The evaluated cross-section data constitute an
array of points (*E _{i}*,σ

First the energy *E _{i}*

_{},

which can be integrated analytically. The corresponding formulas are as follows:

_{},

_{},

_{},

where θ is a scattering angle, *E*_{2} is the energy of the
outgoing particle immediately after an interaction and *k* is a kinematical factor.

The interaction yield *Y*_{1}(*E*_{1i}) at the depth *x _{i}*
is obtained by a convolution of the cross-section with the beam spreading
function which is assumed to be represented by Bohr’s straggling theory:

_{},

where

_{}

with *Z _{t}* and

The yield of the registered particles *Y*_{3}(*E*_{3i}) is calculated as a convolution of the yield *Y*_{1}(*E*_{1i}) with the
Gaussian spreading function, the variance _{} including both
straggling on the way out and the detector resolution:

_{}.

The yield per a MCA channel of width Δ*E*_{3} is

_{},

where *Q* and Ω are the number of projectiles and the detector
solid angle respectively, and

_{}.

The stopping power approximation used in the
calculations is accurate up to tenths of percent in the energy range of
interest as can be seen from the following figure.