Self-Consistent Field in Self-Bound Finite Nucleus

概要

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Starting from the antisymmetrized product of plane waves, we derive the shell model wave function A[П^^A__<i=1> u_<a_i>(i)] in the nucleon system which is self-bound. Each wave function u_<α_<i>>(i) has the tail being exponentially small at large distances from the origin. In the final result, the self-consistent field is given by U_i=Σ^^A__<j≠i> (u_<α_<j>>(j)|t_<ij>|u_<α_<j>>(j)). Here the t-matrix has just the same meaning as the Brueckner's but with a difference in the boundary condition of Green's function in the t-matrix. Ours is so defined that it vanishes at large distances from the origin. Therefore, it is suited for treating the finite system. It has further advantage that the Neumann series converges for nuclear potentials. Three points are essential in derivation: (1) The Pauli principle. (2) The nuclear force is "weak", having only one bound state in free space. (3) The number of constituent particles is very large, so 1/A≪1. The extension of the present method to the independent pair model is made. In the limit of infinite matter, the precise equivalence of the present method and the Brueckner's method is shown for a weak interaction.
理論物理学刊行会の論文
1964-10-25