Two-neutron transfer analysis of the ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}$ reaction

Recently a quantitative description of the two-neutron transfer reaction ${}^{12}\mathrm{C}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{14}\mathrm{C}$ was performed and the measured cross sections were successfully reproduced [M. Cavallaro et al., Phys. Rev. C 88, 054601 (2013)]. This task was accomplished by combining nuclear structure calculations of spectroscopic amplitudes and a full quantum description of the reaction mechanism. Verification of such a theoretical approach to other heavy nuclear systems is mandatory in order to use (${}^{18}\mathrm{O},{}^{16}\mathrm{O}$) reactions to assess pair configurations in nuclear states. In this work we apply this methodology to the ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}$ reaction at 84 MeV. Experimental angular distributions for the two-neutron transfer to the ground state and $2_1^{+}$ state of ${}^{18}\mathrm{O}$ were obtained using the MAGNEX spectrometer at INFN-LNS. The roles of one- and two-step processes are analyzed under the exact finite range coupled reaction channel and the second order distorted wave Born approximation. We conclude that the one-step transfer mechanism is dominant in this system.

Figure 1

Energy spectra for the angular range between $5.5^{\circ }$ and $6.5^{\circ }$ in the laboratory frame. Peaks are numerically labeled as reported in Table 1.

Figure 2

Estimation of the effect of elastic cross section by simple macroscopic calculation of (a) the final ${}^{16}\mathrm{O}$ and (b) the complementary ${}^{18}\mathrm{O}$ channels cross sections.

Figure 3

Coupling for (a) direct CRC and (b) two-step DWBA transfers.

Figure 4

Comparison of angular distributions in the cluster model in the case of the spin antiparallel [ClustA(1)] and parallel [ClustP(1)] transfer with the experimental data for the ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}_{\text{gs}}$ (bottom) and ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}_{2^{+}}$ (top) channels. The value of the spectroscopic amplitude for the all overlaps is 1. The ClustP(1) curve for the ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}_{2^{+}}$ channel was arbitrarily multiplied by 10 in order to guide the eye.

Figure 5

Comparison of angular distributions in the cluster model in the case of the spin antiparallel [ClustA($-0.32$)] and parallel [ClustP($-0.32$)] transfer with the experimental data for the ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}_{\text{gs}}$ (bottom) and ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}_{2^{+}}$ (top) channels. The value of the spectroscopic amplitude for the $2^{+}$ overlaps is $-0.32$. For a better visibility the ClustP($-0.32$) calculation for the transition to the ${}^{18}\mathrm{O}_{2+}$ state is multiplied by 100.

Figure 6

Comparison of angular distributions in independent coordinate scheme and two-step DWBA transfer calculations with the experimental data for the ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}_{\text{gs}}$ (bottom) and ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}_{2^{+}}$ (top) channels. For a better visibility the two-step DWBA curve for transition to the ${}^{18}\mathrm{O}_{2+}$ state is shifted upward 100 times.

Figure 7

Comparison of the experimental angular distributions with the coherent sum of the independent coordinate scheme and two-step DWBA calculations for the reaction ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}_{\text{g.s.}}$ at 84 MeV. The spectroscopic amplitudes of Tables 1 and 2 are used.

Figure 8

Comparison of the angular distributions in the independent coordinate scheme and two-step DWBA transfer calculations with the spectroscopic amplitudes obtained by ZBM interaction and those obtained by psdmod interaction for the ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}_{\text{g.s.}}$ (bottom) and ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}_{2^{+}}$ (top) channels. The two-step DWBA curve, derived using the ZBM spectroscopic amplitudes, for the ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}_{2^{+}}$ channel was arbitrarily multiplied by 100 in order to guide the eye.

Figure 9

Comparison of the experimental angular distributions with the coherent sum of independent coordinates and the two-step DWBA calculations for the reaction ${}^{16}\mathrm{O}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{18}\mathrm{O}_{\text{gs}}$ at 84 MeV. The spectroscopic amplitudes of Tables 1 and 2, 3, and 4 are used.