Physics and Engineering of Radiation Detection

4.4. Commonly Used Liquid Detection Media 233

where we have used the approximationr−a≈r+a≈rsincer>>a. Substitution
ofN 1 from equation 4.3.2 into the above equation gives

N 2 =

N 0

1+K/E(r)

exp

[

−r

{

A+

rB

2 V

ln

(

b

a

)}]

. (4.3.9)

As a reminder,N 2 represents the number electrons that have survived the recombi-
nation and parasitic capture after traveling a distancerin the chamber. These elec-
trons are able to cause avalanche multiplication provided they have gained enough
energy between collisions. The number of electrons produced in the avalanche can
be estimated by substitutingN 2 in equation 4.3.1, that is

N=

N 0

1+K/E(r)

exp

[

−r

{

A+

rB

2 V

ln

(

b

a

)}

+

∫r

a

α(r)dr

]

. (4.3.10)

The multiplication factorM, which represents the ratio of the number of electrons
produced in the avalanche to the initial number of electrons, is then given by

M =

N

N 0

=

1

1+K/E(r)

exp

[

−r

{

A+

rB

2 V

ln

(

b

a

)}

+

∫r

a

α(r)dr

]

. (4.3.11)

The first and second terms in the brackets on right hand side represent the decay
and growth of electron population respectively. The decay is due to the absorption
of electrons by impurities and has a significant effect on the overall amplification.
Therefore in order to predict the multiplication constant correctly one needs to
evaluate this whole expression. However this requires the hard-to-find constantsA,
B,andKfor the particular case under study. Although a number of experimental
studies have been performed to determine these parameters but the fact that they
depend heavily on small changes in impurity concentrations makes their use limited
to the ones used in the experimental setup. For example the constantB,which
is sometimes referred to as thefield dependent capture coefficient, is so sensitive to
the amount of impurity in the gas that it can range from almost zero for very low
impurity levels up to several thousandV/cm^2 for impurity level of a few parts per
million in liquefied noble gases. In gases the variation is not that dramatic and
therefore small changes in impurity levels can be tolerated.

4.4 CommonlyUsedLiquidDetectionMedia................

For liquid filled ionizing detectors, liquid argon is perhaps the most widely used
detection medium. However, this does not mean that other liquefied gases do not
possess favorable properties. In fact, there are a number of liquefied gases that have
been successfully used to build ionizing and scintillating detectors. When it comes
to scintillation detectors, liquid xenon is generally the choice due to its favorable
scintillation light wavelength, refractive index, and Fano factor. In Table??we
list some useful properties of the liquefied noble gases. It is interesting to note
that all three gases listed in the table can act as scintillators, that is, they emit
light after absorbing energy. Hence, in principle, all of them can be used to build