We calculate with a simple classical atom-atom model
some potential parameters of the K-Br_{2} system by fitting calculated deflection functions with specific features of the measured differential cross section
, thus determining simultaneously the exact shape of the deflection function.

The ionization deflection function can be calculated from the potential-energy curves
. Choosing potential parameters by trial and error, the
scattering function has been calculated via fitting with the measured differential cross section for the
K + Br_{2} case by a new
method . The numerical calculation of the classical deflection
angle is performed with a well-known error. For the calculation we
have used the crossing potential curves with the assumption that the
charge exchange occurs exactly at the crossing point.

Because the colliding particles are rather heavy and the kinetic energy is not very low, it will be reasonable to compare the measurements primarily with classical calculations. Small quantum-mechanical interference structures on the differential cross-section curves will be washed out by the large energy spread of the alkali beam, the averaging effect of the internal state distribution and the anisotropy of the halogen molecule, the extent of the crossing region and the finite angular resolution of the detector.

For the ionic-potential curve we have chosen a Rittner potential of the form :

U_{ion}(R) |
= | ||

(E1) |

(E2) |

Because we use for the
ionic and covalent potential formulas many parameters we have looked
for effects in the differential cross section that are mainly due to
only one of these parameters. The parameters that can be determined
rather directly in this way are the endothermicity of the
collision
,
the polarizability of the bromine ion
,
the crossing
distance R_{c}, the resonance energy *H*_{12}, the repulsive steepness coefficient
and the ionic-well depth
.

Firstly
and the electron affinity of Br_{2} are determined via fitting of the relative shifts of the maxima and the small-angle deflection slopes of the deflection function at different energies with the measured shifts. They are found to be
=3.1 eV and
*A* (Br_{2}) = 1.2 eV.

Then
is determined via fitting the scattering angle for collisions with *b*=*R*_{C} with the measured minimum:
.

Substituting the obtained values of
and
in the assumed potential, *R*_{c} can be determined to be *R*_{c}=
5.8 Å.

The well depth of the potential curve is determined using the classical rainbow angle:
= 1.8eV.

The repulsive steepness coefficient is determined via a doubtful classical fit: = 0.3 Å.

The resonance energy is determined by fitting the curve height ratio and found to be H_{12}=4.5 x 10^{12} eV. .

Figure A05-m4bii-F2:
K + BR_{2} ionic and covalent potential. |

Summarizing, we have determined for the
K-Br_{2} system most of the
potential parameters; the missing parameters have been chosen
to construct the potential curves in Fig. A05-m5bi-F2 and the
deflection functions in Fig. A05-m5bi-F3 The values used are:

where the value for

Based on the potential curves of the system, the classical deflection function is calculated
,
. For collisions with two channels, a covalent one and an ionic one
, the deflection function consists of a covalent and an ionic branch which are joined at the crossing radius *R*_{c}, as is shown in figure refA05-m5bi-F3, forming a closed deflection curve.

From the deflection function then, the differential cross section can be calculated .