Interaction of alpha particles in the lead region near the Coulomb barrier

Abstract

The ($\ensuremath{\alpha},n$) cross section on $^{208}\mathrm{Pb}$ and $^{209}\mathrm{Bi}$ has been measured between 16 and 24 MeV by observing the $\ensuremath{\alpha}$ activity of the residual nuclei $^{211}\mathrm{Po}$ and $^{212}\mathrm{At}$. The relative yields to both the ground and metastable states of each residual nucleus were obtained and new half-life determinations have been made for these states. The absolute yield was measured at 20 and 22 MeV to normalize the relative data. Below the ($\ensuremath{\alpha},2n$) threshold, $\ensuremath{\sigma}(\ensuremath{\alpha},n)$ constitutes most of the total reaction cross section, and the ($\ensuremath{\alpha},n$) data, together with accurate elastic scattering measurements at 19, 20, and 22 MeV are reproduced well by a six-parameter optical model. The fits are sensitive to the reaction cross-section data, and serve to define the magnitude and shape of the real potential at a radial distance of about 11 fm. The real potential in this region dominates the interaction at the present energies. The imaginary potential is relatively small; it is not well determined and serves only to absorb those waves which penetrate the real potential. The real potential obtained is interpreted in terms of an $\ensuremath{\alpha}$-folding model using a free $\ensuremath{\alpha}$-nucleon two-body force. The potential near the peak of the Coulomb barrier is determined primarily by the target matter density near 9 fm, where it is approximately 1% of its value at the center of the nucleus. Implications concerning the relative distributions of target neutron and protons are discussed.[NUCLEAR REACTIONS $^{208}\mathrm{Pb}$, $^{209}\mathrm{Bi}(\ensuremath{\alpha},\ensuremath{\alpha}) (\ensuremath{\alpha},n)$; measured $\ensuremath{\sigma}(\ensuremath{\theta})$ elastic, ${E}_{\ensuremath{\alpha}}=19,20,22$ MeV; ${\ensuremath{\sigma}}_{\ensuremath{\alpha}n}(E)$, ${E}_{\ensuremath{\alpha}}=16\ensuremath{-}24$ MeV; ${T}_{\frac{1}{2}}$: $^{211}\mathrm{Po}$, $^{211}\mathrm{Po}^{m}$, $^{212}\mathrm{At}$, $^{212}\mathrm{At}^{m}$. Deduced optical potentials, surface matter density form factors.]