a Theoretical Investigation of State-Changing Thermal Collisions Between Rydberg Atoms and Ground State Noble Gas Atoms.

Two methods for calculating state-changing collisional matrix elements, and hence angular-momentum-mixing cross sections, are presented for a ground state noble gas atom colliding with a Rydberg atom at thermal energies. The first is a fully quantal method using Monte Carlo integration to perform the necessary nonseparable fifteen-dimensional collision integrals. The equations are developed for general treatment in the first and higher Born approximations, the distorted wave approximations, and several close-coupling schemes. The Monte Carlo method is carefully developed and tested for use in the types of integrals involved, and variance reduction techniques are discussed and applied. The second method uses a Gegenbauer polynomial expansion of the -1/r('4) polarization potential to find the necessary matrix elements. It also employs the elliptic functions and elliptic integrals to calculate the classical trajectory of the ground state atom as it passes the ionic Rydberg core. This semiclassical method is easily transformed into a fully quantal method, retaining only the polarization potential feature, by integrating the translational wave function of the incoming ground state atom and the matrix elements calculated via the Gegenbauer polynomials. The equations of scattering for the first quantal method are then specifically developed for ground state helium colliding with Rydberg helium, and a calculation of the l-mixing cross section for He(10('1)P) is performed using over a half million random fifteen-dimensional points. The result, accurate to within a factor of two, gives a result of 1600 A('2) compared to the experimental value of 2580 (+OR-) 590 A('2). This experimental value is within the variance of the Monte Carlo calculation. It is therefore concluded that the method is a viable technique for calculating Rydberg cross sections without the many simplifying assumptions used by other authors to date. Improvements and extensions to calculational methods developed herein are suggested with specific direction given on possible approaches for a continuation of this study. The methods derived are general and thus applicable to a wide variety of Rydberg collision problems.