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Self-consistent field calculations for the nuclear surface and208Pb

Nuclear Physics A
Publication Date
DOI: 10.1016/0375-9474(67)90578-7


Abstract Self-consistent field calculations have been made for the nuclear surface (semi-infinite system) and for 208Pb. A reaction matrix was calculated by the separation method from a spin-independent exponential nucleon potential interacting in S-states only. Only the dispersion (core) term and the long-range part were considered. By expanding the nonlocality of the reaction matrix an effective mass approximation is obtained. This simplifies the self-consistent field calculation considerably. Some parameters were adjusted to give proper saturation of the infinite system. The surface-energy and surface thickness are calculated. Reasonable agreement with experiment is obtained, but both surface energy and thickness tend to be too large. Thus, the calculations give a Bethe-Weiszäcker parameter a 2≈ 27−30 MeV and a surface thickness ΔS ≈ 3.2 fm. Experiments give a 2 ≈ 18−26 MeV and ΔS ≈ 2.4 fm. In view of other calculations the discrepancy may be due partly to the too simplified interaction. However, softening of the core improves the agreement. Thus with no hard core a 2 ≈ 15 MeV, ΔS ≈ 2.0 fm. The interior density of 208Pb with Coulomb field is close to that of the infinite system with the same interaction. Without Coulomb field it is about 15% larger.

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