Energy Gap in Finite Nuclear Systems

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Abstract
Slabs of nuclear matter are studied to assess the finite-nucleus effects on the energy gap, using realistic nucleon-nucleon interactions. The slabs are defined by square wells in one dimension only. The energy gap is found by solving numerically an approximation to the BCS integral equation, and solutions are displayed as functions of the effective mass and the size of the finite system. Empirical estimates of the gap in real nuclei are examined taking into account nuclear "blocking" and particle-umber fluctuation. By identifying structures of the same surface-to-volume ratio, calculated values of the gap can be compared directly with the empirical estimates. It is found that the general trend of the magnitude of the gap as a function of the nucleon number can be reproduced with not too unreasonable values of the effective mass.

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