Analysis of two-proton transfer in the ${}^{40}\mathrm{Ca}({}^{18}\mathrm{O},{}^{20}\mathrm{Ne}){}^{38}\mathrm{Ar}$ reaction at 270 MeV incident energy

Two-nucleon transfer reactions are essential tools to investigate specific features of the nuclear structure, such as the correlation among valence particles in the transfer process. Besides, transfer reactions may be an important channel to take into account in charge-exchange processes since they can represent a competing contribution to the final cross section. The two-proton pickup transfer reaction ${}^{40}\mathrm{Ca}({}^{18}\mathrm{O},{}^{20}\mathrm{Ne}){}^{38}\mathrm{Ar}$ has been measured at 270 MeV, and the angular distributions for transitions to different excited states extracted. This paper shows the analysis of the data performed by finite-range coupled reaction channel and coupled-channel Born approximation methods. Extensive shell-model calculations are performed to derive the one- and two-proton spectroscopic amplitudes for the projectile and target overlaps. The role of the simultaneous and sequential two-proton transfer mechanisms to populate the measured final states or groups of states, mainly characterized by a high collectivity, is also discussed.

Figure 1

Excitation energy spectrum for the ${}^{40}\mathrm{Ca}({}^{18}\mathrm{O},{}^{20}\mathrm{Ne}){}^{38}\mathrm{Ar}$ reaction at 270 MeV in the angular range of $0^{\circ }<{\theta }_{\mathrm{lab}}<+8^{\circ }$. In the inset a zoomed view of the ground-state region is shown.

Figure 2

Comparison between the theoretical and the experimental two-proton transfer angular distribution corresponding to (a) the ${}^{20}\mathrm{Ne}_{\mathrm{g}.\mathrm{s}.}\left(0^{+}\right)+{}^{38}\mathrm{Ar}_{\mathrm{g}.\mathrm{s}.}\left(0^{+}\right)$ channel. (b) Unresolved excited states concerning the second peak in Fig. 1. In both figures the contribution due to the simultaneous (IC), sequential (Seq) transfer, the coherent (Coh), and incoherent (Incoh) sum of the two mechanisms are shown (see the text). In (b) the sum of the different channels contributing to the cross section is plotted.

Figure 3

Comparison between the theoretical and the experimental two-proton transfer angular distribution. (a) The angular distribution related to the contribution of the unresolved excited states of the third peak in Fig. 1. (b) Contribution of the unresolved excited states of the fourth peak in Fig. 1 is shown. The contribution due to the simultaneous (IC), sequential (Seq) transfer, the coherent (Coh), and incoherent (Incoh) sums of the two mechanisms are shown (see the text).

Figure 4

Coordinates considered in the two-nucleon transfer reaction. The upper path corresponds to the direct two-proton transfer, and the lower path is related to the sequential two-proton transfer passing through the intermediate partition.

Figure 5

Coupling scheme considered in the two-proton direct transfer calculations using the independent coordinates scheme.

Figure 6

Coupling scheme considered in the two-proton sequential transfer calculations.

Figure 7

Comparison between the convoluted theoretical and the experimental two-proton transfer angular distribution for the transition to the ${}^{20}\mathrm{Ne}_{\mathrm{g}.\mathrm{s}.}\left(0^{+}\right)+{}^{38}\mathrm{Ar}_{\mathrm{g}.\mathrm{s}.}\left(0^{+}\right)$ channel. The dashed red curve corresponds to the results in which the couplings between the ground states and the inelastic states of the ${}^{20}\mathrm{Ne}$ are switched off in the final partition, whereas in the full green curve these couplings are included.