Np Pairing Correlations Research Articles

Neutron-Proton, Neutron-Neutron, Proton-Proton QRPA for the Gamow-Teller and the M1 Spin Transitions of N ≃ Z Nuclei in the s — d Shell

We study the Gamow-Teller (GT) and the M1 spin transitions of the s — d shell nuclei $^{24}$Mg, $^{26}$Mg, $^{28}$Si, $^{32}$S, and $^{36}$Ar by using a quasiparticle random phase approximation (QRPA) scheme that comprises neutron-proton (np), neutron-neutron (nn) and proton-proton (pp) QRPA owing to the inclusion of the np pairing, as well as nn and pp pairing correlations. At present, we work in spherical symmetry under the assumption that the deformations of the nuclei considered in this work are small enough to neglect, as was customary in past applications. For the GT transition, as well as single and double beta decays, the neutron-proton QRPA (np QRPA) is usually employed. For the M1 spin transition, the pp and nn QRPA is needed due to its neutral current property. The np pairing correlations couple the np QRPA to the nn and pp QRPA. Therefore, the coupled np + nn + pp QRPA enables us to investigate simultaneously the GT and the M1 spin transitions. In particular, in this work, detailed analyses of particle-particle and particle-hole interactions at the QRPA stage are performed for the GT and the M1 spin transitions of the well-known s — d shell N ≃ Z nuclei, and the results are compared to available data. The roles of the np pairing correlations are also discussed for those transitions.

Exact solution of mean-field plus an extended T = 1 nuclear pairing Hamiltonian in the seniority-zero symmetric subspace

An extended pairing Hamiltonian that describes multi-pair interactions among isospin T=1 and angular momentum J=0 neutron–neutron, proton–proton, and neutron–proton pairs in a spherical mean field, such as the spherical shell model, is proposed based on the standard T=1 pairing formalism. The advantage of the model lies in the fact that numerical solutions within the seniority-zero symmetric subspace can be obtained more easily and with less computational time than those calculated from the mean-field plus standard T=1 pairing model. Thus, large-scale calculations within the seniority-zero symmetric subspace of the model is feasible. As an example of the application, the average neutron–proton interaction in even–even N∼Z nuclei that can be suitably described in the f5pg9 shell is estimated in the present model, with a focus on the role of np-pairing correlations.

NUMBER-PROJECTED ELECTRIC QUADRUPOLE MOMENTS OF EVEN–EVEN PROTON-RICH NUCLEI IN THE ISOVECTOR PAIRING CASE

An expression of the number-projected electric quadrupole moment Q2 has been established in the isovector pairing case using the SBCS discrete projection before variation method. It has been verified that this expression reduces to the pairing between like-particles one at the limit when the np pairing gap parameter Δ np goes to zero. The convergence of the projection method has been numerically tested and a fast convergence has been observed. The electric quadrupole moment has been numerically calculated for some even–even proton-rich nuclei such as 16 ≤ Z ≤ 56 and 0 ≤ (N-Z) ≤ 4. The single-particle energies and eigen-states used are those of a Woods–Saxon mean-field. The np pairing effect on Q2 has been studied either before and after the projection; it seems that it is somewhat small since the relative discrepancies do not exceed 12%. Moreover, the np pairing effect is roughly the same in both situations. However, it has been shown that this effect diminishes with increasing values of (N-Z). The projection effect on Q2 has also been studied when including, or not, the np pairing correlations. It appears that this effect is slightly less important in the np pairing case than when only the pairing between like-particles is considered.

Np pairing correlations in low-density region of nuclear matter

In the framework of Green’s function formalism at finite temperatures, superfluidity of nuclear matter with np pairing correlations is studied. It is shown that, at low densities, equations for the energy gap in the spectrum of quasiparticles and chemical potentials of protons and neutrons allow solutions with negative chemical potential, which corresponds to appearance of Bose-Einstein condensation of deuterons in the low-density region of nuclear matter. In this region, np pairing correlations survive even for large isospin asymmetry. Interaction between nucleons is described by the effective zero range force, developed to reproduce the energy gap in the isospin singlet pairing channel, calculated with the use of the Paris N N potential. The obtained results may be of importance for description of thermal properties of outer low-density regions of neutron stars.

Pairing effects in low density domain of nuclear matter

Using equations, governing np pairing correlations in S=1, T=0 pairing channel (PRC 63 (2001) 021304(R)), it is shown that at low densities equations for the energy gap in the spectrum of quasiparticles and chemical potentials of protons and neutrons allow solutions with negative chemical potential. This corresponds to appearance of Bose–Einstein condensate (BEC) of deuterons in low density region of nuclear matter.

Alignment delays in the N = Z nuclei (72)Kr, (76)Sr, and (80)Zr.

The ground state rotational bands of the N = Z nuclei (72)Kr, (76)Sr, and (80)Zr have been extended into the angular momentum region where rotation alignment of particles is normally expected. By measuring the moments of inertia of these bands we have observed a consistent increase in the rotational frequency required to start pair breaking, when compared to neighboring nuclei. (72)Kr shows the most marked effect. It has been widely suggested that these "delayed alignments" arise from np-pairing correlations. However, alignment frequencies are very sensitive to shape degrees of freedom and normal pairing, so the new experimental observations are still open to interpretation.

Competition between T = 0 and T = 1 pairing in proton-rich nuclei

A cranked mean-field model with two-body T = 1 and T = 0 pairing interactions is presented. Approximate projection onto good particle-number is enforced via an extended Lipkin-Nogami scheme. Our calculations suggest the simultaneous presence of both T = 0 and T = 1 pairing modes in N = Z nuclei. The transitions between different pairing phases are discussed as a function of neutron/proton excess, T z , and rotational frequency, ħω. The additional binding energy due to the T = 0 np-pairing correlations, is suggested as a possible microscopic explanation of the Wigner energy term in even-even nuclei.

Total Gamow-Teller strength, ground-state correlations and sum rules in QRPA with neutron-proton pairing

Abstract The sum of the Gamow-Teller (GT) strength in 1p0f shell nuclei is investigated by the Quasiparticle Random Phase Approximation (QRPA), where BCS and RPA ground-state correlations are included with proton-proton and neutron-neutron but in addition also with neutron-proton (np) pairing correlations. Two sums of GT strength with and without closure for the intermediate excited states are derived including different approaches for the ground-state correlations. The sum of the GT strength is compared to the available experimental data and other theoretical calculations. The total GT strength in the usual BCS scheme is reduced by additional neutron-proton (np) pairing correlations. The usual RPA ground-state correlations reduce the total GT strength estimated from the BCS approximation while RPA with np pairing correlations yields an appreciably smaller reduction. Finally, ground-state correlations beyond RPA are also shown to reduce the total GT strength.

Two-neutrino double-beta decay in coupled QRPA with neutron-proton pairing

Two-neutrino double-beta decay rates of 46 20Ca 26, 48 20Ca 28, 76 32Ge 44 and 82 34Se 48 are calculated with inclusion of neutron-proton (np) pairing correlations in describing the ground states of initial and final nuclei. Inclusion of np pairing correlations yields stronger bound nuclei as solutions of the HFB equation. Our results show that even in medium and medium-heavy nuclei, np pairing correlations reduce the Gamow-Teller matrix elements compared to the results without np pairing. Further, the dependence of these matrix elements on the particle-particle strength parameter g pp is reduced remarkably.

Neutron-proton pairing in light nuclei and two-neutrino double-beta decay

We have investigated neutron-proton (np) pairing in light nuclei (2p-lf shell) using a specialized Hartree-Fock-Bogoliubov (HFB) method. For the pairing interaction we used the constant Kisslinger-Sorensen interaction and the realistic G-matrix obtained by solving the Bethe-Goldstone equation with the Bonn one-boson-exchange potential. Our results show that there are at least two minima of the total energy corresponding to two solutions of the HFB equation. The lower solution shows large np pairing. This is confirmed by a recent empirical determination of the np pairing gap, which turns out to be surprisingly large in agreement with our theoretical result. If one renormalizes the Brueckner reaction matrix elements of the Bonn potential by a factor g np multiplying the neutron-proton particle-particle matrix elements to reproduce the experimental np gaps δ np, one obtains large T = 1 np pairing. Preliminary results indicate that the np pairing increases even more if particle-number projection is included. These effects are expected to affect strongly the double-beta decay. The 2 v double-beta decay in 20 48Ca 28 → 22 48Ti 26 is calculated. The Gamow-Teller matrix elements are reduced remarkably by the large np pairing compared to the results without np pairing. The sensitivity of the 2 tv double-beta decay transition on the particle-particle force strength parameter g pp is also reduced compared with the results without np pairing correlations.