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.

It is worth noting that the discrepancy between
different systematics of the stopping power data is
much greater.