As a result of the interactions of matter, beta particles can totally lose their energy and absorb into matter. This process is called “real absorption of the beta radia­tion.” However, during the transmission of beta particles through any substance, the intensity (I) of the beta radiation can also decrease as a result of other processes (e. g., by scattering). These processes have been discussed previously and summa­rized in Figure 5.13. Usually, all decreases in intensity are treated as absorption, regardless of the underlying cause of the decreases.

Quantitatively, the absorption of beta radiation can only be described with diffi­culty due to the continuous nature of the beta spectra. This means that the energy of beta particles when entering matter can range from zero to the maximum energy of the beta spectrum. Therefore, the expressions describing the beta absorption are usually empirical. It is interesting, however, that the empirical equation of beta absorption (Eq. (5.46)) is similar to the general equation of the absorption of radia­tion (Eq. (5.3)):

-r(E)l

where I0 and I are the intensities of the beta radiation before and after the transmis­sion through the matter, l is the thickness of the absorber, and p(E) is the linear absorption coefficient; its dimension is reciprocal length (e. g., mm"1, cm-1, m-1). The value of the linear absorption coefficient depends on both the energy of the radiation and the atomic number and density of the absorber. By introducing the mass absorption coefficient, it can be avoided to determine the linear absorption coefficient for all maximal beta energies and for all substances. For this purpose, the linear absorption coefficient in the exponent of Eq. (5.46) is divided and multi­plied by the density of the absorber (p). Note that the density is the ratio of the mass and volume (p = m/V = m/(l X S)):

p(E) m

I = I0e p l X S (5.47)

where m and S are the mass and the surface area of the absorber, respectively.

(E)

= p is the mass absorption coefficient, and its dimension is surface area/mass.

p

Since l/l = 1, the mass/surface area (m/S) remains in the exponent of Eq. (5.47). This quantity describes the mass of the absorber on a unit surface area; it is called “surface density” (d); its dimension is mass/surface area (e. g., mg/cm2). This leads to:

I = I0 e"^ (5.48)

The relation of the mass absorption coefficient and the maximum beta energy (Epmax) and the atomic number of the absorber (Z) can be approximated by empiri­cal equations. When Z < 13:

When Z> 13:

= 7.7Z031

p e1.14

E(3max

In Eq. (5.47), Ma is the relative atomic mass of the absorber. For compounds and mixtures, the mass absorption coefficient can be calculated by the mass absorp­tion coefficients of the components, taking into consideration their mass ratio (w):

As seen in Eq. (5.48), the absorption of continuous beta radiation can be described by an exponential equation. However, the monoenergetic (> 0.2 MeV)

electron radiations (e. g., conversion electrons) show the linear absorption curve as a function of surface density. Below 0.2 MeV, the absorption curve of the monoe­nergetic electron deviates more or less from linearity.

To characterize the absorption of the beta radiation (exponential law, Eq. (5.48)), the half-thickness of the absorber (d1/2) is defined. This is the thickness where the intensity of the beta radiation decreases by half:

ln 2

d1=2 =——- (5.52)

As seen in Section 5.2.1, alpha radiation has a well-defined range (R). However, the range of beta radiation can be described only by empirical formulas at different maximal beta energies, such as:

In Eqs. (5.53)—(5.57), the dimensions of range and energy are g/cm2 and MeV, respectively.

Cloud chamber photographs show the differences in the pathways of the beta and alpha particles (Figure 5.7 shows the alpha track, and Figure 5.14 shows the alpha and beta tracks). Since alpha particles are much heavier than beta particles/ electrons, the pathway of alpha particles is linear. Beta particles, however, tend to deviate more or less, depending on their energy. The interaction of gamma radia­tion with matter will be discussed later (in Section 5.4); for now, just note that gamma radiation produces secondary electrons, the tracks of which will be shown in the later discussion.

In the presence or two or more beta emitters, Eq. (5.48) consists of several members:

/ = /10 e-ftd 1 /20 e 1 … 1 In0 e2^nd (5.58)

This means that the absorption of each beta radiation has to be taken into account separately. The mass absorption coefficients and the range of some beta emitters as a function of maximal beta energy are plotted in Figure 5.15. These data are widely applied in the characterization of beta absorption and the planning of shielding against radiation. However, Eqs. (5.49) and (5.50) show that the mass

absorption coefficients depend on the atomic number. Therefore, at Z > 13, the mass absorption coefficients calculated on the basis of Eq. (5.50) are about twice as high as the data in Figure 5.15. It should be noted, however, that the plan of shielding uses the principle of the so-called conservative estimation, which means that the plans consider the worst scenario. Therefore, the application of the lower mass absorption coefficient is permitted or even can be desirable.