ONE-AND-A-HALF-CENTERED EXPANSION METHOD IN CHARGE-TRANSFER CALCULATIONS OF PROTON-HYDROGEN SCATTERING

In this paper, we undertake a feasibility study of improving the one-a nd-a-half-centered expansion (OHCE) method of Reading, Ford, and Becke r [J. Phys. B 14, 1995 (198 1); 15, 3257 (1982)]. We have explored the efficacy of an alternative method to evaluate the charge-transfer mat rix elements and improved the estimated time dependence of the charge- transfer scattering amplitudes. More projectile states have been inclu ded in the calculations than used hitherto. A unitary matrix, U matrix , which can propagate the wave functions from -infinity to t, where t denotes time, has been constructed using the single-centered expansion (SCE) method. A complex basis set of nine radial s states and nine ra dial p states has been used in the expansion of trial wave functions f or the target. Charge-transfer matrix elements have been evaluated by a Feynman integral technique; one numerical integral using Gaussian qu adrature is needed. The radial parts of the matrix elements are stored on circles and used for all the impact parameters. In a OHCE calculat ion, we have to choose a function beta(m)(z) to modulate the charge-tr ansfer amplitudes. The only constraints on beta(m)(z) are beta(m)(-inf inity) = 0 and beta(m)(infinity) = 1. In this paper, beta(m)(z) has be en obtained from a SCE calculation. This beta(m)(z) function increases gradually in the whole collision region. It offers an improvement ove r the step function used in previous work. A computer code has been de veloped to include s and p states for the target and projectile. The c alculations have been performed in the proton energy range from 30 to 250 keV. The charge transfer to the Is state has been calculated and g ives good agreement with the experimental data. The proton energy rang es have been extended from the 100 keV used in previous work to 250 ke V. The charge-transfer cross sections to the 2p state fit the experime ntal data at 30 keV and are almost the same as those calculated using the four-state, two-centered expansion method proposed by Cheshire and Gallaher [J. Phys. B 3, 813 (1970)] and Shakeshaft [Phys. Rev. A 14, 1626 (1976)]. The results of the charge exchange to the 2s state are a lso in fairly good agreement with the measurements of Ryding [listed i n Tawara, Kato, and Nakar, At. Data Nucl. Data Tables 32, 235 (1985)].