Energy dependence of nonlocal optical potentials

Recently, a variety of studies have shown the importance of including nonlocality in the description of reactions. The goal of this work is to revisit the phenomenological approach to determining nonlocal optical potentials from elastic scattering. We perform a ${\chi }^2$ analysis of neutron elastic scattering data off ${}^{40}\mathrm{Ca}, {}^{90}\mathrm{Zr}$, and ${}^{208}\mathrm{Pb}$ at energies $E\approx 5–40$ MeV, assuming a Perey and Buck [Nucl. Phys. 32, 353 (1962)] or Tian et al. [Int. J. Mod. Phys. E 24, 1550006 (2015)] nonlocal form for the optical potential. We introduce energy and asymmetry dependencies in the imaginary part of the potential and refit the data to obtain a global parametrization. Independently of the starting point in the minimization procedure, an energy dependence in the imaginary depth is required for a good description of the data across the included energy range. We present two parametrizations, both of which represent an improvement over the original potentials for the fitted nuclei as well as for other nuclei not included in our fit. Our results show that, even when including the standard Gaussian nonlocality in optical potentials, a significant energy dependence is required to describe elastic-scattering data.

Figure 1

Angular distributions for ${}^{208}\mathrm{Pb}(n,n){}^{208}\mathrm{Pb}$ at $E=11$, 20, 30.3, 40 MeV. Data are from Refs. [30, 33, 34].

Figure 2

Angular distributions for ${}^{27}\mathrm{Al}(n,n){}^{27}\mathrm{Al}$ at $E=10.159$, 18, 26 MeV. Data are from Refs. [39, 40].

Figure 3

Angular distributions for ${}^{118}\mathrm{Sn}(n,n){}^{118}\mathrm{Sn}$ at $E=11$, 14, 18, 24 MeV. Data are from Refs. [41, 42].