Woods-Saxon potential

Woods-Saxon potential relative to V ₀ for A  = 50 (i.e. core radius R ≈ 4.6 fm) and a  = 0.5 fm

The Woods-Saxon potential (after Roger Woods and David Saxon , who introduced it in 1954) is an approach for the potential energy of protons and neutrons as a function of their distance from the center of the atomic nucleus . It is used in the shell model of nuclear physics . ${\displaystyle V(r)}$ ${\displaystyle r}$

The Woods-Saxon potential is attractive; i.e. , it increases monotonically with distance from the core center. For large mass numbers , it is approximately constant for distances that are smaller than the core radius, then increases sharply at the core edge and asymptotically approaches zero for larger distances . So it is a box potential with edge blurring.

Mathematically it has the following form:

${\displaystyle V(r)=-{\frac {V_{0}}{1+\exp({\frac {r-R}{a}})}}}$

It is

• V _{0 is} the potential depth (typically V ₀  ≈ 50  MeV );
• r is the distance from the center of the core;
• ${\displaystyle R=r_{0}\cdot {\sqrt[{3}]{A}}}$ the core radius, where
  • r ₀ = 1.25  sc and
  • A is the mass number ;
• a is the edge thickness parameter , which indicates the density of the core matter at the core edge (typically a  ≈ 0.5 fm).

The analytical solution of the Schrödinger equation for the Woods-Saxon potential can be found in the monograph Practical Quantum Mechanics .

Individual evidence

1. ^ Roger D. Woods, 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
2. ^ Siegfried Flügge : Practical Quantum Mechanics . Springer Berlin Heidelberg, 1999, ISBN 978-3-642-61995-3 (624p, limited preview in the Google book search - p. 162 ff .: Problem 64. Wood-Saxon potential ( sic )).