Reaction mechanism of (α,d) transfer inPb208(α,d)Bi210at 33 and 48 MeV

Abstract

The reaction $^{208}\mathrm{Pb}(\ensuremath{\alpha},d)^{210}\mathrm{Bi}$ has been studied at 33 and 48 MeV with particular emphasis on the (${h}_{\frac{9}{2}}{g}_{\frac{9}{2}}$) ground-state multiplet and the high-spin members of other low-lying $n\ensuremath{-}p$ multiplets, which are expected to be of high purity. About 50 angular distributions were obtained and used as a basis for a study of the transfer mechanism in ($\ensuremath{\alpha},d$) reactions. The analysis was made with the microscopic distorted-wave Born approximation and with two-step coupled-reaction-channel calculations. The $L$ transfers observed ranged from $L=1$ to $L=13$ and were consistent with one-step transfer selection rules. Nevertheless, the relative magnitudes of cross sections to levels of the (${h}_{\frac{9}{2}}{g}_{\frac{9}{2}}$) ground-state multiplet disagree with one-step-transfer predictions at either beam energy by factors which vary from 0.5 to 4.0. This phenomenon is explained as a coherent addition of the sequential stripping amplitudes ($\ensuremath{\alpha},t;t,d$) and ($\ensuremath{\alpha},^{3}\mathrm{He};^{3}\mathrm{He},d$) to the one-step amplitude, where the important ($\ensuremath{\alpha},t;t,d$) amplitude typically amounts to about 50% of the one-step ($\ensuremath{\alpha},d$) amplitude for high- and low-spin states alike. Details of the coupled-reaction-channel analysis are provided. The two-step calculations were kept free of arbitrary parameters by a simultaneous analysis of previously published $^{208}\mathrm{Pb}(t,d)$, $^{208}\mathrm{Pb}(^{3}\mathrm{He},d)$, $^{208}\mathrm{Pb}(\ensuremath{\alpha},t)$, and $^{208}\mathrm{Pb}(\ensuremath{\alpha},^{3}\mathrm{He})$ single-particle transfer data. This systematic reanalysis indicated again that most single-particle states in $^{209}\mathrm{Pb}$ and $^{209}\mathrm{Bi}$ show their full spectroscopic strength, but that the $\ensuremath{\pi}{i}_{\frac{13}{2}}$ and $\ensuremath{\nu}{j}_{\frac{15}{2}}$ single-particle states are not pure and have single-nucleon spectroscopic factors of about 0.75\ifmmode\pm\else\textpm\fi{}0.10.NUCLEAR REACTIONS $^{208}\mathrm{Pb}(\ensuremath{\alpha},d)^{210}\mathrm{Bi}$, ${E}_{\ensuremath{\alpha}}=33 \mathrm{and}48$ MeV, measured ${E}_{d}$ and $\ensuremath{\sigma}(\ensuremath{\theta},{E}_{d})$ with QDDD spectrograph. DWBA and CRC analysis, deduced levels, ${L}_{\ensuremath{\alpha},d}$, evidence for sequential stripping.