Woods–Saxon potential

The Woods - Saxon potential is a term used in the shell model of the atomic nucleus approach for the potential energy of protons and neutrons as a function of their distance from the center of the nucleus. It was introduced by Roger Woods and David Saxon 1954.

The Woods - Saxon potential is attractive, that is, it increases monotonically with distance from the core center. For large mass numbers it is for distances that are smaller than the core radius, approximately constant, then increases at the core edge sharply and approaches for greater distances asymptotically to zero, ie, a square-well potential with edge blur.

Mathematically, it has the following form:

It is

  • R is the distance from the center of the core;
  • V0 is the potential depth;
  • A is the edge thickness parameter, which specifies the density curve of nuclear matter at the core edge;
  • The core radius, r0 = 1.25 femtometer (fm), and A is the mass number.

Typical values ​​of the potential depth and the resolution are: V0 ≈ 50 MeV, a ≈ 0.5 fm.

The Schrödinger equation for the Woods - Saxon potential can not be analytically but only numerically solved.

See also

  • Nuclear physics
  • Shell model ( Nuclear Physics )

Credentials

  • Roger D. Woods and David S. Saxon: Diffuse Surface Optical Model for Nucleon - Nuclei Scattering. In: Physical Review. Volume 95, 1954, pp. 577-578. doi: 10.1103/PhysRev.95.577
  • Nuclear physics
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