Elastic, inelastic, and one-nucleon transfer processes in ${}^{48}\mathrm{Ca}+{}^{64}\mathrm{Ni}$

Elastic, inelastic, and one-nucleon transfer channels in the ${}^{48}$Ca + ${}^{64}$Ni reaction have been measured at $\approx 6$ MeV/nucleon with the PRISMA-CLARA setup, at Legnaro National Laboratory, consisting of the coupling of a large solid angle magnetic spectrometer with a germanium array. By trajectory reconstruction the reaction products have been fully identified in mass, nuclear charge, and kinetic energy, while coincident $\gamma$ spectra of binary partners have been constructed after Doppler correction. Absolute differential cross sections have been extracted for the inelastic excitation and one-nucleon transfer, also for specific excited states. The data are in good agreement with semiclassical calculations and distorted wave Born approximation predictions. The work outlines an experimental method which can become valuable to extract structural information from heavy-ion reaction studies.

Figure 1

Top: $\Delta E$-$E$ spectrum of the reaction ${}^{48}$Ca $+$ ${}^{64}$Ni, as measured by the ionization chamber of PRISMA. The most intense distribution is associated to $Z=20$. The diagonal line is a trivial effect due to detector thresholds. Bottom: $E$ versus $\rho v$ spectrum showing the atomic charge state distribution for $Z=20$. The distribution is peaked at $q={18}^{+}$, with less than 7$\%$ intensity going into $q={16}^{+}$ and ${20}^{+}$ (cf. Ref. [16]).

Figure 2

Mass spectra of the most intense isotopic chains produced in the ${}^{48}$Ca $+$ ${}^{64}$Ni experiment, plotted as function of the number of transferred neutrons ($\Delta N$).

Figure 3

Top: Ratio between the elastic cross section ${\sigma }_{el}$ and the Rutherford cross section ${\sigma }_{\mathrm{Ruth}}$. Full dots represent the experimental values normalized at ${\theta }_{\mathrm{lab}}$ $=$ ${17}^{\circ }$, solid and thin lines are the theoretical calculation by the grazing model [11] and by the code ptolemy [12], respectively. Bottom: TKEL spectra for ${}^{48}$Ca ions at the indicated angles. The black spectra are obtained with the only request of a ${}^{48}$Ca ion detected in PRISMA, while the red ones are constructed with the additional request of a $\gamma$ ray in coincidence in the Ge array. The shaded histograms are the difference spectra.

Figure 4

(a) and (b) Correlation matrices $E_{\gamma }$ versus TKEL for ${}^{48}$Ca and ${}^{64}$Ni, integrated over the entire angular range of PRISMA. Projection of the $E_{\gamma }$ axis are shown in (c) and (d). Contaminant lines from the partner nucleus are marked by stars. TKEL spectra gated by specific $\gamma$ transitions of ${}^{48}$Ca and ${}^{64}$Ni are shown in (e) and (f), respectively. The blue histograms are in coincidence with the $2^{+}\to 0^{+}$ transitions, the filled red ones with the feeding transitions. The spectra are background subtracted by setting narrow gates in the 2D matrices, beside the $\gamma$ peaks. The shaded histograms are the difference spectra between the $2^{+}\to 0^{+}$ and the corresponding feeding distributions.

Figure 5

Angular distributions of the $2^{+}$ states of ${}^{48}$Ca (top panel) and ${}^{64}$Ni (bottom panel). Empty (full) symbols refer to the analysis on TKEL ($\gamma$) spectra. The solid lines represents the theoretical values obtained by DWBA calculations with the code ptolemy [12], with parameters given in the text.

Figure 6

Angular distributions for the $\pm 1n$ and $\pm 1p$ transfer channels. The experimental data are shown by symbols while the solid lines give the theoretical predictions from the semiclassical model grazing [11].

Figure 7

(a) Correlation matrix $E_{\gamma }$versus TKEL for ${}^{49}$Ca, integrated over the entire angular range of PRISMA. The projection on the $E_{\gamma }$ axis is shown in (b). The energy of the strongest $\gamma$ transitions of ${}^{49}$Ca are indicated by labels, while contaminant lines from the partner nucleus are marked by stars. (c) gives the TKEL spectra measured by PRISMA (black histogram) and with the requirement of a $\gamma$ coincidence in the Ge array (red curve). The difference spectrum is shown by the shaded distribution, with superposed the Gaussian fit of the main component (with centroid and FWHM equal to 4.3 and 2.5 MeV). (d) and (e) give the TKEL spectra gated by the 2023 and 3991 keV $\gamma$ transitions of ${}^{49}$Ca, with the corresponding Gaussian fit (red line).

Figure 8

Angular distributions of transfer reactions leading to the population of ${}^{49}$Ca ions close to the ground state (a) and to the excited states at 2023 and 3991 keV (b) and (c). The experimental data are given by symbols, theoretical DWBA predictions by red lines. The calculations are obtained by summing the components given by dotted lines, corresponding to the excitation of the partner nucleus ${}^{63}$Ni to states within 2 MeV of excitation energy. In (a) the thin solid, blue line corresponds to the transfer cross section with ${}^{63}$Ni in the ground state.

Figure 9

Single particle level scheme of the neutron states for ${}^{48}$Ca and ${}^{64}$Ni. The yellow areas correspond to the occupied levels below the Fermi surface, which in the case of ${}^{64}$Ni is diffused due to the superfluidity of the nucleus.