1 and e i t h e r ALTABN # -1 o r SMFAC # 1.

940; Input not allowed: IPTPLG < 0 o r IPTPLG > 500.

945; Input not allowed: NDFBCH > 0 and NDFB # 5.

950; Input not allowed: NDFPUN # -1 and e i t h e r NDFB = 5 o r NDFBCH # -1.

955; 11lput not allowed: ALTABN > 1.0 .

T rans fe r s card inpu t from a r r a y s i n t o named va r i ab l e s . ,

Reads ENDFIB LIST record .

L i s t s t h e energy mesh generated by ARMESH.

Ca l l s : PAGE

Moves F i l e 2 ENDFIB d a t a (when formula type i s LRF = 2) i n t o a r r a y s and v a r i a b l e s used i n RESU.

C a l l s : CONT, LIST

Reads ENDFIB card d a t a .

C a l l s : ERR, PAGE

Error s t o p s : More than 5000. ENDFIB d a t a c a r d s i npu t .

F inds i n t e r p o l a t e d v a l u e s f o r ENDFIB unresolved para- m e t e r s.

Ca l l s : TERPO

Writes page headings.

I n i t i a l i z e s v e r s i o n number, d a t e , and time.

Ca lcu la t e s t h e p e n e t r a b i l i t y .

Ca lcu la t e s and p r i n t s unresolved resonance c r o s s sect ions. .

C a l l s : FJCJTB, NEWU1, PAGE, PENTRA, TERPO . Prepares f o r punching and punches ENDF/B d a t a .

Checks t o s e e i f smooth d a t a i s a l l zeroes i n t h e range considered.

C a l l s : TERPO

TERPO

TIM

TMAT

TMF 2

TPOS

TRID

XTND

ZERO

Reads ENDFIB TAB1 r e c o r d ; a s s i g n s permanent s t o r a g e f o r smooth c r o s s s e c t i o n s .

I n t e r p o l a t i o n r o u t i n e .

P r i n t s e l a p s e d and t o t a l . t ime.

P o s i t i o n s t h e ENDFIB t a p e t o t h e d e s i r e d material.

C a l l s : CONT, HOLL

Reads t h e f i r s t ' p a r t ,o f ENDFIB F i l e 1.

Calls: CONT

Reads ENDFIB F i l e 2 d a t a .

Calls: CONT, LIST, LRF2

Reads ENDFIB F i l e 3 d a t a .

Calls: CONT, TAB1, TABlC, TPOS, SMCHK, XTND

P o s i t i o n s t h e ENDFIB t a p e t o t h e d e s i r e d f i l e and r e a c t i o n type .

C a l l s : CONT

Reads and checks the'ENDF/B t a p e i d e n t i f i c a t i o n number.

C a l l s : CONT

Extends i n p u t d a t a over a wider energy r a n g e by add ing z e r o e s o v e r t h e ' e x t e n t i o n s .

I n i t i a l i z e s common v a r i a b l e s .

APPENDIX D

FLOW CHART

1

b Reod Input

Modify Data Stored from Previous Run

Read ENDF/B Data

) Calculate Unresolved Pointwise Cross Sections

Calculate Smooth

PNC-A- 851

4

APPENDIX E

SAMPLE PROBLEM SET

The sample problem s e t c o n s i s t s of a s e t of e leven s tacked problems;

s i x us ing ENDFIB d a t a f o r U-238 and f i v e us ing ENDFIB d a t a f o r Pu-239.

The i n t e n t of t h e s e problems i s t o t e s t t h e major op t ions of C-SURE and

t o demonstrate ' t he u s e of t h e input procedure, p a r t i c u l a r l y t h e u s e of

t h e d e f a u l t va lues .

The reader w i l l n o t i c e t h a t i n some of t h e sample problems i n which

t h e mesh was read i n , such a s run number 3 , t h e r e a r e g r o s s l y d i f f e r e n t

c r o s s s e c t i o n va lues a t apparent ly t h e same energy va lue . This sample

problem was choosen t o show t h a t energy va lues on e i t h e r s i d e of t h e

unresolved range energy l i m i t s may appear t o be t h e same po in t due t o

round of f be fo re p r i n t i n g , whi le t h e c r o s s s e c t i o n r e s u l t s . d i f f e r because

t h e va lues on t h e ENDF/B f i l e s a r e u s u a l l y d iscont inuous a t t h e range

l i m i t s .

The sample problem s e t ou tput fol lows.

I ' C ~ S U ~ E / '31 ll-l~-ll', G. <. SIIJGERI PRODUCES P O I N T W I S E UNRESOLVED CROSS SECTIONS

SAMPLE RUNS FOR U-238, SET 1, NO. I TEST INTERNAL MESH

OATE .OF RUN 0 2 1 1 0 1 7 2 PALE I

ENOFlB MAT. NO. 0

NUMBER OF THE RUN = 1 CONTROLLING INPUT CAROS AS READ

SAMPLE RUNS FOR U-238. SET I t NO. I TEST INTERNAL MESH 1 1 0 3 2 0 1 0 1 3 0 0 U O r 0 0 ' 0 0 0.0 0.0 0.0 0.0 -2.0000E 00-2 .0000E 0 0

INPUT CAROS AFTER OEFAULTS

MATNO I D T A P INUMSH I P T I M E I P T P L G I S K C F S I S O N L Y LETHM MESHRO NOF? NOFBCH NOFPUN lREW

1 1 0 3 2 0 1 5 1 3 -1 - 1 - 1 - 1 9 - 1 - 1 - 1

ALTAMN S l G P SMFAC TKELVN ELOREO EHlREO

-1.OOOOE 0 0 1.0000E 0 7 1.OOOOE 0 0 L.OOOOE-20 -2.OOOOE 0 0 -2.OOOOE 0 0

THERE I S NO SMOOTH F l S S l U N DATA PRESENT FOR T H I S MATERLAL I N THE RANGE CONSIDERED.

I . C - S U K E I 3, 1 1 - 1 0 - 7 1 . G. L. S INGER1 PROWCES P O l N T Y l S E UNRESOLVED CR3SS SECTIONS OATS OF RUN 0 2 1 1 0 1 7 2 PPGE 2

U - 2 3 8 SARPLE RUNS FOR U-238. SET 1. NU- I TEST INTERNAL MESH TIME: 14 .961 14 .96 ISEC.)

ENOFIM-11 TAPE 2 0 1 R E V I S I O N S 2 .3 8-1-10. 8 - 2 5 - 7 0 E N D F I B MAT. NO. 1 1 0 3

*** UNRESOLVEO RESONANCE CROSS SECTIONS *** LOWER UNRESOLVEO RANGE ENERGY L I N I T I N EV.: 3.91OOE 0 3 UPPER UNRESOLVEO RANGE ENERGY L I M I T I N EV.: 4 .5000E 0 4

ENERGY TOTAL CAPTURE

SMOOTH C O N T R l B U T l O N

RESONANCE CONTRl BUTION

S-WAVE CONTRIBUTION

I C - S U H E I 3, 1 1 - 1 0 - 7 1 . G. L. S INGERI PROWCES P O l N T Y l S E UNRESOLVEO CROSS SECTIONS

U - 2 3 0 SAMPLE RUNS FOR U-238. SET 1. NO. 1 TEST I N T E R N A L MESH

O I T E OF RUN 0 2 1 1 0 1 7 2 PAGE 3

T IME: 0 . 2 0 1 15.16 ISEC.1

E N O F I B - I 1 TAPE 2 0 1 R E V I S I O N S 2 . 3 8-7-70. 8 - 2 5 - 7 0 E N O F l B MAT. NO. 1 1 0 3

TOTAL SCATTER

SMOOTH CONTRIBUTION

RESONANCE CONTRL8UTlON

S-WAVE CONTRIBUTION

P-HAVE CONTRIBUTION

I C-SURE1 3. l l - 1 0 - 7 1 . G. L. S INGER) PROOVCES P O I N T Y I S E UNRESOLVED CRJSS SECTIONS DATE OF RUN 0 2 1 1 0 1 7 2 PAGE 4

SET 1 NO. 2 , TEST INPUT MESH, ALSO 1 6 1 1 MATNO - 0 TIME: 0 . 0 3 1 15.11 ISEC.1

E N D F I B MAT. NO- 1 1 0 3

CONTROLLING INPUT CARDS AS REAO NUMBER OF THE RUN = 2

SET I NO. 2, TEST INPUT MESH. ALSO TEST MATNO = 0 O U 0 U U u U U l u U U U

0.0 0.0 0.0 0.0 0.0 0.0

INPUT CAROS AFTER OEFAULTS

MATNO l O T A P INUMSH l P T l M E I P T P L G I S K C F S I S O N L V LETHM MESHRD . NOFB NDFBCH NOFPUN l R E U

1 1 0 3 2 0 1 5 1 3 -I -1 - 1 1 9 -1 -1 -1

A L T I B N S I G P SMFAC TKELVN ELOREO EHIREO

-1.OOOOE 0 0 1.OOOOE 0 7 1.0000E 0 0 1.0000E-20 -2.OOOOE 0 0 -2.0000E 0 0 .

I C-SURE1 3, l l - 1 0 - 7 1 . G. L. S INGER1 PROOUCES POINTWISE UNRESOLVED CROSS SECTIONS DATE OF RUN 0 2 1 1 0 1 7 2 PAGE 5

U - 2 3 8 SET 1 NO. 2, TEST INPUT MESH. ALSO TEST MATNO = 0 T IME: 0 . 0 2 1 15 .21 1SEC.I

ENOFIB MAT. NO. 1 1 0 3

INPUT CARDS FOR MESH

I C-SURE1 3, 1 1 - 1 0 - 7 1 1 G. L. SINGER1 PROOUCES POINTWISE UNRESOLVEO CROSS SECTIONS O A T E OF RUN 0 ~ 1 1 0 1 7 . ? 'PAGE 6

U - 2 3 8 SET 1 NO. 2 , TEST INPUT MESH* ALSO TEST MATNO 0 T IME: 0 .021 15.23 ISEC.1

ENOFIB MAT. NO. 1 1 0 3

1 8 P O I N T ENERGY MESH PRODUCED

I C-SURE1 3. 1 1 - 1 0 - 7 1 . G. L. S INGER) PROWCES POINTWISE UNRESOLVED CROSS SECTIONS DATE OF RUN O 2 l l O l l 2 PAGE 7

u - 2 3 8 S C T I ~IU. 2 . TCST INPUT MCSII, ALSO TEST HATNO - o r l n ~ : u.u 1 1 s . r ~ I ~ ~ L . I

E N O F I B - 1 1 TAPE 2 0 1 R E V I S I O N S 2 .3 8-7-10, 6 -25-70 E N O F l B MAT. NO. 1 1 0 3

*** UNRES3LVEO RESONANCE CROSS SECTIONS *** LOWER UNRESOLVED RANGE ENERG* L I M ~ T IN EV.: 3 . 9 1 0 0 ~ 0 3 UPPER UNRESOLVED RANGE ENERGY L I M I T IN EV.: 4 . 5 0 0 0 ~ 0 4

ENERGY TOTAL SMOOTH RESONANCE S-WAVE P-WAVE CAPTURE C O N T R l 8 U T l O N CONTRIBUTION C O N T R l 8 U T l O N CONTRIBUTION

I C-SURE1 3 r 11-10-71 . G- L. SINGER1 PRODUCES POINTWISE UNRESOLVED CROSS SECTIONS DATE OF RUN 0 2 1 1 0 1 7 2 PAGE B

U - 2 3 8 S E T 1 NO. 2. TEST INPUT MESH. ALSO TEST RATNO = 0 T IRE: 0.521 15.14 ISEC.1

E N O F I R - I 1 TAPF 7.01 9 E V I S I O N S 2 . 3 8 -1-70 , 8 - 2 5 - 7 0 E N D F I B *AT. NO. 1 1 0 3

ENERGY TOTAL SMOOTH RESONANCE S-WAVE SCATTER

P l A V E CONTRIBUTION CONTRIBUTION CONTRIBUTION

I C-SURE1 3, 1 1 - 1 0 - 7 1 , GI L. S INGERI PROWCES P O l N T W l S E UNRESOLVEO CROSS SECTIONS DATE OF RUN 0 2 1 1 0 1 1 2 PAGE 9

SFT 1, NO. 3, TEST L E T H n T I M E : 0 . 0 1 1 15 .81 ISEC.1

ENOF18 HAT. NO. 1 1 0 3

CONTROLLING INPUT CARDS AS READ NUMBER OF THE RUN = 3

SET I, NO. 3, TEST LEfHM 0 0 0 0 0 , 0 0 1 2 0 0 0 0

0.0 0.0 0.0 0.0 0.0 0.0

INPUT CARDS AFTER OEFAULTS

MATNO IOTAP INUMSH I P T l n E I P T P L G I S K C F S I S O N L Y LETHU MESHRO NOFB NDFBCH NDFPUN I R E Y

1 1 0 3 2 0 1 5 1 3 -I - 1 1 2 9 - 1 -I - 1

A L I A B N S I G P SUFAC TKELVN ELORED EHIREO

-1,0000E 0 0 1.UOOOE 0 7 1.OOOOE 0 0 1 .00008-20 -2.OOOOE 0 0 -2.0000E 0 0

1 C-SURE1 3. 1 1 - 1 0 - 7 1 . G. L. S INGER) PRODUCES P O l N T W l S E UNRESOLVED CROSS SECTIONS

U - 2 3 8 5CT 1. 1111. 3, 1TC.T I F T H M

OATE OF RUN 0 2 1 1 0 1 7 2 PAGE LO

I l n t l 0 . 0 3 1 15.04 (5EC.1

E N D F I B MLT. NO- 1 1 0 3

INPUT CARDS FOR MESH

0.0 0 .O 0.0 0 5 0 0 0 0 2

I C-SURE1 3, 1 1 - 1 0 - 7 1 . G. L. SINGER1 PROWCES P O l N T H l S E UNRESOLVED CROSS SECTIONS OdTE OF RUN 0 2 1 1 0 1 7 2 PAGE 1 1

U- 23 8 SET 1, NO. 3. TEST L E T H ~ TIME: 0 . 0 2 1 15.86 1SEC.I

ENUF10 NLT. NO. I 1 0 3

7 POINT ENERGY MESH PRODUCED

I C-SURE1 3 , 1 1 - 1 0 - 7 1 . G. L. S INGER) PROWCES P O l N T W l S E UNRESOLVED CROSS SECTIONS OATE D F RUN 0 2 1 1 0 1 7 2 PAGE I 2

U - 2 3 8 SET 1. NU. 3, TEST L E T M T I M F : 0.0 1 15.06 15CC.l

E N D F I B - I 1 TAPE 2 0 1 R E V I S I O N S 2.3 8-7-70 , 8 - 2 5 - 7 0 ENOF18 MAT. NO. 1 1 0 3

*** UHRESOLVEO RESONANCE CROSS SECTIONS **O

LOWER UNRESDLVEO RANGE ENERGY L I M I T I N EV.: 3.9100E 0 3 UPPER UNRESOLVED RANGE ENERGY L I M I T IN, Ev.: 4 .5000E 0 4

ENERGY TOTAL SMOOTH RESONANCE CaPTURE C O N T R l 8 U T l O N

S-WAVE C O N T R l 8 U T l O N

P-HAVE CONTRIBUTION C O N T R l 8 U T l O N

I C-SURE1 3, 1 1 - 1 0 - 7 1 . G. L. S I N G E R I PRODUCES P O l N T Y l S E UNRESOLVEO CROSS SECTIONS OATE OF RUN 0 2 1 1 0 1 1 2 PAGE 1 3

U - 2 3 8 SET 1 t NU. 3 , TEST LETHM T l R E : 0 . 1 5 1 16.01 1SEC.l

E N D F I B - I 1 TAPE 2 0 1 R E V I S I O N S 2.3 8-7-10, 8 - 2 5 - 7 0 ENOF18 MAT- NO. 1 1 0 3

ENERGY 1 OTAL SUODTH SCATTER

RESONANCE CONTRIBUTION

S-HAVE CONTRIBUTION C O N T R I ~ U T I O N

P-WAVE C O N T R l ~ U T l O N

I C-SURE1 3, 1 1 - 1 0 - 7 1 . G- L. SINGER) PRODUCES P O I N T Y I S E UNRESOLVED CROSS SECTIONS DATE O F R U N . 0 2 / 1 0 / 7 2 PACE n 1 4 L

SET 1. NO. 41 T E S l S l G P T IME: 0 . 0 2 1 16.02 1SEC. I '

ENOFlO MAT. NO. 1 1 0 9

CONTROLLING INPUT CAROS AS READ NUMBER OF THE RUN = 4

{ SET 1. NO. 4 1 TEST S I G P

M U L T I P L E T I T L E

I N P U T CAROS AFTER OEFAULTS

MAT110 I D T A P INUMSH I P T l M E I P T P L G I S K C F S ISONLY LETHM MESHRO NDFB NDFBCH NDFPUN I R E Y -

1 1 0 3 2 0 1 5 I 3 -1 - 1 -1 1 9 - 1 -I -I

ALTABN S l G P SMFAC TKELVN ELOREO EHIREO ,

I C-SURE/ 3 , 11-10-71 , G. L. S INGER1 PRODUCES P O I X T Y I S E UNRESOLVED CROSS SECTIONS DATE OF RUN O 2 1 l O / l Z PACE 1 5

U - 2 9 8 . SET 1, NO. 4. TEST S I G P TIME: 0 .031 1 6 - 0 6 ISEC.1

E N D F I B - 1 1 TAPE 2 0 1 R E V I S I O N S 2 .3 8-7-70. 8 - 2 5 - 7 0 ENOF10 MAT. NO. 1 1 0 3

re* UNRESOLVEO RESONANCE CROSS SECTIONS *** LUWER UNRESOLVEO RANGE ENERGY L I M I T I N EV.: 3.91OOE 0 3 UPPER UNRESOLVED RANGE ENERGY L I M I T I N EV.: 4.5OOOE 0 4

ENERGY TOTAL CPPTURE

RESONANCE CONTRIBUTION

S-UAVE CONTRIBUTION

P-HAVE CONTRIBUTION

I C-SURE/ 3, 11-10-71 , G. L. SINGER1 PROWCES P D l N T Y l S E UNRESOLVED CROSS SECTIONS DATE OF RUN O Z / l O l l 2 PAGE 1 6

U - 2 3 8 SET 1. NO. 4 1 TEST S I G P TIME: 0 . 2 1 1 16.32 1SEC.I

E N U F I B - I 1 TAPE 2 0 1 R E V I S I O N S 2.3 8-7-70. 8 - 2 5 - 7 0 E N D F I B MAT. NO. 1 1 0 3

ENERGY TOTAL SCATTER

SMODTbl RESONANCE S-NAVE P-WAVE CONTRIBUTION CONTRIBUTION CONTRIBUTION CONTRIBUTION

I C-SURE/ 3. 1 1 - 1 0 - 7 1 , G. L . S INGER1 PRODUCES POLNTUISE UNRESOLVED CROSS SECTIONS DATE OF RUN 0 2 1 1 0 1 7 2 PAGE 1 7

SET I, NO. 5. T E S T TKELVN ITEMPERATURE VARIABLEI ~ IHE: 0.03/ 16.36 i s ~ c . 1

E N D F l B MAT. NOr 1 1 0 3

CONTROLLING INPUT CARDS AS READ , NUMBER OF THE RUN = 5

SET 1, NU. 5, TEST TKELVN ITEMPERATURE V A R I A B L E 1 O O 0 . O O O , O O O O b D O

0.0 0.0 0.0 2 .9300E 0 2 0.0 0.0

INPUT CARDS AFTER OEFAULTS

MATNO IDTAP INUMSH I P T I f l E I P T P L G I S K C F S ISONLV L E T M MESHRO NDFB NOFBCH NDFPUN IREW

1 1 0 3 2 0 1 5 1 3 -1 - 1 -1 1 9 - 1 -I -I

AL TAl lN S I G P Sf lFdC TKELVN ELDRED EHIRED

-1.OOOOE 0 0 6 .0000E 0 1 1.OOOOE 0 0 2 .9300E 0 2 -2.0000E 0 0 -2 .0000E 0 0

I C-SURE1 3, 1 1 - 1 0 - 7 1 0 G- L. S INGERI PROOUCES P O l Y T W l S E UNRESOLVED CR3SS SECTIONS DLTE O F RUN 0 2 1 1 0 1 7 2 PAGE 1 8

U - 2 3 8 SET 1, NU. 5 1 TEST TKELVN I rEMPERATURE V A R I A B L E I T I I E : 0 . 0 2 1 16 .37 ISEC.)

E N O F 1 8 - I 1 TAPE 2 0 1 R E V I S I O N S 2 .3 8-7-70, 8 - 2 5 - 7 0 E N D F I B MAT'. NO. 1 1 0 3

*** UNRESOLVED RESONANCE CROSS SECTIONS *+*

LOWER UNRESULVEO RANGE.ENERGY LIM!T I N EV.: 3.9IOOE 0 3 UPPER UNRESOLVED RANGE ENERGY L I M I T I N EV.: 4 . 5 0 0 0 ~ 0 4

ENERGY TOT AL CAPTURE

RESONANCE C O N T R l 8 U T l O N

S-WAVE C O N T R l 8 U T l O N

P-WAVE CONTRIBUTION

I C-SURE1 3, 1 1 - 1 0 - 7 1 1 G. L. SINGER! PRODUCES P O I N T d I S E UNRESOLVEU CHJSS S t C I I U N S ULTE OF RUN 0 2 1 1 0 1 ~ ~ PAGE 1 9

U - 2 3 8 SET I. NO. 5. TEST TKELVN ITEMPERATURE VARIABLE1 T IME: 0 .351 16.72 1SEC.I

E N D F I B - I ! TAPE 2 0 1 R E V I S I O N S 2 .3 8 -7-70 . 8 - 2 5 - 7 0 ENOF18 N I T . ,NO. 1 1 0 3

ENERGY TOTAL ~ ~ 0 0 1 ~ RESONANCE 5 - Y A V t P-WAVE SCATTER C O N T R l 8 U T l O N CDNTRIBUTION C O N T R l 8 U T l O N C O N T R l 8 U T l O N

I C-SURE1 3, 1 1 - 1 0 - 7 1 , G. L. SINGER1 PRODUCES P U l N T W l S E UNRESOLVED CROSS SECTIONS

SET 1, NO. ' 6 , TEST ISONLV = - 2 I S M O r H ONLVI

DATE OF RUN 0 2 1 1 0 1 7 2 P l G E 2 0

T IME: 0 . 0 3 1 16.76 1SEC.I

ENOF18 MAT. NO. 1 1 0 3

NUMBER OF THE RUN = b CONTROLLING INPUT CARDS b S READ

SET 1. NO. 6. ' TEST ISONLY = -2 ISMOOTH ONLY1 0 0 . 0 0 0 0 - 2 0 0 0 0 0 0

-1.OUOOE 0 0 1 .0000E 0 7 1-OOOOE 0 0 1.OOOOE-20 0.0 0.0

INPUT CARDS AFTER DEFAULTS

MATNU I D T A P INUMSH I P T I M E I P T P L G I S K C F S ISONLY LETHM MESHRO NDFB NOFBCH NDFPUN IREW

1 1 m 701 5 I 3 -1 - 2 -1 I 9 -1 -1 -1

ALTALIN S I G P SMFAC TKELVN ELORED E H I R E D

-1.OOOOE 0 0 1.0000E 0 7 1.0000E 0 0 1.OOOOE-20 -2.OOOOE 0 0 -2 .0000E 0 0

THE I N P U T V A R l L 0 L E ISDNLV = - 2 1 THEREFORE W L Y SMOOTH CROSS SECTIONS H I L L BE CALCULATED.

1 C-SURE1 3, 1 1 - 1 0 - 7 1 1 G. L. SINGER1 PRODUCES POINTWISE UNRESOLVED CROSS SECTIONS DATE O F RUN 0 2 1 1 0 1 7 2 PAGE 2 1

U- 2 3 8 SET 1. NU. 6. TEST ISONLY = -2 I S M O T H ONLY) TIME: 0 .021 1 6 . 7 7 1 S E C . I

ENOFIR-11 TAPE 2 0 1 R E V I S I O N S 2 . 3 8-7-70. 8 - 2 5 - 7 0 ' ENOF18 MLT. NO. 1 1 0 3

*** UNRESOLVED RESONANCE CROSS SECTIONS *** LOYER UNRESOCVEO RANGE ENERGY L l n l r IN EV.: 3 . 9 1 0 0 ~ 0 3 UPPER UNRESOLVED RANGE ENERGY LIMIT IN EV.': + .~OOOE 0 6

ENERGY TOTAL CAPTURE

SMOOTH RESONANCE S-WAVE - , P-WAVE C O N T R l 8 U T I O N ' CONTRIBUTION CONTRIBUTION C O N T R l 8 U T l O N

. . I C-SURE/ 3, 11-10-71. G. L. SINGER) PRODUCES POINTWISE UNRESOLVED CROSS SECTIONS OATE OF RUN 0 2 1 1 0 1 1 2 P A G E U 2 2

U - 2 3 8 SET 1. NO. 6, TEST ,I SONLV = - 2 1 S ~ O T H ONLY I TIME: 0 . 1 5 1 .16 .92 ISEC.1 . E N D F I B - I 1 TAPE 2 0 1 R E V I S I O N S 2 1 3 8-7-70. 8 - 2 5 - 1 0 ENOF18 MAT. NU- 1 1 0 3 <

rorm , SCATTER

P-WAVE CONTRIBUTION

I C-SURE1 3. 1 1 - 1 0 - 7 1 . G. L. S INGER) P R O W C E S P Q l N T Y l S E UNRESOLVED CROSS SECTIONS DATE OF RUN 0 2 1 1 0 1 1 2 PAGE 2 3

SET 1 NU. 7 , TEST RANGE L I M I T DEFAULTS T IME: O.O2/ 16.94 1SEC. I

ENOF18 MAT. NO. 1 1 0 3

CONTROLLING INPUT CARDS A S REAO NUMBER OF THE RUN T

SET 1 NO. 7 , TEST RANGE L I M I T OEFAULTS 0 0 0 1 0 - 1 0 0 - 1 0 0 0 0

0.0 0 .0 0.0 0.0 1.OOOOE-20 2-OOOOE 0 7

I N P U T CARDS AFTER OEFAULTS

MATNO I O T A P INUMSH I P T I M E . I P T P L G I S K C F S I S O N L Y LETHM MESHRO NOFB NOFBCH NOFPUN I R E Y

1 1 0 3 2 0 1 5 1 3 - 1 - 2 -1 -1 9 - 1 - 1 - 1

ALTABN S l G P SMF AC T K E L V N ELOREO EHIREO

-1.OOOOE 0 0 1.0000E 0 1 1.0OOOE 0 0 1.OOOOE-26 L.OOOOE-20 2.OOOOE 0 7

THE I N P U T V A R l A 8 L E I S O N L V = - 2 . THEREFORE ONLY SMOOTH CROSS SECTIONS M I L L BE CALCULATED.

I C-SURE1 3 , 11-10-71 . G. L. SINGER1 PROOUCES P O I N T W I S E UNRESOLVEO CROSS SECTIONS

U - 2 3 8 SET 1 NO. 7 , TEST RANGE L I M I T O E F A U T S

OATE OF RUN 0 2 1 1 0 1 1 2 PAGE 2 1

T I M E : 0 . 0 3 1 1 6 . 9 1 ISEC.1

ENOF/@-11 TAPE 2 0 1 R E V I S I O N S 2 .3 8-7-70. 8 - 2 5 - 1 0 E N D F l B MAT- N n r 1 1 0 3

*** UNRESOLVED RESONANCE CROSS SECTIONS a* *

LOYER UNRESOLVEO RANGE ENERGY L I M I T I N EV.: 3.9IOOE 0 3 UPPER UNRESOLVEO RANGE ENERGY L I M I T I N EV.: 4 . 5 0 0 0 ~ 0 1

ENERGY TOTAL CAPTURE

SMOOTH RESONANCE S-WAVE P-WAVE C O N T R l 8 U T l O N C O N T R I B U T I O N C O N T R I B U T I O N C O N T R l 8 U T l O N

I [-SURE/ 3 , 1 1 - 1 0 - 1 1 . G. L. SINGER) PRODUCES POINTWISE UNRESOLVEO CROSS SECTIONS OATE OF RUN 0 2 1 1 0 1 1 2 PAGE 2 5

U - 2 3 8 SET I NO. 7, TEST RANGE L I M I T OEFAULlS T INE: 0 . 1 8 1 17 .16 (SEC.1

ENDFIB-11 TAPE 2 0 1 R E V I S I O N S 2.3 8 -7-70 . 8 - 2 5 - 7 0 ENOF/B HAT. NO. 1103

ENERGY 1OTAL SMOOTH RESONANCE S-UAVE P-WAVE C4PTURE CONTRIBUTION C O N T R l 8 U T l O N , CONTRI B U T I O N CONTRIRUTION

z . z z s 9 ~ - 0 2 3 .639ZE-01 2 .632LE-01 2.032 I E - U I 1 . 9 0 9 l E - 0 1 1 .b545E-01

I C-SURE/ 31 1 1 - 1 0 - 7 1 . G. L. SINGER1 PRODUCES P O l N T Y I S E UNRESOLVED CROSS SECTIONS DATE OF RUN 0 2 / 1 0 1 7 2 PAGE Z b

U - 2 3 8 SET 1 NO- 7 s TEST RLNGE L I M I T DEFAULTS TIRE: 0.70) 17.85 I S E C . ~

E N O F I B - I 1 TAPE 2 0 1 R E V I S I O N S 2 .3 8-7-70. 8-25-70 ENOF18 MAT. NO. I 1 0 3

ENERGY TOTAL SMOOTH RESONANCE S-WAVE P-WAVE SCATTER C O N T R l 8 U T l O N C O N T R l 8 U T l O N C O N T R l 8 U T l O N C O N T R l 8 U T l O N

DATE OF RUN 0 2 / 1 0 1 7 2 PAGE,* 2 7 , r

TIME: O. lZ / 17 .97 1SEC.I '

I C-SURE1 3. 1 1 - 1 0 - 7 1 . G. L. S INGER1 PROWCES P O l N T Y l S E UNRESOLVED CROSS SECTIONS

U - 2 3 8 SET 1 NO. 7 , TEST RANGE L I M I T DEFAULTS

E N D F I B - I 1 l A P E 2 0 1 R E V I S I O N S 2 .3 8 -7-70 . 8 - 2 5 - 7 0 1 .5427E 0 2 0.0 0.0 E - L b Z T E OZ 0.0 0.0 3.0317E 0 2 0.0 0.0 4 .2500E 0 2 0.0 0.0

E N D F l 8 MAT. NO. 1 1 0 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

I C-SURE/ 3 1 11-10-71 . G. L. SINGER1 PROWCES P o l ~ T u l s E UNRESOLVEO CROSS SECTIONS

SAMPLE RUNS FOR PU-239. SET 2, NO. 11 RESET INTERNAL MESH

DATE O F RUN 0 2 1 1 0 1 7 2 PAGE 2 8

T IME: 0 . 0 8 1 18.05 1SEC.I

ENOF18 MAT. NO. 1 1 0 3

NUMBER OF THE RUN . 8 CONTROLLING INPUT CARDS AS REAO

SAMPLE RUNS FOR PU-239. SET 2, NO. I. RESET INTERNAL M E s n 1 1 0 4 0 0 1 0 - 1 0 - 1 0 0 0 0 0.0 L.0000E 0 7 0.0 1.0000E-20-2.0000E OO-2.0000E 0 0

INPUT CAROS AFTER OEFAULTS

MATNO IOTAP INUMSH I P T I M E I P T P L G ISUCFS ISONLY LETHM MESHRO NOFR N O F B W NOFPUN IREW

1 1 0 4 2 0 1 5 1 4 - 1 -1 -1 -1 9 - 1 - 1 - 1

ALTABN S l G P SMFAC TKELVN ELOREO EHIREO

-1.OOOOE 0 0 1 .0000E 0 7 L.0000E 0 0 1.OOOOE-20 -2.0000E 0 0 -2.OOOOE 0 0

I C-SURE1 3 1 1 1 - 1 0 - 7 1 1 G. L. S INGER1 PROOUCES POINTWISE UNRESOLVED CROSS SECTIONS DATE OF RUN 0 2 1 1 0 1 7 2 PAGE 2 9

PU-239 SAMPLE RUNS FOR PU-239, SET 2 1 NO. 11 RESET INTERNAL MESH TIME: 6 - 0 6 / 24.11 1SEC.I

E N O F I B - I 1 TAPE 2 0 1 R E V I S I O N S 2.3 8-7-70. 8 - 2 5 - 1 0 E N O F I B MAT. NO. I 1 0 4

*** UNRESOLVED RESONANCE CROSS SECTIONS *** LOWER UNRESOLVEO RANGE ENERGY L I M I T I N EV.: 3 .0000E 0 2 UPPER UNRESOLVEO RANGE ENERGY L I M I T I N E V . : 2-5OOOE 0 4

TOTAL

ENElGY CAPTURE F I S S I O N

RESONANCE C O N T R l 8 U T l O N

CAPTURE . F I S S I O N

SMOOTH CONTR18UTlON

CPPTURE F I S S I O N

I C-SURE1 3. 1 1 - 1 0 - 7 1 . G. L. S INGER) PROOUCES,POINTWISE UNRESOLVED CROSS SECTIONS DATE OF RUN 0 2 1 1 0 1 1 2 PAGE 3 0

P U - 2 3 9 SAMPLL HUNS FOR PU-239. SET 2. NO. 1. RESET INTERNAL *ESH TIME: 0 . 6 8 1 24.79 1SEC.I

E N D F I B - 1 1 T A P E 2 0 1 R E V I S I O N S 2 . 3 8 -7-70 , 8 - 2 5 - 7 0 ENOF18 MAT. NO. 1 1 0 4

S-YAVt KtSUNANCE C U N I K l M U l l U N P - Y A V t R ~ S U N A N L ~ L U N I K I M U I I L I N

ENERGY CAPTURE F I S S I O N CAPTURE F I S S I O N

I C-SURE1 3 1 1 1 - 1 0 - 1 1 . G. L. S INGER) PKOWCES POINTWISE UNRESOLVEO CROSS SECTIONS DATE OF RUN 0 2 1 1 0 1 7 2 PAGE

TIME: 0 . 0 5 1 24.84 I

ENOF18 MAT. NO. 1 1 0 4

3 1

1 SEC. PU-239 SAMPLE RUNS FOR PU-239. SET 2. NO. 1, RESET INTERNAL MESH

ENOFIB-11 TAPE 2 0 1 R E V I S I O N S 2 . 3 8-1-70. 8 - 2 5 - 7 0

ENERGY TOTAL SCATTER

SMOOTH RESONANCE C O N T R l 8 U T l O N CONTRIBUTION

S-WAVE P-WAVE C O N l R l 8 U T l O N CONTRIBUTION

I C-SURF1 3, 1 1 - 1 0 - 7 1 , G. L. S I N G E R I PROWCES P O l N T Y l S E UNRESOLVEO CROSS SECTIONS

SET 2. NU. 2 1 TEST REWIND AN0 PUNCH

DATE OF RUN 0 2 1 l O l 7 2 PPGE 3 2

T I M E : 0 .031 24.88 ISEC.1

ENOFIR MAT. NO. 1 1 0 4

NUMBER OF THE RUN = 9 CONTROLLING INPUT CAROS AS READ

SET 2, NO. 2. TEST REWIND AND PUNCH 0 0 0 0 0 0 0 0 1 0 0 1 1

0.0 0.0 0.0 0.0 0.0 0.0

I N P U T CAROS AFTER OEFAULTS

MAIN0 IOTAP INUMSH I P T I M E I P T P L G I S K C F S ISONLY LETHM MESHRO NOFB NOFBCH NOFPUN IREW

1 1 0 4 2 0 1 5 I 4 -1 - 1 -1 1 9 -1 1 1

ALTABN S I G P SMFAC TKELVN ELOREO EHIREO

-1.0000E 0 0 1.OOOOE 0 7 1 .0000E 0 0 1 .0000E-20 -2.0000E 0 0 -2.OOOOE 0 0

THERE I S NO SMOOTH S C I T T E R OATA PRESENT FOR T H l S MATERIAL I N THE RLNGE CONSIOEREO.

THERE I S NO SMOOTH F l S S l U N OATA PRESENT FOR T H l S MATERIAL I N THE RANGE CONSIDERED.

THERE I S NO SMOOTH CAPTURE OATA PRESENT FOR T H I S MATERIAL I N THE RANGE CONSIOEREO.

I C-SURE1 3. 11-10-71 , G. L. S INGER1 PRODUCES P O I N T Y I S E UNRESOLVED CROSS SECTIONS

r u - 2 3 9 SET 2 . NO. 2 , T E S T n e u l N o m o r u ~ c n

ENOFIO-11 TAPE 2 0 1 R E V I S I O N S 2 .3 8-7-70. 6 - 2 5 - 7 0

THE FOLLOYING ENOF18 DATA CARDS HAVE BEEN PUNCHEO I N C-SURE TYPE FORMAT:

I C-SURE1 3, 11-10-71 . G. L. S INGER1 PROWCES P O I N T Y I S E UNRESOLVED CROSS SECTIONS

PU-239 SET 2. NU. 2. TEST REYINO AN0 PUNCH

E N D F I B - 1 1 TAPE 2 0 1 R E V I S I O N S 2.3 8-7-70. 8 - 2 5 - 1 0

8 .7000E 9.30OOE 9.7500E 1 .0500E 1 .0750E 1 .2250E 1 .3250E 1 .5500E 2.OOOOE 2.lOOOE 2 .2000E 2 .4000E 2.8OOOE 3 .5000E 6.5000E 8.5000E 1.OOOOE 1.7000E 2.5000E 2 .3700E 0.0 0.0 3.0000E 3. IOOOE 3.40UOE 3.6500E 4 .7500E 5 .2500E 5 .8000E 6. IOOUE 6.6500E 7.2500E 8 .2500E 8 .1000E 9.30OOE 9.7500E 1 .0500E 1.075OE 1.225OE

0.0 i i o c 0.0 1 1 0 4 0.0 1 1 0 4 0.0 1 1 0 4 0.0 1 1 0 4 0.0 1 1 0 4 0.0 1 1 0 4

DATE OF RUN 0 2 1 1 0 1 7 2 PAGE 3 3

T I M E : 10 .931 35 .81 ISEC.1

ENOF18 HAT. NO. 1 1 0 4

DATE OF RUN 0 2 1 1 0 1 7 2 PAGE 3 4

T IME: 0 . 3 0 1 3 b . l l I S E C . I

E N D F I B M4T. NU. 1 1 0 4

3 .5000E 0 3 8.7800E 0 0 0.0 1 .3170E-03 4.1600E-02 0.0 1 1 0 4 2 1 5 1 9 8 6 .5000E 0 3 8 .7800E 0 0 0.0 1 .3170E-03 4. lbOOE-02 0.0 1 1 0 4 2 1 5 1 9 9 8.50OOE 0 3 . 8 .7800E 0 0 0.0 1.3170E-03 4 .1600E-02 0.0 1 1 0 4 2 1 5 1 LOO 1.0000E 0 4 8.7800E 0 0 0.0 1.317OE-03 4.1600E-02 0.0 1 1 0 4 2 1 5 1 1 0 1 1.7000E 0 4 8.78OOE 0 0 0.0 1.317OE-03 4 .1600E-02 0.0 1 1 0 4 2 1 5 1 1 0 2

I C-SUREI 3 , 11-10-71, G. L . SINGERI PRODUCES POINTUISE UNRESOLVED CROSS SECTIONS

PU-239 SET 2, NO. 2. TEST REWIND AN0 PUNCH ,

ENDFIB-11 TAPE 2 0 1 R E V I S I O N S 2 .3 8-7-70, 8 - 2 5 - 7 0

DATE OF RUN 0 2 1 1 0 1 7 2 P4GE 3 5

T IME: 0 .271 36.38 ISEC.1

ENOF18 MAT. NO. 1 1 0 4

2.50UOE I. OOOOE 0.0 3.OOOOE J. LUUUt 3 .4000E 3 .6500E 4 .1500E 5. 25OOE 5 .8000E 6 .1000E 6 . 6 5 0 0 8 7.2500E 8.250UE 8.7000E 9.30OOE 9 . 7 5 0 0 1 1 .0500E

I C-SURE1 3, 11-10-71 . Gr L . SINGER1 PROOUCES POINTWISE UNRESOLVED CROSS SECTIONS DATE O F RUN 0 2 1 1 0 1 7 2 PAGE 3 6

P U - 2 3 9 SET 2 . NO- 2. TEST REWIND I N 0 PUNCH TIME: 0 - 1 7 1 36.54 1SEC.I

ENOFIB-11 TAPE 2 0 1 R E V I S I O N S 2 .3 8-7-70, 8 - 2 5 - 7 0 ENOF18 RAT. NO. 1 1 0 4

I C-SURE/ 3 1 11-10-71 . G. L. S INGER1 PRODUCES P O l N T Y l S E UNRESOLVED CROSS SECTIONS 0 4 7 E OF RUN 0 2 1 1 0 1 7 2 PAGE 3 7

PU-239 SET 2 , NU. 2 , TEST R E u l N O AN0 PUNCH TIME: O.27/ 36 .81 ISEC.1

E N O F I B - I 1 T I P E 2 0 1 R E V I S I O N S 2,) 8-7-70. 8 - 2 5 - 7 0 ENOF18 MAT. NO. 1 1 0 4

9 .6000E-01 1.OOOOE 0 0 4. OOOOE 00 L.0000E 0 1

I C-SURE/ 3, 11-10-71 . G. L. SINGER) PROOUCES POIN~YISE UNRESOLVEO CROSS SECTIONS

PU-239 SET 2 , NU. 2 , TEST REMIND AND PUNCH

ENDFIB-11 TAPE 2 0 1 R E V I S I O N S 2.3 8-7-70, 8 - 2 5 - 7 0

DATE O F RUN 0 2 / 1 0 / 7 2 PAGE 3 8

T I R E : ' 0 . 3 0 1 37.11 1SEC.I

E N O F l 8 MAT. NO. 1 1 0 4

I C-SURE/ 3, 11-10-11 , G. L. S INGER] PRODUCES P O l N T Y l S E UNRESOLVEO CROSS SECTIONS

PU-239 SET 2 1 NU. 2. TEST REWIND AN0 PUNCH

E X O F I B - I 1 TAPE 2 0 1 R E V I S I O N S 2.3 8-7-70, 8 - 2 5 - 7 0

I C-SURE1 3 1 11-10-71 . G- L. SINGER1 PRODUCES P O I N T W I S E UNRESOLVED CROSS SECTIONS

PU-239 SET 2, NU. 2 1 TEST REWIND AN0 PUNCH

ENOFIB-11 TAPE 2 0 1 R E V I S I O N S 2 . 3 8-1-10, 8 - 2 5 - 7 0

DATE OF RUN 0 2 1 1 0 1 7 2 PAGE 3 9

T IME: 0 .27 / 37.'31 ISEC.1

ENOF18 MAT. NO. I I O I

DATE OF RUN 0 2 1 1 0 1 7 2 PAGE 4 0

TIME: 0.231 37 .61 1SEC.I

E N D F I B MAT. NO. LLO*

I C-SURE1 3 , 1 1 - 1 0 - 7 1 . G. L . SINGER1 PROOUCES POINTWISE UNRESOLVEO CROSS SECTIONS DATE OF RUN 0 2 1 1 0 1 7 2 PAGE 4 1

P U - 2 3 9 SET 2, NU. 2. TEST REWIND 4NO PUNCH T I R E : 0 . 2 8 1 37.89 1SEC.I

ENOFIB-11 TAPE 2 0 1 R E V I S I O N S 2 ,3 8-7-10. 8 - 2 5 - 7 0 ENOF10 MAT. NO. 1 1 0 4

I C-SURE1 3. 1 1 - 1 0 - 7 1 , G. L. S INGERI PROOUCES POINTWISE UNRESOLVEO CROSS SECTIONS

PU-239 SET 2, NO. 2. TEST REWlNO AN0 PUNCH

E N D F I B - I 1 TAPE 2 0 1 R E V I S I O N S 2.3 8-7-10. 8 - 2 5 - 7 0

OATE OF RUN 0 2 1 1 0 1 7 2 P I C E 4 2

T I R E : 0 .221 38.11 1SEC.l

ENOF18 MAT. NO. 1 1 0 4

I C-SURE/ 3 , 1 1 - 1 0 - 7 1 9 G. L. S INGERI PRODJCES POINTWISE UNRESOLVEO CROSS SECTIONS DATE OF RUN 0 2 1 1 0 1 7 2 PAGE 4 3

PU-239 SET 2, NU. 2. T E S T REWINO AND PUNCH TIME: 0 . 2 3 1 38.34 ISEC.1

E N D F I B - I 1 TAPE 2 0 1 R E V I S I O N S 2 .3 8-7-70. 8 - 2 5 - 7 0 . ENOF18 MAT. NO. 1 1 0 4

I C-SURE1 3 , l l - 1 0 - 7 1 . G. L. SINGER) PRODUCES POINTWISE UNRESOLVED CROSS SECTIONS DATE O F RUN 0 2 1 1 0 1 7 2 PAGE 4 4

PU-239 SET 2. NO. 2. TEST REMIND AN0 PUNCH TIME: 0.0 1 38.34 1SEC.I

E N O F I B - I 1 TAPE 2 0 1 R E V I S I O N S 2 1 3 8-7-70, 8 -25-70 E N O F l 8 MAT. NO. 1 1 0 4

*** UNRESOLVEO RESONANCE CROSS SECTIONS *** LOWER UNRESOLVEO RANGE ENERGY L I M I T I N EV.:. 3.0000E 0 2 UPPER UNRESOLVEO RANGE ENERGY L I M I T I N EV.: 2.5000E 0 4

ENERGV

TOTAL

CAPTURE F I S S I O N

RESONANCE C O N T R l 8 U T l O N

CAPTURE F I S S I O N

SMOOTU CONTRIBUTION

CAPTURE F I S S I O N

.. . . . .

1 C-SURE1 3. 1 1 - 1 0 - 7 1 , G. L. SINGER1 PROOUCES POINTWISE UNRESOLVEO CROSS SECTIONS

PU-239 SET 2 , NU. 2. TEST REMIND AND PUNCH

E N D F I B - I 1 TAPE 2 0 1 R E V I S I O N S 2 .3 8-7-70. 8 - 2 5 L 7 O

S-HAVE RESONANCE CONTRIBUTION

ENERGY CAPTURE F I S S I O N

I C-SURE1 3. 1 1 - 1 0 - 7 1 . G. L . SINGER1 PROOUCES P O I Y T M I S E UNRESOLVEO CROSS SECTIONS

PU-239 SET 2. NO. 2 , TEST REWIND &NO PUNCH

ENOF18-11 TAPE 2 0 1 R E V I S I O N S 2 1 3 8-7-70. 8 -25-70

ENERGY TOTAL SCATTER

SMOOTH CONTRIBUTION

RESONANCE C O N T R l 8 U T l O N

DATE O F RUN 0 2 1 1 0 1 7 2 PAGE 4 5

T IME: 0 . 2 5 1 38.59 1SEC.I

ENOF18 MAT. NO. 1 1 0 4

P-WAVE RESONANCE C O N T R l 8 U T l O N

CAPTURE F I S S I O N

5 . 9 2 8 l E - 0 2 3 .1601E-01 6 .0T75E-02 ' 3.2CBOE-01 6 .22 IOE-02 3.3333E-01 6 .3589E-02 3 . 4 1 6 I E - 0 1 6 .4916E-02 3 .4967E-01 6 .6194E-02 3 .5751E-01 6 .7427E-02 3 .6516E-01

OATE O F RUN 0 2 1 1 0 1 7 2 PAGE 4 6

T IME: 0 . 0 3 1 38 .b2 ISEC.)

ENOF18 MAT. NO. I 1 0 4

S-HAVE P-MAVE CONTRIBUTION C O N T R l 8 U T l O N

I C-SURE1 3 1 11-10-71 . G. L. S INGER1 PRODUCES P O I N T W I S E UNRESOLVED CROSS SECTIONS DATE OF RUN 0 2 1 1 0 1 7 2 PAGE 4 7

SET 2 1 NO. 3. TEST ALTABN A N 0 SMFAC U S I N G I S O N L Y 5 1 T I M E : 0 . 0 5 1 38 .67 ISEC.1

E N O F I B MAT. NO. 1 1 0 4

CONTROLLING I N P U T CARDS A S READ NUMBER OF THE RUN = 1 0

I N P U T CARDS AFTER DEFAULTS

MATNO I O T A P INUMSH I P T I M E I P T P L G I S K C F S I S O N L Y LETHM MESHRO NOFB NDFBCH NOFPUN I R E Y

1 1 0 4 2 0 1 5 1 4 - -1 1 -I 1 9 -1 -1 - 1

A L T A B N S I G P SMFAC TKELVN ELOREO 'EHIREO

5 . 0 0 0 0 E - 0 1 1.0000E 0 7 2.5OOOE-01 1 .0000E-20 -2 .0000E 0 0 -2 .0000E 0 0

THE I N P U T V A R I A B L E I S U N L Y H A S BEEN USEO. ONLY ISOTOPE NUMBER 1 M I L L B E PROCESSED

THE I N P U T V A R I A B L E A L T A B N HAS BEEN USEO. THUS THE ABUNDANCE Y E I G H T I N G FOR T H I S ISOTOPE H I L L B E 5 . 0 0 0 0 E - 0 1

TnE I N P U T V A R I A B L E SMFAC HAS BEEN USEO. A L L SMOOTH CROSS SECTIONS PROOUCED W I L L BE M U L T I P L I E O BY 2 .5000E-01

I C-SURE1 3. 11-10-71 . G. L - S INGER1 P R O W C E S P O I N T Y I S E UNRESOLVEO CROSS SECTIONS OATE OF RUN O Z 1 1 0 1 7 2 PAGE 4 8

PI)-?a9 SET 2. NO. 3 r TEST A L T A I N A N 0 SMFAC U S I N G ISDULY = 1 T I M C t 0 .021 30 .b9 1SEC.I

E N O F I B - 1 1 TAPE 2 0 1 R E V I S I O N S 2.3 8 -7 -70 . 8 - 2 5 - 7 0 E N O F l B MAT. NO. 1 1 0 4

*** UNRESOLVEO RESONANCE CROSS SECTIONS **a

L W C R UNRESOLVED RANGE ENERGY L I M I T I N FV.: 3.OOOOE 0 2 UPPER UNRESOLVED R 4 N b E ENERBI L I n L I I N tV.: Z.5UUUE 0 4

TOTAL

ENERGY CAPTURE F I S S I O N

RESONANCE C O N T R I B U T I O N

CAPTURE F I S S I O N

SMOOTH C O N T R I B U T I O N

CAPTURE F I S S I O N

I C-SURE1 3. 1 1 - 1 0 - 7 1 . G. L. S INGER1 P R O W C E S P O I N T V I S E UNRESOLVED CROSS SECTIONS DATE OF RUN 0 2 1 1 0 1 7 2 PAGE 4 9

PU-239 SET 2. NO. 3. TEST ALTABN AN0 SMFAC U S I N G ISONLY I T I M E : 0 . 2 8 1 38.97 1 S E C - l

E N D F I B - 1 1 TAPE 201 R E V I S I O N S 2 1 3 6-7-70, 6 - 2 5 - 7 0 E N O F 1 0 MAT. NO. 1 1 0 4

S-WAVE RESONANCE C O N T R I B U T I O N P-HAVE RESONANCE C O N T R I B U T I O N

ENERGY CAPTURE F I S S I O N CAPTURE F I S S I O N

I C-SURE1 3. 1 1 - 1 0 - 7 1 . G. L. S I N G E R 1 PRODUCES P O I N T Y I S E UNRESOLVED CROSS SECTIONS D A T E OF RUN 0 2 1 1 0 1 7 2 PAGE 5 0

PU-239 SET 2 . NU. 3. TEST ALTABN AND SMFAC U S I N G I S O N L Y = 1 T I M E : 0 . 0 2 1 38.99 1SEC.I

E N O F I B - I 1 TAPE 2 0 1 R E V I S I O N S 2 .3 8 -7 -70 . 8 - 2 5 - 7 0 E N D F I B MAT. NO. 1 1 0 4

ENERGY

3 .10742 0 3

TOTAL SCATTER

S M O T H RESONANCE , S-WAVE P-WAVE C O N T R I B U T I O N C O N T R I B U T I O N .CONTRIBUTION C O N T R I B U T I O N

I C-SURE1 3, l l - 1 0 - 1 1 . G. L. S INGER) PRODUCES POINTWISE UNRESOLVED CROSS SECTIONS

SET 2, NO. 4. TEST NDFB = 5 LENOF18 CARD I N P U T )

OATE O F RUN 0 2 1 1 0 1 7 2 PAGE 5 1

T IME: 0.03/ 39.02 ISEC.1

ENOF18 MAT. NO. 1 1 0 4

NUMBER OF TnE RUN = I 1 CONTROLLING INPUT CAROS AS READ

SET 2 . NO. 4. TEST NDFB = 5 l E N D F l 8 CARO I N P U T 1 1 1 0 4 0 5 1 0 0 - 1 0 2 5 0 0 1

-1 .0000E 0 0 1.OOOOE 0 1 1.OOOOE 0 0 1 .0000E-20 0.0 0.0

I N P U T CAROS AFTER DEFAULTS

MATNO IOTAP INUMSH I P l l M E I P T P L G I S K C F S LSONLY LETHM

1 1 0 4 2 0 1 5 I 4 - 1 - 1 -1

MESHRO NOF8 NDFBCH NOFPUN I R E U

2 5 - 1 - 1 I

ALTAON s l c r S ~ F A C TKCLVN CLORCD

-1.0000E 0 0 1.OOOOE 0 7 1.0000E 0 0 1.0000E-20 -2.0000E 0 0

OATE OF RUN O L l l O l l 2 PAGE 5 2

T IME: 0 . 0 3 1 39.05 'lSEC.1

I C-SURE1 3 , 11-10-11 . G. L. S INGERI P R O W C t S P U I N I W L 5 t UNReSOLVEU CROSS SECTIONS

P u - 2 3 9 SET 2. NU. 4. TEST NDFB E 5 l E N D F l 8 CARO INPUT)

ENWIB MAT. NO. 1104

INPUT CAROS FOR MESH

I C-SURE1 3, l l - 1 0 - 1 1 . G. L. S I N G E R I PRODUCES P O l N T W l S E UNRESOLVED CROSS SECTIONS

P U - 2 3 9 SET 2. NU. 4. TEST NOFB = 5 l E N D F l 8 CARO I N P U T 1

DATE O F RUN 0 2 / 1 0 1 7 2 PAGE 5 3

T IME: 0.0 1 39.05 1SEC.l

ENOF18 MAT. NO. 1 1 0 4

I C-SURE1 3. 1 1 - 1 0 - 7 1 , G. L. S I N G E R I PRODUCES P O I N T W I S E UURESOLVEO CROSS SECTIONS

SET 2. NO. 4. TEST NDFB = 5 ( E N D F I B CARD I N P U T 1

PU-239 1 1 0 4 1 4 5 1 1

ENOF18 CARD DATA I N P U T

PU-239 1 1 0 4 1 4 5 1 1

OATE OF RUN 0 2 / 1 0 / 7 2 PAGE 5 1

TIME: 0.0 1 39.05 ISEC.1

ENOF18 MAT. NO. 1 1 0 4

. .- 9 . 4 2 3 9 1 9 . 4 2 3 9 1 3 .0000E 5 .0000E 2 .3100E 0.0 0.0 3.0000E 3.1000E 3.4000E 3.6500E 4.7500E 5.250UE 5 .8000E 6. LOOOE 6.6500E 1.2500E 8.25OOE 8 .7000E 9 .3000E 9 .75008 1 .0500E 1.0750E l . 2 2 5 0 E 1.3250E I. 5 5 0 0 E 2.OOOOE 2.IOOOE 2 .2000E 2.4000E 2.8000E 3 .5000E 6 . 5 0 0 0 6 8 .5000E 1.OOOOE 1 .7000E 2.5000E 1.OOOOE 0.0 3. OOOOE 3 .1000E 3 .4000E 3 .6500E 4 .7500E 5 .2500E 5.8000E 6.IOOOE 6 .65008 1 .2500E 8 .2500E 8 .7000E 9 .3000E 9 .7500E

I C-SURE1 3, 11-10-71 . G. L. S I N G E R I PRODUCES P O l N T Y l S E UNRESOLVED CROSS SECTIONS

SET 2 , NU. 4 , TEST NOFB = 5 l E N O F 1 8 CARO I N P U T I

3 , 11-10-71 . G.

SET 2 1 NU. 4.

L. S I N G E R I PRODUCES P O l N T Y l S E UNRESOLVED CROSS SECTIONS

TEST NOFB - 5 l E N O F l 8 CARO I N P U T I

1 1 0 4 1 4 5 1 1

OATE OF RUN 0 2 1 1 0 1 1 2 PAGE 5 5

TIME: 0 . 2 7 1 39.32 ISEC.1

ENOF18 MAT. NO. 1 1 0 4

OATE OF RUN O Z l l O l

TIME: 0 .221

MAT. NO. 1 1 0 4

7 2 PACE 5 6

39.54 ISEC.1

I C-SURE1 3 , 11-10-11. G. L . SINGER) PROOVCES POlNTYlSE UNRESOLVEO CROSS SECTIONS DATE OF RUN 02110172 PAGE 57

SET 2 . NU. 4 , TEST NDFB = 5 lENOFl0 CAR0 INPUT) TIME: 0.251 39.79 ISEC. I

3 , 11-10-71, G. L. SINGER) PRODUCES POlNrYlfE UNRESOLVEO CROSS SECTIONS

SET 2 . NO. 4 , TEST NOFB = 5 lENOFl8 CARO INPUT1

1104 1 4 5 1 1

1.5950E 0 0 4.50OOE 0 4 1.515JE 00 5.0000E 04 1.5580E OOllOO 3 i 8 232 1.5500E 0 0 5.7300E 04 1.5430E 0 0 6.0000E 04 1.5350E 001104 3 1 8 233 1.5200E 0 0 7.0000E 0 4 1.5080E 00 7.50WE 0 4 1.5000E 001104 3 1 8 234 1.4990E 0 0 8.0000E 0 4 1.4980E 00 8.5000E 04 1.4930E 001104 3 1 8 235 1.5850E 0 0 9.5000E 04 1.4900E 0 0 1.OOOOE 05 1.4970E 001104 3 18 236 1.4970E 0 0 1.4000E 05 1.4980E 00 1.6000E 05 1.501OE 001104 3 1 8 2 3 1 1.50LOE 0 0 1.8000E 05 1.5030E 0 0 1.9300E 05 1.5030E 001104 3 18 238 1.5030E 00 2.2000E 0 5 1.5050E 0 0 2.4OOOE 05 1.5050E OOllO4 3 1 8 239 1.5050E 0 0 2.8OOOE 0 5 1.5030E 0 0 2.8730E 05 1.5030E 001104 3 1 8 240 1.5030E 0 0 3.2OOOE 05 1.5090E 0 0 3.3140E 05 1.512OE 001104 3 1 8 211 1.5140E 0 0 3.6000E 05 1.512OE 0 0 3.8000E 05 1.5150E 001104 3 I 8 242 1.5170E 0 0 3.9370E 05 1.518OE 00 4.0000E 05 1.5200E 001104 3 1 8 243 1.52IOE 0 0 4.3380E 05 1.52OOE 0 0 4.3690E 05 1.520OE 001104 3 1 8 244 1.5200E 0 0 4.6000E 0 5 1.5ZZOE 0 0 4.6300E 05 1.52ZOE 001104 3 1 8 245 1.5240E 0 0 4.8000E 0 5 1.5250E 0 0 4.8200E 05 1.5260E O O l l O I 3 1 8 246 1.5270E 0 0 5.0000E 0 5 1.5290E 0 0 5.0700E 05 1.5300E 001104 3 1 8 247 1.5320.5 0 0 5.2OOOE 05 1.5330E 0 0 5.40M)E 05 1.5370E 001104 3 1 8 248 1.5410E 0 0 5.60M)E 0 5 1.54ZOE 0 0 5.8000E 05 1.5510E 001104 3 1 8 249 1.4590E 0 0 b.2000E 0 3 1.SblOE 0 0 6.4000E 05 1.575OE 001104 3 1 8 250 1.5820E 0 0 6.8000E 0 5 1.594OE 0 0 7.OOOOE 05 1.6130E 001104 3 1 8 2 5 1

1.6800E 0 0 8.8OOOE 0 5 1.6560E 0 0 9.0000E 05 1.6440E 001104 3 1 8 255 1.6410E 0 0 9.4000E 05 1.6490E 0 0 9.6000E 0 5 1.66308 001104 3 1 8 2 5 6 1.6810E 0 0 1.0000E 0 6 1.7000E 00 1.1000E 0 6 1.1530E O O l l O I 3 1 8 257 1.7550E 0 0 1.3000E 0 6 1.7640E 0 0 1.4000E 06 1.804OE 001104 3 1 8 258 1.8650E 0 0 1.6000E 0 6 1.9290E 0 0 1.7OOOE 0 6 1.9750E 001104 3 1 8 259 2.0000E 0 0 1.9000E 0 6 2.0070E 00 2.OOOOE 0 6 2.OOIOE O O l l O I 3 I 8 260 1.9800E 0 0 2.2OOOE 0 6 1.9560E 00 2.3000E 0 6 1.9180E 001104 3 I 8 2 6 1 1.8820E 0 0 2.5000E 0 6 1.8560E 0 0 2.6000E 06 1.8380E 001104 3 1 8 262 1.827OE 0 0 2.8OOOE 0 6 1.8250E 00 2.9000E 0 6 1.827OE 001104 3 1 8 263 1.8310E 0 0 3.1000E 0 6 1.8320E 0 0 3.2000E 0 6 1.8320E 001104 3 I 8 265 1.8290E 0 0 3.4000E 0 6 1.8240E 00 3.5000E 0 6 1.8150E 001104 3 I 8 265 1.8060E 0 0 3.7000E 0 6 1.7940E 0 0 3.8000E 0 6 1.7820E 001104 3 I 8 2 6 6 1.1710E 0 0 4.0000E 0 6 1.7570E 00 4.1000E 0 6 1.7450E 001104 3 1 8 267 1.732OE 0 0 4.3000E 0 6 1.72OOE 0 0 4.4000E 06 1.7090E 001104 3 1 8 268 1.6980E 0 0 4.6000E 0 6 1.6890E 00 4.7OOOE 0 6 1.6780E O O l l O I 3 1 8 269 1.6690E 0 0 4.9000E 0 6 1.6600E 00 5.OOOOE 0 6 1.6540E 001104 3 1 8 2 7 0

ENOF18 MAT. NO. I

DATE OF RUN 02110172 PAGE 5 8

TIME: 0.231 40.02 LSEC.1

ENOF18 MAT. NO. 1104

3, 11-10-71 , G. L. SINGER1 PRODUCES P O l N T Y l S E UNRESOLVEO CROSS SECTIONS

SET 2 , NU. 4. TEST NOFB = 5 IENOFIB CARD INPUT)

1 1 0 4 1 4 5 1 1

I C-SURE1 3 1 11-10-71 . G. L. S INGER) PROWCES P O l N T Y l S E UNRESOLVEO CROSS SECTIONS

SET 2. NO. 4, TEST NDFB = 5 I E N O F I B CARD I N P U T 1

5 .5000E 6.5000E 7.b400E 9.0000E 1.2OOOE 1.6470E 2. OOOOE 2.6OOOE 3 .0000E 3 .4000E 3 . 8 9 1 0 1 4.2OOOE 4 .4000E 4.72OOE 4 .88008 5.142OE 5.5860E 6 .0000E 6.6000E 7.2000E 7.6300E 8.2000E 8.6000E 9. ZOOOE 9. UOOOE L.2OOOE I. SOOOE

OATE O F RUN O 2 l l O l

T INE: . O.22/

MAT. NO. 1 1 0 4

7 2 PLGE 8 5 9

40.24 1SEC.J

OATE OF RUN 0 2 1 1 0 1 7 2 PLGE 6 0

T IME: 0 .201 40.44 ISEC.1

E N D F I B MAT. NO. 1 1 0 4

I C-SURE1 3. 11-10-71 . G. L. SINGER) PROOUCES P O l N T Y l S E UNRESOL,VEO CROSS SECTIONS

SET 2. NO. 4 1 TEST NDFB 3 5 I E N O F I B CARD I N P U T 1

DATE OF RUN 0 2 1 1 0 1 7 2 PAGE 6 1

T I H E : O.LO/ 40.63 ISEC.1

PU-239 I 1 0 4 1 6 5 1 1 ENOF18 HAT. NO. 1 1 0 4

1 .9000E 2.2OOOE 2.5000E 2 .8000E 3. LOOOE 3 .4000E 3 .7000E 4 .0000E 4.3000E 4.6000E 4.9000E 5 .2OWE 5 .5000E 5 .8000E 6 . I O W E 6 .4000E 6.7OOOE t.UUUUE 7.3000E 7 .6000E 7.9000E 8 .4000E 9 . 0 0 0 0 E 9.6000E 1.0500E L.2OOOE L.3000E 1 .4500E

I C-SURE1 3 r 11-10-71 . G- L. S INGER1 PROWCES P O l N T Y l S E UNRESOLVED CROSS SECTIONS DATE OF RUN O Z l l O l 7 2 . PAGE 6 2

SET 2. NO. 4 , TEST NOFB = 5 l E N O F l 8 CARO I N P U T 1 T IME: 1.45/ 42.08 1SEC.I

PU-239 - 1 1 0 4 1 4 5 1 1 ENOF18 MAT. NO. 1 1 0 4

*** UNRESOLVEO RESONANCE CROSS SECTIONS

L W E R UNRESOLVEO RANGE ENERGY L I M I T I N EV., 3.0OOOC 0 2 UPPCR UNRCSOLVCD RANGC CNERGY L I M I T I N EV.: 2.5OOOE 0 4

TOTAL

ENERGY CAPTURE . F I S S I O N

RESONANCE CONTRIBUTION

CAPTURE ' F I S S I O N

SMOOTH C O N T R ~ ~ U T ~ O N

CAPTURE F l SSlON

I C-SURE1 3. 11-10-71 . G. L. S INGER1 PROOUCES POINTWISE UNRESOLVEO CROSS SECTIONS DATE OF RUN O 2 / l O l 7 Z PbGE 6 3

SET 2. NO. 4 1 TEST NOFB = 5 I E N O F I B CARO I N P U T ) T I M E : 0 .131 42.22 1SEC.I

PU-239 1 1 0 4 1 6 5 1 1 E N O F l 8 MAT. NO. I 1 0 4

S-HAVE RESONANCE CONTRIBUTION P-WAVE RESONANCE C O N T R l 8 U l l O N

ENERGY CAPTURE F I S S I O N CAPTURE F I S S I O N

I C-SURE/ 3 r 11-10-71 . G. L - SINGER) PROOUCES P O I N T U I S E UNRESOLVED CROSS SECTIONS OATE OF RUN O Z / l O l 7 2 PAGE 6 4

SET 2 1 NO- 4 , TEST NOF8 = 5 I E N O F I B CARO I N P U T 1 T IME: 0.031 4 2 - 2 5 ISEC.)

PU-239 1 1 0 4 1 1 5 1 1 ENOF18 MAT- NO. 1 1 0 4

ENERGY TOTAL SCATTER

SMOOTH C O N T R l 8 U T l O N

RESONANCE S-WAVE . C O N T R l 8 U T l O N CONTRIBUT I O N

P-HAVE C O N T R l 8 U T l O N

I C-SURE1 3, 1 1 - 1 0 - 7 1 . G. L. S INGER1 PROOUCES P O I N T Y I S E UNRESOLVED CROSS SECTIONS

SET 2. NO. 5 . TEST NOFBCH I W A N G I N G I N O I V I O U A L ENOF18 DATA CAROSl

CONTROLLING I N P U T CARDS A S REAO

0 4 T E OF RUN 0 2 1 1 0 1 7 2 PAGE 65

TIME: 0 . 0 5 1 42.30 ISEC.1

E N O F I B M4T. NO. 1 1 0 4

NUMBER OF THE RUN = 1 2

SET 2. NO. 5, TEST N O f B C l l l C l l 4 N G l N G I N O I V I O U A L E N O P I B D A l 4 CAROSl 0 0 0 1 0 0 0 - 1 5 2 0 0

0.0 0.0 0.0 0.0 0.0 0.0

I N P U T C4RO.5 L F T F R n C F A I I L T S

MATNO 1OT4P INUMSH 1 P T l l E I P T P L G I S K C F S I S O N L Y LETHM MESHRO ' NOFU NDFBCH NOFPUN I R E Y

1 1 0 4 2 0 1 5 I 4 - 1 - 1 -I -1 5 2 -1 -1

A L T A B N S l G P SMFAC TKELVN ELOREO EHIREO

-1 .0000E 0 0 1 .0000E 0 7 1.0000E 0 0 1 .0000E-20 -2.0000E 0 0 -2 .0000E 0 0

I C-SURE1 3. 1 1 - 1 0 - 7 1 . G. L.. S INGER1 PROOUCES P O I N T Y I S E UNRESOLVED CROSS SECTIONS

SET 2. NO. 5. T E S T NOFBCH I C H A N G I N G l N O l V I O U 4 L ENOF18 OATA CARDS1

P U - 2 3 9 1 1 0 4 1 4 5 1 1

ALTERED ENOF18 I N P U T OATA

DATE OF RUN 0 2 l l 0 1 7 2 P I C E 66

TIME: 0 .021 42.32 ISEC.1

ENOF18 MAT. NO- 1 1 0 4

3 . 0 0 0 0 ~ 3. LOOOE 3 .4000E 3.6500E 4.7500E 5. 25OOE 5.8000E 6. IOOOE 6 .6500E . 7.2500E 8.2500E 8.7OOOE 9.3000E 9.1500E 1.0500E 1.0150E 1.225OE 1.3250E 1 .5500F 2.0000E 2. IOOOE

3. 1 1 - 1 0 - 1 1 . G. LI

SET 2. NO. 5 1

, SINGER1 PRODUCES P O l N T H l S E UNRESOLVED CROSS 51

TEST NOFBCH LCHANGING l N D l V l O U A L ENOF18 OPTA C1

NE U

NEW

DATE Of

T IRE:

MAT. NO.

: RUN 0 2 1 1 0 1 1

0.301

1 1 0 4

' 6 7

I SEC. I

4.6000E OOllOI 3 I8 0.0 1104 3 18 4.900OC OOllOI 3 18 0.0 1104 3 18 1.6200E 001104 3 18 1.5580E 001104 3 18 1.5350E 001104 3 18 1.5000E 001104 3 18 1.4930E 001104 3 18 1.4970E 001104 3 I8 1.5OIOE 001104 3 I8 1.5030E 001104 3 1B 1.5050E 001104 3 I8 1.5030E 001104 3 18 1.5120E 001104 3 18 1.5150E OOllOI 3 18 1.520Ut 001104 3 18 1.5200E OOllOI 3 18 1.522OE OOllOI 3 I8 1.5260E OOllOI 3 18 1.5300E OOllO4 3 18 1.5370E 001104 3 18 1.551OE 001104 3 I8 1.5750E OOllOI 3' 18 1.6130E 001104 3 I8 1.65lOE 001104 3 18 1.7170E 001104 3 18 1.69001 OOllOI 3 10 1.6440E 001104 3 18 1.6630E 001104 3 18 1.7530E 001104 3 18 1.8040E 001104 3 18 1.9750E 001104 3 18 Z.OO4OE 001104 3 18 1.918OE 001104 3 I8 1.8380E 001104 3 18 1-B27OE OOllOI 3 18 1.8320E 001104 3 18 1.8150E 001104 3 I8 1.78ZOE OOllOI 3 I8 1.7450E 001104 3 18 1.709OE 001104 3 18 1.6780E OOllOI 3 18 1-654OE 001104 3 18 1.6520E 001104 3 18 1.6610E 001104 3 18 1.6890E 001104 3 I8 1.7660E 001104 3 18 L.YUZOE OOllOI 3 18 2.OO9OE 001104 3 I8 2.0870E 001104 3 18 2.15bOE 001104 3 18 2.1830E 001104 3 I8 2.214OE 001104 3 18 2.229OE OOllOI 3 I8 2.2560E OOllO4 3 I8 2.2480E 001104 3 I8 2.2430E 001104 3 18 2.ZBOOE 001104 3 18 2.2940E OOllO4 3 18 2.321OE 001104 3 18

01104 3 0 01104 3102

I C-SURE/ 3 , 11-10-71 . G. L. S INGER1 PRODUCES P O l N T Y l S E UNRESOLVED CROSS SECTIONS DATE OF RUN 0 2 / 1 0 / 7 2 PACE 6 8

SET 2 , NO. 5. TEST NOFBCH (CHANGING I N O l V l D U A L E N D F l 8 DATA CARDS) TIME: 2.65/ 45.26 I S E C - I

PU-239 1 1 0 4 1 1 5 1 1 ENOF18 MAT. NO. 1 1 0 4

*** UNRESOLVED RESONANCE CROSS SECTIONS *** LWER UNRESOLVED RANGE ENERGY L I M I T IN EV.: 3 . 0 0 0 0 ~ 0 2 UPPER UNRESOLVED RANGE ENERGY LIMIT IN EV.: Z.SOOOE 0 4

TOTAL

ENERGY CAPTURE F I S S I O N

RESONANCE W N T R I B U T I O N

CAPTURE F I S S I O N

SMOOTH CONTRIBUTION

CAPTURE F I S S I O N

I C-SURE1 3. 11-10-71 . G. L - S INGER1 PROWCES P O l N T Y l S E UNRESOLVED CROSS SECTIONS DATE OF RUN O 2 1 1 0 / 7 2 PACE 6 9

SET 2. ND. 5 r TEST NDFBCH I C H A M i l H ; I N O l V I O U A L 6 N O F I 8 DATA CAR051 T i a t : 0.631 45 .89 ISEC.]

PU-239 . 1 1 0 4 1 4 5 1 1 E N O F l B MAT. NO. 1 1 0 4 . S-WAVE RESON~NCE C O N T R l 8 U T l O N P-HAVE RESONANCE C O N T R l 8 U T l O N

ENERGY CAPTURE F I S S I O N CAPTURE F I S S I O N

I C-SURE/ 3 1 1 1 - 1 0 - 7 1 . G. L. 5 I M i t R I PRODUCES P O l N T Y l S E UN(ESOLVE0 CROSS SECTIONS O l T E OF RUN 0 2 1 1 0 1 7 2 PAGE 7 0

SET 2 1 NO. 5. TEST NOFBCH ICHANGIUG l N O l V I O U A L ENOF18 DATA CARDS1 T IME: 0.05/ 45.94 lSEC.1

P U - 2 3 9 1 1 0 1 1 1 5 1 1 ENDF18 MAT. ND. 1 1 0 4

EYERGV SMOOTH c o N T R l 8 U r l O N

RESONANCE C o N T R l s U r l o ~

S-YAVE P-WAVE C O N T R l 8 U T l O N C O N T R ~ B U T I O N

EN0 OF OATA. END OF PROBLEM