Ôèçèêà/5. Ãåîôèçèêà
À. Blochshitsyna, D.
Pak, F. Karabalinova
Karaganda State Technical University, Kazakhstan
Effective
atomic number determination
A
conception of an effective atomic number is introduced for understanding of
interaction characteristic of gamma-quantum within a composite medium. An
effective atomic number determination is based on substitution of a composite
medium to a hypothetical element. The parameter in question is the same for
such element and composite medium. In other words, Z of composite medium is
numerically equal to an atomic number of a hypothetical element. The
attenuation coefficient of gamma-quantum with certain energy is the same for
such element and composite medium. This means that a value of Z is defined not
only by a composition of medium but by an incident radiant energy.
Effective atomic number of composite medium is evaluated from following
consideration. The atomic number of an element markedly affects on
photoelectric absorption of gamma-quantum. For composite medium mass
photoelectric absorption coefficient of gamma-quantum is evaluated by following
formula:
In low-energy band a photo-effect cross-section is proportional to Z4.
Taking this and Z determination it is easy
to define the formula for 
value estimation.
On
condition that E0 < 300 keV and not less than absorption energy of
K-layer the effective atomic number of element 
can be calculated by the following formula:
ãäå 
- concentration of i-element in a
composite medium;
- atomic number of i-element.
In processing of gamma-irradiation of substance and registration of gamma-rays
scattered by substance, additionally testing its probed samples it is possible
to determined sensitivity – effective atomic number of substance relationships
for different energies E0
of primary gamma-radiation. Based on these relationships it is possible
to determine interrelation between optimal values of 
and energy
, conforming to maximal sensitivity to
. Also optimal primary
gamma-radiation energy
, which irradiates substance, is
selected by assuming Z average value of analyzable substance as 
optimal value. Effective atomic number of irradiated substance is
determined by scattered gamma-radiation intensity.
While quantitative analyzing of composite medium by gamma-gamma method
sensitivity is the main metrological parameter which characterizes relative
increment of scattered gamma-radiation intensity in case of unit change of
effective atomic number. In general case sensitivity of the method is a complicated
function of primary gamma-radiation energy, substance composition and effective
atomic number 
and geometrical conditions of
measurement.
Samples of substance with known 
value are used to determine sensitivity 
- effective atomic number
dependencies for different
primary gamma-radiation energies ÅÎ. Sensitivity
dependencies 
have inversion character with
maximums are related on substance Z-value and primary gamma-radiation energy ÅÎ. The more primary
gamma-radiation energy ÅÎ becomes the better maximal sensitivity to 
value of substance with 
increased values. Sensitivity absolute values to 
in inversion region decrease consistently with increasing of
energy ÅÎ and effective atomic number of substance.
This allows to find interrelation
between 
optimal values and energy
, conforming to maximal sensitivity to 
. 
average value of analyzable substance is taken as 
optimal value whereby optimal primary gamma-radiation energy 
is selected. Analyzable
substance is irradiated by selected optimal primary gamma-radiation energy;
effective atomic number is determined by intensity of scattered
gamma-radiation.
So to every substance of certain effective
atomic number value conform optimal value 
of primary gamma-radiation whereby maximal sensitivity to 
presents.
Offered method was approved for coal quality control. In whole coal
quality varies in wide range. Effective atomic number of coals is subject to
variation from 6 to 11. Dependencies of sensitivity 
from effective atomic number of
coals were determined by testing coal samples of known composition (
varied from 6 to 11 with the
step size 0,2 unit) and using primary gamma-radiation of different energies (5.9 keV; 8
keV; 16 keV; 22 keV; 60 keV).
Interrelation between optimal values of 
and 
, conforming to maximal sensitivity to 
, was defined based on
determinate dependencies which have inversion (extremal) from 
-value character. For cleaned
coals with 
=6,2-6,9 optimal value of primary
gamma-radiation is 20keV. For high ash and raw coals with 
=9,6-10,8 primary
gamma-radiation 
is 55 keV. Cd-109 (22 keV) was
chosen, for cleaned coals with average value 
=6,5, as a source of primary
gamma-radiation. Am-241 (60 keV) was
chosen, for high ash and raw coals with average value 
≈6,5, as a source of
primary gamma-radiation.
Effective atomic number determination method is characterized by increased
its sensitivity to 
in broad range of its change.