Quantal Stark mixing at ultralow collision energies

D Vrinceanu, M R Flannery
2000 Journal of Physics B: Atomic, Molecular and Optical Physics  
A new exact solution of the time-dependent quantal equation is obtained for the full array of angular momentum mixing transitions n → n in atomic hydrogen induced by collisions with charged particles at ultralow energies. Based on this new solution, efficient numerical procedures are devised. It is proven that the present (fixed-frame) solution is equivalent to the rotating-frame approach described by Kazansky and Ostrovsky (Kazansky A K and Ostrovsky V N 1996 Phys. Rev. Lett. 77 3094) and that
more » ... . 77 3094) and that it overcomes the difficulties therein. Analytic expressions for low quantum numbers n are presented. Numerical results for the transition array with n = 28 are reported. Stark mixing occurs when the electron of a Rydberg atom (in a state with principal quantum number n) changes its angular momentum , without changing its energy, as a result of a collision, at large impact parameter b, with a slow massive particle of charge Z 1 e moving with velocity v. It is important in many areas of atomic physics, as in the Auger (or autoionization) process which follows the collision between ions and atoms (Miraglia and Macek 1990), in ZEKE spectroscopy (Merkt and Zare 1994), in astrophysics (e.g. Percival 1983), in recent efforts (Mensh'ikov and Fedichev 1995) to produce anti-hydrogen at 4 K and for general three-body recombination (Flannery and Vrinceanu 1998) at ultralow energies. The first stage in ultralow energy electron-ion recombination (Flannery and Vrinceanu 1998) at temperature T e is a very rapid collisional capture into high Rydberg states with high angular momentum and large radiative lifetimes at a rate proportional to T −4.5 e . Thus the -mixing is an essential step in producing the low-angular-momentum states required to radiatively decay at a relatively high rate to low levels, thereby stabilizing the recombination. On considering the Rydberg atom in a frame rotating with the internuclear axis, the Stark mixing problem can be reduced to the problem of the Rydberg atom in mixed static fields: electric, provided by the projectile ion, and magnetic, produced by the non-inertial (Coriolis) forces. In this way, the well known equations, in both classical (Born 1960) and quantum (Demkov et al 1970) mechanics, for the problem of interaction between weak fields and an atom, can be adopted to provide, in principle, a solution for the Stark mixing problem. Both quantal (Kazansky and Ostrovsky 1996a, b) and classical (Kazansky and Ostrovsky 1996b, c) versions of this approach have succeeded only for = 0 to higher angular momentum transitions, appropriate to the experiments described in a paper by Sun and MacAdam (1993) . This letter presents a new exact solution for the Stark mixing process, valid for transitions n → n between any states within the shell of energy E n . The present theory in the fixed-frame representation is shown to be formally equivalent to the rotating-frame approach (Kazansky and Ostrovski 1996a, b), but, in contrast to it, the full array of transition amplitudes can be obtained at once by efficient numerical procedures. Results for transitions within the 0953-4075/00/200721+08$30.00
doi:10.1088/0953-4075/33/20/10a fatcat:nwivajqhxfaxzjzuplgm6bkzi4