Coupled-Channel Optical Potential Method For Positron-excited Hydrogen (2s) Collisions

In recent years, with the development of experimental technique, the process of electron impact excited atoms is receiving more and more attention. There are significant differences between the behavior of cross sections for excited atom system and ground atom system. The unique features of excited atoms indeed enrich the dynamics of collision process. As the antimatter of electron, positron collisions are different from the analogous collisions involving electrons. Factors contributing to these differences include the absence of exchange interaction for positrons; the repulsive short-range static interaction; and the positronium channel. So we realized that positron-excited atoms collisions are expected to create some different phenomena from the positron-ground atoms collisions. We expect that the studies of interaction of positron with excited atoms can not only enrich our knowledge about positron-atom collisions, but also provide us a new means to investigate the correlation effect between electrons and new tests of our understanding of basic physics.In this paper, we have applied the momentum-space coupled-channel optical (CCO) method to investigate the positron collisions with excited hydrogen. An ab-initial complex optical potential is developed to describe the ionization continuum and positronium formation channels. The CCO method is given by I. E. McCarthy and A. T. Stelbovics【33-34】firstly. In this method, the whole space is split into P and Q spaces, which are orthogonal to each other, by the Feshbach projection operators. The P space consists of some discrete channels, including the entrance channel; the rest discrete channels and the ionization continuum are included in the Q spaces. We solved the Lippmann-Schwinger coupled equations in the P space with a complex nonlocal optical potential which describes the contribution of Q space. For computational convenience, we approximate the nonlocal potential by an equivalent local potential. So we can get the T matrix elements and the formulae for cross sections.In the present calculation, we calculated the positronium formation cross sections and the ionization cross sections. And by adding the obtained polarization which describes the positronium formation channels and ionization channels, we got the total cross sections, the elastic cross sections and the 2s-3s excitation differential cross sections. 8 discrete states of hydrogen are included in the P space. They are 2,3,4s, 2, 3, 4p, 3,4d. The optical potentials that describe the target continuum are in the couplings 2s-2s, 2s-2p and 2p-2p. The optical potential that represents the formation of positronium is included in the coupling 2s-2s. We describe the target bound states by configuration inertaction wave functions. Because there are no experimental results available, we compare our results with the corresponding results of positron scattering with ground hydrogen and some other theoretical results. To check the contribution from the positronium formation and ionization optical potential, we make a comparison among three theory model when we calculate the elastic cross sections.Through the analysis and comparison, we could obtain the following conclusions:There is an essential difference in the energy dependence relation of the Ps-formation cross sections between positron collision with ground-state and excited state hydrogen. And Ps-formation and ionization cross sections have large values comparing with the ground-state hydrogen, especially for Ps-formation cross sections. The differences are due to the low ionization threshold of 2s of hydrogen that is lesser than the bound energy of Ps-formation 6.8eV, the smaller ionization potential makes the values of Ps-formation cross section very large. And the higher polarizability in the excited hydrogen causes an enhancement in the ionization cross section's magnitude.Unlike the ground-state hydrogen, the Ps-formation channel is not important for positron scattering with excited hydrogen. But the contribution of the ionization continuum can not be neglectable. Because the long-range dipole polarization potential plays a significant role and dominates the whole scattering process. So we should consider the ionization polarization potential more precisely.In the comparison between the theoretical results, the 2s-3s excitation differential cross sections differ from each other. In the absence of any differential cross section measurements it is difficult to justify the present theory methods.The comparison of the present total scattering cross section with that for positron impact on the ground state hydrogen shows that the cross sections for excited state exceeds that for ground state for about two orders of magnitude. And the total cross sections are mostly from the 2s-2p excitation cross sections. These behaviors are also attributed to the much higher value of the dipole polarizatbitity of H (2s) compared to H (1s).Some defects exist in our theory model. For instance, we got extremely large Ps-formation cross sections in the very low energy range. We think that the difference may be attributed to the plane wave representation of the incident positron and the centre-of-mass motion of Ps. And the weak-coupling approximation omits some coupling in the Q space. Extensive improvements would be made in the future.