Single and pair neutron transfers at sub-barrier energies

Multinucleon transfer cross sections in the ${}^{96}$Zr+${}^{40}$Ca system have been measured, in inverse kinematics, at bombarding energies ranging from the Coulomb barrier to $\sim$25$\%$ below. Targetlike recoils have been identified in A, Z and velocity with the large solid angle magnetic spectrometer PRISMA. The experimental data for one- and two-neutron transfer channels have been compared with semiclassical microscopic calculations. For the two-neutron transfer channels the relevance of the transitions to the ground state and to the 0${}^{+}$ excited states of ${}^{42}$Ca are discussed by employing, for the reaction mechanism, the successive approximation. It is found that the transition to the 0${}^{+}$ state at $\sim$6 MeV, whose wave function is dominated by the two neutrons in the $2p_{3/2}$ shell, is much larger than the ground state one. The comparison with the inclusive data reveals that transitions to states with high multipolarity and non-natural parity are important. This suggests that more complex two-particle correlations have to be incorporated in the treatment of the transfer process.

Figure 1

Velocity ($\beta =v/c$) vs in-plane scattering angle (${\theta }_{\mathrm{lab}}$) for the reaction ${}^{96}$Zr+${}^{40}$Ca at $E_{\mathrm{lab}}=330$ MeV. The magnetic fields of the spectrometer were set to bring the Ca ions with maximum yield near the center of the focal plane area. The events at large $\beta$ correspond to Ca-like recoils, and those at lower $\beta$ to Zr-like ions scattered from Ca, as well as from other elements (see text for details).

Figure 2

$\Delta E-E$ matrix obtained at the indicated bombarding energy and with the spectrometer at ${\theta }_{\mathrm{lab}}$ = 20${}^{\circ }$. The most intense spot corresponds to $Z=20$ (Ca isotopes), the lower ones to $Z=19$ and $Z=18$, respectively. The tail of events corresponding to Zr-like ions entering into the spectrometer are also visible.

Figure 3

Mass distributions for pure neutron transfer channels obtained in the reaction ${}^{96}$Zr+${}^{40}$Ca at the indicated bombarding energies of ${}^{96}$Zr. Ca-like recoils have been detected with the spectrometer at ${\theta }_{\mathrm{lab}}$ = 20${}^{\circ }$. The obtained resolution is $\Delta A/A$ $\sim$ 1/150, which allows clear separation of the different isotopes.

Figure 4

Experimental TKEL distributions for the elastic(+inelastic) and $+1n$ and $+2n$ transfer channels obtained in the reaction ${}^{96}$Zr+${}^{40}$Ca at the indicated bombarding energies. The vertical dotted lines represent the ground-state Q values.

Figure 5

Transfer probabilities as a function of the distance of closest approach for neutron transfer channels. Points are the experimental data: $+1n$ (full circles), $+2n$ (empty circles), $+3n$ (full triangles), and $+4n$ (empty triangles). For the $+1n$ channel we indicated in black the data obtained from the nominal bombarding energy. The energies, in the center of the target, are 329.2, 315.9, 298.4, 287.7, 276.1, and 262.6 MeV, corresponding to the distances of closest approach 12.28, 12.80, 13.55, 14.05, 14.64, and 15.40 fm. With red and cyan colors we indicated the data obtained with one and two degraders, respectively. Quoted errors are statistical only, errors on $D$, reflecting energy indetermination, are $⩽$$1\%$. The full line is a fit according to the expression $P_{1n}=\exp (13.95-1.25D)$. In the fit we excluded the points at the highest measured energies where absorption starts to be a significant fraction of the elastic channel. The dashed lines correspond to the shown equations.

Figure 6

Neutron single-particle levels in ${}^{96}$Zr and ${}^{40}$Ca.

Figure 7

Theoretical transfer probabilities for one- and two-particle transfer (lines) in comparison with the experimental data (points). The full line represents the inclusive transfer probability for one-neutron transfer, the dotted line the ground-ground state transition for the two-neutron transfer, and the dashed line the transition to the first 0${}^{+}$ excited state at 5.76 MeV in ${}^{42}$Ca (see text).

Figure 8

Level schemes and observed intensities for the ${}^{42}$Ca and ${}^{94}$Zr nuclei reconstructed from the measured $\gamma$ transitions in ${}^{40}$Ca+${}^{96}$Zr at E${}_{\mathrm{lab}}$ = 152 MeV [20]. The experiment has been performed with the PRISMA and CLARA [30] setup. The $\gamma$-ray spectra of binary partners have been obtained after Doppler correction. The correction for the projectilelike ions is based on the knowledge of their velocity vector measured with the spectrometer. The correction of the (undetected) targetlike ions is based on the assumption of binary kinematics and the corresponding calculated velocity. The intensities (reported in the figure as normalized counts, bold numbers) have been obtained taking into account the branching ratios [31] and the efficiency of the CLARA $\gamma$ array.