Precision energy measurement of gamma rays from the decay of 75Se and 133Ba

Nuclear Instruments and Methods in Physics Research A238 (1985) 431-442 North-Holland, Amsterdam

431

PRECISION ENERGY MEASUREMENT OF GAMMA RAYS FROM THE DECAY OF 75 Se AND 133 Ba Hiroki KUMAHORA

Department of Physics, Faculty of Science, Hiroshima University, Hiroshima, Japan

Received 5 November 1984 and in revised form 6 February 1985 Energies of gamma rays in the decays of 75 Se and 133Ba were precisely measured with uncertainties of 0.6 to 2.7 eV . A Ge detector was calibrated with the gamma-ray energy standards of 169 Yb and 19sAu by means of the attenuation method. The observed gamma-ray energies are useful for energy calibration of the Ge detector in the range of 50 to 400 keV. 1. Introduction Gamma-ray energies have been measured with a Ge detector or a crystal spectrometer relative to the 198Au 412 keV gamma-ray energy . The resolution of the crystal spectrometer is better than that of the Ge detector in the energy range up to about 500 keV. Intense sources are strongly required for the crystal spectrometer measurement but not for the Ge detector measurement. Therefore the Ge detector is fitted for measurements of weak gamma rays emitted from long-lived nuclides and of higher energy gamma rays . Gamma-ray wavelengths of 169Yb, 1921r and 198Au were precisely measured with a double flat crystal spectrometer by Kessler et al . [1,2] . The crystal lattice spacings of this spectrometer were calibrated by the wavelength of an IZ stabilized He-Ne laser, which was referred to the length standard . Thus these gamma rays are the best measured standards. Gamma-ray energies in the range from 450 to 600 keV were measured with a Ge(Li) detector, and a new Table 1 Gamma-ray energy standards Nuclide 1691

.b

198Au

Energy (eV)

63120.77 93615.14 109779 .87 118190 .18 130523 .68 177214 .02 197957 .88 261078 .23 307737 .58 411804 .41

Error (eV) 0.06 0.12 0.05 0.18 0.03 0.05 0.06 0.74 0.12 0.07

0168-9002/85/$03 .30 C Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

attenuation method was adopted for the calibration of the detector systems in the previous paper [3]. In the present experiment, gamma-ray energies of 7s Se and 133B a were determined with a high purity Ge detector with uncertainties of 0.6 to 2.7 eV . We used only gamma-ray energies of 169Yb and 198Au as standards, which are listed in table 1. The 192Ir gamma rays were also available for standards in the present energy region . However, we did not use them, because X-rays and gamma rays of 192Ir lie close to some 75 Se and 133 Ba gamma rays. Several gamma-ray energies were deduced from the difference between two gamma-ray energies on the basis of the level scheme. The energies of gamma rays in the decay of 75 Se and 133Ba have been measured with Ge detectors by Helmer et al . [4,5] within an uncertainty of several eV. They used many energy standards and reevaluated the gamma-ray energies on the basis of the 198Au and 192 Ir gamma rays . 2. Experimental method A high purity Ge detector, Ortec amplifiers and a multichannel analyzer were used for the present measurement . The resolution of the detector system was about 580 eV at the 136 keV "Co gamma ray. Since the gains and nonlinearities of the amplifiers and the AD converter change with temperature, room temperature was kept within 2°C . The distance between the sources and the detector was set to 20 cm, so that the source position effect [6] was negligible . In order to decrease the ambiguity of the energy interpolation, the internal calibration method and the attenuation method [3] were adopted. The main part of the ambiguity is attributed to the linearity of the AD converter and/or the amplifier. The linearity of the

H. Kumahora / Precision energy measurement of gamma rays

H. Kumahora / Precision energy measurement of gamma rays

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H. Kumahora / Precision energy measurement of gamma rays

43 4

amplifier changes with its gain, and the gain drifts a little for each measurement. Thus the internal calibration is important, that is, both reference gamma rays and objective gamma rays must be measured simultaneously. The calibration for the integral nonlinearity was performed by the attenuation method. An attenuator of about 39 2 was connected between the preamplifier and the main amplifier in series . Measurements were alternately repeated, at the same amplifier gain, with the attenuator and without the attenuator . Details of the integral nonlinearity can be tested in comparisons between spectra with and without the attenuator . The number of calibration points for this method is twice more than that for the usual case . A second advantage is that peaks of the standard gamma rays in one spectrum can be set very close to observed gamma-ray peaks in the other spectrum by choosing the appropriate attenuator. Therefore the nonlinearity correction must be reliable in the vicinity of the gamma ray of interest . Since a set of measurements with and without attenuator was repeated 20 times for "Se and 133Ba, 40 spectra were taken for each source . The integral nonlinearity calibration and the energy determination were performed for each set of measurements. Examples of the set of spectra are shown in figs . 1 and 2. The differential nonlinearity was obtained from a measurement of the Compton flat part of the 6° Co gamma-ray spectrum . The counts per channels of the flat part were summed to emphasize the differential nonlinearity as follows : (k-1,2, . . .,16),

Ck-YN16l+k+ l

where N16J+kts the number of counts at the (16j + k)th channel and the sum is extended over the flat part of the 6° Co gamma-ray spectrum. The sum Ck shows the systematic deviation (fig . 3) . The sum counts at odd

number channels are lower and the counts at even number channels are higher in the figure . The line shape of the gamma ray must be distorted by this differential nonlinearity . But this effect for the energy determination is estimated to be less than 0.2 eV by using the observed differential nonlinearity as mentioned later. 3. Analysis The peak analysis was performed by a Gaussian fitting procedure [3,71. A linear background was adopted for each peak, because there were no Compton edges of higher energy gamma rays or peaks of other weak gamma rays near the peak of interest . Several monochromatic gamma rays were measured in the present energy region and the tail shapes were obtained from the ratios of the counts at the lower energy part to those at the top of the peak . We subtracted the linear background in order to reproduce these ratios. After the background subtraction, the peak was fitted by a Gaussian function between a channel at the half-maximum on the low-energy side and the tenth-maximum on the high-energy side . A typical example of a peak is shown in fig. 4 . The 169Yb 198 keV line was not used as an energy standard in the measurement of "Se gamma rays, because this line was very close to the 75 Se 198 keV line. Integral nonlinearity curves are made for each set of measurements by using the following equations: E=A1 +A 2 X+A3X2 +A 4 X3 +A 5X4 +A 6 X5 , E = (A 7 + A 2X' +A 3 X' 2 +A4 X,3 +A5 X,4 +A 6 X' 5)/A8 ,

where E is the energy at channels X and X' . The first and second equations correspond to the spectra without

J

N +(T

LU z z

N

w z 0 U

N- a-

1

5

CHANNEL

10

NUMBER

15

Fig. 3 . Sum counts of the Compton flat part of the 6° Co gamma-ray spectrum . N ]s the mean value and o is the

estimated standard deviation .

(2)

10`' 10 3 10 2 10

6400

6500

6600

CHANNEL NUMBER 133 Fig. 4 . Spectrum of the Ba 356 keV gamma ray. The broken line shows the linear background . The peak at the 6480 channel is the chance coincidence sum peak.

43 5

H. Kumahora / Precision energy measurement of gamma rays 100

50

ILI z

0 Q

0

w 0

-50

2000

4000

6000

CHANNEL NUMBER

8000

Fig. 5. Example of integral nonlinearity curve. Vertical axis indicates the energy differences between the calibrated curve and the straight line . The open and closed circles show the calibration points in the spectra without and with the attenuator. and with the attenuator, respectively . The parameters A l, A2 , . . . . A, are obtained from the least-squares method . In the previous paper [3], terms to X2 were used for the integral nonlinearity curve. But terms to X5 are used for curve (2) in the present measurement, because the energy region of interest is wide and the integral nonlinearity curves are not symmetric, as shown in fig. 5 . The reduced chi-squares are between 0.8 and 1.2 for all the measurements where the degree of freedom is taken to be 5. The reference lines far from the

line of interest were rejected in the determination of the parameters by using eq. (2), since the effect of these lines was negligible for the determination . Gamma-ray energies were obtained from eq. (2) and small corrections were performed as follows: Let E) and Eh represent the energies obtained from eq . (2) for close-lying reference lines at the low- and high-energy sides, and let El and E2 denote the standard energies listed in table 1 for these lines. This correction is performed by interpolating the differences E) - E7 and Eh - E2. Values of the corrections are generally less than 0.2 eV . The components of errors are listed in table 2. The peak fitting error S is obtained from eqs. (3) and (4) in the previous paper [3]. The energy deviation of each line is estimated by the square root of the unbiased variance u as shown in eq . (5) in the previous paper [3]. The systematic error consists of three components . The first component, denoted by S indicates the ambiguity of the .integral nonlinearity curve. The second component, denoted by 8d, indicates the ambiguity of the differential nonlinearity . The effect of the differential nonlinearity for the energy determination is estimated as follows: Sd =IPN-PN'J, where PN is the given peak center of the Gaussian function . PN' denotes the peak center obtained from the fitting procedure, in which the base line of the Gaussian function includes the systematic deviation due to the differential nonlinearity as shown in fig. 3. This estimation of the ambiguity 8d is generally less than 0.2 eV, and this limit is used for all gamma rays . The third component, 8r, is due to the errors of close-lying refer-

Table 2 Error estimations Nuclide 133

75

Ba

Se

Gamma-ray energy (keV) 276 303 356 383 66 97 121 264 279 303 400

Error (eV) s a) 0.8 0.5 0.9 2.2 0.5 0.7 0.2 1.0 0.6 1.2 0.9

u/v~n_ 0.5 0.5 0.6 0.7 0.5 0.4 0.2 0.4 0 .5 1.4 0.6

b)

0

So 1.9 0.8 0.4 0.4 0.3 0.5 0 .3 0.7 0.5 0.6 0.3

Peak fitting error. b) Square root of the unbiased variance divided by the number of measurements. c) Uncertainty of the integral nonlinearity curve. d) Uncertainty due to the differential nonlinearity. e) Error due to reference gamma rays. Total error obtained from eq . (4). a)

ad d)

ge)

0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

0.3 0.1 0.1 0.1 0.1 0.1 0.1 0.7 0.5 0.1 0.1

E

n

2.7 1.2 1.1 2.3 0.8 1.1 0.6 1.9 1.3 1.7 1.1

H. Kumahora / Precision energy measurement of gamma rays

436

Table 3 Observed gamma-ray energies in eV. The average values of energies and their errors are given in the last entry . u/~n- means the square root of unbiased variance divided by the number of measurements . Nuclide 75 se

Energy (keV)

Without attenuator Energy

Error

Energy

Error

66

66046 .5 66044.5 66050 .5 66051 .6 66046.1 66054 .8 66053.5 66053.9 66053 .2 66050 .6 66052 .9 66050 .7 66049.1 66052 .1 66052 .3 66051 .5 66052 .7 66049 .0 66045 .1 66053 .4

4.5 2.8 2.8 3.0 3.4 2.0 3.0 1 .6 2.4 2 .2 2.2 2 .5 2.6 2.3 2 .7 4.3 3 .7 3 .2 3 .7 3 .2

66055 .2 66053 .8 66058 .9 66051 .2 66052 .5 66054 .3 66053 .3 66055 .2 66055 .2 66058 .1 66052 .2 66051 .8 66053 .3 66054 .3 66049 .3 66055 .8 66050 .7 66051 .3 66055 .2 66053 .2

3 .0 4 .5 3 .0 3 .4 2 .8 3 .3 2 .9 1 .9 2 .0 2 .3 2 .2 2 .4 2 .7 2 .6 3 .6 3 .2 3 .0 2 .9 3 .3 2 .9

66050 .7

0 .7

66053 .7

0 .5

average u/ vrn 75

Se

96

average

0 .7

Se

121

0 .7

96740 .8 96735 .4 96732 .9 96735 .5 96734 .8 96736 .5 96733 .3 96741 .3 96729 .3 96735 .8 96736 .4 96725 .9 96740.4 96733 .9 96730.1 96745 .9 96731 .3 96733 .8 96729.5 96727 .5

3 .0 1 .7 1 .8 2 .1 2 .1 1 .6 2 .3 1 .4 1 .7 2 .2 1 .9 1 .8 1 .7 1 .8 2 .2 2 .1 2.0 2.0 1 .9 1 .9

96732 .6 96733 .7 96738 .5 96738 .4 96734 .3 96732 .2 96733 .5 96735 .1 96736 .9 96740 .6 96733 .5 96735 .5 96739 .5 96739.2 96735 .1 96730.5 96728 .5 96729.7 96734.4 96728.2

2 .0 2 .4 2 .7 2 .4 2 .7 2 .6 2 .5 2 .1 2 .2 2 .5 2 .3 3 .2 3 .1 2.9 2.9 2.9 2.9 2.7 3.0 2.8

96734.5

1 .1

96734.5

0.8

u / v'n 75

With attenuator

0 .6

0 .4 121112 .3 121115 .1 121120 .9 121115 .2 121121 .1 121116 .3 121112 .2

1 .3 1 .0 1 .2 1 .1 1 .0 0 .9 1 .2

121113 .9 121115 .6 121117 .2 121120 .5 121120 .8 121117 .9 121116 .9

1 .0 0 .9 1 .0 1 .1 1 .0 1 .3 1 .3

437

H. Kumahora / Precision energy measurement of gamma rays Table 3 (continued) Nuclide 75 Se

Energy (keV)

Without attenuator Energy

Error

Energy

Error

121

121117 .4 121112 .0 121115 .9 121118 .3 121115 .8 121119 .0 121114 .4 121111 .0 121120 .0 121117 .0 121111 .8 121119 .6 121117 .7

0.8 0.9 1 .0 1 .3 1 .1 1 .1 1 .1 1 .3 1 .3 1 .2 1 .2 1 .1 1 .2

121120 .1 121116 .4 121116 .0 121116 .2 121116 .0 121117 .0 121116 .2 121115 .9 121117 .9 121115 .0 121120.6 121114.5 121116.8

1 .1 0 .9 1 .1 1 .0 1 .2 1 .3 1 .3 1 .3 1 .3 1 .3 1 .2 1 .2 1 .2

121116 .2

0.7

121117 .1

0.5

average 75 se

136

u/f

average 75

Se

264

u/r

With attenuator

0.3

0.3

136002.0 136001 .6 136001 .8 136002 .9 135999.6 136002.0 135998.0 136003.8 136002.2 136002.7 136002.6 136002.0 135999.5 136002.1 136001 .1 136001 .3 135999.6 136002 .2 136000 .6 136002 .3

1 .2 1 .0 1 .2 1 .2 1 .3 1 .1 1 .7 1 .3 1 .5 1 .5 1 .9 1 .7 1 .8 1 .8 1 .7 1 .5 1 .6 1 .5 1 .5 1 .6

135999.9 135999.3 135999.8 135999.3 136000.9 135998.5 136000.2 136001 .5 135999 .8 136000.8 136001 .3 135998.9 136000 .2 135998 .2 135999.8 136001 .9 135999 .9 135999 .6 136001 .1 136001 .6

1 .1 1 .0 1 .2 1 .4 1 .2 1 .5 1 .6 1 .2 1 .2 1 .4 1 .3 1 .4 1 .5 1 .6 1 .5 1 .7 1 .4 1 .4 1 .5 1 .5

136001 .5

0 .3

136000 .1

0 .2

0.3 264661 .9 264658 .2 264662.7 264654 .5 264658 .1 264655 .5 264654 .6 264668 .0 264650 .4 264651 .9 264667 .0 264662 .4 264662 .5 264659 .5 264659 .7 264659 .2

2.4 1 .8 2.0 2.1 2.4 2.0 2.6 2.0 1 .8 2.3 2.2 2.1 2.4 2.3 2.5 2.5

0 .3 264653 .2 264663 .6 264660 .1 264651 .2 264661 .1 264653 .6 264667 .2 264647 .6 264656 .3 264660 .5 264655 .6 264675 .8 264663 .2 264659 .6 264666 .1 264659 .7

2 .5 2.4 2 .8 2.8 3 .5 3.1 3.4 3.0 2.5 3 .3 2.8 3.0 3.4 3 .1 3 .7 3 .0

H. Kumahora / Precision energy measurement of gamma rays

438 Table 3 (continued) Nuclide 75

Se

Energy (keV)

Without attenuator Energy

Error

Energy

Error

264

264644.1 264656.2 264653 .7 264657 .1

2.3 2.3 2.3 2.7

264655 .4 264661 .2 264657 .4 264652.0

2 .9 3 .0 3 .0 3 .2

264657.8

1 .3

264659 .0

1 .4

average 75

Se

279

u /C

average u 75

Se

303

/r

average u/v~n-

With attenuator

0 .5

0 .7

279545 .6 279544 .1 279544 .3 279541 .1 279545 .2 279542.5 279541 .5 279550.7 279540.6 279540.1 279547 .5 279545 .6 279545 .8 279546 .0 279542 .8 279543 .6 279534.2 279542 .5 279542.9 279543 .8

3 .6 2.4 2.4 2.8 2.6 2.2 3.2 2.1 2.0 2.7 2.6 2.4 2.6 2.9 2.7 2.8 2.8 2.7 2.8 3.1

279543 .5 279548 .6 279541 .1 279539 .8 279543 .5 279543 .1 279550 .4 279537 .0 279541 .6 279545 .8 279542 .8 279553.8 279546.2 279546.1 279549.7 279545.2 279541 .5 279545.1 279545.8 279542.0

3 .1 2 .9 3 .3 3 .3 4 .0 3 .4 3 .7 3 .2 2 .7 3 .5 2 .8 3 .2 3 .7 3 .3 4 .2 3 .5 3 .3 3 .3 3 .4 3 .5

279543 .5

0.7

279544.6

0 .9

303910.4 303917 .5 303926 .3 303918 .8 303928 .9 303928 .2 303921 .9 303933 .9 303930 .3 303919 .9 303910 .2 303932 .7 303933 .9 303927 .8 303933 .0 303936 .6 303931 .0 303930 .2 303935 .0 303924.3

12.4 9.4 8 .8 9.6 8 .2 6 .0 9.3 4.8 7 .4 9.7 8 .4 7 .6 7 .4 8 .5 7 .7 9.5 9.3 10.1 10.0 9.5

303921 .0 303926.7 303927.2 303911 .1 303913.3 303931 .9 303916.8 303926.9 303937.3 303921 .0 303931 .1 303915 .2 303919.4 303920.4 303932.4 303920.1 303921 .4 303931 .0 303935 .0 303917.1

10 .0 8 .9 9 .7 8 .5 8 .8 9 .4 8 .8 6 .9 6 .3 8 .9 5 .9 9 .8 8 .6 7 .9 9 .9 10 .7 10.1 10 .9 10 .5 11 .2

303926 .5

1 .7

303923.8

1 .7

0.6

2.0

0 .8

2 .1

H. Kumahora / Precision energy measurement of gamma rays Table 3 (continued) Nuclide 75

Se

Energy (keV)

Without attenuator Energy

Error

Energy

Error

400

400635 .5 400640 .9 400654 .5 400645 .1 400648 .4 400636 .0 400646 .3 400644.0 400643 .8 400634.7 400643 .7 400644.6 400642.6 400637.0 400645 .7 400651 .1 400645 .9 400645 .8 400651 .0 400647 .6

6 .7 4.3 4.6 4.7 4.3 3 .8 4.8 3 .8 3.4 4.1 4 .3 4 .4 4 .0 4 .0 4 .5 4 .9 5 .4 4 .4 4 .6 4 .6

400663 .0 400658 .1 400654 .6 400654 .7 400646 .5 400652 .7 400649 .3 400661 .5 400656 .9 400657 .0 400656 .1 400654.0 400649.7 400650.4 400653 .8 400657.4 400648.6 400653 .9 400654.6 400653.1

4 .4 3 .9 3 .8 4 .0 4 .7 4.2 4.2 4.1 2.5 3 .3 3 .0 3.5 3.5 3.5 4.8 4.7 4.1 4.5 4 .2 4 .2

400644 .2

1 .2

400654.3

0 .9

average 133

u/V-n Ba

276

average 133

Ba

303

u/V-n

With attenuator

1 .0

0 .9

276389 .8 276400 .7 276400 .2 276395 .9 276393 .3 276399 .0 276398 .8 276400 .2 276398 .4 276390 .3 276395 .1 276397 .1 276402 .: 276412 .3 276399 .7 276397 .6 276400 .5 276399 .0 276404 .8 276409 .2

2 .9 3 .0 2 .8 3 .2 2 .9 2 .6 2 .4 3 .6 2 .6 2 .7 2 .8 2 .7 3 .2 2 .9 2 .8 2 .7 3 .0 2 .9 3 .1 3 .0

276390 .4 276406 .7 276404 .4 276399 .1 276399 .3 276397 .7 276402 .7 276393 .1 276399 .5 276403 .3 276401 .1 276404 .4 276394 .2 276390 .5 276399 .8 276400 .9 276390 .4 276392 .5 276404 .4 276402 .2

3 .3 3 .2 3 .2 3 .2 3 .0 3 .0 2 .9 2 .9 2 .9 3 .0 3 .8 3 .4 5 .8 3 .4 3 .1 3 .6 3 .4 3 .2 3 .3 3 .4

276399 .2

1 .2

276398 .8

1 .2

0.6 302855 .2 302854 .0 302854.1 302853 .6 302853 .6 302852 .7 302853 .7 302855 .5 302857 .1

3 .0 3 .2 3 .1 3 .3 2 .7 2.4 2.5 2.5 2.4

0 .8 302852 .9 302850 .0 302857 .3 302858 .6 302853 .2 302855 .5 302852 .5 302852 .5 302855 .2

3 .0 3 .0 2 .9 3 .1 2 .8 2 .7 2 .6 3 .1 2 .8

440

H. Kumahora / Precision energy measurement of gamma rays

Table 3 (continued) Nuclide 33

Ba

Energy (keV)

Without attenuator Energy

Error

Energy

Error

303

302851 .1 302853 .2 302850.6 302857 .6 302858 .1 302853 .1 302852.0 302849.1 302849.7 302857.6 302861 .4

2 .7 2 .9 2 .7 3 .4 3 .2 2.8 2 .8 3 .3 3 .0 3 .2 3 .6

302853.2 302852.5 302856.9 302851 .2 302852.9 302855.0 302857.0 302851 .6 302847 .9 302855 .5 302860 .3

3.2 3.1 3.6 5 .7 3.6 3.1 3.1 3 .4 3 .4 3 .4 3 .5

302854 .1

0.7

302854 .1

0 .7

average 133

Ba

u/v~n356

average 133

Ba

383

u/r

With attenuator

0.7

0 .7

356017 .2 356019 .1 356013 .9 356015 .0 356014 .7 356014 .1 356014 .8 356022 .1 356018 .8 356017 .1 356019 .5 356019 .2 356024.7 356022 .6 356016 .5 356015 .8 356008 .7 356018.8 356020.8 356019.5

4 .0 4 .0 3 .9 4 .4 3 .6 3 .4 3 .3 3 .6 3 .4 3 .7 4 .2 4 .3 5 .9 4.5 4.0 4.1 4.5 4.3 4.6 4.9

356009 .5 356005 .2 356010 .9 356007 .3 356004 .3 356009 .8 356007 .0 356007 .1 356010.5 356004.8 356005 .9 356007.4 356010.2 356008.7 356008 .0 356007 .7 356002 .6 356005 .1 356010 .2 356011 .8

2 .3 2 .5 2 .3 2 .5 2 .2 2 .1 2 .1 2 .4 2.2 2.3 2.6 2.7 4.3 2.7 2 .5 2.5 2 .6 2 .6 2 .7 2 .8

356017.6

0 .8

356007 .7

0 .6

0 .9 383831 .3 383867 .0 383870 .7 383868 .9 383867 .7 383864 .2 383868 .4 383875 .5 383869 .4 383866 .9 383864.8 383868 .3 383870.7 383865 .0 383861 .6 383861 .0 383854 .6 383863 .2

4 .7 4 .6 4 .6 5 .3 4 .6 4 .9 4 .2 4.4 4.1 4.5 4.7 4.9 6 .9 5 .0 4.7 4.7 5 .0 4.8

0.6 383840.5 383837 .3 383844.2 383841 .3 383828.4 383840.2 383839.3 383842.7 383846.1 383838.6 383841 .8 383840 .8 383857 .3 383840 .9 383840 .4 383840 .7 383838 .2 383839 .4

3 .2 3 .5 3 .2 3 .9 4.3 3 .8 3.1 3.3 3.1 3 .7 3.7 3.3 6.4 4 .1 3 .4 3 .7 3 .1 4 .3

441

H. Kumahora / Precision energy measurement of gamma rays

Table 3 (continued) Nuclide

Energy (keV)

Without attenuator Energy

Error

133

383

383850.4 383856.4 383863 .3

Ba

average

ence gamma rays. The details of the error estimation were mentioned in the previous paper [3]. The total error E is given by the equation, 2 =S 2 +(Si +Sd +Sr )2 ,

or E

Energy

Error

5 .6 5 .2

383838.3 383841 .7

3 .2 3 .2

2 .1

383840.9

1 .2

1 .1

u /~n

E

2 =u 2/n+(S,+Sd +Sr )2 ,

(4)

0 .8

keV and 223 keV lines of t33Ba are too weak to analyze. Thus the energies of these gamma rays were deduced from the energy differences between the two following transitions on the basis of the well-established level schemes: 133 Ba 53 = 356 - 302, 79 = 356 - 276, 81 = 383 - 302,

where n is the number of measurements. The larger one was adopted as the error in table 2.

Examples of observed values and equal-weight averages are listed in table 3. These values agree with each other within the statistical error. Final values of gammaray energies are given by the mean of individual sets of measurements, and are shown in table 4. The 53 keV gamma ray of t33Ba is out of the present calibration region. The 79 keV and 81 keV lines of t33Ba and the 198 keV line of 75 Se are complicated peaks. The 160

°) a

Q1 O

223 = 302 + 276 - 356 ;

se 198 = 264 - 66,

where energies are written in keV. A recoil correction was performed for these transition energies. To examine the reliability of our measurements, the three following cascades for the 7S Se 400 keV line were

Table 4 Final values of gamma-ray energies Nuclide Present

Helmer et al .

Energy (eV) Error (eV) Energy (eV) Error (eV)

m z m r

160 = 79 + 81 = (356 - 276) + (383 - 302), 75

4. Result and discussion

CD

With attenuator

75 se

r-

_ m

o o° , V

< -

O

y w 400 96 + 303 121 + 279 135+ 264

Fig. 6 Reliability test of the measurements . Three sum energies for the 75 Se 400 keV line are shown. Numerals in the figure indicate gamma-ray energies in keV. Errors indicate only the statistical component.

133

Ba

66052.2 96734.5 121116 .6 136000.8 198606 .4') 264658 .4 279544 .1 303925 .2 400660 .0

0.8 1 .1 1 .6 0.6 2.1 1 .9 1 .3 1 .7 1 .1

66060 96734 ' 121119 136000 198596 264656 279538 303924 400657

7 2 3 3 6 4 3 3 2

53158 .7') 79613 .9'~ 80998 .2') 160612 .0') 223249 .4a) 276399 .0 302854 .1 356012 .7 383852 .1

1 .6 2 .9 2 .6 3 .9 3 .2 2 .7 1 .2 1 .1 2 .3

53161

1

276398 302853 356017 383851

2 1 2 3

') The energy is deduced from the energy difference between

two gamma rays on the basis of the level scheme .

442

> ar

H. Kumahora / Precision energy measurement of gamma rays

10

I

PRESENT

8

HELMER et al

w

U z

w w

0

i 100

200

300

400

ENERGY (keV)

Fig. 7. Comparison between present values and Helmers' for the 75 Se gamma-ray energies. Closed circles with flags show present values and rectangles show values of Helmer et al . [5]. compared after correction for the recoil energy : 400 = 96 + 303 = 121 + 279

(6)

= 136 + 264,

where values are in keV. In all cases the sums agree with each other within the statistical errors as shown in fig. 6. The final values are compared with those of Helmer et al . [4,51 in table 4 and figs. 7 and 8. The present values agree with those of Helmer et al. except for the 75 Se 66 and 279 keV lines and the 133Ba 356 keV line . The errors of the present measurements are generally smaller than those of Helmer et al . The gamma-ray energies of Helmer et al . are generally larger than the present values in the energy region of 60 to 200 keV and smaller in the region of 200 to 400 keV as shown in fig. 7. A systematic deviation seems to appear between these two measurements . This deviation may be attributed to the standard gamma-ray energies used for calibration or to their reevaluation method . In conclusion the gamma-ray energies of 75 Se and 133 Ba were determined with uncertainties of 0.6 to 2.7 eV . They are useful for the calibration of the Ge detector. The author is grateful to Prof. Y. Yoshizawa for valuable guidance and discussions . He also thanks Dr . H. Inoue for valuable suggestions . He wishes to thank the referees for their comments. References

d

5

w

U z

w w LL u0

0

-5

300

400 ENERGY (keV)

500

Fig. 8. Comparison between present values and Helmers' for the 133 Ba gamma-ray energies. Closed circles show present values and rectangles show values of Helmer et al. [5].

E.G. Kessler, R.D. Deslattes, A. Hennis and W.C . Sauder, Phys . Rev. Lett. 40 (1978) 171. [2] E.G. Kessler, L. Jacobs, W. Schwitz and R.D . Deslattes, Nucl . Instr. and Meth . 160 (1979) 435. H. Kumahora, H. Inoue and Y. Yoshizawa, Nucl. Instr. and Meth . 206 (1983) 489. [4] R.G. Helmer, R.C . Greenwood and R.J . Gehrke, Nuci . Instr. and Meth . 155 (1978) 189. R.G. Helmer, A.J . Caffrey, R.J. Gehrke and R.C Greenwood, Nucl . Instr. and Meth. 188 (1981) 671. [6] K. Shizuma, H. Inoue, Y. Yoshizawa, E. Sakai and M. Katagiri, Nucl. Instr. and Meth . 157 (1978) 117. K. Shizuma, Nucl. Instr. and Meth . 150 (1978) 447.