Competition of isoscalar and isovector proton-neutron pairing in nuclei
Abstract We use shell model techniques in the complete pf shell to study pair correlations in nuclei. Particular attention is paid to the competition of isoscalar and isovector proton-neutron pairing modes which is investigated in the odd-odd N = Z nucleus 46 V and in the chain of even Fe-isotopes. We confirm the dominance of isovector pairing in the ground states. An inspection of the level density and pair correlation strength in 46 V, however, shows the increasing relative importance of isoscalar correlations with increasing excitation energy. In the Fe-isotopes we find the expected strong dependence of the proton-neutron isovector pairing strength on the neutron excess, while the dominant J = 1 isoscalar pair correlations scale much more gently with neutron number. We demonstrate that the isoscalar pair correlations depend strongly on the spin-orbit splitting.
An Algebraic pairing model with Sp(4) symmetry and its deformation
A fermion realization of the compact symplectic sp(4) algebra provides a natural framework for studying isovector-pairing correlations in nuclei. While these correlations manifest themselves most clearly in the binding energies of 0+ ground states, they also have a large effect on the energies of excited states, including especially excited 0+ states. In this paper, we consider non-deformed as well as deformed algebraic descriptions of pairing through the reductions of sp(q)(4) to different realizations of u(q)(2) for single-j and multi-j orbitals. The model yields a classification scheme for completely paired 0+ states of even–even and odd–odd nuclei in the 1d3/2, 1f7/2 and 1f5/2 2p1/2 2p3/2 1g9/2 shells. Phenomenological non-deformed and deformed isospin-breaking Hamiltonians are expressed in terms of the generators of the dynamical symmetry groups Sp(4) and Spq(4). These Hamiltonians are related to the most general microscopic pairing problem, including isovector pairing and isoscalar proton–neutron interaction along with nonlinear interaction in the deformed extension. In both the non-deformed and deformed cases the eigenvalues of the Hamiltonian are fit to the relevant Coulomb corrected experimental 0+ energies and this, in turn, allows us to estimate the interaction strength parameters, to investigate isovector-pairing properties and symmetries breaking and to predict the corresponding energies. While the non-deformed theory yields results that are comparable to other theories for light nuclei, the deformed extension, which takes into account higher order interactions between the particles, gives a better fit to the data. The multi-shell applications of the model provide for reasonable predictions of energies of exotic nuclei.
Shell model Monte Carlo methods
We review quantum Monte Carlo methods for dealing with large shell model problems. These methods reduce the imaginary-time many-body evolution operator to a coherent superposition of one-body evolutions in fluctuating one-body fields; resultant path integral is evaluated stochastically. We first discuss the motivation, formalism, and implementation of such Shell Model Monte Carlo methods. There then follows a sampler of results and insights obtained from a number of applications. These include the ground state and thermal properties of pf-shell nuclei, thermal behavior of {gamma}-soft nuclei, and calculation of double beta-decay matrix elements. Finally, prospects for further progress in such calculations are discussed. 87 refs.