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# Geiger Muller device: description

### 1. Description

A Geiger M�ller (GM) Counter consists of a GM tube with a thin mica end-window exposed to a source of radiation, a filling gas to be ionized, a high voltage supply for the tube. The peripheral consists of a scaler to record the number of particles detected, and a timer to stop the action of the scaler at the end of ad defined interval of time.

A particle entering a tube ionizes a single atom of the filling gas of the tube. this single particle initiates an avalanche of ionization in the tube. This avalanche consists of many secondary ionizations which causes the extracted electrons, since they are accelerated, to move towards the anode (positive lectrode).

Each ionizing particle corresponds to an avalanche, then to a current outside the tube, called a pulse of voltage.

During a fixed interval of time, many particles can enter the tube, then many pulses can occur. If the scaler records x pulses, then we had x ionizing particles. The amplitude of such pulse is the order of a volt or so.

The GM Counter is used for counting alpha particles, beta particles, and gamma rays with. This device does not define the nature of these particles. It just count them.

The electrons travel to the anode very quickly. However, it takes a certain time called the dead time (or down time)to the positive ions to reach the cathode (negative electrode). During this dead time, the tube remains insensitive; and even an ionizing particle arrives inside the tube, it will not ionize the atoms of the filling gas, and therefore, it will not be counted. To give the true counting rate, we must take account of this gap.This dead time (or recovery time) is about 100 - 400 microseconds. During this dead time, one or more other ionizing particles come in the tube. This phenomenon is known as coincidence and the correction applied is known as the coincidence correction.

### 2. Resolving time

1. Definition:
Resolving time is defined as the smallest time interval which elapse between the occurrence of two consecutive ionizing events or signal pulses, in order that the measuring device could be capable of fulfilling its function for each of the two occurrences separately.

2. The coincidence correction formula: If the counter were perfect, it would measure N counts in the time interval t; then the rate R = N/t. But during the dead time td (or down time), the counter was inoperative and missed R x td counts. It follows then that the true count is:
True = missed + mesured
N = R x td + M
R x t - R x td = M

R = r/(1 - td/t)
with r = M/t, the measured rate.

If we assume that the dead time td is constant for a filling gas, we can understand that it will be proportional to the counting time t and the true collected number of counts N. Let's write then:

td = constant x N, or with constant = T:
td = T x N
T is called the resolving time

The relationship above becomes:
R = r/(1 - TR), that gives:
R2T + r - R = 0
At low count rates N &asym; N and the realtionship becomes:
R = r/(1 - rT)

Other radiation called background radiation is always present. Gamma rays emitted by certain radioisotopes in the ground, the air, various building materials, and cosmic radiation from outer space can all provide counts in a detector in addition to those from a sample being measured. This background counting rate should always be subtracted from a sample counting rate in order to obtain the rate from the sample alone.

### 4. Measurement of the resolving time

The resolving time can be measured by the method known as the method of paired sources. The rate corresponding to the activities of two sources are measured individually (r1 and r2) and then together (r12).

Having a small quantity of radioactive material (split source), split in two parts, we measure the rate r1 for the first part and r2 for the second part and r12 for the two combined parts.

If we neglect the background for the three measurements, we can set the equality for the related true rates:
R1 + R2 = R12
That is:
r1/(1 - r1T) + r2/(1- r2T) = = r12/(1 - r12T)

Solving for T, we have:

T = 2r1r2 - [4r12r22 - 4r1r2r12 (r1 + r 2 - r12)]1/2/ 2r1r2r12

We can write it as: T = 2r1r2 - 2r1r2[1 - r12(r1 + r2 - r12)/r1r2]1/2/ 2r1r2r12 Using the MacLaurin series:
(1 + x)n = 1 + n x + n(n-1)x2/2! + n(n-1)(n-2) x3/3! + ...
for n = 1/2, that is: (1 - x)1/2 = 1 - x/2 + ...; we find:
T = 2r1r2 - 2r1r2[1 - r12(r1 + r2 - r12)/2r1r2 + ... ]/ 2r1r2r12
T = r12(r1 + r2 - r12)/ 2r1r2r12 = (r1 + r2 - r12)/ 2r1r2

T = (r1 + r2 - r12)/ 2r1r2

### 5. Statistical treatment of counting data

The emission of particles by radioactive nuclei is a random process. If during the period of time t, we get N pulses corresponding to N detected particles; this individual measurement of N particles per unit of time "t" vary while we repeat these measurements under the same conditions. The variation of this series of measurements has a little value about the mean of these measurements.

We know from Statistics that the true mean, μ, can be determined only by averaging an infinite number of measurements.

The observed or measured m mean is a good approximation of the true mean. It is set by a finite (and large) number of observations. It is expressed by its arithmetic average:

m = ∑ ni/N
where ni is the ith measurement and is the total number of measurements. The index i vary from 1 to N.

The difference between a measurement and its mean is called deviation = ni - m ( observed) or ni - μ (theoritical).

The variance, denoted σ2, is the average of the squared deviations. σ2 = &sum (ni - μ)/N, or for a sample: σ2 = &sum (ni - m)/N

The standard deviation is the square root of the variance. More precisely, the root-mean-square: rms.

The radioactive decays occur commonly with a large number N(t) for a fixed time "t". N(t) is a random variable described by a Poisson distribution; with a Standard Deviation is the square root of the true mean. Fore more details, see Probability & Statistics section. Web ScientificSentence