COUNTING ERRORS: BACKGROUND AND DEAD TIME 



At the starting potential the pulses produced by the Geiger tube are 

 somewhat variable in size since this potential is in the transition region of 

 Figure 31.1, and the amplitude of the output pulses is still governed to some 

 extent by the number of ion pairs formed by the incident radiation. Under 

 these conditions only the largest pulses are able to trigger the scaler. As the 

 applied potential is raised, more and more of the pulses exceed the threshold 

 of the scaling circuit, and the counting rate increases rapidly, until when the 

 Geiger-MiJller region is reached the pulses are uniform in size and are all 

 large enough to be recorded. A further rise in potential beyond this point 

 makes the pulses even larger but has little effect on the counting rate, so that 

 the characteristic curve shows a flat plateau. The normal operating voltage 

 of a Geiger tube is in the centre of this plateau, where small variations in the 

 applied potential cause the minimum error in the recorded count. In a well 

 designed tube the length of the plateau should be about 200 V, so that some 

 latitude is permissible in choosing the operating potential. At the upper end 

 of the plateau the counting rate begins to rise steeply again, largely because 

 at excessive operating potentials the quenching vapour ceases to be able to 

 suppress all the spurious counts; the tube is apt to be damaged if it is 

 operated for any appreciable period at such a potential. 



The slope of the plateau is not zero, although in a good tube it should not 

 be greater than about 0-1 per cent per V. The finite slope arises partly 

 through an increase in the sensitive volume with operating potential, and 

 partly through production of a small but increasing proportion of spurious 

 pulses. The change in sensitive volume is an end-effect which is most marked 

 in small tubes, and which can never be avoided altogether. The effect of 

 spurious counts can, however, be virtually eliminated by using a quench 

 probe, which enables an appreciably flatter plateau to be attained; but in 

 general it is unnecessary to take great pains to flatten the plateau, since it is 

 not difficult to design an EHT supply unit (see Chapter 37) whose output is 

 sufficiently well stabilized for errors arising from shifts up and down the 

 characteristic curve to be small compared with those from other sources. 



When Geiger tubes have been in use for some time there may be a tendency 

 for the plateau to shorten or alter its position. In order to keep a check on 

 the condition of a tube it is therefore highly desirable to make routine 

 measurements of the starting potential and plateau characteristics. 



COUNTING ERRORS: BACKGROUND AND DEAD TIME 



The quantity ultimately to be measured in almost all tracer experiments is, 

 in effect, the number of labelled atoms in a given sample. The observation 

 actually made consists in counting the number of atoms which, over a known 

 period, disintegrate to give detectable radiation. It is convenient at this 

 point to consider briefly the various sources of error that have to be taken 

 into account when making such observations. 



The rate at which a given species of radioactive isotope decays is a property 

 of its nuclear constitution, and for all practical purposes is independent of 

 its physical and chemical state. The law of radioactive decay can be written 

 as 



dNIdt = -A7V 



431 



