Getting Coincidence Information from Analysis of Sum Peaks in Singles Ge(Li) Spectra

Test, Evaluation and Improvement of the Method

ISTVAN TijRijK, ISTVAN URAY, PANNA BORNEMISZA-PAUSPERTL. and PAL KOVACS

Institute of Nuclear Research of the Hungarian Academy of Sciences. Debrecen. H-4001. Pf. 5 I. Hungary

Analysis of sum peaks from singles spectra obtained by a large volume Ge(Li) detector in many cases gives more coincidence information than traditional two-detector gamma-gamma coincidence measure- ments do. Approximate methods are given to obtain and use coincidence information from sum peaks of a single spectrum. The method gives numbers of coincidence counts several orders of magnitude higher than the traditional two detector methods do, without the use of sophisticated multiparameter analysis equipment and during comparable time. The sum peak analysis method requires much less instrumenta- tion and memory capacity, than the traditional methods. and also multiple coincidences can be measured with rather good efficiency. The possibilities and limitations of the sum peak analysis method are discussed. illustrated by different measurements as examples.

Introduction

THE HIGH efficiency of large volume Ge(Li) detectors combined with a large solid angle source-detector geometry, results in considerable summing effects, if the source, even at relatively low count rates, gives ;I-rays in a cascade (in true coincidence). The detector may “see” a single event instead of the real two or more, with the amplitudes summed. By this way real “sum peaks” occur in the spectra at the energy sum of the components. Because all the summed signals are missing from the photopeaks, different methods were developed for the correction against summing effect losses in the single photopeaks (e.g.“m4)). In current nuclear physics measurements, sum peaks are gener- ally used only for corrections against the above men-

tioned “unavoidable” and “useless” effect, despite the known fact that they also comprise coincidence’” “). source activity”s- z2’, cross-over fraction’23’, effi- ciency’z4~2h’, de cay mode, life time12” and probably even further information. As it is seen from the litera- ture cited above, the basic concept to get coincidence information from the sum peaks is not new, but the method is not yet in general use. An explanation might be that it seemed difficult to distinguish a small sum peak from small peaks of other origin. A further possible explanation: the advantages and limitations of the method have not been considered thoroughly.

We have to mention that contrary to the single-

detector and single-spectrum “sum peak analysis” method described here, there is another completely different method, the “sum coincidence” method of HooGENMx)M(**-~~’ which uses two detectors, thus only the names of the methods are similar.

Methods

In our several nuclear spectroscopy measurements on fast neutron produced radioactive nuclei by using high resolution Ge(Li) y-spectroscopy, we found empirically that the ratio of the product of the number of counts I,Ij in the single ;j-peaks of a ;-cas- cade of energies of Ei and Ej to the number of counts I,j in the corresponding true summing coincidence peak with energy Ei + Ej is constant in a single measurement. For a given isotope emitting several ;-rays in a cascade, the value Kij must be about the same for every pair of these y-rays:

Iilj Kij = I

1113

‘.I

= K,2 zz I;!’ = K,3 zz _

12 I 1.1

= K13 = !+ = (I)

I23

In 1963 BKINKM,W cl ctl. ” ‘) for Nal (TI) scintillation

785

786 1. Tiiriik et al

counters gave the formula:

for the absolute activity of radioisotopes emitting two y-rays in coincidence, where N is the absolute activity, A, and A2 are the areas under the photopeaks of the two y-rays respectively. A, 2 is the area under the sum- peak, and T is the area under the whole spectrum, all normalized to unit time. (Later different authors applied this formula to Ge(Li) and other solid state

detectors as well. e.g.” ‘) Formulae (I) and (2) are closely related. R in (2) is

equivalent to Kij in (I) not regarding the measure- ment time. (In reference (18) BRINKMAN rr trl. gave a

formula similar to (I) for the R,i values for 21 multiple

cascade.) BRINKMAN et d. discussed in the above mentioned

works. that formula (2) is strictly valid if one of the y-rays in a cascade has the abundance of IOO”,, and there is no angular correlation between the y-rays. In practical cases, during our experiments, evaluable sum peak can be resulted only if the abundance of one of the components is nearly 100”. (more than about SO”,,) and the angular correlation in most cases gives less than 2&30’:, errors (4). This means, that the near constancy of K,, (within a factor of 2 or within an order of magnitude) as observed by us, is true in most of the practical cases within the rather large statistical error limits of Kij, which are mainly due to the low number of counts in the sum peak.

BRINKMAN et cd. used the formula (2) for absolute activity measurements with a well type Nal(TI) scintil-

lation counter. They advised to place the source inside the well, to keep the term A,A,iA,, as small as possible. In this case, using an almost 47~ geometry the term T is the dominant. This mode of mcasure- ments is excellent in work with monoisotopic sources. In practice one often works with multi-isotopic sources. and it is difficult to determine which fraction of the measured T value stems from the isotope in question.

In such cases it is advantageous to keep the term T as small as possible. We measured with common co- axial Ge(Li) detector. that means a geometry always much less than 2n. In all of our practical cases the term R was dominant in the formula (2) T << R it means a small total detection efficiency. This small detection efficiency is compensated by the high energy resolution of the semiconductor detectors, and per- mitted to work in a high background of other iso- topes, because the dominant R (or K) is calculated only from the photo and sum peaks. The partition of R and T in the absolute activity of a source depends on the s ~ d distance, e.g. for a 100cm” Ge(Li) “‘Co source, ,S - d = 10 cm: T < 0.05 R. These questions will be discussed by the authors in detail in a future

paper on absolute activity measurements using sum

peaks.

The above considerations on branching, angular

correlation and statistical errors are valid throughout the following discussions of getting coincidence infor- mation from the sum peaks.

We have to emphasize that for practical work the experimentalist must thoroughly analyse the measured peak at energy Ei + Ej. because it may be combined of components of different origin:

(I) The true summing coincidence, the random summing peak and a possible crossover transition appear exactly at the same energy.

The random summing can be kept negligibly low by choosing a small source strength or a longer source detector distance (resulting in low count rates). if not, special corrections arc necessary vvhrch will not be discussed in this paper.

Where ;I cross-over transition exists. the measured I,, will he respectively larger and so K will be orders of magnitude smaller for such peaks. If the statistics are good. one can estimate the relative intensity of the cross-over peak. The crossover intensrties should be calculated as

I,,,,.. = 1112 IlIZ

K,2 - K,,

(3)

where I CrlJ\< is the crossover component of the inten- sity at El + E,. K,? is the K value obtained from the measured intensity ilL at E, + El. K,, is the K value for the clean sum peak (e.g. obtained from any other coinciding pair in the spectrum of the same isotope without crossover).

(2) Because of the tinite energy resolution of the detector used, the true coincidence sum peak and a peak of other origin (e.g. contamination, background) may remain unresolved. The Kij value for such peaks differs in most cases from the K,, vjalue for the clean sum peaks. and this difference changes with the measurement geometry.

The value of K is very sensitivje to these disturbing effects, but fortunately, in many cases it is possible to distinguish between the above effects, by using the formulae (I) and (2). and in most measurements the disturbing effects can be more or less eliminated and the experimental conditions can be optimized for the sum peak analysis.

For the combinations of ;‘-rays. where at the energy (Ei + E, + .) there is no detectable sum peak, this fact may indicate the lack of the coincidence or simply the unsatisfactory statistics of the measure- ment at this energy. In such cases only lower limits can be calculated for K,, from the fuctuation of the spectrum around the expected energy value. The maximum intensity of the peak. which may bc hidden in the tluctuation. gives the upper limit for I,,. and using this value we obtain from formula (I) the lower limit of K. These lower limits may be spread ovscr ;I

wide range of orders of magnitude Their meaning

TABLE 1. The constancy of K value obtained from the rough evaluation of the ;-ray spectrum of 52Mn taken

from Ref. (32)

Sum peak energy Components K (kev) (kev) ( x 109)

1446 935 + 511 3.8 1679 935 + 744 5.1 1945 1434 + 511 4.2 2178 1434 f 744 5.2 2369 1434 + 935 5.2

from the point of view of coincidence information is the following:

(a) For all the limits higher than the K values for true sum peaks plus their errors: a true coincidence is very improbable.

(b) For all the limits positioned near K values for true sum peaks: there is no definite argument for or against true coincidences.

(c) For all the limits positioned below K values for true sum peaks: the situation is similar as in case (b) but also a crossover transition may exist, for which an intensity limit can be calculated. In cases like (b) and (c) the traditional two detector coincidence method cannot say anything either.

To illustrate the constancy of Kij for true coinci- dence sum peaks we took the y-ray spectrum of 52Mn from the spectrum catalogue of HEATH’~” and calcu- lated K,, for the five marked sum peaks. using ap-

proximate values for Ii and Ii, deduced from the peak heights. The result is given in Table I.

The constancy is true within a factor of K,,,/K,,,, = 1.4. In this case a four-stage cascade was considered for several evaluable sum peaks.

Similar calculations were made by us on the spec- trum of 5hNi from the same spectrum catologue. Here the decay scheme also contains crossover transitions. The results for different pairing combinations of the single photopeaks are given in Fig. I. The estimated errors were calculated as

A= K 1.1. I

_‘I =L!.t_ll

1,) ‘II Ii; (4)

\

The true sum-peaks are ordered again in a band of a factor of 1.65, whereas Kij - s of the cross-overs are by one or two orders of magnitude less, than in the

case of clean true sum peaks. The upward arrows show lower limits for other possible combinations of y-rays.

Formula (1) is comfortable as it uses just the measured peak areas. In the case of a cascade the K values of the true sum peaks lie in a band as seen above. Consequently, if the K values for several pairs of y-rays for a measured spectrum lie in such a band, these y-rays are probably in a cascade. The existence of such a band alone, however, is a weak argument

values in a band (i.e. the number of observed y-ray

pairs in a cascade) grows. the argument becomes stronger and stronger. Anyhow, the argument needs more support, e.g. if the absolute activity of the source measured is known, the K value can be tested against the activity through (2). This can be done even in the case of a source giving only a two-member cascade, which means that the “band” of Kii values is restric-

ted to a single point. So the weak argument turns into a rather strong one.

Summing of mow than two y-rays

For the case of three member cascades BRINKMAN et u/.“~~**’ gave also a formula like (1). with the

proper definition of R and T:

A,A, A,A, A,A, R=-=--=_ A 12 A 23 A 13

A,ZAZJAIJ = L412,)’

= N - T (5)

where AI23 is the intensity of the triple sum peak

(E 123 = E, + EI + E,). The same R is defined here with the three pair summing (Ai,; i,j = 1,2,3) and the single triple summing (A,,,). For the triple summing case we rearrange formula (5). by substituting

getting an improved expression:

A,AzA3

J __=N-T=R

A 123

:

i

‘os6_____n-----~-py_____~ ___ E I’

105 I ----I--

I

1 Llmlt

I I 5ou

I 1000

I 15Xi

E, *El (keV)

(6)

FIG. 1. Kij = liIj/f,, values for a p-ray spectrum of ‘hNi vs for the existence of the cascade. As the number of K energy.

Considering the triple sum peak. this form of the for- mula for R is more convenient for calculation because

(a) it contains the single photopeak areas instead of those of the double sum peaks, and according to the better statistics the relative errors are smaller.

(b) it can be easily generalized for multiple sum- ming. c.g. for an rl-fold summing:

Formula (7) can bc obtained also directly from the following approximation:

for the single photopeaks

.tnd 4, ,, 1 :L’E,E~ t,, for the r7-fold sum peak. So

Here l i is the total detection efficiency including the intrinsic efficiency of the detector. all absorption factors (self-absorption in the sample. absorption in the detector housing, and absorption in any other absorber between the source and detector). the solid angle (geometry) and also the probability of the con- sidered :-ray in the decay. It can be seen that the resulting formula does not depend on these factors.

therefore it is very useful. All these considerations arc valid in the case of relatively simple cascades. In the case of branching at certain levels. the branching ratios should bc taken into consideration.” ‘~“I

On the other hand. formula (8) is valid for the case when 7 < R. ;I condition generally fulfilled for Ge(Li)

detectors.

The expression (7) is normalized to unit time. As in the case of double coincidences we may use the total number of counts during the measurement time in the formula for r7-fold coincidence

which is again constant for a given measurement. and for any combination of double. triple. quadruple. or ,I-fold sum peaks.

As an illustration for the wide-range usefulness of this method, a ;‘-ray spectrum from a neutron acti- vation measurement of osmium isotopes will be presented.‘““’ Among others, the isotope ““‘“OS was produced in the activation. This isomer decays by a

five-member gamma cascade with 38.Y: 616.5: 502.5: 361.2: 186.7 kcV energies. All possible combinations of double and triple sum peaks were found in the spectrum with a considerably large number of counts

for the latter four energies. Even at the energy of the quadruple sum peak we could tind 247 counts above the background. of course with ;I high error value for

K. The actual value, however. is in the order of the K

values obtained from the double and triple summlng.

(The 3X.9 keV transition did not give signilicanc xlm

peaks because at this low energy the absorption

factors and the hiph conversion rate strongly dc-

crcascs the dctcction etticiency).

Figure 2 shows the K values as the function of the energy of the sum peaks. Up to triple summing NC

have a factor I .2 illustrating the constancy of K.

In Fig. 3 we made an illustration ho\v the summing

effect simplified the possible multiparnmctcr cxperl-

ment for the above 10”“‘Os isomer.

On the left-hand side and on the bottom of the

figure ;I simplified. bar-type ;‘-ray spectrum on ;I

logarithmic intensity scale can be seen (twice). which H;IS actually recorded with ;I single Ge( Li) detector. At the top and on the right-hand part of the figure the

right angle representation of the t%o-dimensional address field of :I possible dual parameter mcasurc- mcnt using tno Ge(Li) detectors of identical par-

ameters is shown. The vertical and horirontnl lines in Fig. 3 represent the single and sum peak energies

using the same address energy scale as in the single spectra. Along the I35 lines the sum of the cncrgies

of the ;‘-rays detected in the two detectors are con-

stant. At the crossings the possible coincidence peaks

are marked. In our case the single spectrum \\a tahen

in 2048 channels. the dual parameter measurement

would need 204X’ = 4.194.?04 channels supposmg

that the traditionaI on-Iinc two parameter method bvould h:~bc been applied. If one stores the address

K

x10

_

. double comctdence

. triple colnctdence

. quadruple co,nc,dence

I I I 1 I 1 I / I I I 1 I

500 1000 1500 IE, CkeV)

7x9

1667=A+B+C+O

lL79=B+C+O

6c

:5

E4 t

- 3

z2

FIG. 3. Single spectrum vs multiparameter analysis in the case of 19”mOs. for getting coincidence mfor- mation. (See text for explanation.)

pairs of the coincidence events and later generates the spectrum, the required memory would again be of the

order of several million words. (Though here the memory is e.g. a magnetic tape, the evaluation of the data is a rather time consuming task, regarding both the computer time and the physicist’s amount of work.) It can be seen that the information on multiple coincidences can be extracted from the several poss- ible summing peaks in one of the detectors of the multiparameter experiment, and this is in coincidence with a single or another sum peak in the other detec- tor. It can also be seen from the figure, that in the dual parameter address network-an inherently small number of coincidence events (caused by the disad- vantageous geometry) is distributed among a great number of possible address pairs. Every double co- incidence is separated into two places, the triple co- incidences into 6 places for each, the quadruple coin- cidence-with even much less probability already into 14 places, giving more and more hopelessly small peaks at a given place. On the contrary, a single measurement can be performed by using a much more advantageous geometrical arrangement. and on

the other hand, the coincidences at a given energy will

be automatically summed up into a single peak, and that is the reason that even the multiple coincidences

are measurable. It is remarkable that the number of counts in the n-fold sum peaks (n = 1, 2, 3. 4; where 1 stands for the single peaks) is decreasing with only about one order of magnitude, with increasing order of summing, which is not common in the case of tra- ditional two-detector experiments.

Several measurements have been performed in our neutron generator laboratory for getting coincidence information on the y-transitions in the de-excitation of 2”hmTl produced by fast neutron activation from z”yBi.‘“5.“5’ Here we applied the formula (1) for a formerly unknown spectrum.

Traditional ;’ 7 coincidence measurements have been made by using a 100 cm3 Ge(Li) and a 30 cm3 Ge(Li) for testing the results. In both branches high resolution semiconductor detectors should be used. because of the rather close vicinity of the y-lines in the single spectrum. not well resolved by NaI(TI). Because of absorption. geometry and backscattering reasons only a 7.50 g (0.70 mm x 36 mm dia. disc) piece of the activated material could be used in the geometry shown on Fig. 4a. The bismuth disc itself served as a

shielding against backscattered ;-rays. One of the raw. uncorrected coincidence spectra (gate at

a)

channel number

265.7 keV) obtained in a j-day run wjith periodic acti- vation is shown in Fig. 4b. (The gating 265.7 keV peak is of much lower intensity relative to other peaks in the single spectrum.)

On the other hand. single spectra have been taken with the 100 cm3 Ge(Li) detector and analysed on the base of the formula (I). The geometry of the single measurements was the arrangement shown in Fig. 5a.

Here a large mass (43.35 g) of Bi in annular shape was

arranged around the aluminium housing of the detec- tor. The single elements were I mm thick M. 30 mm x 12 mm sheets of Bi metal placed in pockets on a polyethylene band. A single spectrum taken in H

6-day run. with about the same specilic activity. is

shown in Fig. 5b. The proposed decay scheme of “‘h”Tl is given in

Fig. 6. For all possible combinations of the strong y-transitions, not disturbed by confusing single peaks originated from contaminations, the K,j - s were cal-

culated and these values are plotted vs the energy of the sum peaks in Fig. 7. In Table 2 we give the combi- nations of the single peaks and the K values calcu- lated from them. (Above 1330 keV no measurements were performed.) The K values of the real coincidence sum peaks are positioned in a band around 1.7 x IO’. despite of the fact that they were calculated from the raw. measured number of counts, without any correc- tion for the rather divergent transition probabilities and internal conversion coeficients. also given in Table 2. The sum-peaks, where a crossover exists. are placed under this band. The upward arrows of lowjer limits for other possible combinations of ;‘-rays spread over a wide range.

In our measurements the count rate was rather low (a few hundred counts/s). so random summing from pile-up was not disturbing.

The constancy of K,, - s in this case is true wnithin a factor of 2.X but regarding the errors it is remark-

able that I5 out of the I6 analyzed sum-peaks have the value 1.7 x IO’ inside the f3., I,j error limit of their K,, and the only exception at 1287.2 keV is only 1.45 times higher than this value. The K value was

tested against the activity (measured in other ways) with an agreement of the results within the error limits. In the case of ‘OhmTI. evaluable sum peaks could be obtained composed of y-rays of nearly IOO”,, relative intensity with about 5 x IO5 pulses in their photopeaks, and of coinciding ;‘-ray of about IO”,, relative intensity. Table 3 gives an impression on the intensity gain obtained by using sum peak analysis. vs a two detector coincidence measurement. For inter- comparison Fig. 8 summarizes the coincidence infor- mation drawn from the above mentioned traditional two detector coincidence measurement, and from the sum peak analysis of the single spectrum. As can be seen from the measuring times and numbers of neu- tron monitor counts. the two measurements were made well inside a factor of two, regarding the specific activities of the sample. In the sum peaks. however. we found counts almost two orders of magnitude more than in the corresponding coincidence peaks obtained with two detectors.

Conclusions

Based on our experience in sum peak corrections. in this paper we should like to show that the analysis of the sum peaks is possible with simple methods. and one can obtain some new information of the kind mentioned above. e.g. coincidence information with a similar if not better accuracy than with the tra- ditional. highly sophisticated two detector methods.

We tested and generalized the basic formula taken from literature. We found that the basic formula. wzithout any correction works even under rather poor circumstances. Our generalization permitted us to

791

N 066 keV/ch

Energy n keV b)

a)

Xl/L I 1 I 1 I r 1 n I I lcoo 1100 1200 1300 1400 1500 1600 1700 1800 1930 zoo0

Channel number

FE. 5. (a) Arrangement of a big amount of active sample around the Ge(Li) detector. (b) The single .;-ray spectrum of Zo6mTl (Reproduced from Ref. (35) with the written permission of the copyrIght owner

Springer Verlag, Heidelberg.)

792 I. TtirGk et al.

I I

6’ t zw 1710.4

7’ 1 ,

;pzi 1621 9

FIG. 6. The proposed decay scheme of the 2obmTl. (Reproduced from Ref. (35) with the written permis- sion of the copyright owner Springer Verlag. Heidelberg.)

find a quadruple summing peak in a spectrum, which has not been reported, to our best knowledge, in the literature. We found that the absolute activity of the source and the coincidence information can be tested against each other (to decide whether it is a real sum peak) and thus a strong argument can be obtained

x:9 ‘11

loa-

ms-

ma-

m’ I-

lo’ -

lo5 -

10' -

--.

. .

ll13d 200 500 1000

E, + E, IkcV)

FIG. 7. ,K,, values for Zo6mTl.

from the sum peak analysis for coincidence. Even in the case when the absolute activity is not known, but the isotope in question emits several cascades, the constancy of the K value (see later) gives an argument for coincidence. Lastly, we compared the traditional and sum peak analysis coincidence methods in our

own experiments, investigating the decay of the new 206mTl isomeric state. We made several absolute ac- tivity measurements too, with good results, but their discussion is the subject of another paper.

We do not say that the sum peak analysis is the only or the best method to obtain coincidence infor- mation, but its simplicity and other inherent advan- tages--e.g. the fact that significant sum peaks are in

most cases present in a singles spectrum from y-ray sources emitting y-rays in a cascade-makes it easy to

utilize the additional information contained in these sum peaks, information which must not be thrown away. With a slight modification of the experimental geometry, the measurements can be easily optimised for the sum peak formation.

Traditional two-detector coincidence measurements cs

sum peak analysis

The data above suggest that the sum peak analysis has some advantages in several cases:

1. It needs only a single detector, electronic ampli- fier chain and power supply. All instruments necess-

Coincidence informution in Gr(Li) sum peak.5 793

TABLE 2. The sum peaks and K values of zoamTl from the spectrum shown in Fig. 5b. Notice the big differences in the transition probabilities and in the internal conversion coefficients of the components

Sum peak energy

tkeV)

Components

(keV)

Transition probability

of the components

(%)

Internal conversion coefficient of

the components

463.6 216.4 f 247.2 97 14 0.28 0.66 (1.33 * 0.21) x IO’ 482.1 216.4 + 265.1 97 100 0.28 0.15 (1.59 + 0.05) x 10’ 669.7 216.4 + 453.3 97 94 0.28 0.01 (1.74 + 0.08) x 10’ 673.6 216.4 + 451.2 97 25 0.28 0.13 (1.94 * 0.20) x IO’ 700.5 247.2 + 453.3 14 94 0.66 0.01 (2.10 f 0.21) x IO’ 719.0 265.7 + 453.3 100 94 0.15 0.01 (1.69 + 0.04) x IO’ 722.9 265.7 t 451.2 100 25 0.15 0.13 (2.26 + 0.22) x IO’ 780.6 216.4 + 564.2 91 12 0.28 1.15 (3.75 f 2.52) x 10’ 829.9 265.7 + 564.2 100 12 0.15 1.15 (3.35 k 1.69) x IO’ 902.9 216.4 + 686.5 97 92 0.28 0.01 (1.77 f 0.11) x IO’ 910.5 453.3 f 457.2 94 25 0.01 0.13 (2.27 + 0.21) x IO’ 933.7 247.2 + 686.5 14 92 0.66 0.01 (1.68 + 0.27) x IO’ 952.2 265.7 + 686.5 100 92 0.15 0.01 (1.58 f 0.05) x 10’

1237.9 216.4 + 1021.5 97 I3 0.28 0.06 (1.52 + 0.08) x IO’ 1250.7 564.2 + 686.5 12 92 1.15 0.01 (1.96 + 0.42) x 10’ 1287.2 265.7 + 1021.5 100 73 0.15 0.06 (2.46 f 0.10) x 10’

ary to perform the two-detector coincidence measure-

ment (analogue and digital delays, coincidence units) and also the second detector chain can be spared. This is a big saving, mainly in setting time and in avoiding measurement ambiguities, not to mention the costs.

All these measurements can be performed not only in a well type but also with usual coaxial large volume Ge(Li) detectors.

2. If some y-rays are in coincidence with others, the sum peak analysis may supply this information in many cases (often sufficient to decide between poss- ible decay schemes), and it does it simultaneously, in the same run. So a lot of normalizations can be spared, together with a lot of accelerator time. The traditional coincidence techniques either make suc-

cessive coincidence measurements with different gat- ings, or use expensive and complicated multipara- meter analysis instruments, with big memory require- ments.

As the information is accumulated for all possible coincidences in the same run, the long-time stability requirements on the electronic analogue system are less strict.

Also multiple (triple, quadruple) coincidences can be measured with rather good efficiency.

3. Traditional coincidence measurements are very sensitive to geometry, they often give backscattered phantom peaks, and need special shielding between the detectors. In the case of the sum peak analysis of a single spectrum, the source can be placed as close to

the detector as possible. This results in a more con-

TABLE 3. Intensity gain obtained by using sum-peak analysis. vs a two detector coincidence measurement of comparable measurement time and activation

;-ray energy Ckevl

Coincidence peak areas from two

detector 7-7 coincidence.

gate at 265.7 keV 216.4

Sum peak areas with y-rays of energy in keV

247.2 265.7 453.3 457.2 564.2

216.4 174 & 24 247.2 24$- 18 265.7 0 * 21 453.3 185 k 19 451.2 38 f I2 564.2 8*7 686.6 107 * 12

1021.5 9*5 1139.9 4+2 511 127 + 20

Measurement time (s)

Neutron monitor (times 10’ counts)

43 680

96.65

< 259 1800 + 280

15838 + 517 11353 + 547 2472 k 250

265 + 178 7387 f 449 4457 + 237

<I35

< 256 <167

1016 f 209 13274 + 320 <94 2418 + 240 1885 f 170 <96

337 * 170 <80 843 f 138 9418 k 283 299 f 64

3128 f 130

<135 <82 <82 <80

49 280

153.28

794 I. TiirGk et al

316 6 .

2 5((0 - - - - - -

* 56L 2 0

&&5OOO l -0

1021.5 0 0

1139.9

FIG. 8. Coincidence information obtained from a Ge(Li)- Ge(Li) coincidence measurement and from sum peak analysis of a single Ge(Li) spectrum. (In the case of coinci- dence: the larger the circle the more accurate is peak area.

See Table 3 for the errors.)

venient solid angle, and thus in improved detection efficiency. So the method is useful in the cases of sources which are hard to produce, have low activity, and a short half-life. The necessity of shielding between the detector is also avoided in the sum peak

analysis case. 4. From the same single measurement one can get

source activity information and distinguish to a cer- tain extent between true sum coincidences and cross- overs. This method generally leads to an order of magnitude estimation, but in several cases an accu-

racy of about 10”; or even better may be obtained. 5. In the range of the resolving time of the analyser

system excited level life-time information can be obtained.“”

6. In the case of samples with low specific activity the sum-peak analysis method permits the use of a big quantity of material contrary to the case of the two detector coincidence method.

Limitations of the method

(a) It needs a large volume, high efficiency Ge(Li) detector, or equivalent.

(b) The evaluation of the spectra in several cases needs the determination of areas of small peaks on a high background with appropriate accuracy, which requires special spectrum analyzing computer codes.

(c) Statistical error of photo and sum peaks, strongly influenced by the statistical error of back- ground under them (mainly at the sum peaks).

(d) Disturbing peaks from background or from con- tamination near the,interesting photo or sum peaks.

I.

2.

3.

4.

5. 6.

7

8

9

10

II I2 I3

I4

15

I6

17

I8

19.

20.

21.

22.

23.

24. 25.

26

27

28

29

30

VERPLANKE J. C. Nucl. Instrum. Methods 96, 557 1971).

~NDREEV D. S., EROKHINA K. I., ZVONOV V. S. and LEMBERG I. KH. Instrum. Exp. Tech. 15, 1358 (1972). MCCALLUM G. J., CHUTE G. E. Nucl. Inswum. Methods 130, 189 (1975). SEHRKE R. J., HELMER R. G., GREENWOOD R. C. Nucl. Instrum. Methods 147, 405 (1977). Lu D. C., WIEDENBECK M. L. Phy.7. Rec. 34,501 (1954). Lu D. C., KELLY W. H.. WIEDENBECK M. L. Phys. Rev.

95, 121 (1954). Lu D. C., KELLY W. H., WIEDENBECK M. L. Phys. Rev. 95, 1533 (1954). Lu D. C., KELLY W. H., WIEDENBECK M. L. Phw Rec. 97, 139 (1955). SCHERRER V. E., FAUST W. R.. ALLIXIN B. A. Phw. Rrr. 98, 224A (1955). FAUST W. R., SCHERRER V. E.. ALLISON B. A. Phys. Rec. 98, 224A (1955). GUPTA R. K., JHA S. Nucl. P~vs. 1. 2 (1956). SHAPIRO P., HIGGS R. W. Phy.k. Rec. lb, 760 (1957). GIRGIS R. K.. VAN LIESHOUT R. Nucl. Phw. 12. 672 (1959). VINGIANI G. B.. MONARO S. Nucl. Insrrum. Merhods 14, 138 (1961). SANTHANAM S.. MONARO S. Nucl. Insrrum. Methods 76, 322 (1969). SANTHANAM S., WEBB P. P., MONARO S. IEEE Truns. Nucl. Sci. 16, 75 (1969). BRAUER F. P., MITZLAFF W. A. IEEE Trans. NW/. Sci. 25, 398 (1978). BRINKMAN G. A., ATEN A. H. W., JR, VEENBOER J. Th. Inr. J. Appl. Radiar. Isor. 14, 153 (1963). BRINKMAN G. A.. ATEN A. H. W. JR. VEEN~IOER J. Th. Int. J. Appl. Radial. Isot. 14, 433 (1963). BRINKMAN G. A., ATEN A. H. W. JR, Inr. J. Appl. Radiat. Isor. 14, 503 (1963). BRINKMAN G. A., ATEN A. H. W. JR. VEENBOER J. Th. Int. J. Appl. Radiut. Isot. 16, 15 (1965). BRINKMAN G. A.. ATEN A. H. W. JR. Int. J. Appl. Radiat. Isor. 16, 177 (1965). SHAPIRO P.. HIGGS R. W. Rec. Sci. Instrum. 28, 939 (1957). SCHMIDT-OTT W. D.. Z. Phys. 154, 294 (1959). MANNHARDT W.. VONACH H. Nucl. Instrum. Methods 151, 157 (1978). LUNKKO A.. HOLMBERG P. Nucl. Insrrum. Methods 65, 121 (1968). TAFF L. M.. VAN KLINKEN J. Nucl. Inswum. Methods

151, 189 (1978). H~~GENB~~M A. M. Nucl. Instrum. Methods 3, 57

(1958). MATHS Gy., BER~NYI D.. SCHARBERT T. Nucl. Instrum. Methods 14, 209 (1961). KANTELE J., FINK R. W. Nucl. Instrum. Methods 15. 69 (1962). EGAN A., SPYRON N. M. Anal. Chem. 48, 1959 (1976). 31

(e) A possible high degree of angular correlation between the coinciding y-rays!*@ The larger the solid angle is, the smaller the error originated from these effects is.

(f) In the case of very high count rates the effect of random summing distorts the sum peaks and this requires special corrections.

References

Coincidence i!formation in Ge( Li) sum peaks 795

32. HEATH R. L. Gamma-ray Spectrum Cotalogue, Ge(Li) 34. URAY I., T~R~K I., BORNEMISZA-PAUSPERTL P., V&H L. and Si(Li) Specrrometry. 3rd edn, Vol. 2. ANCR-1000-2 Int. Symp. on High-spin States and Nuclear Structure

(1974). (Dresden, 19-24 Sept. 1977) ZfK-336. p. 58 (1977). 33. Kovics P. Thesis (Kossuth University. Debrecen, 35. URAY I., TGRGK I., BORNEMISZA-PAUSPERTL P., V&H L.

1974). Z. Phys. A287, 51 (1978).

Koinzidenzinformationen erhalten aus Summe$inien eines mit einem einzigen Ge(Li) Detektor gemessenem Spektrums (Uberpriifung, Auswertung und

Verbesserung der Methode)

Die Untersuchung der Summenlinien eines. mit der Hilfe eines gross-volumigen Ge(Li) Detektors aufgenommenen Spektrums gibt ofters mehr Koinzidenzinformation als die traditionelle Koinzidenz- messung mit Verwendung von zwei Detektoren. Es wird eine Nlherungsmethode gegeben womit man von den Summenlinien des Spektrums die Koinzidenzinformationen auswerten kann. Die Summenlinien erhalten einiger Grossenordnungen mehr Impulsen als die mit zwei Detektoren. wahrend gleichen Messzeiten, ohne kompliziertes Multiparameteranalysator System, aufgenommenen Spektren. Die Methode der Summenlinienuntersuchung beansprucht weit weniger Messapparatur und Rechen- maschinenkapacitat als die traditionellen Methoden. daneben bietet sie such Moglichkeiten fur die Messung von Mehrfachkoinzidenzen mit ziemlich gutem Wirkungsgrad. Die Moglichkeiten und die Grenzen der Methode der Summenlinienuntersuchung werden besprochen und mit einigen Messexemplaren illustriert.