The form of the potential, in terms of the distance r from the center of nucleus, is:
where V0 (having dimension of energy) represents the potential well depth,
a is a length representing the "surface thickness" of the nucleus, and is the
nuclear radius where r0 = 1.25
fm and A is the
mass number.
Typical values for the parameters are: V0 ≈ 50
MeV, a ≈ 0.5 fm.
For large atomic number A this potential is similar to a
potential well. It has the following desired properties
It is monotonically increasing with distance, i.e. attracting.
For large A, it is approximately flat in the center.
Nucleons near the surface of the nucleus (i.e. having r ≈ R within a distance of order a) experience a large force towards the center.
It rapidly approaches zero as r goes to infinity (r − R >> a), reflecting the short-distance nature of the
strong nuclear force.
The Schrödinger equation of this potential can be solved analytically, by transforming it into a hypergeometric differential equation. The radial part of the wavefunction solution is given by
Schwierz, N.; Wiedenhover, I.; Volya, A. (2007). "Parameterization of the Woods–Saxon Potential for Shell-Model Calculations".
arXiv:0709.3525 [
nucl-th].
Flügge, Siegfried (1999). Practical Quantum Mechanics. Springer Berlin Heidelberg. pp. 162ff.
ISBN978-3-642-61995-3.