Systematic treatment of the photopeak efficiency

NUCLEAR INSTRUMENTS &METHODS IN PHYSICS RESEARCH

Nuclear Instruments and Methods in Physics Research A309 (1991) 236-247 North-Holland

Section A

Systematic treatment of the photopeak efficiency H. Baba, A. Yokoyama, Y. Sakuraba, N. Nitani and T. Saito

Department of Chemistry and Laboratory of Nuclear Studies, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan

S. Baba

Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-11, Japan Received 29 January 1991 and in revised form 30 May 1991

The method introducing the effective interaction depth for the photopeak efficiency proposed for small detectors was applied to three large germanium detectors and found feasible for large detectors too, except for soft y-rays measured at small source-to-detector distances. These exceptional cases, are caused by attenuation by the absorption layer, or by ineffective core in the case of coaxial Ge(Li) detectors. Coincidence summing effects are also discussed in order to extract a simple relationship between the magnitude of the coincidence summing and the source-to-effective-volume distance regardless the details of individual cascade relations . This enabled us to devise a correction method for the coincidence summing even when the decay scheme is unknown for the relevant -y-ray .

1. Introduction A quarter of a century has already passed since germanium detectors came into use in high-resolution y-ray spectrometry . Numerous works have been devoted to various aspects of the accurate measurement of -y-ray intensities with the detectors [1]. Absolute

measurement of the photon intensity, however, still depends on empirically determined photopeak efficiency of the detector at a given geometry using secondary standard sources with known photon intensi-

ties; one must go through the whole procedure of constructing the efficiency curve all over again when the counting condition is changed. It has been pointed out [2-5] that a Ge(Li) detector has a photopeak efficiency E(E,, d) for a point source

at source-to-detector distance d that is proportional to

(d +x i,) - 2 if d is not too small. Here, x,) is called the effective interaction depth which is supposed to depend on the photon energy Ey only. That is, the photopeak efficiency may be considered to be controlled by a purely geometrical factor of the solid angle subtended by the detector surface locating at d + x(i

instead of d . Then, the photopeak efficiency e(Ey , d) may be expressed as

E(Ey,

Eo~ Ey ) d) - [d +x i,(E y )

1-

where e,, is a specific function of the photon energy Ey only

and is considered to

photopeak efficiency .

be an effective intrinsic

Eq . (1) is, however, reported invalid for small d,

particularly in the case of large detectors [6]. One of the sources responsible for the deviation of y efficiency from eq . (1) may be the detector edge effect .

Cline [7] demonstrates that the ratio of the full-energy

peak intensity at a close distance to that of a distant position increases below 500 keV for a coaxial-type detector while it remains constant for a planar detec-

tor. This is ascribed to a lower relative probability for detecting high-energy photons at the smaller distances

where the y-rays entering the detector surface near the edge have considerably off-normal angles and are likely to escape without depositing all their energy in the detector .

There is another correction which is attenuation of the incident -y-rays in the layer of casing and the dead layer of the detector surface. -y-rays impinging with a large angle with respect to the normal direction tra-

* Present address: Osaka Gas Co. Ltd., Konohana-ku, Osaka 554, Japan.

verse a longer distance in the layers and consequently suffer more attenuation for a shorter source-to-detec-

0168-9002/91/$03 .50 Oc 1991 - Elsevier Science Publishers S.V . All rights reserved

H. Baba / Systematic treatment of the photopeak efficiency

for distance . The relative attenuation should be then more substantial for low-energy -y-rays than high-energy ones . We must further consider the coincidence sum effect with multi-gamma emitters . In order to construct the efficiency curve, we should use a sufficient number of standard y-rays whose energies spread uniformly over the required energy range. This requirement can hardly be realized with single-gamma emitters only, and we are forced to add some multi-gamma emitters . It follows that we must isolate the sum effect for multi-gamma sources from the other effects in determining full-energy peak efficiencies . The coincidence summing effects in germanium detectors were demonstrated by Luukko and Holmberg [8] for two -y-rays in cascade. This effect has been formulated in a complete form by Andreev et al . [9] for ,y-rays in the case of complex decay scheme . They also demonstrate [10] that the sum effect appearing in the -y-ray spectrum of 152Eu measured in a close geometry can be corrected by these formulas . Several authors have studied this problem experimentally and found a satisfactory solution for a large number of multiple -y-ray emitters by solving the complete correction formulas that take into account the established complex decay scheme of the relevant nuclide completely [4,1113]. The coincident detection of two photons may occur in measurements of multiple -y-ray emitters . The sum effect becomes prominent in the y-ray measurement at a close source-to-detector distance . That is, a decrease in the full-energy peak area is observed for a -y-ray accompanying cascade -y-rays. Furthermore, ß +-decaying nuclides such as 22 Na reveal the sum effect with the annihilation photons and coincidence summing with X-rays is observed for nuclides in which X-ray emission from electron capture or the internal conversion process is involved . All of ß-decaying nuclides may produce a coincidence with a ß-ray directly or via a bremsstrahlung photon . These ß-rays may hence cause the sum effect with the -y-rays of the daughter nuclei though it is usually less prominent. All the above sum effects result in a decrease of the relevant full-energy peak area, whereas for the crossover -y-rays there is an increase of the relevant peak area . Finally, there is a sum effect due to chance coincidences between mutually independent -y-rays. The effect is, however, insignificant except for the case of high counting rate so that one can get rid of the effect by keeping the counting rate well below the inverse of the time constant of the circuitry. So let us focus on the real or essential coincidence summing phenomena only in the following consideration . Though the theoretical treatments have been proved to describe the sum effect well, they generally concern relatively low degrees of coincidence summing. Even

237

though such correction formulas are theoretically correct, we must introduce several sources of the error into actual calculation as discussed later. Debertin [14] also discussed problems involved in the coincidence summing correction for radionuclides with complex decay schemes. Therefore, we like to elucidate how far the relevant treatment of the sum effect is valid as the rate of correction increases by comparing the observed sum effect with the predicted values . To do so, we need to construct the photopeak efficiency with sufficient accuracy . In the present work, we first describe a systematic method of deducing the photopeak efficiency of coaxial-type germanium -y-ray detectors, in which the efficiencies determined with point sources of monochromatic -y-ray emitters and point sources giving rather insignificant sum effects were corrected for attenuation by calculation . Comparison of this efficiency curve with apparent photopeak efficiencies enabled us to evaluate the magnitudes of the coincidence sum effect for multiple y-ray standard sources. Next, we give a simple formula describing the coincidence sum effect without taking into account the details of the relevant decay scheme . We then propose a method correcting for coincidence summing in such cases and study the feasibility with -y-rays emitted from 152Eu and 133Ba. This solves a problem frequently encountered in studies of nuclei far from the stability line that necessarily possess short half-lives and are not produced in large quantities . One can not undertake the measurement with such short-lived weak activities at long source-detector distance so that one needs to make a correction for the coincidence summing in the observed full-energy peak with unknown decay scheme . A decayscheme-independent method for the correction would thus be useful .

2. Germanium detectors and -y-ray sources Three coaxial-type germanium detectors, 93 cm 3 hyperpure germanium detector (HPGe) and 75 cm 3 and 134 cm 3 Ge(Li) detectors were used in the present study. The two Ge(Li) detectors are of true coaxial type whereas the HPGe is a closed-end detector . Specifications of the three detectors are listed in table 1. The HPGe detector is expected to have a small ineffective hole at its back but it is neglected because it is insignificant for the present purpose as seen in the succeeding treatment . The y-rays utilized in the measurement are summarized in table 2. Emission probabilities and conversion coefficients given in the table were taken from ref. [15] .

238

H. Baba / Systematic treatment of the photopeak efficiency

Table 1 Characteristics of the three germanium detectors used in the present study

3. Systematic treatment of the photopeak efficiency

HPGe

Ge(Li) (75 cm 3)

1/2 . 1/( e(E 3 d))1/2= [d+xl~(E Y )1l(eo(Ey ))

47 .0 55 .5

46.6 48.2

0a

4.1

2 .625

0 .7 1 .3

0 0.5

0 0.5

3 93 .2

5 75 .4

5 134.2

Diameter 2R [mm] Length [mm] Diam . of ineffective core 2r [mm] Absorbing layers [mm] germanium aluminum teflon Window-to-detector distance s [mm] Total active volume [cm3] a

0

1.0

Ge(Li) (134 cm 3) 53 .9 69 .0

From eq . (1), one obtains the relation : 1

It follows that one should find a straight line by plotting the inverse of the square root of the observed photopeak efficiency vs the source-to-detector distance d for a monochromatic 1'-ray. In order to elucidate the validity of eq . (2), several -y-ray sources that are generally used as the standard in the -y-ray spectrometry

1.0

The detector has a hole of 8 mm in diameter and about 37 mm in depth at the back, the effect of which is negligible .

Table 2 Standard -y-ray sources used in the present study Nuclide 139 11-3

Emission probabilities of -y-rays from 152Eu were, however, taken from ref. [16] except for the 122- and 245-keV y-rays. A mixed -y-ray source supplied by LMRI, France, was used after re-evaluating the photon intensities of individual -y-rays when necessary. 152 Eu and 133Ba sources were also obtained from LMRI . A 152Eu source prepared and calibrated by ourselves [17] was also used in the measurements with the two Ge(Li) detectors. An evaluated 24 Na source was offered by the inspection group of Isotope Division of JAERI. In the present work, we intended to consider the photopeak efficiency systematically from the practicable viewpoint rather than from the metrologically strict point of view . We restricted ourselves to point sources measured with coaxial-type germanium detectors. We did not consider the source-volume effect for the photopeak efficiency nor investigate other types of the detector . Furthermore, the standard sources obtained from LMRI accompanied errors in the photon intensities amounting more than 2% . We did not attempt to re-evaluate the photon intensities from the metrological point of view but merely tried to reduce the involved errors within 1% by secondary standardization of several standard sources by means of -y-ray spectrometry . The statistical errors were constrained within 0.2% and uncertainties in the peak area determination are estimated to be less than 0.2% [18] . Considering other sources of the error, such as uncertainty in the source position, deviation in the source size from the point, etc., the total error is estimated to be 2% in which the systematic error is 1% . Consequently, we try to explain the photopeak efficiency for practically all -y-ray energies at various distances to near the detector surface with allowable fluctuations of 2% .

(2)

Ce

Sn

85 Sr

137c

,54

s

Mn

57Co

60 Co 88 Y 22 24

Na Na

133

Ba

152 E u

a

Ey

Emission probability

a

165 .85 391 .69 514.00 661 .65 834.83 14.4125 122,058 136,471 1173.21 133247 898.03 1836.00 1274.26 1368.53 2754.14 53 .16 79.63 80.998 160.63 223.10 276.38 302 .85 356.005 383.851 121 .78 244.69 344 .27 411 .11 443 .9 778 .90 867 .39 963 .4 964 .0 1085 .80 1112 .07 1212 .89 1299 .19 1408 .02 1528 .12

100 99 .9 99 .99 94 .6 100 9 .77 85 .6 11 .13 99 .88 100 91 .9 100 100 100 100 2 .3 2.8 34 .3 0 .75 0 .46 7 .1 18 .2 62 9 .0 29 .3 a 7 .7 a 27 .2 2.32 3 .20 13 .22 4.32 14 .92

0 .251

Taken from ref. [21].

10 .24 13 .75 146 1 .01 21 .27 0.286

9 .1 0 .027 0 .166

5 .0 1 .76 1 .665 0 .253 0 .080 0 .057 0.044 0 .025 0 .021

239

H. Baba / Systematic treatment of the photopeak efficiency

were measured at various distances with the three coaxial-type germanium detectors . Resulting relationships of e on d are exemplified in fig. 1 for several standard -y-rays measured with the 134 cm 3 Ge(Li) detector. Linear dependences of s on d were obtained as expected except for soft -y-rays measured at shortest distances. The inverse of square of the slope of the straight line gives the constant s,,(E,), the "intrinsic efficiency", and its intersect on the abscissa corresponds to the effective interaction depth, x(E,) [2-5]. Deviations for soft -y-rays at small d always appear upward from the linear line as shown for the 166 keV ,y-ray in fig. 1 . This implies that a detection loss with large geometry appears in the case of soft 1'-rays. Observed photopeak efficiencies of high-energy -y-rays follow eq . (2) quite well even in the case of as large a detector as the 134 cm 3 Ge(Li) . If one takes the ratio of the efficiency of a low-energy -y-ray to that of a high-energy one instead, one

50

40

I wo

30

N 1 ~

20

10

1

3p

Ó \\

rui Fig. 2. A pictorial illustration of the geometrical arrangement of a coaxial Ge(L0 detector . The dotted zone indicates the sensitive volume and the hatched core of the crystal corre sponds to the ineffective core . The double-hatched regions are responsible to the attenuation of y-rays obtains larger values as the sources approach the detector surface as pointed out by Cline [7]. This suggests that the edge effect, more effective to high-energy photons, has been almost completely compensated by introducing a phenomenological "effective interaction depth" to leave a secondary effect which works in the opposite direction from the edge effect . We ascribe this secondary effect, the deviation from linearity, to the attenuation of incident -y-rays by the absorption layer on the top of the detector or by the ineffective core in the case of the true coaxial detectors. The rate of attenuation was calculated as demonstrated in fig. 2 and formulated by eq . (3): w(d) = (cos 0b -cos Be X exp[ X

0 Fig. 1. Inverse of the square root of observed photopeak efficiency plotted versus the source-to-detector distance d for various standard y-rays measured with a 134 cm 3 Ge(L0 detector. The intersect of the resulting linear line on the abscissa gives the effective interaction depth xo while one obtains the "intrinsic photopeak efficiency Eo" from the slope of the line .

) -t I 0. exp( - pS/cos 0) n

-S(B - 0, »

(r/sin 0 - d/cos 0) ] sin 0 dB,

where j.$ is the effective absorption coefficient which is obtained by computing the individual total absorption coefficient for each absorption layer described in table 1 and the total absorption cross section given in ref. [19] . Furthermore jut is the total absorption cross section of germanium and S denotes a step function defined by S( x)

= l1 l0

for x < 0, for x > 0.

240

H. Baba / Systematic treatment of the photopeak efficiency

The correction factor was deduced as the calculated attenuation at a given distance d normalized by that for the largest observed distance . The second factor in the integrand of eq . (3) gives absorption in the ineffective core of the Ge(Li) detector which turned out to be crucial to compensate the large efficiency deficit observed for soft -y-rays measured at a close source-to-detector distance . In the cases of pure germanium detectors and planar-type Ge(Li) detectors, r in fig. 2 equals zero and hence 0, = 0 so that the second factor in the integrand of eq . (3) disappears . The consequences are more appropriately demonstrated in fig. 3, where the ratios of the corrected efficiency to the efficiency given by eq . (1) are plotted vs d. Deviations from unity are found to be mostly within the estimated error of measurement amounting to 2% . Coincidence summing proved to be not too large among -y-rays emitted from popular standard sources such as 6° Co, S7Co, or 88 Y as discussed in the next section. This assures good linear relationships given by eq . (2) and enables us to determine a number of x, and Eo values accurate enough to deduce their

0.9 1.1

ó

0

61 39Ce 166 keV

+-ó ó-~ °

á

" Sn 319keV

° ó

0.9 1 .1

e6Sr

1-f ó-"a

~

1

60 C°

° °

0

5

514keV

137C5 662keV

0.9 1 .1

09

3

t

d (cm)

10

1332keV

15

Fig. 3 . The ratios of observed photopeak efficiencies to corresponding calculated efficiencies for various standard -y-rays; measured with the 134 cm" Ge(Li) detector. Open circles represent uncorrected value and solid circles are for corrected data . Triangles designate those corrected for the coincidence summing only .

4 3 2 E V

0 x

L 3 á

0 c 0 V ro v

c

v

2 1 4

û

w 3 w 2 0.1

Et (MeV)

1 0

Fig. 4. Effective interaction depths deduced for the three germanium detectors plotted versus -y-ray energies . Solid curves are drawn to guide the eye, while the dashed lines indicate the depth to the crystal center.

energy dependences for any of the three detectors as shown in figs . 4 and 5, respectively . According to the consequences of fig. 4, obtained xo values seem to merge in more or less the same range among the three detectors as the photon energy increases though the features somewhat differ from one another . Furthermore, they exceed the depths to the center of crystals indicated by dashed lines in fig. 4 except for the case of the largest detector . Fig. 4 suggests that the effective geometry of a detector is rather independent of the detector length, which conflicts with the observation with small crystals that the effective interaction depth appears to approach to the center of the crystal as the photon energy increases [3,61. The presently obtained consequence is, however, feasible bacause x o is to reflect the edge effect for incident y-rays not depositing all the energies in the detector, which would be affected by the detector diameter but rather indifferent to the detector length . Results of fig. 5 demonstrate that eo takes its maximum value around 150 keV and starts to decrease as energy increases showing an energy dependence well represented for any of the three detectors by log £o = a log Ey + b,

241

H. Baba / Systematic treatment of the photopeak efficiency

where a and b are appropriate constants. Though the essential feature of e as a function of E y is visualized in the photopeak efficiency, it is generally the case that the energy dependence of the photopeak efficiency is much more complicated as shown in fig. 6. Making use of eqs. (1) and (5) one obtains

2

d log ey

d log Ey

0 .01

0001

0 .1

1 .0 Er (MeV)

Fig. 5. Intrinsic efficiencies as functions of the energy obtained for the three germanium detectors.

_a

dx 

d +x  d log Ey

(6)

for E y > 200 keV. That is, the non-linear slope of log ey is generally brought in via the second term of eq . (6), unless the derivative of x with respect to Ey is 0 or sufficiently small. As depicted in fig. 7, however, photopeak efficiencies exhibited linear relationship in the case of the 75 cm 3 Ge(Li) detector, whose x  was found linearly depending on log Ey and consequently giving a constant derivative value above 200 keV. This would result in a constant contribution of the second term despite the small changes in x. The contribution of the second term in the righthand side of eq . (6) becomes less pronounced as the source-to-detector distance increases so that the energy dependence of eY resembles that of e more and more for far distant geometry . This is seen even in the case of the 75 cm 3 Ge(Li) detector of fig. 7, where the second term in the region of unsaturated x eventually

10-1

10-2

10-3

0-1

Er. (MeV )

1 .0

Fig. 6. Observed (circles) and calculated (solid curves) photopeak efficiencies at various distances from the top of the 93 cm 3 HPGe detector. In the case of d = 26 mm, both corrected (open circles) and uncorrected (closed circles) are depicted .

Fig. 7. Observed (circles) and calculated (solid curves) photo peak efficiencies at various distances from the top of the 75 cm 3 Ge(Li) detector .

242

H Baba / Systematic treatment of the photopeak efficiency

to renormalize the effective distance, d +x o . Finally, one need not worry about exact reproduction of the counting condition to measure E o because it is not affected by the change in the counting condition at all. 4. Coincidence summing correction

0 W

The observed photopeak intensity N,' of the ith y-ray at distance d is expressed as

01

N,' = Nofe(E  d)-Nof_-(E d)

X F_WJ(0)p,(y,)e,(E,, d) +N Lfm .Wmn( 0 )E(Em, d)E(E., d), m,n

1 0 ET (MeV) Fig. 8. Effective interaction depths and the intrinsic efficiencies measured at two different occasions. Solid marks represent those at the normal condition whereas open marks give corresponding data measured under the condition in which the position of sample holder has eventually moved by about 8 mm . 0.1

extends the linear portion further down whereas the feature of E o is gradually recovered for distant geometries. Since the intrinsic efficiency E  is a characteristic of the relevant detector and is a function of EY only, the value once determined ought to be valid all the time indifferent to the change in the counting conditions though spurious values of x o may incidentally change from time to time . This expectation was proved as shown in fig. 8 in which the initially determined values of E  and x, (open circles) are plotted together with those measured in another occasion (closed circles) . During the first and second measurements the source holder happened to be moved to make apparent x O value smaller by about 8 mm as seen in the bottom section of fig. 8. Nevertheless, observed e o values coincided almost perfectly between the two measurements (cf . the top section of fig. 8.) . This assures the following three items: First, one can predict the photopeak efficiency at a given EY with any geometry without carrying out any further measurements once one has determined E, and x, with a set of standard y-ray sources. Second, in case where the exact source-to-detector distance is unknown, all one has to do in order to get photopeak efficiencies are to measure the photopeak intensity of a standard y-ray at an appropriate position

where No is the disintegration rate of the source activity, f, gives the emission probability of the ith -y-ray, and E(E, d) and E,(E, d) are, respectively, the photopeak and total efficiencies of the -y-ray with energy E . Furthermore, W,,(O) implies the angular correlation of y, and y averaged over the solid angle subtended by the detector, p,(y) is the fraction of y cascading with y,, and f,., denotes the coincident fraction of ym and y that are in the cross-over relation with y, . The summations in eq . (7) are to be carried out for all of the relevant -y-rays. For simplicity, contributions of triple coincidences are not included in the second and third terms of the right-hand side of eq . (7) though they were taken into account in the actual individual computation in the text . The first term of eq . (7) is equal to the photopeak intensity N, obtained in the condition where the summing effect is negligible, that is N = Nof E(E d) .

(8)

The second and third terms correspond to the correction due to the coincidence summing. The random summing that depends on the counting rate of the detector is not taken into account here as mentioned in the introduction . In order to evaluate the coincidence summing one needs to know the total efficiency as well as the photopeak efficiency. Determining e t experimentally is not easy, however, because the very low-energy part of the , y-ray spectrum is generally dropped by setting a discriminating level in the amplifier to cut noise signals out. According to Griffiths [20], E, is computed by E,(E, d)

4Tr

ƒ [1 - exp{

wt(E)t)1 df,

where t is the path-length of the -y-ray in the detector and p, t is the total attenuation coefficient [19] . Integration is performed over the solid angle subtended by the detector .

243

H. Baba / Systematic treatment of thephotopeak efficiency

Et

0 .1

0.01

0 .1

Er (MeV )

1

Fig. 9. Observed (circles) and calculated (dashed and solid curves) total efficiencies of the 134 cm3 Ge(L0 detector at d=2 cm . The dashed curve gives the total efficiency computed without absorption correction (eq. (9)) while the solid curve represents corrected efficiencies computed with eq . (9').

1 .1

10

1 .0

0.9

09 10 d

+_~_~

+

60C0

~1 .0 0

" 0.9

0

0

22Na

1173 keV

1275keV

0

0 .9 1 .1

w

10

w0

0.9 1 .1

0

10

10

60

0.9 "- t -t

4

0

0.9 0

5

4

10

d (cm)

Co

1332 keV

b

53

0

10

`

0.9

o a

0 .8

88 y 698 keV

0

0

0 .9

8

~

.b

0

1836keV

15

Fig. 10 . Ratios of the observed photopeak efficiencies to the calculated values for typical standard -y-rays measured with the 93 cm3 HPGe detector . Open marks represent uncor rected values, while solid marks are for those corrected for the coincidence summings .

81 keV

276

keV

356

keV

b

1 .1 1 .0

88y

keV

0.9

384 keV

0

5

10

d (cm)

15

Fig. 11 . Ratios of the observed photopeak efficiencies to the calculated values for principal -y-rays of 133Ba measured with the 93 cm 3 HPGe detector . Open circles represent uncorrected values, triangles give those corrected for the absorption only, and solid circles are for those corrected for both absorption and coincidence summing.

H. Baba / Systematic treatment of the photopeak efficiency

244

Eq . (9) is, however, valid only if attenuation of -y-rays by the absorption layer is negligible . For systems in which the rate of attenuation is substantial, eq . (9) must be modified as

{ r/sin 0 - d/cos 0) 1

X

(1 - exp(- li t t)} sin 0 dB,

where li p is the photoelectric cross section of the y-ray with energy E. For comparison the total efficiencies Et were measured with the 134 cm 3 Ge(Li) detector by assuming the missing part of the observed spectrum being constant at the height in the lowest observed channel. The resulting total efficiencies are plotted with circles in fig. 9 together with two computed efficiency curves ; one calculated with eq . (9) (dashed line) and the other with eq . (9') (solid line). Agreement between the measured E t and calculated one is acceptable considering the ambiguity involved in the low-energy part of the spectrum . Though either of the alternatives resulted satisfactory consequences, the total efficiencies given by eq. (9') proved to improve the coincidence summing correction . This suppression in the low-energy region was crucial in the reproduction of the coincidence summing for some y-rays . In order to investigate how well eq . (7) reproduces the amount of the coincidence summing, we made use of the main y-rays of 133Ba and 152Eu, which are summarized in table 3, in addition to the -y-ray sources given in table 2 . Some of the results of investigation are shown in figs . 10 and 11 . The coincidence summing with annihilation photons was found to be explained well within the framework of eq . (7) as shown for 22 Na, while no sizeable coincidence summing between -y-rays and accompanying X-rays was observed with presently used 0'- and/or EC-decaying nuclides such as 85 Sr, 139 Cc and so forth. Many of the -y-rays emitted from 133 Ba and 152 Eu revealed significant amounts of coincidence summings as displayed for 133 Ba in fig. 11, which proved to be reproduced satisfactorily by the treatment based on eq . (7) (Corrections for triple coincidence summing were of course taken into account here .) . The only exception was the 1529 keV -y-ray from 152 Eu . An abnormally large coincidence summing effect is always observed with this y-ray. The energy of the sum peak between the 1408 and 122 keV -y-rays is very close to 1528 keV so that they are spuriously in the cross-over relation with the 1528 keV -y-ray . Furthermore, the initensity of the cascading -y-rays is 31 .5 times [151 that of the 1528 keV y-ray. This is responsible for the large summing

1

0.9 11

S/cos 0) exp[ -S(6 - Bt)wp et(E, d) = z I o°exp( - ~_ o,, X

245 keV

10

0.9 11

344 keV

C

1

444 keV

0.9 0

1 .0 09

a a

867 keV

t

4d

--0

1086 keV 0

5 3

0

0

1529 keV

1 0.2

0.4

d-1 (crn1 )

0.6

0.8

Fig. 12. Ratios of the observed photopeak efficiencies to the computed efficiencies (open circles) for main -y-rays of 152 Eu measured with the 93 cm ; HPGe detector. Attenuation by the absorption layer was corrected. Coincidence summings computed with eq . (7) are represented by solid curves while the approximate linear relationship with respect to d-1 is de picted by the dotted line . Vertical arrows designate the positions where individual solid lines take the value of unity. amounting as large as 400% as shown in fig. 12 but it is not completely explained yet by eq . (7). In conclusion, eq . (7) explains the correction for coincidence summing that one encounters in ordinary -y-ray spectrometry . 5. Presentation of the coincidence summing in a simple functional form In the preceding section, it was verified that eq . (7) reproduced the coincidence summing corrections satisfactorily. Although the computation procedure following eq . (7) is easy, there is no way of evaluating the correction for a nuclide whose decay scheme is unknown. We will demonstrate a simple functional form enabling the estimation of such summing corrections empirically. Suppose both E and Et are approximately expressed in the product form of a factor depending on the

24 5

H. Baba / Systematic treatment of the photopeak efficiency

energy only and a factor dependent of the geometry only :

X103

E(E d) =E"(E,)F(d),

3.0

(10)

We further assume that F' approximately equals F. Then, we can rewrite eq . (7) in a simple form : N,'/N,=1-k,F(d),

where k, is the quantity characteristic of y, but independent of the geometry ; that is, k, -

LWJ( 0 )p,(yj )e0 ( E,) Winn( O )fmnEO ( Em) E()( E,) f,Eo(E)

m,re

In order to study the validity of eq . (11), observed and calculated coincidence summings were plotted vs d- ' for the three detectors as exemplified in fig. 12, in which observed values are represented with circles and calculated ones are given by solid lines. The contribution of triple coincidences was taken into consideration as well in the calculation . Observed values are seen to be satisfactorily reproduced by calculated ones, except for the 1529 keV -y-ray of IS2 Eu . Furthermore, observed coincidence summing corrections were found to satisfy a linear relationship vs d -) for d greater than 2.5 cm, as shown with dotted lines in fig. 12. It follows that the above proposition, eq . (11), proved feasible and we can introduce the following equation for F(d) ; 0

F,(d)-~d-'-d

c)

for

d > d,,,

for

d
a

245keV

X I04 1 .2

344keV

Fn C X103 ap 1 .8

c

867keV

C 0

a

O

L X103

cO (12)

a.

3.2

4.5

v d 4 .0 0Q. 4 X103 9

1066 keV 1408 keV

0

8 X102 8 4 0

1529 keV

0

0.2

0.4 0.6 0.8 d -1 (cM-' ) Fig. 13 . Apparent photon intensities plotted versus d-1 for some -y-rays of )SZ Eu measured with the 93 cm 3 HPGe detector . Solid lines represent obtained linear relation among observed data uncorrected for the coincidence summings . The vertical dotted line designated the position of the minimum critical distance dm'n of the relevant detector (see text). Hatched zones demonstrate ambiguities expected in the proposed method .

(13)

where d, is a critical distance for the relevant -y-ray . Though each -y-ray gives a specific value for d. which must be empirically found, one shuold be able to find the minimum value dm'" among those critical distances in each detector system . These findings then suggest a phenomenological method of the correction of coincidence summing for an unknown short-lived y activity as described below . The relevant activity is to be measured at a few positions close to a detector for which the intrinsic efficiency £(, and effective interaction depth xo are known as functions of energy and the minimum critical distance dm" needs to be known also . Observed photopeak areas are divided by the photopeak efficiencies calculated by means of E o and x (, to deduce apparent absolute intensities. For soft -y-rays attenuation by the absorbing layer should also be taken into account. Resulting apparent intensities are then plotted vs d - ' as depicted in fig. 13 .

One should find the plotted data points lying on a straight line if experimental fluctuations have been carefully removed. The obtained linear line is expected to level off at a certain position in the region from 1/dm'" to 0 unless the apparent intensities are constant from the beginning. It follows that the true photopeak intensity should be contained in the hatched zone illustrated in fig. 13, which gives the ambiguity involved in the deduced photopeak intensity. In order to see the feasibility of the proposed treatment of the coincidence summing, it was applied to main -y-rays of '52Eu and 133 Ba and the resulting photopeak intensities were divided by individual emission probabilities to obtain the disintegration rates. In fig. 14 each of the deduced disintegration rates is plotted as a vertical segment of a line vs the -y-ray energy and the disintegration rate given to the relevant ,y-ray source is displayed as the horizontal line with hatched band indicating the attached error. Considering the fairly difficult experimental condition postu-

246

H. Baba / Systematic treatment of the photopeak efficiency 350

152E u

300

=svAMr5ZISIi

a -0 250 ro 0

x104 ~, 1 2

ro

j, 1 1 ~ 0 10 x104 40 35 30

bi-

Ge(Li) 75cc 1 0

01

c

s It

152 Eu

HPGe

above absorption and therefore were studied to see how well the logical treatment [4,9-13] reproduces the magnitude of the coincidence summings among cascading and/or cross-over -y-rays and between -y-rays and accompanying annihilation -y-rays or X-rays . It was furhter found that the coincidence summings showed good linear relationship with respect to the inverse of the distance between the source and the sensitive volume surface, d, over nearly the whole range of d. It suggests a promising correction method for the coincidence summing of unknown -y-rays . Acknowledgements

01

133g a 01

HPGe

Et (MeV )

10

Fig. 14 . Determined absolute intensities of two 152Eu and a 133Ba sources whose intensities are known as depicted with horizontal lines associated with the errors shown by the hatched bands. Vertical segments of a line correspond to the ranges of individual allowance of individual estimated values .

lated here it is concluded that the proposed method gives satisfactory consequences . 6. Summary The method introducing the effective interaction depth for the photopeak intensity that is proposed for small germanium detectors [2-5] was applied to three coaxial-type detectors and found to reproduce the photopeak efficiencies quite well except for soft -y-rays measured at close source-to-detector distances. This exceptional deviation was then studied to show it being almost completely explainable in terms of the attenuation of incident -y-rays by the absorbing layers . Above all, absorption in the ineffective core proved to be crucial for reproducing the large efficiency deficit for soft -y-rays in the coaxial Ge(Li) detector while it is rather insignificant in the pure germanium or planartype Ge(Li) detector . It was then concluded that the edge effect pointed out by Cline [7] was completely absorbed by the "effective interaction depth" . Coincidence summing effects which occur in most -y-ray sources are recognized to be a factor next to the

The authors express their gratefulness to Drs. M. Fujioka, T. Katoh and K. Kawade for their useful discussions . They are indebted to the inspection team of Isotope Division of Japan Atomic Energy Research Institute for preparing a Z4 Na standard source for us . They are also grateful to Messrs . H. Kusawake and T. Miyauchi for carrying out various numerical computations to check several models that we introduced and to Miss T. Maruoka for her preparing of a number of drawings. References [1] K. Debertin and R.G . Helmer, Gamma- and X-ray Spectrometry with Semiconductor Detectors (North-Holland, Amsterdam, 1988). [2] A. Notea, Nucl . Instr. and Meth . 91 (1971) 513. [3] D.F . Crisler, J.J . Jarmer and H.B . Eldridge, Nucl . Instr. and Meth 94 (1971) 285 . [41 G.J . McCallum and G .E . Coote, Nucl . Instr. and Meth . 130 (1975) 189. [5] R. Gunnik, W.D . Ruhter and J.B . Niday, VCRL-53861, vol. 1 (1988) . [6] K. Kawade, M. Ezuka, H. Yamamoto, K. Sugioka and T. Katoh, Nucl . Instr. and Meth . 190 (1981) 101 . [7] J.E . Cline, IEEE Trans. Nucl . Sci. NS-15 (3) (1968) 198. [8] A. Luukko and P. Holmberg, Nucl . Instr . and Meth . 65 (1968) 121. [9] D.S . Andreev, K .I . Erokhina, V.S. Zvonov and I .Kh. Lemberg, Instr. Exp . Techn., 25 (1972) 1358 . [10] D.S . Andreev, K.I . Erokhina, V.S. Zvonov and I.Kh. Lemberg, Izv. Acad . Nauk . SSR, Ser. Fiz. 37 (1973) 1609 . [III R.J . Gehrke, R.G . Helmer and R.C. Greenwood, Nucl Instr. and Meth . 147 (1977) 405. [12] K. Debertin and U. Sch6tzig, Nucl . Instr. and Meth . 158 (1979) 471 . [13] T.M . Semkow, G. Mehmood, P.P . Parekh and M. Virgil, Nucl . Instr. and Meth . A290 (1990) 437. [14] K. Debertin, Low-Level Measurements of Man-Made Radionuclides in the Environment, ed . M. Garcia-Léon and G. Madurga (World Scientific, Singapore, 1990) p. 15 .

H. Baba / Systematic treatment of the photopeak efficiency [151 C.M . Lederer and V.S . Shirley, Table of Isotopes, 7th ed . (Wiley, New York, 1978). [161 Y. Yoshizawa, Y. Iwata and Y. Iinuma, Nucl . Instr . and

Meth . 174 (1980) 133. [171 S. Baba, S. Ichikawa, T. Sekine, I . Ishikawa and H. Baba, Nucl . Instr. and Meth . 203 (1982) 273. [181 H. Baba, T. Sekine, S. Baba and H. Okashita, JAERI Report, JAERI 1227 (1972) ; and

247

H. Baba, S. Baba and T. Suzuki, Nucl . Instr. and Meth . 145 (1977) 517.

[19] E. Storm and H.I. Israel, Nucl . Data Tables A7 (1970) 565 . [201 R. Griffiths, Nucl . Instr. and Meth . 91 (1971) 377. [211 S. Baba and T. Suzuki, J. Radioanal. Chem . 29 (1976) 301 .