Non adiabatic theory of collisions in a radiative field. Semi-classical limit

The quantal theory of atomic collisions in a radiative field is now well established for weak fields which we consider here. Several calculations of radiative cross sections and redistribution of polarization compare extremely well with experimental results. Semi-classical approaches often allow a better physical interpretation. However, the above mentioned results show that trajectory and internuclear reorientation effects during the collision play an essential role so that sophisticated methods have to be developed. In this paper (paper 1), we derive the semi-classical close coupled equations in the limit of large quantum numbers of the quantal equations thereby avoiding the rectilinear trajectory assumption. An adequate choice of the axis frame of reference allows us to show the exact correspondence between this approach and the direct semi - classical derivation of the close coupled equations. This leads us to interpret physically the P, Q, R spectroscopic branches in terms of the rotation of the internuclear axis during the collision