7.1 Basic Concepts and Formulae 373
Fig. 7.4Rutherford
scattering
R 0 is also the minimum distance of approach in head-on collision for positively
charged particles of energy below Coulomb barrier (Fig. 7.4).
Impact parameter (b) and scattering angle (θ)
tan (θ/2)=R 0 / 2 b (7.16)Minimum distance of approach
R 0
2[
1 +
(
1 +
4 b^2
R 02) 1 / 2 ]
=(R 0 /2)[1+cosec (θ/2)] (7.17)Multiple scattering angle
The root mean square angle of multiple scattering
√
<Θ^2 >=k
√
tze/pv (7.18)wherekis the scattering constant
k=[8πNZ^2 e^2 ln(bmax/bmin)]^1 /^2t=thickness,N=number of atoms/cm^3 , Ze and ze are the charge of nuclei of medium
and projectile, pv is momentum times the velocity of the incident particle. For pho-
tographic emulsions, ln(bmax/bmin) is of the order of 10.
Cross-section and mean free path
Ifnis the number of atoms/cm^3 , then the macroscopic cross-section
Σ=nσ (cm−^1 ) (7.19)And mean free path
λ= 1 /Σ (7.20)
Also,n=N 0 ρ/A (7.21)whereN 0 =Avagadro’s number,ρ=density,Athe atomic weight.