Dispersion relations for $\mathrm{}(n,n),$ $\mathrm{}(n,p),$ and $(n,\alpha )$ reactions on ${}^{39}\mathrm{K}$ and ${}^{40}\mathrm{Ca}$

Cross sections and differential cross sections of ${}^{39}\mathrm{K}(n,\alpha {)}^{36}\mathrm{Cl}$ at $En=4.5,$ 5.5, and 6.5 MeV, and that of ${}^{40}\mathrm{Ca}(n,\alpha {)}^{37}\mathrm{Ar}$ at $En=5\mathrm{}$ and 6 MeV were measured. These data and other available experimental data were used in optical model calculations which contain a dispersion relation term. One set of parameters for dispersive optical potentials of ${}^{39}\mathrm{K}\mathrm{}(n,n),$ $\mathrm{}(n,p),$ and $(n,\alpha )$ reactions is determined, and subsequently used in the dispersive optical model (DOM) calculations for ${}^{40}\mathrm{Ca}\mathrm{}(n,n),$ $\mathrm{}(n,p),$ and $(n,\alpha )$ reactions. A good description of the experimental data with DOM is achieved, and the results are compared with that of the spherical optical model.