Investigating nuclear pairing correlations via microscopic two-particle transfer reactions: The cases of ${}^{112}\mathrm{Sn}$, ${}^{32}\mathrm{Mg}$, and ${}^{68}\mathrm{Ni}$

We investigate the selectivity of different two-particle transfer reactions [($t,p$), (${}^{18}\mathrm{O}$,${}^{16}\mathrm{O}$), and (${}^{14}\mathrm{C}$,${}^{12}\mathrm{C}$)] with respect to detailed microscopic configuration in initial and final target states. In particular the relative magnitude of the cross sections associated with processes in which the pair is transferred in pure single-particle orbitals depends on the specific reaction and its kinematical conditions. As a consequence also enhancement factors due to pairing correlations may differ in different reactions, and the extraction of information on the correlated wave functions may imply the blending of data from different projectiles. As test cases we have chosen ${}^{112}\mathrm{Sn}$ as an example of superfluid nuclei, and ${}^{32}\mathrm{Mg}$ and ${}^{68}\mathrm{Ni}$ to study shell evolution for exotic nuclei.

Figure 1

Angular distributions obtained in DWBA for the ${}^{110}\mathrm{Sn}$($t,p$)${}^{112}\mathrm{Sn}$ reaction at $E=15.7$ MeV. Each curve corresponds to the transfer of the two neutrons to the single-particle orbitals indicated in the inset, either pure configurations (dashed lines) or the mixed configuration (solid line) according to the BCS calculation. We compare with the experimental data from the reverse reaction measured in Ref. [23]. Optical parameters are taken from [24, 25]. The normalization factor in this case is 4200.

Figure 2

Cross sections for two-neutron transfer reactions to various configurations in ${}^{112}\mathrm{Sn}$ (horizontal axis) starting from several configurations in different projectiles as indicated in the legend.

Figure 3

Angular distributions obtained in DWBA for the ${}^{30}\mathrm{Mg}$($t,p$)${}^{32}\mathrm{Mg}$ reaction at $E=5.4$ MeV. Each curve corresponds to the transfer of the two neutrons to the single-particle orbital indicated in the legend. We compare with the experimental data from [29]. Optical parameters are taken from [24]. The normalization factor in this case is 1000.

Figure 4

Ratio of cross sections obtained in DWBA for the excited and ground $0^{+}$ states in the ${}^{30}\mathrm{Mg}$($t,p$)${}^{32}\mathrm{Mg}$ reaction at $E=5.4$ MeV, as a function of the mixing probability parameter ${\alpha }^2$. The different curves correspond to different choices of the structure of the addition pair, with the removal pair assumed to be pure ${\left(d_{3/2}\right)}^2$. The horizontal line corresponds to the experimental value [29]. Optical parameters are taken from [24]. This figure is consistent with Fig. 1 in [26] plotted in terms of ${\beta }^2=1-{\alpha }^2$.

Figure 5

Ratio of cross sections obtained for the excited and ground $0^{+}$ states in the reaction ${}^{30}\mathrm{Mg}$${(}^{18}$O,${}^{16}\mathrm{O}$)${}^{32}\mathrm{Mg}$ at $E=26$ MeV, as a function of the mixing probability parameter ${\alpha }^2$. The different curves correspond to different choices of the structure of the addition and removal pairs. Ion-ion potentials are taken from the Akyüz-Winther parametrization [5, 30].

Figure 6

Angular distributions obtained in DWBA for the ${}^{66}\mathrm{Ni}$($t,p$)${}^{68}\mathrm{Ni}$ reaction at $E=7.8$ MeV. Each curve corresponds to the transfer of the two neutrons to the single-particle orbital indicated in the legend. Optical parameters are taken from [25, 32].

Figure 7

Ratio of cross sections obtained in DWBA for the excited and ground $0^{+}$ states in the ${}^{66}\mathrm{Ni}$($t,p$)${}^{68}\mathrm{Ni}$ reaction at $E=7.8$ MeV, as a function of the mixing probability parameter ${\alpha }^2$. The horizontal line corresponds to the experimental value [31]. Optical parameters are taken from [25, 32].

Figure 8

Ratio of cross sections obtained for the excited and ground $0^{+}$ states in the reaction ${}^{66}\mathrm{Ni}$${(}^{14}$C,${}^{12}\mathrm{C}$)${}^{68}\mathrm{Ni}$ at $E=32.4$ MeV, as a function of the mixing probability parameter ${\alpha }^2$. Ion-ion potentials are taken from the Akyüz-Winther parametrization [5, 30]. The colored circle covers the region that approximately corresponds to the ${\alpha }^2$ value extracted from the ($t$,$p$) reaction, Fig. 7.