Nucleon Energy Levels in a Diffuse Potential

Phys. Rev. 102, 1613 – Published 15 June 1956
A. A. Ross, Hans Mark, and R. D. Lawson


The level sequence and shell structure for the bound single-particle states of nucleons moving in the spherically symmetric potential V(r)=-V0[1+expα(r-a)] have been examined. For protons, a Coulomb potential was added corresponding to a uniform charge distribution out to the "nuclear radius," a, and the potential depth was increased to give sufficient binding energy for the last proton level in the nucleus under consideration. For α=1.45×10+13 cm-1 (implying a surface layer of approximately 3×10-13 cm, which is constant for all A), a spin-orbit coupling 39.5 times the Thomas term and a=1.3A13×10-13 cm, good shell structure is obtained for both neutrons and protons. The level sequences obtained are in close agreement with experiment except in the region of strong distortion from sphericity. For V0=42.8 Mev the neutron binding energies are in reasonable agreement with experiment. With these parameters the 3s and 4s giant resonances in the low-energy neutron scattering cross section occur at A=56 and 166 respectively. The neutron and proton distributions in Au19779 are examined. With the values of α, r0, and λ given above, the thickness of the surface layer on the proton distribution is 1.92×10-13 cm and the radius is 6.77×10-13 cm.


  • Received 20 February 1956
  • Published in the issue dated June 1956

© 1956 The American Physical Society

Authors & Affiliations

A. A. Ross*, Hans Mark, and R. D. Lawson

  • Department of Physics, University of California, Berkeley, California

  • *Whiting Fellow in Physics, Department of Physics, University of California.


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