PHYSICAL REVIEW C VOLUME 18, NUMBER 1 JULY 1978

Energy levels of Fe populated by the Fe( &,p) Fe reaction

Eric B. Norman*Physics Division, Argonne National Laboratory, Argonne, Illinois 60439

and University of Chicago, ChicagoIl, linois 60637

Cary N. DavidsPhysics Division, Argonne National Laboratory, Argonne, Illinois 60439

Calvin E. MossLos Alarnos Scientific Laboratory, Los Alamos, ¹eMexico 87545

(Received 23 January 1978)

Thirteen levels below 3.8-MeV excitation in Fe have been identified using the "Fe(t,p) Fe reaction.Analysis of the proton angular distributions has yielded spins and parities of most states observed below 3.1MeV. The ground-state Q value is 6913+4 keV, yielding a mass excess for Fe of —61404+5 keV. Thelevel structure of Fe deduced from this experiment is compared with previous measurements and is discussedin terms of a vibrational model.

NUCLEAR REACTIONS Fe(t,p) Fe, E,=17.0 MeV, QBD spectrograph; en-riched targets, measured excitation energies, do/dO(0, E&), DWBA analysis.

6 Fe levels deduced I.,J,x.

INTRODUCTION

In recent years the iron isotopes have been thesubjects of many theoretical and experimental in-vestigations. These nuclei are of interest becauseof their proximity to the closure of the fv&, protonshell, and because they bracket the closure of the

f», neutron shell. Until recently, however, verylittle was known about the structure of the neutron-rich isotope "Fe.

The half life of "Fe is thought to be approxi-mately 1 && 10' yr 'The (t., p) reaction on "Fe wasfirst performed by Casten et al. ' at a bombardingenergy of 13 MeV. They measured a ground-stateQ value of 690 I + 15 keV and a ground-state dif-ferential cross section of 2.51 mb/sr at 12.5' inthe laboratory. Sakai' observed four p rays in the~'Ca("0, ct2ny)" Fe reaction which he tentativelyattributed to the decays of levels at 0.823-,1.668-, 1.833-, and 2.114-MeV excitation energyin "Fe. Steele et al. ' used the ('He, 'Be) reactionon ~Ni to study "Fe. The mass excess of 60Fe

was measured to be -61437 +10 keV. In addition,states at 0.835, 2.11, and 3.08 MeV were observed inthis investigation. Recently Warburtonetal. 'report-ed the results obtained in ~Ca("N, 2npy)eoFe4'Ca("0, a.2ny)eoFe, and "Fe(t,py)eoFe experiments.A number of new states in "Fe were observed,and spins, parities, and lifetimes were deter-mined for some levels. Hansen et al. ' have studied"Fe using the (d, 'I i) reaction on "Ni. Severalstates were observed in this experiment includinga previously unreported level at 2370 keV.

The present study was undertaken as a result ofthe observation by Norman et aL' of the p decayof the new isotope "Mn. In order to determinethe spin and parity of "Mn, it was necessary toknow the spins and parities of the levels in "Feto which it P decays. In addition, it was hopedthat by using a higher triton bombarding energythan had been used previously, more detailed in-forfnation could be obtained on higher excitedstates. .

EXPERIMENTAL METHOD

A 100-p,g/cm' "Fe target, enriched to 82.5'"Fe was bombarded with a 17-MeV triton beamfrom the Los Alamos tandem Van de Graaff ac-celerator. Beam currents of approximately 100nA were used in measurements at forward anglesin order to reduce dead time corrections, but wereincreased to 300 nA at back angles. Charges of600 p C were collected for all angles up to 70 .The reaction protons were momentum analyzed:with the Los Alamos quadrupole-dipole-dipole-dipole (QSD) type II spectrograph and detected atthe focal surface with a helical-cathode position-sensitive proportional counter. ' The spectrographwas calibrated using the (t, p) reactions on "Fe,"Co, and "Ni targets because these reactionshave Q values comparable to that of the"Fe(t,P)"Fe reaction and because the masses andlevel schemes of "Fe, "Co, and "Ni are accurate-ly known. ' " From these reactions a calibrationcurve was obtained by making a least-squares fit

102 1978 The American Physical Society

ENERGY LEVELS OF Fe POPULATED BY THE Fe(t, p)6 Fe. . . I03

to a fourth-order polynomial of proton momentumversus channel number. The peak centroid chan-nels of the proton groups from the "Fe(t,p)60Fereaction were then used to find the Q values andhence excitation energies of the "Fe states. Ex-citation energies. in "Fe were measured up to 3.7MeV. Angular distributions, taken in 5' stepsfrom 10' to 70', were measure'd for states ob-served below 3.1 MeV.

Elastically scattered tritons were monitoredwith a silicon surface-barrier detector positionedat 30' in the scattering chamber in order to de-tect possible changes in target thickness frombeam heating. These elastically scattered tritonswere also used to establish an absolute cross-sec-tion scale by normalizing the observed yields tooptical-model calculations. The accuracy of theabsolute cross section is estimated to be +20'%%uo.

RESULTS AND ANALYSIS

The proton spectrum measured at a laboratoryangle of 15' is shown in Fig. 1. The resolutionwas approximately 15 keV [full width at half maxi-mum (FWHM)]. Many of. the peaks in this spec-trum are attributed to levels in "Fe produced bythe (f, P) reaction on the "Fe contaminant in thetarget. Those peaks identified by energy only havebeen attributed to levels in "Fe. The ground-stateQ value for the "Fe(t,p) "Fe reaction was found tobe 6913+4 keV. Using the value -62151.8 keV forthe mass excess of "Fe,"one obtains for the massexcess of "Fe -61404+5 keV. This value dis-agrees with the result -61437 +10 keV of Steele

et al. by 33 keV, but agrees very well with thevalue -61 398 + 15 keV calculated using the ground-state Q value measured by Casten et al. ' in theirprevious (t, p) study.

Table I shows the excitation energies, spins,parities, and peak differential cross sections mea-sured in the present work together with previouslyreported data on "Fe. The errors quoted for theexcitation energies measured in this investigationtake into account uncertainties in the beam energyand spectrograph angle, uncertainties in calibra-tion, and statistical errors. Figure 2 shows theproton angular distributions obtained in the pres-ent work for 10 levels in "Fe. The results of thedistorted-wave Born approximation (DWBA) cal-culations described below are shown along withempirical curves taken from angular distributionsobtained from states of known spin.

The spins and parities of the levels in "Fe re-ported here have been determined in two ways.We have used the results of DWBA calculationsand also those of an empirical method in which theI transfers are determined by comparing theshapes of the distributions from the states in ques-tion with those obtained from levels whose spinsare known. Both of these methods rely on a use-ful feature that has been observed in (t, p) reac-tions on even-even (0') targets. The transferredangular momentum and parity appear to be unique-ly determined by the orbital angular momentum I-with which the two neutrons enter the target nu-cleus. The resulting angular momentum and parityof the final state are thus I and (-1), respec-tively x3

1000-

800—

LLj

~ 600

~ 400-OC3

200—

CO

OJCo0 0

fO

OO &LAlA ~&

CO

OCO

OlA

I 0co

O0N)CO CO

uI

O

4 CI+ CTI

g N

0

+ -CJcoIA

Ocdp

co

LACOPO

co

nJ 0cf CO

uI

pC7I iu)

Fe(t, pj Fe

ELAe 17 MeV

19 =15

PO

CUY)

cn

COIO

OOCOOJ

co

I

200I I

400 600 800 1000 1200CHANNEL NUMBER

hII

I A '~- i I

I I I I I

1400 1600 1800 2000

FIG. 1. Proton spectrum observed at a laboratory angle of 15 . The peaks identified by energy only have been at-tributed to levels in Fe.

I

104 ERIC B. NORMAN, CARY N. DA VIDS, AND CALVIN E. MOSS 18

100—

EMP I RI CAL:————DIN BA

1=0

IO

- I'

I'

I

C

The two-nucleon transfer code TWOPAH - wasused to carry out the DWBA calculations. Thetriton optical model parameters used were essen-tially those obtained by Flynn et a/. "from theelastic scattering of tritons on ' Fe. The protonparameters were taken from the global parameterset of Percy. '6 However, in order to obtain rea-sonable phase agreement between the experimentaland calculated results both the real and imaginarywell depths had to be increased. The triton and

10—IO—

100—

E

bIO—

10—

I—l. I . I ~ I . I, I, I—

10 20 30 40 50 60 70C.fTl.

(a) 10—

I'

I'

1'

I'

I'

I

10—

l

100—

10 20 30 40 50 60 70e,

10—-I, I, t, I i I i. l i I-10 20 30 40 50 60 7(f

ec.m.

(c) (b)

FIG. 2. Proton angular distributions observed fromthe ~8Fe(t,p) ~Fe reaction at K&=17.0 MeV. The errorbars shown in the figure represent relative errors only.

The systematic uncertainty in the absolute magnitudes

of the cross sections is estimated to be +20%. The

dashed curves are the results of DWBA calculationsperformed using the two-nucleon transfer programTwoPAR (Ref. 14) for (a) I.= 0, (b) L =2, and (c) L =4transfers; the solid curves are empirical shapes takenfrom the known (a) I.= 0 (g.s.), (b) L = 2 (824-keV), and

(c) L = 4 (2116-keV) distributions.

* proton parameters used in this analysis are listedin Table II.

The shapes of the calculated proton angular dis-tributions are insensitive to th0 particular two-neutron configuration chosen. Thus the J' valuesdetermined from these shapes are not influencedby this choice. Since no wave functions for statesin "Fe are presently available, we have simplyused the (2p, &,)' configuration for L = 0 and 2

transfers, the (If,&„ lg, &,) configuration for L=1transfers, the (If,&„ lg, &,) configuration for L= 3

and 5 transfers, and the (1f»» 2P, &,) configura-tion for L = 4 transfers. The two-nucleon formfactors were calculated for a 'Woods-Saxon poten-tial with ~,=1.25 fm and a=0.65 fm. The depth ofthe well was adjusted to give each neutron a bind-ing energy of half the two-neutron separation en-ergy. The calculated angular distributions, eachnormalized (to obtain the best visual fit) to thedata, are shown as the dashed curves in Fig. 2.The data are systematically low 4ith respect tothe calculations at small angles. This may be theresult of underestimating the dead time at theseangles. The shapes of the known I = 0 (g.s.) andL= 4 (2116-keV) angular distributions are reason-ably well reproduced by the DWBA calculations.However, the other observed distributions show

more variations with respect to the calculations.As a result, we have employed an additional tech-nique to determine the spins and parities of thestates observed in "Fe.

The results of our DWBA calculations and thoseof previous workers indicate that the shape of aproton angular distribution is mainly determined

by the L transfer and does not depend strongly on

the Q value of the reaction. Cohen et al."'"alsofound in their '""Fe(t,P)56 ~ 58Fe experiments atE,= 12 MeV that the shapes of all proton angulardistributions from states of a. particular spin and

parity were fairly similar to one another. In par-ticular, they found that the position of the firstmaximum in an angular distribution was a reliableindicator of the L transfer involved in the reaction.These observations form the basis of a secondmethod by which we have attempted to determinethe spins and parities of states in "Fe. The spinsand parities of the "Fe ground state, the 824-keV

18 KNKRGY LEVELS OF 60 Fe POPULATED BY THK 58 Fe(t, p)6 o Fe. . . 105

TABLE I. States in Fe from the present work and from previous experiments.

Present workExcitation

energy(keV)

Fe(t,p 7) Fe(Ref. 5)

0 eV)

48' a (18P 0,2 ~)SDFe(Refs. 3,5)(keV) J'

Ni( He, Be)6 Fe(Ref. 4)

(keV)

~Ni(d 'Li)"Fe(Ref. 6)

(keV)

0824 +3

1975+32116+32301+32358+32668+42749 +43032 + 1P3067+103289 ~10

3634 +103701+ 10

(0')4+

2+

2'2+

(2')

18832.9

5.412.231.714

13142.250.180.0

0 0'824+1 2'

2673 +22756 +23039+33072 +3

1-3p

1-32, 4

3308+3 1-4

3648371438753930

1975+1 0-32114+1 2, 42305+2 2

0 0'823.64 + 0.15 2'

(1668) (2')0.833) (0')

2114.52 + 0.23 4'

3516.10+ 0.30 (5)

3954.38 +0.33 (6}4292.99+0.354359.11+ 0.585002.96+ 0.35

0835 +10

2110+20

0830+20

2130+20

2370+ 20

3040 +20

3330+20

3610+20

5220+ 20

level, and the 2116-keV level are known to be 0'„2', and 4', respectively. %e have taken the ob-served shapes of the angular distributions fromthese states as representatiVe of L = 0, 2, and 4transfers, respective1y. The solid curves shownin Fig. 2 are simply smooth curves drawn throughthe angular dj.stribution data obtained from theseparticular levels. In Fig. 2(a), the ground-statedistribution is compared with other levels whosedistributions most nearly resemble it; in Fig. 2(b),a similar comparison is made with levels whosedistributions resemble that obtained from the 824-keV level. As a result of both the DWBA analysis

and this empirical technique, spins and paritieshave been determined for most of the levels ob-served below 3.1 MeV in "Fe. In all cases, bothmethods of analysis gave the same results for thespins and parities, and these values are given inTable I.

DISCUSSION

The results of the present investigations are in

very good agreement with the data previouslyavailable on 'Fe. As can be seen in Table I, theenergies of those levels observed in the present

TABLE II. Optical-model parameters used in the DWBA analysis.

wv(MeV)

)vs(MeV)

a(fm)

Fp a'

51.0

163.3 20.5

16.0

Protons

1.25

Tritons

1.16

0.65

0.705 1.50

0.47

0.795 '

106 ERIC B. NORMAN, CARY N. DA VIDS, AND CALVIN E. MOSS 18

(t, p) study agree within the quoted errors withessentially all the previous measurements. How-ever, no evidence was seen in our data for the lev-els at 1668 and 1833 keV tentatively proposed bySakai. ' The present results confirm the spin andparity assignments of 2' and 4' to the levels at 824and 2116 keV, respectively. The angular distribu-tion obtained from the 1975-keV level is very simi-lar in shape to that of the ground state, but appearsto be shifted towards larger angles by approxi-mately 5'. The DWBA calculations do not predictsuch a shift for an L= 0 transfer, but the shapesof the distributions predicted for all other possibleL transfers do not at all resemble the observedshape. As a result, we have tentatively assigneda spin and parity of 0' to this level. The angulardistributions from the levels at 2301, 2668, 2749,3032, and 3067 keV all have a first maximum atapproximately the same position as does that fromthe 824-keV level. The general shapes of the dis-tributions from the 2301-, 2668-, and 2749-keVlevels are also reasonably well reproduced by theDWBA calculations. Therefore, we have assigneda spin and parity of 2' to each of these levels. The3032-keV level has been given a probable spin andparity of 2', but it was felt that the shape of thedistribution from the 3067-keV level was suchthat no spin assignment could be made. The 2358-keV level observed in the present study may beidentified with the 2370-keV state found by Hansenet al. ' The shape of the angular distribution ob-tained from this state is similar to that of theground-state distribution, although it appears tobe shifted toward smaller angles by about 5 . Theposition of the first minimum appears to be ap-proximately 30', though only an upper limit forthe value of the cross section at this angle couldbe obtained. As a result, we have not assigned aspin and parity to this level.

The major results of the present "Fe(t,j)"Festudy at E~ = 17 MeV are summarized in Fig. 3along with those of Cohen et a/. "'"from the' '"Fe(t, p)56 ~ 58Fe reactions performed at F, = 12MeV. The relative peak intensities for all statesobserved below 3.5-MeV excitation are shown forall three reactions. In each case the peak ground-state yield is larger than that to any of the excitedstates observed below 3.5 MeV. More strength isobserved to excited states in "Fe, however, thanis seen for "Fe or "Fe. This may be due to thehigher beam energy used in the present study.The peak yield to the 2668-keV level in "Fe is, infact, only 30Vo less than that to the ground state.No strongly populated 0' excited states are ob-served in any of these reactions. This is consis-tent with the results of previous studies of (t,P)reactions leading to final nuclei with ¹ 30.""""

—5(6)20 -2

-2xl/5

(2)

~ 2—LLLLJ

LIJ

zO

l—ULLJ

4-(0)

xl/5 «l/5 xl/5

54F (f )56F 56F (f )58F 58F (f ) 60F

FIG. 3. Relative intensities of states below 3.5 MeVin 6Fe (Ref. 13), +Fe (Ref. 17), and 6 Fe (present work)populated by the {t,p) reaction.

ACKNOWLEDGMENTS

The authors would like to thank R. V. Poore forassistance in operating the computer facilities

The low-lying levels of ' Fe are essentially thoseexpected for vibrational excitations of an even-even nucleus. The 824-keV first excited state isthe one-phonon X= 2 state. The 1975-, 2116-, and2301-keV levels can be identified, respectively,as the (0'), 4', and 2' members of the two-phononX = 2 triplet of states expected in a vibrationalmodel. The centroid of these three states is 2168keV, which is approximately 2.6 times the energyof the first excited state. The ratio of the energyof the two-phonon X= 2 triplet to that of the one-phonon X= 2 state is expected to be equal to 2 forvibrational nuclei, but considerable variationsof this quantity have been observed in other nuclei,For example, this ratio is approximately 2.8 in' Fe and 2.4 in "Fe. The collective nature of someof these states in "Fe was indicated by the ob-servations of Warburton et al. ' of significant en-hancements over single-particle estimates for thestrengths of the 2116-824 and 824- g.s. E2 tran-sitions.

The Z'= 3 collective octopole vibration statewas not identified in the present (t, p) study. Thelocation of this state is at 4.5 MeV in "Fe and at3.9 MeV in "Fe. Thus, if angular distributionshad been obtained for states above 3.1 MeV in"Fe, this state might have been observed.

ENERGY LEVELS OF ee Fe POPULATED BY THE Fe(t, p) Fe 107

used in taking and analyzing data. Two of us (E.N.and G.D.) wish to thank LASL and the tandem stafffor their hospitality and assistance during thisexperiment. We also wish to thank J. P. Schiffer

J

for several helpful discussions and W. F. Henningfor a careful reading of the manuscript. Workperformed under the auspices of the Departmentof Energy.

*This work is submitted in partial fulfillment of the re-quirements for the Ph. D. degree at the University ofChicago.

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