#### Abstract

Solutions are given for the $S$ states of the potential $V\left(r\right)=-\frac{{V}_{0}}{[1+{e}^{\alpha \mathrm{}(r-a)\mathrm{}}]}$. These are used to calculate the position of the giant $S$-wave neutron resonances at low (zero) energy and the bound states of the potential. If one chooses ${V}_{0}=39.8\mathrm{}$ Mev, $\alpha =2\mathrm{}\times {10}^{13}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $a=1.35\mathrm{}{A}^{\frac{1}{3}}\times {10}^{-13\mathrm{}}$ cm, the potential binds the right number of particles. $S$-wave maxima in the elastic scattering cross sections then occur at $A=13,64,\mathrm{and}183$. The experimental curves show a rise in the total scattering cross section in the region $A\sim 60\mathrm{and}180$ for small neutron energies.

DOI: http://dx.doi.org/10.1103/PhysRev.101.311

- Received 20 September 1955
- Published in the issue dated January 1956

© 1956 The American Physical Society