Excitation functions for quasielastic transfer reactions induced with heavy ions in bismuth

Abstract

The excitation functions for the production of $^{210}\mathrm{Bi}$, $^{210}\mathrm{Po}$, $^{207\ensuremath{-}211}\mathrm{At}$, and $^{211}\mathrm{Rn}$ through quasielastic transfer reactions induced with heavy ions in $^{209}\mathrm{Bi}$ have been measured. The corresponding reactions involved the transfer of one neutron, one proton, two charges, and three charges from projectile to target. The projectiles used were $^{12}\mathrm{C}$, $^{14}\mathrm{N}$, $^{16}\mathrm{O}$, $^{19}\mathrm{F}$, $^{20}\mathrm{Ne}$, $^{40}\mathrm{Ar}$, $^{40}\mathrm{Ca}$, $^{56}\mathrm{Fe}$, and $^{63}\mathrm{Cu}$. The experimental techniques involved target irradiations and off-line $\ensuremath{\alpha}$ and $\ensuremath{\gamma}$ activity measurements. Chemical separations were used to solve specific problems. Careful measurements of incident energies and cross sections were performed close to the reaction thresholds. All excitation functions exhibit the typical features of quasielastic transfer reactions: a sharp increase at low energy, and a constant value at high incident energy. The position of the thresholds are strongly influenced by the energetics of the reaction: High cross sections are observed under the strong interaction barrier if the energy balance at the minimum distance of approach is positive. This balance is equal to the difference between the interaction potentials in the entrance and exit channels, corrected for the mass balance. The constant cross sections observed for the high energy part of a given excitation function are consistent with the assumption that the curve $P(R)$ which represents the transfer probability versus the distance between the nucleus centers does not vary with incident energy. This assumption implies the constancy of the optimum distance of approach ${R}_{\mathrm{opt}}$, of the $R$ window $\ensuremath{\Delta}R$ for which $P(R)$ is significant, and of the magnitude of $P(R)$. Moreover the data show that the high energy cross sections for one-proton transfer are independent of the projectile, while odd-even effects of the projectile atomic number $Z$ on the two-charge transfer cross sections are observed for the lightest incident ions $^{14}\mathrm{N}$ to $^{20}\mathrm{Ne}$.NUCLEAR REACTIONS $^{209}\mathrm{Bi}(\mathrm{HI}, X)$, $^{211,210,209,208,207}\mathrm{At}$, $^{211}\mathrm{Rn}$, with HI=$^{12}\mathrm{C}$, $^{14}\mathrm{N}$, $^{16}\mathrm{O}$, $^{19}\mathrm{F}$, $^{20}\mathrm{Ne}$, $^{40}\mathrm{Ar}$, $^{56}\mathrm{Fe}$, $^{63}\mathrm{Cu}$. $\frac{E}{A}\ensuremath{\simeq}4.5\ensuremath{-}10$ MeV/nucleon. Measured $\ensuremath{\sigma}(E)$.