Neutron transfer in the ${}^{13}\mathrm{C}+{}^{197}\mathrm{Au}$ reaction from gold isotope residuals

Residual gold nuclei were produced via neutron transfer at multiple energies using a 130-MeV ${}^{13}\mathrm{C}$ beam incident on a stacked-foil target consisting of alternating layers of ${}^{197}\mathrm{Au}$ and ${}^{27}\mathrm{Al}$. Production cross sections, over an energy range of 56 to 129 MeV, for seven gold isotopes and two gold isomers were determined through activation analysis. By using the Wilczyński binary transfer model with a modified version of the recoil formula and a standard evaporation model, we were able to reproduce the isotopic production cross sections at high beam energy, with some disagreement at lower beam energies. This limiting angular momentum model does not predict the transfer of sufficient angular momentum to reproduce the observed isomeric populations.

Figure 1

A portion of the characteristic $\gamma$-ray spectra from foil 1, counted for 2 h. The spectra were taken before (blue, top) and after (red, bottom) chemical separation. Peaks labeled indicate the gold isotopes.

Figure 2

Residual gold production cross sections (data points) as a function of ${}^{13}\mathrm{C}$ energy in the laboratory frame. Connecting lines are added only to guide the eye. Data points for ${}^{192}\mathrm{Au}$ have been slightly downshifted in energy for clarity (see text for details).

Figure 3

Measured cross sections (black squares) versus those predicted from the Wilczyński binary transfer model (blue circles) with the assumption that the dissipated energy in the entrance channel is proportional to the beam energy per nucleon. Parameters are $T=2.52$ MeV, $R_c=12.7$ fm, ${\mathrm{\Delta }}_{\ell }=5.11$, and with $E_{\mathrm{diss}}=0.22E_{\mathrm{beam}}$ MeV/u. Calculations with zero cross-section values are not plotted. The ${}^{192}\mathrm{Au}$ cross sections could not be reproduced using the binary transfer model.

Figure 4

Comparison of measured isomer to ground-state ratios (black circles) with those predicted using talys (blue squares) and dicebox (red diamonds) to calculate the statistical $\gamma$-ray cascade for both ${}^{198}\mathrm{Au}$ (a) and ${}^{196}\mathrm{Au}$ (b). Both isomers show much higher relative population in the data than is predicted by the binary transfer model, with a particularly large discrepancy from ${}^{196}\mathrm{Au}$. Calculations with zero cross-section values are not plotted.