Quantum-mechanical study of the Landau-Zener resonances in nuclear heavy-ion collisions

In order to resolve the well-known defects in classical or semi-classical approaches, we solve a two-state Landau-Zener problem fully quantum -mechanically with a localized radial coupling. An analytic expression of the T-matrix is derived by using distorted-wave Born approximation (DWBA). The convergence of the expansion formula is shown to be rapid enough for a reasonable range of the coupling. The transition probabilities calculated with the formula are shown to well agree with those calculated by the coupled-channels method even for the strength of the coupling, which is five times as strong as that extracted from the two-center shell model. Therefore, the analytic DWBA formula is extremely useful for discussion of the Landau-Zener transition in nuclear heavy-ion collisions. Qualitative features of the resonancelike behaviour are discussed for three different forms of the coupling. For light systems such as 12C + 17O, the resonancelike structures are shown to survive in the excitation function even for a realistic finite range coupling, though the calculated cross sections are much reduced in comparison with those for a constant coupling in semi-classical calculations. For heavier systems such as 40Ca + 57Ni, however, no resonancelike structure can survive because of the broad width resulting from the strong Coulomb potential. (author)