Physics and Engineering of Radiation Detection

160 Chapter 3. Gas Filled Detectors

the capture mean free path can be written as

μc = fNmησ (3.2.16)

λc =

1

fNmησ

. (3.2.17)

Now sinceλcis the capture mean free path, we can simply divide it by the average
electron velocityvto get itscapture mean lifetimeτc.

τc=

1

fNmησv

(3.2.18)

The exponential relation 3.2.14 can then also be written in terms of time as

N=N 0 e−t/τc, (3.2.19)

whereN 0 is the initial electron intensity andNis the intensity at timet.
The factorsh,σ,andvin the above relations depend on the electron energy
whileNmhas dependence on temperature and pressure. It is therefore not possible
to find the values of these parameters in literature for all possible energy and working
conditions. Further complications arise if there are more than one electronegative
elements in the gas. This is because the charge exchange reactions between these
elements can amount to significantly higher electron attachment coefficients as com-
pared to the ones obtained by simple weighted mean. In such cases, one should
resort to the experimentally determined values ofλcorτc, which are available for
some of the most commonly used gas mixtures.

Example:

Compute the percent loss of 6eVelectrons created at a distance of 5mmfrom

the collecting electrode in a gaseous detector filled with argon at standard

temperature and pressure. Assume a 1% contamination of air withη=10−^5.

The total scattering cross section of air for 6eV electrons is 5× 10 −^14 cm^2.

Solution:

The given parameters are

f =0. 01 ,

η =10−^5 ,

σ =5× 10 −^14 cm^2 ,

and x =0. 5 cm.

To estimateNmwe note that the contamination level in argon is very low

(1%) and therefore we can safely use the argon number density in place of

the overall density of the gas. The number density of argon atoms can be

calculated from

Nm=

NAρ

A

,