Accurate elastic scattering cross sections for 17-MeV deuterons

Angular distributions for 17.0-MeV ($d,d$) scattering on 23 isotopically pure targets (${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$, ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$, ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$, ${}_{}{}^{100}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{105}{}_{}{}^{}\mathrm{Pd}$, ${}_{}{}^{112}{}_{}{}^{}\mathrm{Cd}$, ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$, ${}_{}{}^{112}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$ ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$, ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$) have been measured from ${\theta }_{\mathrm{lab}}\le 10 \mathrm{to} 165°$ in 5° steps. Relative experimental errors are always less than 2% and absolute scale errors range from 2 to 5%. Optical model searches have been performed on all angular distributions. Good fits were obtained (with four free parameters) for three values of the real radius parameter $r_0=1.0, 1.1, \mathrm{and} 1.2$ fm using starting values of $V_0\approx 100$ MeV. The best fit parameters are presented for these searches, as well as for the best over-all nine-parameter fits. The data show some preference for parameter values close to $r_0=1.1\mathrm{}$ fm (with $a\approx 0.82$) for all targets heavier than ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, although very acceptable fits are also obtained for all three sets with restricted parameters. The searches with nine free parameters resulted in overly perfect fits (${\chi }^2\lesssim 1$) indicative of considerable ambiguity for so large a parameter space. Preliminary global fits to our 17-MeV data yielded a formula for generating usable optical model parameters for other near-spherical nuclei of mass $A>\mathrm{}48\mathrm{}$.

NUCLEAR REACTIONS ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$, ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$, ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$, ${}_{}{}^{100}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{105}{}_{}{}^{}\mathrm{Pd}$, ${}_{}{}^{112}{}_{}{}^{}\mathrm{Cd}$, ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$, ${}_{}{}^{112}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(d,d)$, $E=17.00\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$ and ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}(d,d^{\prime })$, $E=17.00\mathrm{}$ MeV, measured $\sigma (E_d,\theta )$ optical model analysis, deduced $A$ dependence in optical model parameter prescription. Enriched targets.