Global optical model potential for elastic deuteron scattering from 12 to 90 MeV

A set of about 4000 data points has been used in a global search for a general optical model parameter prescription. This potential for deuteron-nucleus scattering was confined to remain within the range given by folding model calculations. The data set spans the energy range from 11.8 to 90 MeV and includes many targets ranging in mass from ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ to ${}_{}{}^{238}{}_{}{}^{}\mathrm{Th}$. The set includes 50 reaction cross sections, 13 angular distributions for vector polarization at and above 15 MeV, and 103 angular distributions for elastic scattering. A successful 11-parameter potential of the conventional form fits all data analyzed to about 18% rms. Two of these parameters, $V_R$ and $a_I$, are functions of proton number and target mass, while five ($V_R$, $a_o$, $W_S$, $W_D$, $V_{\mathrm{LS}}$) are smooth functions of bombarding energy. The remainder ($r_o$, $r_I$, $r_c$, $r_{\mathrm{LS}}$, $a_{\mathrm{LS}}$) are constants. A simple functional dependence for $a_I\mathrm{}(A,Z)\mathrm{}$ approximately reproduces the rapid changes in $\sigma \left(\theta \right)$ found experimentally for nuclei at or near neutron shell closure. A comparison with earlier work suggests that the optical model analyses furnish the rms radii for the real and imaginary potentials with little ambiguity. General agreement but with a somewhat larger scatter (10%) is also found for the real and the imaginary volume integrals deduced. However, little consistency is seen for the imaginary volume integral if the bombarding energy is below 15 MeV. The rms radii and volume integrals have a small but distinct energy dependence. It was found that the 11-parameter potential occasionally has difficulty delivering good simultaneous fits for cross sections and vector polarizations. This situation was improved by the addition of a small, three-parameter imaginary spin-orbit term, which in our global prescription required short range and very small diffuseness.