Particle-particle Matrix Elements Research Articles

Global microscopic calculations of ground-state spins and parities for odd-mass nuclei

Systematic calculations of ground-state spins and parities of odd-mass nuclei have been performed within the Hartree-Fock-BCS (HFBCS) approach and the finite-range droplet model for nuclei for which experimental data are available. The unpaired nucleon has been treated perturbatively, and axial and left-right reflection symmetries have been assumed. As for the HFBCS approach, three different Skyrme forces have been used in the particle-hole channel, whereas the particle-particle matrix elements have been approximated by a seniority force. The calculations have been done for the 621 nuclei for which the Nubase 2003 data set gives assignments of spins and parities with strong arguments. The agreement of both spin and parity in the self-consistent model reaches about 80% for spherical nuclei, and about 40% for well-deformed nuclei regardless of the Skyrme force used. As for the macroscopic-microscopic approach, the agreement for spherical nuclei is about 90% and about 40% for well-deformed nuclei, with different sets of spherical and deformed nuclei found in each model.

Competition between particle-hole and particle-particle correlations in forbidden electron capture: The case of123Te

The K-electron capture half-life of $^{123}$Te has been recently measured to be $t^K_{exp}=2.4\times 10^{19}$ yr, and constitutes the longest half-life ever measured in a single $\beta$-transition of any nuclear species. We have calculated this second unique forbidden transition within the framework of the proton-neutron quasi-particle random phase approximation, making use of Skyrme-type effective interactions. A strong cancellation effect between particle-hole and particle-particle correlations is found. The model, without any renormalization of the force, provides a lower limit for the K-electron capture half-life of $\sim 10^{17}$ yr, which unambiguously rules out the old experimental values of $10^{13} - 10^{14}$ yr. A few percent increase of the particle-particle matrix elements of the Skyrme interaction allows to reproduce the experimental findings.

Nuclear structure with Dirac phenomenology

With non-relativistic Bonn A G matrix elements, it appears that the spin-orbit interaction in a nucleus is too small. As a consequence the wave functions in the 0 p shell are too close to the LS limit. The introduction of a Dirac nucleon effective mass m ∗ less than the free mass enhances the spin-orbit interaction and affects nuclear structure in a very significant way. For example, the B(M1) in 12C to the J π = 1 1 +, T = 1 state is increased by a factor of 2.5 when m ∗/m is decreased from 1 to 0.67. In the above analyses, large-space shell-model calculations are essential to prevent collapse of 1 + states below the ground state. A superficial analysis suggests that the tensor interaction in the nucleus is too large despite the small percentage of the D-state admixture for Bonn A (about 4.4%). However, there are some complications in the analysis. It is emphasized that in order to see large effects of the Dirac phenomenology in nuclear structure, it is essential to calculate single-particle energies with the same interaction that is used for the particle-particle matrix elements in the open shell. This also holds for the core polarization corrections.

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.

Skyrme-Landau particle-particle interaction and application to 18O and 18F

Patterned after Landau's Fermi-liquid theory of nuclear matter, we develop an extension of the theory for finite nuclei. Since the particle-hole interaction V ph derived from the Skyrme-Landau HF ground state is antisymmetric and the exchange term of the phonon-induced interaction is added to V ph when the renormalization of the HF single-particles due to the particle-phonon coupling is included, the total effective particle-particle interaction is anti-symmetric. We use the newly developed Skyrme-Landau interaction SL1 to evaluate the particle-particle matrix elements in the s-, d-shells. Except for a few cases, the results agree well with those calculated from the G-matrix and those from the empirical study. The spectra of 18O and 18F are predicted which indicate that except for the 5 + state of 18F, the results are similar to those obtained from the Kuo-Brown G-matrix. These results represent great improvement from predictions of the other Skyrme-type interactions which are plagued with either the anti-pairing effect or the lack of anti-symmetry in the particle-particle matrix elements.

91Zr(τ, α) 90Zr and the [formula omitted] matrix elements: Test of an average effective interaction

The 91Zr(τ, α) 90Zr reaction has been studied and members of the ( g 9 2 ) −1 d 5 2 multiplet were identified, yielding the g 9 2 − d 5 2 particle-particle matrix elements in both isospin states. The results are compared with calculations using an interaction that had been deduced from other data.

Method of Correlated Quasiparticles. II.0+Particle-Particle Residual Interactions

The method of correlated quasiparticles is extended to treat the problem of attractive particle-particle matrix elements in the generalized ${0}^{+}$ mode. A computationally convenient approach to the problem is presented. Sample calculations are performed and compared with the results of pairing model calculations. It is concluded that the nonpairing ${0}^{+}$ matrix elements play an important role in determining the ground-state properties of deformed nuclei.