From the Laboratory of Zoophysiology, Copenhagen University.

A Method of Correcting for Counting Losses in Geiger-Muller Counters with Special Reference

to the Geiger-Muller Counter Arrangement Described by Hilde Levi (1941).

BY

IB HOLM-JENSEN.

Received 11 January 1943.

A GE~GER-M ~;.LLICR counter arrangement mainly designed in accordance with the description given by HILDE LEVI, has been used in this laboratory during the last two years. We found that it was possible to get reliable results up to 500 counts per minute or even more. The limiting factor is the mechanical recorder, which was found to require frequent readjustments, when the impulses registered exceeded about 500 per minute for more than a very short time.

However, when the counting rate exceeded about 180 impulses per minute, and it is often important t o be able t o coiiiit such strong preparations, we found it necessary to apply it more ac- curate correction for counting loss, than that employed by HILDE LEVI, who carried out the correction from the following formula:

I

where N was the actual number of incoming impulses per minute and Nobs the number of impulses recorded per minute. The con- stant k was determined empirically and was found to be 1,500.

As the statistical fluctuations in the number of disintegrations

272 I& HOLM-JEPl'SEiY.

from a radioactive substance is about f y , y being the number of impulses considered, and as a total of 10,000 impulses is practic- ally the maximum counted from any sample in biological work,

the probable fluctuation will be 2 2 - 100 = 1 per cent. 10,000

It is therefore desirable to keep the error clue to approxiniate correction for counting losses below this figure in order t o obtain the highest possible accuracy.

The counting losses are caused by the finite recovery time of the GEIGER-MULLER circuit, the amplifier and the recorder, because impulses arriving during these recovery periods are not transmitted respectively not recorded.

The recovery times of the GEIGER-MWLLER circuit arid of the amplifier are negligible compared with that of the mechanical recorder, and need not be Considered a t the counting rates in question.

IJntil recently it was customary to compute the actual incoming impulses per minute from the following formula (VOLZ, 1935):

VlGG

Nobs = N . epN' . . . . . . . . . . 11

where t is the recovery time. N and Nabs are here used in the same sense as in equation I. However, RUARK and BRAMMLR (1937) stressed the fact t8hat the above equation is based upon the assumption that an impulse in order to be registered must he preceded by an interval t dvring which no impulses arrive. I n other words, if another impulse comes in during the recovery period this (even if i t is not registered) should re-excite the recorder and add to the recovery time and thereby cause a further in- crease in counting loss. When, on the other hand, a recorder is completely unaffected by additional impulses coming in during the recovery period N may be computed from a much simpler equation.

. . . . . . . . . N I t t . N Nabs x= I11

The deduction of RUARK and BRAMMIER is as follows: Consider the interval t following the arrival of an impulse. The average number of impulses lying in this interval is z * N, but there are Nobs such intervals per minute. Thus N = Nobs + Nob,N ' t which gives the above equation.

A METHOD OF CORRECTING FOR COUNTING LOSSES. 273

Equation I1 may be written N

thus it is seen that there is only a minor difference between formula I1 and 111 if t - N is small. The difference, however, is by no mems negligible a t our counting rates.

Example: 1

If N = 5 0 0 and t=- 1,500

equation I1 will give 500

1.396 N == 500. e-33 = __ = 3.58 obs

whereas equation I11 will give 500

= 375 500 N =----

1 f '/a 1.333 - obs

The difference is 5 per cent. It may be quite difficult to find out whether a recorder should

be considered as belonging to one type or the other from theoretical considerations regarding its construction; but the problem can easily be solved experimentally by isolating the grid of the thyr- athrone valve; the recorder will now behave as if it received im- pulses transmitted from a radioactive source of infinite strength.

From equation I1 is derived

if N -+ w, lini No,, = 0

and from equation 111 1

if N -+ co, lim Nabs = - z

Thus, when the number of impulses received approach infinity, a recorder of one type will stop recording, whereas a recorder of the other type will work a t its maximum speed.

The values of Nobs thus determined for the mechanical recorder in question are found to be 1,200 t o 2,000, dependiiig on the adjustment of the recorder, and of the strength of the anode current in the thyrathrone circuit.

1 8 4 2 4 0 7 5 . Acta &us. Scandinav. Vol. 5.

274 IB HOLM-JENSEN.

The valiie of Nobs obtained in the above test is about 10 per

cent smaller than - found as shown below. So we may conclzcde

thut our counter i s practically unaffected by impulses urrivirzg during the recovery period, and for our purpose tL'e 'may safely upply the correctioia formula 111.

We have also tested counters of different design which clearly belonged to the group to be corrected by equation 11.

The constant t is readily determined in the same way as used by HILDE LEVY for determination of her constant k which is

seen to be nearly equal to - when N is small.

1 z

1 t

t can also be computed from the following equation derived from equation 111:

nx, -- x1 (n - l)x, * x,

z =

where xI and x, are countings per minute from the decay of some suitably shortlived radioactive substance, e. g. ThB with a half period of 10.6 h, n being the ratio bstween the corrected counting corresponding to xI and x, which is computed from the time in- terval considered and the known length of the half period. E. g. if the time interval considered is equal to the half period, n will be equal to 2 and

2*xz-x, t = ___-

xs * XI

for this computation i t is best to use readings from a smoothed decay curve.

As a standard of the radioactive preparation used in our exper- iments is always counted regularly during the decay, and as this standard for practical reasons is generally chosen a t least of equal activity to the strongest sample, we usuadly obtain the necessary facts to recalculate the length of our recovery period and thus check the adjustment of our counter. When t is com- puted the correction for counting loss is easily carried out by equation 111 which may be written

A METHOD OF CORRECTINQ FOR COUNTINQ LOSSES. 275

or T N O L N == Nabs + -~ - TNobs

thus being the counting loss. %a -___ - ZNobs We found i t most convenient to carry out the correction.in the

following way: I11 is written

N* =; 1 - T. Nobs

The straight line representing the relation thus given between

N

NObS and Nobs is drawn. (Fig. 1). N

I I , , 1 I

100 200 300 400 JOQ 4 Pig. 1.

5

Nabs 1 - - l---Nobs 1,600

Nobs . When Nobs is given the corresponding value of ~ IS fourid N on this line and N is computed from

Nabs I N = Nabs: ---

N

I n this way the cornputations are reduced to a minimum.

I am greatly indebted to Mr. H. K. ROLTVED, Civil Ingineer of the Telephone Company Automatic in Copenhagen for kindly placing at my disposal mechanical recorders of different design.

276 IB HOLM-JENSEN.

Summary.

The theoretical basis of correcting for counting losses in a simple GEIGER-M~LLER counting arrangement is outlined and a convenient procedure for carrying out the correction is presented.

Literature.

LEVI, H., Acta Physiol. scand. 1941. 2. 311. RUARK, A. E., and F. E. BRAMMER, Physical Rev. 1937. 52. 322. VOLZ, H., Z. Physik 1935. 93. 539.