Deep-inelastic multinucleon transfer processes in the ${}^{16}\mathrm{O}+{}^{27}\mathrm{Al}$ reaction

The reaction mechanism of deep-inelastic multinucleon transfer processes in the ${}^{16}\mathrm{O}+{}^{27}\mathrm{Al}$ reaction at an incident ${}^{16}\mathrm{O}$ energy ($E_{\mathrm{lab}}=134$ MeV) substantially above the Coulomb barrier has been studied both experimentally and theoretically. Elastic-scattering angular distribution, total kinetic energy loss spectra, and angular distributions for various transfer channels have been measured. The $Q$-value- and angle-integrated isotope production cross sections have been deduced. To obtain deeper insight into the underlying reaction mechanism, we have carried out a detailed analysis based on the time-dependent Hartree-Fock (TDHF) theory. A recently developed method, TDHF+GEMINI, has been applied to evaluate production cross sections for secondary products. From a comparison between the experimental and theoretical cross sections, we find that the theory qualitatively reproduces the experimental data. Significant effects of secondary light-particle emissions are demonstrated. Possible interplay among fusion-fission, deep-inelastic, multinucleon transfer, and particle evaporation processes is discussed.

Figure 1

A typical two-dimensional $\mathrm{\Delta }E\text{−}E$ spectrum from ${}^{27}\mathrm{Al}$(${}^{16}\mathrm{O}$, $x$) reactions at $E_{\mathrm{lab}}=134$ MeV showing the various projectile-like fragments: (upper panel) oxygen, nitrogen, carbon, and boron isotopes; (lower panel) beryllium and lithium isotopes.

Figure 2

The ratio of the elastic scattering to the Rutherford cross sections for the ${}^{16}\mathrm{O}+{}^{27}\mathrm{Al}$ reaction at $E_{\mathrm{lab}}=134$ MeV plotted as a function of the scattering angle in the center-of-mass frame. Fitted result by the optical model calculation with the sfresco code [51] is shown by a blue solid curve. The potential parameters obtained from the fitting to the data are given in Table 1.

Figure 3

Experimental total kinetic energy loss (TKEL) distributions (histogram plot) for various projectile-like fragments in the ${}^{16}\mathrm{O}+{}^{27}\mathrm{Al}$ reaction at $E_{\mathrm{lab}}=134$ MeV, for a fixed scattering angle of ${\theta }_{\mathrm{lab}}={10}^{\circ }$ (${\theta }_{\mathrm{c}.\mathrm{m}.}=15.9^{\circ }$). The blue vertical dashed lines indicate the position of ground-to-ground-state $Q$ values.

Figure 4

The experimental total kinetic energy loss spectra of ${}^{15}\mathrm{N}$, ${}^{14}\mathrm{N}$, ${}^{13}\mathrm{C}$, ${}^{12}\mathrm{C}$, and ${}^{11}\mathrm{B}$ (top row, from left to right) and ${}^{10}\mathrm{B}$, ${}^9\mathrm{Be}$, ${}^7\mathrm{Be}$, ${}^7\mathrm{Li}$, and ${}^6\mathrm{Li}$ (bottom row, from left to right) reaction products from the ${}^{16}\mathrm{O}+{}^{27}\mathrm{Al}$ reaction at $E_{\mathrm{lab}}=134$ MeV. Note that the vertical axis was adjusted case by case for better visibility. Note also that the data shown in the top row (${\theta }_{\mathrm{c}.\mathrm{m}.}=15.9^{\circ }$) are the same data as shown in Fig. 3.

Figure 5

The measured $Q$-value-integrated angular distributions for various channels in the ${}^{16}\mathrm{O}+{}^{27}\mathrm{Al}$ reaction at $E_{\mathrm{lab}}=134$ MeV. The errors indicate the statistical error.

Figure 6

A schematic illustration of the initial orientations of ${}^{27}\mathrm{Al}$ in the TDHF calculations. Red (blue) disk represents cross sections of the density of ${}^{27}\mathrm{Al}$ (${}^{16}\mathrm{O}$) nucleus in the reaction plane ($xy$ plane). The incident direction is indicated by thick arrows which are parallel to the $x$ axis (at infinitely large distance), and the impact parameter vector is parallel to the $y$ axis. By a blue dashed arrow or a circle attached to ${}^{27}\mathrm{Al}$, the direction of shrinking is represented. This direction would correspond to the symmetry axis if ${}^{27}\mathrm{Al}$ were purely deformed in an oblate shape.

Figure 7

Results of the TDHF calculations for the ${}^{16}\mathrm{O}+{}^{27}\mathrm{Al}$ reaction at $E_{\mathrm{lab}}=134$ MeV. (a) Total kinetic energy loss (TKEL), (b) scattering angle in the center-of-mass frame, and (c) sticking time are shown as a function of the impact parameter, $b$. In panel (b), the scattering angle for the Coulomb trajectory is indicated by a dotted curve. In panel (c), the sticking time is shown in zeptoseconds (1 zs $={10}^{-21}$ s).

Figure 8

(a) The Wilczyński plot and (b) the TKE-$A$ distribution obtained from the TDHF calculations for the ${}^{16}\mathrm{O}+{}^{27}\mathrm{Al}$ reaction at $E_{\mathrm{lab}}=134$ MeV.

Figure 9

Average numbers of neutrons (a) and protons (b) of the projectile-like fragment (PLF) in ${}^{16}\mathrm{O}+{}^{27}\mathrm{Al}$ reaction at $E_{\mathrm{lab}}=134$ MeV are shown as a function of the impact parameter, $b$. In panel (c), the average $N/Z$ ratios of the PLF and the targetlike fragment (TLF) are shown.

Figure 10

Snapshots of the density of the colliding nuclei in the reaction plane at various times obtained from the TDHF calculations for the ${}^{16}\mathrm{O}+{}^{27}\mathrm{Al}$ reaction at $E_{\mathrm{lab}}=134$ MeV. In upper panels (a), dynamics for the shrinking $y$ case are shown, while those for the shrinking $z$ case are shown in lower panels (b). In each panel, the elapsed time is indicated in zeptoseconds (1 zs $={10}^{-21}$ s). It is to mention that the whole simulation box ($60\mathrm{fm}\times 52\mathrm{fm}$) is not shown in the figure.

Figure 11

The $Q$-value- and angle-integrated isotope production cross sections for various proton-transfer channels in the ${}^{16}\mathrm{O}+{}^{27}\mathrm{Al}$ reaction at $E_{\mathrm{lab}}=134$ MeV. The change in the number of protons compared with the projectile ($Z=8$) is indicated as ($\pm x\mathrm{p}$; $X$), where $X$ stands for the corresponding element. Red filled circles show the experimental data. The results of TDHF(+GEMINI) calculations are shown by histograms. Calculated results for primary (secondary) products are shown in the left (right) figure. grazing results [90] are also shown by gray shaded histograms for comparison.