COUNTING ERRORS: BACKGROUND AND DEAD TIME 



which are almost always to be found in the floor and walls of a room. 

 Geiger tubes are also sensitive to light, and the background will be further 

 increased if they are not operated in complete darkness. In order to reduce 

 the background to a minimum, both the Geiger tube and the sample are, if 

 possible, enclosed within a thick lead shield or castle, but even with 3 in. of 

 lead on all sides a Geiger tube of conventional size (say 1 in. in diameter and 

 3 in. long) gives a background of the order of 10 counts/minute. The back- 

 ground tends to be proportional to the sensitive volume of the tube, so that 

 larger tubes will inevitably give still higher background counts no matter 

 how well shielded they are. The background can normally be treated as 

 constant, but it is subject to the same statistical fluctuations in rate as the 

 count given by a radioactive sample. When dealing with weak samples it is 

 therefore necessary to determine the background in the absence of the 

 sample, and to subtract it from the total counting rate obtained for sample 

 plus background. The S.E. of the background determination can often be 

 made small enough to be neglected, by taking very long background 

 counts, but the S.E. of the corrected counting rate for the sample is calculated 

 from the square root of the total counts given by sample plus background, so 

 that for samples giving counts not much greater than background, the S.E. 

 of the final result is apt to be unsatisfactorily high in comparison with the 

 result. Furthermore there are, in the hmit, statistically significant variations 

 in the background from time to time, arising from phenomena such as 

 cosmic ray showers. It is, consequently, difficult to make reliable measure- 

 ments of samples giving less than, say, half the background count. When 

 confronted with samples as weak as this, little can be gained by greatly 

 prolonging the counting periods, and it is necessary to resort to other means 

 of improving the accuracy of the measurements. Thus it may be possible to 

 re-design the experiments so as to increase the activity of the samples, or to 

 improve the geometry of the counting arrangement (see below) so that a 

 higher proportion of the ionizing particles emitted by the sample penetrates 

 the sensitive volume of the Geiger tube. The eifective background can also 

 be reduced, at the cost of appreciable complications in the apparatus, by 

 employing coincidence counting techniques. 



In the other direction, when excessively active samples are to be counted a 

 limitation is set by errors arising from the dead time of the Geiger tube and 

 associated equipment. As has already been mentioned, once a Geiger tube 

 has been triggered by an ionizing particle there is a period of the order of 

 100 ^sec during which a second particle entering the sensitive volume will 

 not be detected. This dead time is irreducible, and may, in fact, be deliber- 

 ately increased by operating the tube in conjunction with a quench probe set 

 to give a quenching pulse which lasts appreciably longer than 100 //sec. In 

 view of the random spacing between disintegrations some particles are bound 

 to arrive during the dead time, so that the apparatus always fails to record a 

 certain proportion of them. This proportion is not fixed, but rises steeply 

 with counting rate; thus for a dead time of 100 /isec, less than 2 counts/min 

 are missed at a true rate of 1,000 counts/min, but at 5,000 counts/min about 

 40 counts/min are lost — an error of nearly 1 per cent. Provided that the dead 

 time (t) is known, it is simple to calculate the correction that should be made 

 to the recorded counting rate (N) in order to arrive at the true counting rate 



433 



