Nuclear Physics A90 (1967) 650-----656; (~) North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

MEASUREMENT OF SOME GAMMA-RAY ENERGIES

SUITABLE FOR ROUTINE ENERGY CALIBRATION

w. w. BLACK and R. L. HEATH National Reactor Testing Station, Idaho Nuclear Corp., Idaho Falls, Idaho t

Received 12 July 1966

Abstract: The energies of several gamma-ray transitions have been measured using a Ge(Li) spectro- meter. The isotopes and the corresponding transition energy measurements in keV are

1'1Ce(145.44:4=0.05), ls'Ce(165.85±0.05), 51Cr(320.07-t-0.05), ~Be(477.57±0.05), ssSr(513.95~0.07), 9SNb(765.83--0.07), 5+Mn(834.84=[=0.07), 4sSc(889.25±0.07, 1120.50~0.07), 88Y(898.01 =t=0.07, 1836.08+0.07), 92Nb(934.51 ±0.07), 2°7Bi(1063.63-i-0.07), e6Zn(1115.51 =t=0.07) and 22Na(1274.52~0.07).

RADIOACTIVITY ~Be, ~2Na, 4eSc, 5tCr, ~Mn, 66Zn, s6Sr, 88y, [ E 'z,'SNb, tag,~+tCe, 2°7Bi; measured E r- I

1. Introduction

With the accuracy presently being realized in gamma-ray energy measurements using Ge(Li) detectors, it has become imperative to measure the energies of several gamma rays with sufficient accuracy so that they may be used for routine energy

calibrations. These energy values are needed because there are presently very few gamma-ray energies known with enough accuracy to use for this purpose. In fact, there are currently no gamma-ray energies known with an accuracy significantly better than that one might hope to attain with present Ge(Li) spectrometers. Since

these spectrometers cannot measure absolute energies but only energy ratios we have chosen some of the best known transition energies presently available for spectrometer calibration. It is hoped that the resulting energy determinations can be used as secondary energy standards for daily calibration, where many points along the energy

scale are desired, but the utmost accuracy is not required.

2. Experimental apparatus

2.1. A P P A R A T U S U S E D

The spectrometer used for all measurements consisted of a Ge(Li) detector, a cryogenic field-effect-transistor (FET) preamplifier, a low-noise linear amplifier and a ~096-channel multi-channel analyser. The Ge(Li) detector used was manufactured

t Work performed under the auspices of the U. S. Atomic Energy Commission. 650

y - R A Y E N E R G I E S 6 5 1

by ORTEC with dimensions 2.5 cm 2 x 0.8 cm. The FET preamplifier was the result of an extensive development program in this laboratory 1). The linear amplifier was a TENNELEC Model TC 200 and the multichannel analyser was a Nuclear Data Corp. Model ND 161.

2.2. L I N E A R I T Y O F T H E A M P L I F I E R - M U L T I C H A N N E L A N A L Y S E R SYSTEM

One of the largest errors that can be introduced into energy measurements of the type being discussed is due to the non-linearity of the amplifier-ADC (analogue-to- digital converter) system. Techniques have been developed to measure deviations of the system from linearity using a precision mercury-switch pulse generator. A brief description of the method may be found in ref. 2) and a detailed description in ref. 3).

+05: - ........ ]

I ' , :

° °

I r i

~z

I

9-0 .5 ' ~J

G 1 .. u - 0 . 1 0 0

i

1000 1500

! i

i 5 0 0 2 0 0 0 2 5 0 0 3000 _'3500 4000

Channel

Fig. 1. The deviat ions f rom linearity o f the ampl i f ie r -ADC system used for the energy measuremen t s .

Fig. l shows the results of such a measurement on the amplifier-ADC system used in the present experiments. This is a plot of correction versus channel number, i.e., the amount that must be added or subtracted to make the response at a given channel location linear. The dots represent the measured deviations and the smooth line passing through these dots the result of a least-squares fit of the data to a polynomial. The data presented in this paper were corrected using values from the smooth curve. It is interesting to note that the deviation from linearity is not greater than about 0.20 channels in the region from approximately channel 250 to 3800. Gains were always adjusted so that photopeaks of interest fell in this most linear region.

3. Data collection

In all cases the data were collected by simultaneously obtaining a spectrum of several unknown lines along with a minimum of four calibration lines. Source-to- detector distances were always adjusted to give count rates (less than 5000 counts/sec) low enough to avoid smearing of the photopeaks due to pile-up effects. In order that

652 W. W. BLACK AND R. L. HEATH

the photopeak positions might be located with the best possible accuracy, sufficient data were collected to obtain several thousand counts in each of several channels of a photopeak. At least three sets of data were taken for each energy determination.

= - - ~ - " r - - ~ . . . . . " . . . . . . . . . . ] L - __ " : : -I. " / -: ' - - - - - - " - :

• . : . . . . . . I ~ . . . . J . . . . : . . . . . . i 2 65Zn ' I I I 5 5~-e-V -- I - - - . . . . , . . . . ~- " ~

I I 4 .~.:,C.11%0 5 0 k~ v -- "~I60~. ] 1%~ "~ 2~- ~-V . . . . . / . . . . . . . . . . . . i - _ _ !

~ - - - ~ - - ~ i : ~ s : ~ - -: i--:: ~ - - - - - : T - . ~ ! 5 , - ~ , ~ . - - . . . . . • . . . . . ~ ~ . . . . . . . . . . . . . ~ ~ I k~ I [ I------I " ~

. . . . . . . . T t : ] ~ . . . . . . . . . . . . [ _ _ _ . i ~ , . ~ ( F W H M ) I . . . . > ~ : - . - - ~ .', . . . . . . . . ' . . . . . . . . I . . . . . . . . ~ , o ~ z . [ f

. i , ~ 1 ~ - - - ! : : - ------.~: : - + ' - = _ - 7 : .----- . . . . . : t_, . . . . . . . . . . ,~ • " I " ~ [ , ~ . " ' - i

5 ' ~ m , ~ , ~ , f f . . . : ~ . . . ~ , , , ~ ~,, l . L ~ _;,,;.~,.~ " ~ . " . . . . . . . . . . . . .'-Lr.._--t-3:.__ . . . . . . . . . :

2 ' - - - [ - - - - [ . . . . .

1 0 2 . . . . . . C h a n n e l . . . . . . . . . . ] _ _ . I

3000 --3100 3200 3300

Fig. 2. A portion of a typical spectrum showing lines from the decay of 6sZn, 4eSc and '°Co.

Fig. 2 shows a portion of a typical spectrum including the 1173 keV line of 6°Co, the 1116 keV line of 65Zn and the 1121 keV line of 46Sc. Table 1 gives a list of the isotopes and transitions used for calibration and the energies quoted for these lines by other authors.

TABLE 1

Calibration energies used and their quoted values

Isotope Energy (keV) Ref.

24XAm 59.568 +0.017 4)

XS3Gd 97.43 -t-0.02 6) 103.18 -2:0.02

17~Lu 112.952 F0.003 s) 208.359±0.010

2°°Hg 279.16 :!:0.02 ~)

I'SAu 411.795 -t-0.009 s)

annihilation 511.006 +0.002 ~)

2°7Bi 569.62 --0.06 x0)

x~Cs 661.595 --0.076 H)

'°Co 1173.226 + 0.040 ' ) 1332.483 4-0.046

~4Na 1368.526-k0.044 8)

"/-RAY ENERGIES 653

4. Data analysis

4.1. DETERMINATION OF PHOTOPEAK LOCATIONS

Photopeak locations were determined by a simple computer routine which calculates the width of a photopeak at a designated height. Half the value of this calculated width is taken as the centre of the photopeak. Experience has shown that the routine can determine photopeak locations to about +0.05 channels with data of the quality under consideration.

4.2. CORRECTION FOR SYSTEM NON-LINEARITIES

As mentioned in subsect. 2.2, the linearity data were least-squares fit to a polynomial. The polynomial used was a simple power series of the following form:

N

1, = ~ a.cL n = 0

where li is the linearity correction for the ith channel and c~ the ith channel. Once the values of the coefficients an have been obtained a computer routine is used to calculate the linearity correction. It can be seen from fig. 1 that the deviation from linearity is known to an accuracy of 0.1 channels or better.

4.3. ENERGY CALCULATIONS

The energy of a line in a spectrum is then given by the following expression:

N

Et = B(ci + A + ~ a,(ci + A)n), n=O

where B is the gain of the system in keV/channel, A is the intercept of the ADC in channels, and the summation term is the linearity correction taking account of the intercept. If one makes the assumption that A/ci << 1, then this expression reduces to a form suitable for a linear least-squares calculation. A detailed discussion of this derivation may be found in ref. 3).

The energy calculations were made using a computer program which incorporates the routines for locating photopeak positions and linearity calculations. First, all photopeak positions of a spectrum are determined. Then the energies and photopeak positions corresponding to the calibration lines, along with the linearity coefficients a n, are used in the linear least-squares calculation to determine the parameters A and B. Using A, B and the linearity coefficients the unknown line energies can be determined from their channel positions. Table 2 outlines the results of a typical measurement. In this measurement a determination of the gamma-ray energies for x*lCe, 139Ce, SXCr and 7Be was made. The energy scale was established with lines from the decay of ~53Gd, 2°3Hg, t9SAu, 2°7Bi and 137Cs. It is important that as many calibration lines as possible be used to minimize the errors in A and B resulting from the least-squares calculation. The usual procedure is to use a minimum of two

654 W, ~V. BLACK AND R. L. HEATH

ca l i b r a t i on l ines a b o v e and be low the energy reg ion o f interest . T h e first c o l u m n o f

tab le 2 m a r k e d ca lcu la ted energy gives va lues o f the ca l ib ra t ion t r ans i t ions ca lcu la ted

f r o m the p a r a m e t e r s A and B. T h e th i rd c o l u m n shows the d i f ference be tween these

ca lcu la ted va lues and the q u o t e d values fo r the ca l i b r a t i on lines. These differences,

w h e n c o m p a r e d with the er rors q u o t e d for the ca l ib ra t ion lines, serve to d e m o n s t r a t e

the prec i s ion which m a y be ach ieved in the l oca t i on o f p h o t o p e a k pos i t ions . I t a lso

subs tan t ia tes the m e t h o d used to d e t e r m i n e the non- l inea r i ty o f the e lec t ron ic system.

TABLE 2

Results of a typical energy measurement ")

Results of least-squares

Isotope calculated energy correct energy difference

~3Gd 97.430 97.43 :!:0.02 0.00

*~Gd 103.163 103.18 ~0.02 --0.017

~°3Hg 279.197 279.160±0.02 0.037 19SAu 411.776 411.795 ~'0.009 --0.019

2°7Bi 569.624 569.62 -0 .06 0.004

137Cs 661.591 661.595 !- 0.076 --0.004

Calculated energies of unknowns

145.44(NICe)

165.86(13'Ce)

320.09(61Cr) 477.55(7Be)

a) All energies in keV.

TABLE 3

Results of energy measurements and comparison with previous measurements a)

Isotope This Study Previous Studies

H1Ce 145.44'--0.05 145.6 , 0 .3 1,)

13'Ce 165.85_+_0.05 165.84--0.03 a)

51Cr 320.074-0.05 319.8 "-0.3 e.) ~Be 477.57--0.05 477.4 4-0.2 e)

85Sr 513.95--0.07 9SNb 765.83 !~0.07 54Mn 834.84-0.07 835.50:'0.15 J)

'6Sc 889.25--0.07 889.60~0.15 J) say 898.01 ±0.07 898.2 -_k0.4 e)

°~Nb 934.51 --0.07 ~°TBi 1063.63±0.07 1063.44--0.09 n) ~sZn 1115.51±0.07 1115.6 ~0.4 e)

4~Sc 1120.50t-0.07 1120.65_-1z0.12 ~) tuNa 1274.524-0.07 1274.6 ~0.3 e) say 1836.081-0.07 1836.2 ~0.3 e)

145.5 :!:0.3 e)

320.3 -t-0.3 t) 320.28 -i-0.66 ¢) 320.3±0.3 ~) 320.18"-0.21 1)

834.9 --1.1 k) 835.0 ~0.3 e)

889.15+0.13 l) 888.3 --0.4 TM) 897.5 :t:_0.5 m) 898.2 ±0.2 h)

1063.7 _±0.2 e) 1063.9 J-_0.3 o) 1114.5 "-1.0 t) 1115.6 "-0.2 h) 1120.30.::0.22 t) 1119.2 4-0.6 m) 1274.8 ±0.3h)

1836.6 , 0 . 9 m) 1836.2 ~0.3 h)

834.5 ~:0.2 h)

1063.9_+_0.3 v)

a) All energies in keY. e) Ref. *s). J) Ref. 19). m) Ref. =3). ~) Ref. 12). t) Ref. 16). J) Ref. 2,J). a) Refi 1o). e) Ref. la). g) Ref. l~). k) Ref. 21). ") Ref. 2.L). a) Ref. H). h) Ref. is). l) Ref. m). P) Ref. ~5).

?'-RAY ENERGIES 655

The energies of the fourth co lumn are the values determined for the unknow n lines

in this part icular measurement .

As ment ioned earlier a m i n i m u m of three measurements was made for each

transit ion. The three or more resulting energy values for a given line exhibited a

max imum spread of about 0.10 keV with an average spread of about 0.05 keV.

5. Results

Table 3 lists the energies determined in this study and some previous measurements

of these t ransi t ion energies. In the case of 88y thc value of the 1836 keV line was

determined by measuring the energy of its second escape peak and adding 1022.01

kcV 9) (2 m c 2) to this value.

In order to estimate the errors in the energy measurements, a calculation of the

most probable crror was made which took into account the errors in A, B, c~ and l~.

The smaller energy values of table 3 with an assigned error of 0.05 keV werc measured

with a gain of approximately 0.19 keV/channe l . This error assignment is about three

times the most probable crror. The energy values with an error assignment of 0.07

keV were measured with a gain of approximately 0.37 keV/channel. This error as-

s ignment is approximately twice the most probable error.

6. Conclusions

These measurements have resulted in better determinat ions of the t ransi t ion

energies for a number of convenient cal ibrat ion lines. The measurements demonst ra te

that energy determinat ions with Ge(Li) spectrometers are limited by the accuracy

of presently available cal ibrat ion transit ions. This result emphasizes the need for

more precise energy determinat ions with other types of instruments .

References

1 ) K. F. Smith and J. E. Cline, Proc. Tenth Scientillation and Semiconductor Counter Symposium, Washington, D.C. (1966) IRE Trans. Nucl. Sci., Vol. NS-13, No. 3, June 1966, p. 468

2) R. L. Heath, W. W. Black and J. E. Cline, ibid; Nucleonics 24, No. 5 (1966) 3) W. W. Black, U. S. AEC Report No. IDO-17140 (1965) 4) P. B. Day, Phys. Rev. 97 (1955) 689 5) R. L. Graham, G. T. Ewan and J. S. Geiger, private communication to Nuclear Data Sheets 6) B. P. Maier, thesis, Technische Hochschule Miinchen (1964) 7) C. J. Herrlander and R. L. Graham, Nuclear Physics 58 (1964) 544 8) G. Murray, R. L. Graham and J. S. Geiger, Nuclear Physics 63 (1965) 353 9) E. R. Cohen and J. W. M. DuMond, Revs. Mod. Phys. 37 (1965) 537

10) F. P. Brady, N. F. Peek and R. A. Warner, Nuclear Physics 66 (1965) 365 11) R. L. Graham, Nucl. Instr. 9 (1960) 245 12) D. W. Martin, K. M. Brice, J. M. Cork and S. B. Burson, Phys. Rev. 101 (1956) 182 13) J. S. Geiger, unpublished results quoted in Nuclear Data Sheets 14) R. L. Graham and J. S. Geiger, private communication to Ewan and Tavendale, Can. J. Phys

42 (1964) 2315

656 W. W. BLACK AND R. L. HEATH

15) R. L. Robinson et aL, Nuclear Physics 74 (1965) 281 16) G. T. Ewan and A. J. Tavendale, Can. J. Phys. 42 (1964) 2286 17) W. R. Pierson, Phys. Rev. 140 (1965) B1516 18) K. W. Dolan, D. K. McDaniels and D. O. Wells, to be published 19) D. H. White, W. John, B. G. Saunders and R. W. Jewell, Nuclear Physics 72 (1965) 241 20) D. Parsignault, Phys. Lett. 18 (1965) 36 21) R. R. Wilson et al., Phys. Rev. 125 (1962) 1655 22) J. J. Reidy and M. L. Wiedenbeck, Nuclear Physics 70 (1965) 518 23) A. A. Bartlett, J. R. Keith and W. D. King, Bull. Am. Phys. Soc. 8 (1963) Q8 24) G. Backstrom, Ark. Fys. 10 (1956) 393 25) D. E. Alburger, Phys. Rev. 92 (1953) 1257