Multinucleon transfer processes in ${}^{40}\mathrm{Ca}+{}^{208}\mathrm{Pb}$

Multinucleon transfer reactions in ${}^{40}\mathrm{Ca}+{}^{208}\mathrm{Pb}$ have been studied at bombarding energies close to the Coulomb barrier. Projectilelike fragments have been identified in nuclear mass and charge with a time-of-flight spectrometer. Angular and total kinetic energy loss distributions and inclusive cross sections have been compared with those of semiclassical models. The analysis shows that a successive transfer mechanism of single nucleons does not account for the data, and a direct nucleon pair transfer has to be included in the description. Nucleon evaporation effects are taken into account.

Figure 1

$E\text{−}\Delta E$ two-dimensional spectra (left panel) and mass-charge distribution (right panel) of the ${}^{40}\mathrm{Ca}{+}^{208}$Pb reaction at $E_{\mathrm{lab}}\hspace{1em}=235$ MeV obtained at the grazing angle, ${\theta }_{\mathrm{lab}}\hspace{1em}=\hspace{1em}{84}^{°}$. The dash-dotted lines correspond to the pure proton stripping $(\Delta Z)$ and to the pure neutron pickup $(\Delta N)$ channels, crossing at $Z=20$ and $A=40$. The full line shows the charge equilibrization, namely the $N/Z$ ratio of the compound nucleus.

Figure 2

Angle and Q-value integrated cross sections for pure proton stripping and pure neutron pickup channels of the ${}^{40}\mathrm{Ca}+{}^{208}\mathrm{Pb}$ reaction at $E_{\mathrm{lab}}\hspace{1em}=\hspace{1em}235$ (top) and 249 (bottom) MeV as a function of transferred nucleons. The points and histograms are experimental and theoretical (CWKB) values, respectively. The dashed lines are the results of CWKB calculations using sequential transfer only, whereas the solid lines also include pair-transfer modes.

Figure 3

Angle and energy integrated cross sections at 235 (upper panel) and 249 (lower panel) MeV. The left and middle panels show total cross sections as a function of transferred protons for neutron pickup and neutron stripping reactions, respectively. The right panels show the total cross sections as a function of the number of transferred neutrons. For the sake of clarity, no experimental errors are plotted.

Figure 4

Experimental (histogram) and theoretical (shaded areas) total kinetic energy loss distributions at ${\theta }_{\mathrm{lab}}\hspace{1em}=\hspace{1em}{84}^{°}$ at $E_{\mathrm{lab}}\hspace{1em}=\hspace{1em}235\hspace{1em}\mathrm{MeV}$ for the strongest transfer channels. Vertical lines indicate the total kinetic energy loss corresponding to the two-touching-sphere configuration of the appropriate $Z_1$ and $Z_2$ in the exit channels.

Figure 5

Experimental (histogram) and theoretical (shaded areas) total kinetic energy loss distributions for the pure neutron pickup and proton stripping channels at ${\theta }_{\mathrm{lab}}={60}^{°},{65}^{°},{75}^{°}$, and ${80}^{°}$ at $E_{\mathrm{lab}}=249\hspace{1em}\mathrm{MeV}$.

Figure 6

Experimental (dots) and theoretical (lines) angular distributions of dominant transfer channels measured at $E_{\mathrm{lab}}\hspace{1em}=\hspace{1em}235$ (left) and 249 (right) MeV and integrated over all detected energies. The full and dashed lines are results of CWKB and GRAZING calculations, respectively.

Figure 7

(Color online) Single-particle levels for projectile and target used in the calculations. The gray areas indicate the occupied levels.

Figure 8

Measured (points) and calculated (lines) quasielastic angular distributions. The calculations are obtained in the coupled-channel approach using the code PTOLEMY. The full lines represent quasielastic cross sections defined as the sum of the elastic (dash-dotted) and of all inelastic cross sections. With a dotted line we reported also the Optical Model elastic angular distributions.

Figure 9

Total angle and Q-value integrated cross sections for the transfer channels at $E_{\mathrm{lab}}\hspace{1em}=\hspace{1em}249\hspace{1em}$ Points and histograms are the experimental and theoretical values, respectively. The calculations shown include single and pair nucleon transfer modes and evaporation effects.