Bi209(He3, d)Po210andBi209(He4, t)Po210reactions and some matrix elements of the residual interaction

Abstract

The ($^{3}\mathrm{He}$, $d$) and ($^{4}\mathrm{He}$, $t$) single proton transfer reactions on $^{208}\mathrm{Pb}$ and $^{209}\mathrm{Bi}$ were studied using 30 and 40 MeV He beams. The outgoing reaction products were detected by a position sensitive proportional counter in the focal plane of a quadrupole-three-dipole spectrometer. The resolution varied between 10 and 14 keV full width at half maximum. Using the ratio of cross sections for the ($^{3}\mathrm{He}$, $d$) and ($^{4}\mathrm{He}$, $t$) reactions to determine $l$ transfers, spectroscopic factors for the reactions on $^{209}\mathrm{Bi}$ have been measured relative to the transitions to the single-particle states observed in reactions on $^{208}\mathrm{Pb}$. Sum rules are applied and diagonal matrix elements of the effective interaction between valence protons around the $^{208}\mathrm{Pb}$ core are deduced. The matrix elements obtained from empirical interactions and from realistic calculations are compared to these extracted matrix elements.NUCLEAR REACTIONS $^{209}\mathrm{Bi}(^{3}\mathrm{He}, d)^{210}\mathrm{Po}$, $^{208}\mathrm{Pb}(^{3}\mathrm{He}, d)^{209}\mathrm{Bi}$ ${E}_{^{3}\mathrm{He}}=30$ MeV and $^{209}\mathrm{Bi}(^{4}\mathrm{He}, t)^{210}\mathrm{Po}$, $^{208}\mathrm{Pb}(^{4}\mathrm{He}, t)^{209}\mathrm{Bi}$ ${E}_{^{4}\mathrm{He}}=40$ MeV. Measured differential cross sections with a resolution of 10-14 keV (FWHM). Sum rule analysis and deduction of matrix elements of the residual interaction in nuclei.