We review several experimental and theoretical advances that emphasize common aspects of the study of spin-singlet, T = 1, and spin-triplet, T = 0, pairing correlations in nuclei. We first discuss various empirical evidence of the special role played by the T = 1 pairing interaction. In particular, we show the peculiar features of the nuclear pairing interaction in the low-density regime, and possible outcomes such as the BCS–BEC crossover in nuclear matter and, in an analogous way, in loosely bound nuclei. We then move to the competition between T = 1 and T = 0 pairing correlations. The effect of such competition on the low-lying spectra is studied in N = Z odd-odd nuclei by using a three-body model; in this case, it is shown that the inversion of the and states near the ground state, and the strong magnetic dipole transitions between them, can be considered as a clear manifestation of strong T = 0 pairing correlations in these nuclei. The effect of T = 0 pairing correlations is also quite evident if one studies charge-changing transitions. The Gamow–Teller (GT) states in nuclei are studied here by using self-consistent Hartree–Fock–Bogoliubov (HFB) plus quasiparticle random-phase approximation calculations in which the T = 0 pairing interaction is taken into account. Strong GT states are found, near the ground state of daughter nuclei; these are compared with available experimental data from charge-exchange reactions, and such comparison can pinpoint the value of the strength of the T = 0 interaction. Pair transfer reactions are eventually discussed. While two-neutron transfer has long been proposed as a tool to measure the T = 1 superfluidity in the nuclear ground states, the study of deuteron transfer is still in its infancy, despite its potential interest for revealing effects coming from both T = 1 and T = 0 interactions. We also point out that the reaction mechanism may mask the strong pair transfer amplitudes predicted by the HFB calculations, because of the complexity arising from simultaneous and sequential pair transfer processes.

High-resolution study of Gamow-Teller excitations in thê {42}Ca(^{3}He,t)^{42}Sc reaction and the observation of a "low-energy super-Gamow-Teller state"Phys. Rev. C 91, 064316

We performed self-consistent Hartree-Fock plus random-phase approximation (HF+RPA) calculations for charge-exchange 1 + states in 90 Zr and 208 Pb by using Skyrme interactions with tensor terms. We employed a parameter set in which the tensor terms are added to the SGII interaction. It is pointed out that Gamow-Teller (GT) states can couple strongly with the spin-quadrupole (SQ) 1 + states in the high-energy region above E x = 30 MeV due to the tensor interactions. As a result of this coupling, more than 10% of the GT strength is shifted to the energy region above 30 MeV, and the main GT peak is moved 2 MeV downward. At the same time, the main SQ 1 + peak is moved upward by more than 10 MeV due to the tensor correlations. Schematic separable interactions are proposed to elucidate the quenching mechanism induced by the tensor interaction on the GT state.

The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree-Fock plus Random Phase Approximation (HF+RPA) model. The Gamow-Teller (GT) strength function of 90 Zr and 208 Pb are calculated with and without the tensor terms. The main peaks are moved downwards by about 2 MeV when including the tensor contribution. About 10% of the non-energy weighted sum rule is shifted to the excitation energy region above 30 MeV by the RPA tensor correlations. The contribution of the tensor terms to the energy weighted sum rule is given analytically, and compared to the outcome of RPA.

The Gamow-Teller (GT) strength distributions and isobaric analog resonance (IAR) states of several N = Z + 2 nuclei with mass number A = 42-58 are studied by using a self-consistent Skyrme Hartree-Fock-Bogoliubov method plus quasiparticle random phase approximation (HFB+QRPA) formalism. The isoscalar spin-triplet pairing interaction is included in QRPA on top of the isovector spin-singlet one in the HFB method. It is found that the isoscalar pairing correlations mix largely the (νj > → πj < ) configurations into the low-energy states, and this mixing plays an important role in the formation and in the collectivity of these low-energy states. Furthermore, the observed excitation energy of the low-energy GT state with respect to the IAR can be well reproduced when the strength of isoscalar pairing is about 1.0-1.05 times that of the isovector pairing, irrespective of the adopted Skyrme interactions. In N = Z + 2 nuclei in the middle of the pf -shell, a mutual cooperative effect of isoscalar pairing and tensor interaction is found; namely, the tensor force reduces the spin-orbit splittings and enhances the effect of the isoscalar pairing.

Gamow-Teller (GT) transitions in atomic nuclei are sensitive to both nuclear shell structure and effective residual interactions. The nuclear GT excitations were studied for the mass number A ¼ 42, 46, 50, and 54 "f-shell" nuclei in ( 3 He, t) charge-exchange reactions. In the 42 Ca → 42 Sc reaction, most of the GT strength is concentrated in the lowest excited state at 0.6 MeV, suggesting the existence of a low-energy GT phonon excitation. As A increases, a high-energy GT phonon excitation develops in the 6-11 MeV region. In the 54 Fe → 54 Co reaction, the high-energy GT phonon excitation mainly carries the GT strength. The existence of these two GT phonon excitations are attributed to the 2 fermionic degrees of freedom in nuclei.

Gamow-Teller (GT) and charge-exchange spin-dipole (SD) excitation energies in 90 Zr and 208 Pb are systematically studied to determine the appropriate magnitude of the tensor terms of the Skyrme interactions. We have found that the centroid energies of GT and SD excitations are sensitive to the adopted strengths of the triplet-even and triplet-odd tensor interactions. Especially, the 1 − SD state plays a crucial role in constraining the triplet-even part while the triplet-odd part is related rather to the GT peaks. Among the 36 TI J parameter sets that include nonperturbatively the tensor terms, the four sets, T21, T32, T43, and T54, give reasonable results for the centroid energies in comparison with the experimental data. The sign and magnitude of the tensor terms are also discussed when these terms are added to the existing Skyrme interactions SGII and SLy5. The triplet-even strength can be constrained in a narrow range by using the available experimental data while further empirical data are needed to set a constraint on the triplet-odd term.

This corrects the article DOI: 10.1103/PhysRevLett.110.122501.