F. Grümmer

Backbending: Coriolis antipairing or rotational alignment?

Abstract A theoretical description of the ground-state bands m even-mass nuclei is given which includes the possibility of Coriolis antipairing (CAP) and rotational alignment (RAL) in the explanation of backbending. The method is based on a combination of Hartree-Fock- Bogoliubov, cranking model and particle number projection and applied to the high ( ≦ 18 h ) and very high ( ≦ 80 h ) spin states of 162 Er. The results indicate that the nucleus behaves according to a combination of CAP and RAL effects. Pairing for all neutron pairs near the Fermi surface is markedly reduced although the two i 13 2 pairs nearest to the Fermi level are somewhat more affected. However the dominant contribution to the total angular momentum for spins greater than 12 ħ comes from one i 13 2 pair, (with large components Ω = 1 2 3 2 5 2 ). For the very high spin states ( 30 h h ) the nucleus becomes triaxial and well defined shape isomers appear.

Neutrinoless ββ decay and a new limit on the right-handed current

Abstract We have calculated the 0νββ and 2νββ decay rates of the transition 76 Ge(0 + 1 ) → 76 Se(0 + 1 ). We took into account a relativistic correction to the nuclear current including weak magnetism. The nuclear two-body transition operator for the 0νββ decay originating from this correction acquires a finite range due to the finite extension of the nucleon and the short-range NN correlations reduce its matrix element only moderately. The contribution from this “second-forbidden” transition plays a dramatic role in the 0νββ decay caused by a specific admixture of a right-handed leptonic current because of the high momentum of the virtual neutrino exchanged between nucleons and systematic cancellations in “allowed” and other “second-forbidden” 0νββ transitions. A new limit on the right-handed current coupling strength |〈 η 〉| −8 was obtained, which is more stringent by an order of magnitude than that obtained recently by the Osaka group.

Complex mean fields and unnatural parity pairing in the Hartree-Fock-Bogoliubov problem with symmetry-projection before the variation☆

Abstract The Hartree-Fock-Bogoliuboy problem with restoration of the broken symmetries before the variation as it has been formulated recently within the VAMPIR and EXCITED VAMPIR approaches is studied in more detail. Special emphasis is put on the implications of various symmetry restrictions imposed on the quasiparticle transformations. It is shown that the use of essentially complex transformations provides a possibility to account for time-odd unnatural parity pairing correlations in the wavefunctions without being forced to give up axial and time-reversal symmetry. It is illustrated that together with parity and neutron-proton mixing the use of such complex mean fields extends the applicability of the VAMPIR and EXCITED VAMPIR approaches to states with arbitrary spin and parity in both doubly even and doubly odd nuclear systems. The corresponding variational equations are explicitly evaluated and the numerical feasibility of their solution is investigated.

Hartree-Fock-Bogoliubov theory with spin and number projection before the variation: An application to 20Ne and 22Ne

Abstract After rederiving the variational equations for the Hartree-Fock-Bogoliubov problem with spin and number projection before the variation a numerical method for their solution in realistic model spaces is presented. This method is then applied to the two nuclei 20 Ne and 22 Ne. Furthermore, on the basis of the obtained spin-dependent mean Hartree-Fock-Bogoliubov fields multi-configuration calculations are performed. The results are compared with those of complete diagonalizations of the effective many-nucleon hamiltonian. Finally, the shortcomings as well as possible extensions and improvements of the method are discussed.

The physical nature of the strange oscillating behaviour of the Yrast-Yrare interaction in the i132 shell

Abstract The oscillating behaviour of the yrast-yrare interaction as a function of the chemical potential found in various calculations using mostly the Hartree-Fock-Bogoliubov cranking approach is reexamined with the help of an exactly solvable angular momentum conserving model. It is shown, that the oscillations of the yrast-yrare coupling can be explained as being due to the mixing of states with different particle numbers inside the valence shell.

Microscopic description of low-lying states in even Ge and Se nuclei

Abstract The Hartree-Fock-Bogoliubov approach with spin and number projection before the variation extended to the description of nonyrast states (EXCITED VAMPIR) is used to describe simultaneously many properties of the 68,70,72,74 Ge and 72,74 Se nuclei. Low-lying spectra, neutron and proton occupation numbers for the spherical-basis orbitals, E0 and E2 transitions, and quadrupole moments are calculated and a fairly good agreement is obtained with experiment. The analysis of the EXCITED VAMPIR mean fields reveals that a strong mixing of prolate and oblate intrinsic quasiparticle determinants is responsible for the complex behaviour of the nuclei in A =70 region.

Microscopic description of odd-mass nuclei in the mass A = 130 region

Abstract We present a systematic study of low- and medium-spin properties of odd-mass nuclei in the mass A = 130 region using a microscopic spin- and number-conserving nuclear structure model with a realistic two-nucleon interaction. In this model the wave functions are approximated by linear combinations of number- and spin-projected one-quasiparticle determinants obtained from a selfconsistent Hartree-Fock-Bogoliubov mean field. The choice of the model space and the renormalization of the two-nucleon force extracted via a G -matrix description from nucleon-nucleon scattering data are discussed in detail. We demonstrate that the model can account for the main systematic trends of odd-mass nuclei in the region considered and is even able to reproduce rather fine details. It can hence be used to predict e.g. even such complicated level sequences as displayed here by the positive-parity neutron and proton excitations. The calculated spectroscopic amplitudes for singlenucleon transfer are compared with experiments and an extensive set of predictions is made. Throughout the paper we discuss the limitations of the presently used projected one-quasiparticle approach.

Beyond symmetry-projected quasi-particle mean fields: A new variational procedure for nuclear structure calculations

Abstract The solution of the Hartree-Fock-Bogoliubov problem with restoration of the broken symmetries before the variation, as it has been formulated within the VAMPIR and EXCITED VAMPIR approaches yields a description of each state of the nucleus by essentially one single symmetry-projected quasi-particle determinant. In the present paper we propose a procedure which allows to go beyond this mean-field approximation and to include the most important additional correlations in a systematic way. In this new approach each state is approximated by a linear combination of several symmetry-projected quasi-particle determinants, and the corresponding quasi-particle transformations are determined successively together with the configuration mixing via a chain of variational calculations. In this way the selection of the relevant configurations for each state is entirely left to the dynamics of the considered system. The method is applied to some selected examples within the 1sOd shell (the lowest three I π = 1 + states in 20 Ne and the 0 + , 2 + , 4 + members of the 28 Si ground-state band). The results are compared to the exact as well as to the VAMPIR and EXCITED VAMPIR results. Considerable improvements with respect to the latter approaches are obtained.

Discontinuities and angular momentum fluctuations in the self-consistent cranking model

Abstract Two main shortcomings of the cranking model in band crossing regions, namely the possible occurrence of discontinuities and the strongly varying angular momentum fluctuations, are investigated. It is found that because of these drawbacks the reliability of the cranking approximation in regions of band crossing is more than doubtful, and that even the suggestions to overcome the difficulties by including the so-called physical parts of the 2qp trajectory do not improve the situation, at least as far as the wave functions are considered.

Pairing vibrational states and the generator coordinate method

The pairing vibrational states and the two-neutron transfer cross sections between these states are calculated in Ni, Sn and Pb isotopes by the generator coordinate method (GCM). The particle number fluctuation of the BCS functions is handled by projecting in a good approximation on sharp particle numbers. The results agree quite well with the experimental data.