Multinucleon transfer study in ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},x)$ at energies above the Coulomb barrier

Single- and multi-nucleon transfer reactions, namely, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{20}\mathrm{O})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{19}\mathrm{O})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{17}\mathrm{O})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{16}\mathrm{O})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{18}\mathrm{N})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{17}\mathrm{N})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{16}\mathrm{N})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{15}\mathrm{N})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{14}\mathrm{N})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{16}\mathrm{C})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{15}\mathrm{C})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{14}\mathrm{C})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{13}\mathrm{C})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{12}\mathrm{C})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{12}\mathrm{B})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{11}\mathrm{B})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{10}\mathrm{B})$, ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^{10}\mathrm{Be})$, and ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},{}^9\mathrm{Be})$, have been studied at an incident ${}^{18}\mathrm{O}$ energy of 139 MeV. The total kinetic energy loss (TKEL) spectrum and angular distribution of reaction products have been measured. The $Q$ value and angle integrated cross sections are deduced. Angular distributions for the elastically scattered ${}^{18}\mathrm{O}$ particles are also measured. Fully microscopic time-dependent Hartree-Fock (TDHF) calculations, based on the independent single-nucleon transfer mode, have been carried out and are compared with experimental data of multinucleon transfer reactions. The TDHF calculations provide reasonable agreement with the experimental data for cases where one- and two-nucleon transfer is involved; the discrepancy is large for multinucleon transfer reactions. The effect of particle evaporation on the production cross sections has been studied. Inclusion of particle evaporation effects, though improving the results, could not reproduce the measured cross sections. Possible origins of these discrepancies are discussed.

Figure 1

Typical two-dimensional $\mathrm{\Delta }E-E$ spectra from ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},x)$ reactions for the angle ${\theta }_{\mathrm{lab}}={30}^{\circ }$: (a) oxygen and nitrogen isotopes and (b) carbon, boron and beryllium isotopes.

Figure 2

Calibration curve showing mass identification of the projectile-like particles in ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},x)$ reactions. The elastically scattered ${}^{18}\mathrm{O}$ particles and beryllium isotopes (${}^{7,9}\mathrm{Be}$) were used for calibration. The identification of ${}^7\mathrm{Be}$ and ${}^9\mathrm{Be}$ was straightforward as ${}^8\mathrm{Be}$, being unstable, is absent in the two-dimensional $\mathrm{\Delta }E-E$ spectrum (Fig. 1).

Figure 3

Ratio of elastic scattering to Rutherford cross section for ${}^{18}\mathrm{O}+{}^{206}\mathrm{Pb}$ at $E_{\mathrm{lab}}\left({}^{18}\mathrm{O}\right)=140$ MeV plotted as a function of the scattering angle. The fit shown is the optical model calculation using the code sfresco.

Figure 4

Experimental total kinetic energy loss distribution (histogram plot) for quasielastic and various transfer processes in the ${}^{18}\mathrm{O}+{}^{206}\mathrm{Pb}$ reaction at $E\left({}^{18}\mathrm{O}\right)=139$ MeV and ${\theta }_{\mathrm{lab}}={38}^{\circ }$. The vertical dashed lines (blue) indicate the position of ground-to-ground state $Q$ values. The cross section scale (mb/MeV) has been obtained by normalizing each distribution to its total integrated cross section.

Figure 5

Experimental $Q\mathrm{-value}$ integrated angular distributions for the indicated reactions at $E_{\mathrm{lab}}\left({}^{18}\mathrm{O}\right)=139$ MeV.

Figure 6

The total integrated cross section for various transfer channels in the ${}^{18}\mathrm{O}+{}^{206}\mathrm{Pb}$ reaction at $E\left({}^{18}\mathrm{O}\right)=139$ MeV. Points are the experimental data and the histograms represented by the red solid lines correspond to the results of present TDHF calculations. The predicted cross sections after inclusion of particle evaporation effects in the TDHF calculations are shown as blue dashed lines (details are given in the text).

Figure 7

The $Q\mathrm{-value}$ and angle-integrated cross section for single- and multi-nucleon stripping reactions ${}^{206}\mathrm{Pb}({}^{18}\mathrm{O},x)$ measured at an incident ${}^{18}\mathrm{O}$ energy of 139 MeV plotted as a function of the number of nucleons transferred $\mathrm{\Delta }N$. The solid lines are a guide for the eye and are drawn as a straight line to connect different isotopes of a particular element. All lines have the same slope.

Figure 8

Average numbers of (a) protons and (b) neutrons in the PLF in ${}^{18}\mathrm{O}+{}^{206}\mathrm{Pb}$ reaction at $E_{\mathrm{lab}}=139$ MeV plotted as a function of the impact parameter. Red open circles, green crosses, and blue open triangles connected with dotted lines show results for $x-$, $y-$, and $z\mathrm{-direction}$ configurations, respectively. The initial number of protons (neutrons) in ${}^{18}\mathrm{O}$ is shown by a horizontal dotted line.

Figure 9

Differential cross sections of representative transfer channels as a function of the scattering angle for the ${}^{18}\mathrm{O}+{}^{206}\mathrm{Pb}$ reaction at $E_{\mathrm{lab}}=139$ MeV compared with the TDHF calculations. The blue curves are the TDHF results and the red vertical lines indicate the position of the Coulomb rainbow angle obtained from the TDHF trajectories.

Figure 10

The decomposed transfer cross sections as defined in Eq. (4) for various transfer reaction channels plotted as a function of TKEL (details are given in the text).