Coupled-Channels Optical Potential Method For Positron-magnesium Collisions

In recent years, positron-atom collision has simulated more and more scientific research. Great successes have been achieved both experimentally and theoretically, a number of theoretical calculations have given successful predictions that cover almost all aspects of the positron-hydrogen system (Igarashi and Toshima 1994, Kernoghan et al 1995, 1996, Mitroy and Stelbovics 1994, Ratnavelu et al 1996, Kuang and Gien 1997, Kadyrov A S and Bray I 2002, Zhou et al in press). However, as to the many-electron atoms scattering with positron, there remain obvious discrepancies between the experimental measurements and the theoretical predictions, for the various reaction within the complex collision system. Nowadays, with the remarkably improvement on the experimental technology, corresponding descriptions from the theory are expected urgently, which comes into being the great challenge to our theoretical workers.In the past 20 years, some theoretical models have been developed to the positron-atom collision, wherein the common models include the distorted-wave Born approximation method (DWBA), the R-matrix method, the convergent close coupling method (CCC) and the coupled-channels optical potential method (CCO). The DWBA method are more valid for the collision in the high energy range; the R-matrix method, which was proposed by Burke, Noble and Scott, and then developed by the Belfast groups, is more suitable for the collision in the low energy range and when the incident energy reach to the intermediate range, a series of pseudo-structure are caused due to the use of the large number of pseudo-states; the CCC method has advantage over the simple target atom, for example, the H and , and there are some difficulty in treating the more complex target atoms. So it is necessary to develop a more common theory model, which can descript the positron collision with the many-electrons atom explicitly. HeThe CCO method, developed in 1980's by McCarthy et al, has been widely applied to the electron scattered by various atoms and molecules and has achieved great success. In the recent year, Prof Zhou Ya-jun et al have successfully developed the CCO method to the positron collision with atom H. In the present paper, we propose a complex, local polarization to represent the Positronium formation (Ps) arrangement channel and the ionization continuum channel, and develop the CCO method to the positron collision with the complex atom.In the present paper, we investigate the positron-Mg collision in the low and intermediate energy, and calculated the Ps, ionization, elastic, excitation and the total cross sections. We found resonance phenomena and calculated both the resonant cross sections and the partial resonant cross sections. In the intermediate energy collision, infinite reaction channels are open including the Ps and ionization channels, which must be considered effectively in order to descript the collision process explicitly. In the low and intermediate energy range, the ionization and Ps channels play a prominent role in the positron-Mg collision and must be considered carefully. We developed a complex, local polarization potential representing the Ps and ionization effects and add it to the polarization potential to the first order coupled potential, then through the CCO method, we can consider all the reaction channels effectively. To test the validity of the polarization potential model and the developed CCO method, we calculate the important channels cross sections including the Ps, ionization, elastic, excitation the total cross sections.In this paper, we have done the following calculation: Firstly: By using the obtained polarization model, we calculated the Ps and ionization cross sections of the positron-Mg collision in the low and intermediate energy, and compared the results with the latest experimental measurements and other theoretical calculations. We found that the present Ps results agree quite well with the latest experiment and also in accord with the recent R-matrix and CCC calculations. For the ionization cross section, through there are no experimental results available, our calculations agree with the explicit DWBA calculation perfectly. The successful predictions of the Ps and ionization cross sections validate our polarization potential.Secondly: We add the polarization potential to the first order coupled potential and calculate the elastic, 3s-3p excitation cross section in the low and intermediate energy positron-Mg collision, furthermore, we calculated total cross section considering or omitting the Ps and ionization effect respectively. We found that, the effect of the Ps formation and the ionization on the total cross section is significant at lower energies. For there are no experiments data about the elastic and excitation cross sections in the positron-Mg collision, we just compare our calculations with the available theoretical results. We found that, our results accord well with the explicit R-matrix calculations on the whole, and in the higher incident energy range, our results converge to the other theoretical predictions. Through the theoretical calculation results, we could obtain the following conclusions:1. The complex, local polarization potential model successful predicted the Ps cross section in low energy positron-Mg collision and the ionization cross section in the intermediate energy positron-Mg collision, which validated the polarization model. In the low energy range, the Ps channel plays a prominent role in the positron-Mg atom collision and this effect is not negligible even in the intermediate energy range. In the intermediate energy range, the ionization channel is important and must be carefully considered in the positron-Mg collision.2. We add the polarization potential to the CCO method formalism and successfully predict the elastic, 3s-3p excitation and the total cross section. The effect of the Ps formation and the ionization on the total cross section is significant at lower energies. Accordingly it is necessary to take into account the ionization and Ps formation channels in the investigation of the positron-Mg collision at the intermediate energies. 3. In the very low energy range, there are difference between our prediction and the experimental data of the Ps cross section. We think that the difference may be due to the use of the plane wave representation of the incident positron and the centre-of-mass motion of Ps, omitting the polarization effect of the incident positron and the residual target ion, and the single configuration Hartree-Fock wave function that is used in our calculation, which does not include the many configuration interactions. In the following work, we will center on the polarization effect and the higher-order electron-electron correlations to improve the calculations.