Quantum-Mechanical Study of the Landau-Zener Resonances in Nuclear Heavy-lon Collisions

概要

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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 ^<12>C+^<17>O, 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 ^<40>Ca +^<57>Ni, however, no resonancelike structure can survive because of the broad width resulting from the strong Coulomb potential.
理論物理学刊行会の論文
1991-03-25