A. Bobyk

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

Abstract 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 48 Ca 28 → 22 48 Ti 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.

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

Abstract Two-neutrino double-beta decay rates of 46 20 Ca 26 , 48 20 Ca 28 , 76 32 Ge 44 and 82 34 Se 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.

Two-vacua RPA and the two-neutrino double-beta decay

Abstract A new method “two-vacua random-phase approximation” (TVRPA) for the description of the two-neutrino nuclear double-beta decay is developed. The nuclear wave functions of the intermediate odd-odd nucleus are constructed as linear combinations of proton-particle neutron-hole excitations from the ground state of the initial even-even ( N , Z ) nucleus and, at the same time, as neutron-particle proton-hole excitations from the ground state of the final ( N − 2, Z + 2) nucleus. The Ritz variational principle is used to obtain RPA-like equations. The ground state in the initial and final nucleus is approximated with HFB wave functions including proton-neutron pairing. A projection on numbers of protons and neutrons is performed additionally on the wave functions in both nuclei to restore the exact number of particles, broken by the quasi-particle transformation. The method is applied, as a preliminary test, to the 2ν double-beta decay in 20 48 Ca 28 . More realistic B (GT − ) and B (GT + ) Gamow-Teller strength distributions than QRPA and PQRPA are obtained. No dependence is found on the particle-particle strength parameter g pp , renormalizing Brueckner reaction matrix elements of the Bonn potential.

Two vacua particle number projected random phase approximation

Abstract A new Two Vacua Particle Number Projected Random Phase Approximation (TVRPA) method for nuclear structure calculations is presented. In the framework of this method excited states of the odd-odd nucleus (A,Z+1) are given as configuration mixing of the particle-hole excitations from the ground states of two even-even nuclei, (A,Z) and (A,Z+2). TVRPA has been applied for the study of the two neutrino mode of the nuclear double beta decay of 48 Ca.

Pauli principle and pion distortion in the p-wave pionic double charge exchange reaction

We propose an approach which takes the Pauli principle and pion distortion into account to investigate the p-wave absorption/emission mechanism of the double charge exchange reaction. The ground state to ground-state processes and are discussed in the new approach. Excitation functions with a maximum energy distribution at have been obtained. The calculated differential cross sections at with and their ratio agree well with experimental data and depend only slightly on the particle-particle interaction parameter . Results indicate that the Pauli principle lowers the cross section and stabilizes its dependence on evidently while pion distortion reduces the cross section in the energy region above the resonance.

Distortion of the pion wavefunction and the DCX reaction

Effects of the distortion of the pion wavefunction in the pionic double charge exchange on are studied in the framework of the pion - nucleus optical potential and in the proton - neutron quasiparticle random phase approximation. The agreement of the calculated p-wave cross section with existing experimental data is improved with respect to the plane wavefunction results. The resonant behaviour of the cross section at 50 MeV is analysed.