Realistic Shell-model Interactions Research Articles

Shell-model study of octupole collectivity near Pb208

We show that the collectivity of the particle-hole wave function of low-lying octupole 3^- states in doubly magic nuclei is mainly due to the neutron-proton interaction. Both the enhanced reduced transition probability to the ground state, B(E3;3-_1 -> 0+_1), and the coupling of the octupole excitation to a nucleon result from the coherent action of all the components of the collective state. The results obtained with a realistic shell-model interaction both for 208Pb and 209Pb agree with the geometric collective model of Bohr and Mottelson, where octupole excitations are associated with phonons corresponding to collective shape oscillations of the surface of the nucleus.

Contrasting properties of particle-particle and hole-hole excitations in 206Tl and 210Bi nuclei

A complete-spectroscopy investigation of low-lying, low-spin states in the one-proton-hole and one-neutron-hole nucleus 206Tl has been performed by using thermal neutron capture and γ-coincidence technique with the FIPPS Ge array at ILL Grenoble. The new experimental results, together with data for the one-proton-particle and one-neutron-particle nucleus 210Bi (taken from a previous study done at ILL in the EXILL campaign), allowed for an extensive comparison with predictions of shell-model calculations performed with realistic interactions. No phenomenological adjustments were introduced in the calculations. In 210Bi, state energies, transition multipolarities and decay branchings agree well with theory for the three well separated multiplets of states which dominate the low-lying excitations. On the contrary, in 206Tl significant discrepancies are observed: in the same energy region, six multiplets were identified, with a significant mixing among them being predicted, as a consequence of the smaller energy separation between the active orbitals. The discrepancies in 206Tl are attributed to the larger uncertainties in the determination of the off-diagonal matrix elements of the realistic shell-model interaction with respect to the calculated diagonal matrix elements, the only ones playing a major role in the case of 210Bi. The work points to the need of more advanced approaches in the construction of the realistic interactions.

Quartet structure of self-conjugate nuclei

We provide a description of even-even N = Z nuclei in a formalism of quartets. Quartets are four-body correlated structures characterized by isospin T and angular momentum J. We show that the ground state correlations induced by a realistic shell model interaction can be well accounted for in terms of a restricted set of T = 0 low–J quartets, the J = 0 one playing by far a leading role among them. A conceptually similar description of odd-odd self-conjugate nuclei is given in terms of two distinct families of building blocks, one formed by the same T = 0 quartets employed for the even-even systems and the other by collective pairs with either T = 0 or T = 1. Some applications of this formalism are discussed for nuclei in the sd shell.

Quartetting in even-even and odd-odd N=Z nuclei

We report on a microscopic description of even-even N = Z nuclei in a formalism of quartets. Quartets are four-body correlated structures characterized by isospin T and angular momentum J. We show that the ground state correlations induced by a realistic shell model interaction can be well accounted for in terms of a restricted set of T = 0 low-J quartets, the J = 0 one playing by far a leading role among them. A conceptually similar description of odd-odd self-conjugate nuclei is given in terms of two distinct families of building blocks, one formed by the same T = 0 quartets employed for the even-even systems and the other by collective pairs with either T = 0 or T = 1. Some applications of this formalism are discussed for nuclei in the sd shell.

Neutrinoless double- β decay matrix elements in large shell-model spaces with the generator-coordinate method

We use the generator-coordinate method with realistic shell-model interactions to closely approximate full shell-model calculations of the matrix elements for the neutrinoless double-beta decay of $^{48}$Ca, $^{76}$Ge, and $^{82}$Se. We work in one major shell for the first isotope, in the $f_{5/2}pg_{9/2}$ space for the second and third, and finally in two major shells for all three. Our coordinates include not only the usual axial deformation parameter $\beta$, but also the triaxiality angle $\gamma$ and neutron-proton pairing amplitudes. In the smaller model spaces our matrix elements agree well with those of full shell-model diagonalization, suggesting that our Hamiltonian-based GCM captures most of the important valence-space correlations. In two major shells, where exact diagonalization is not currently possible, our matrix elements are only slightly different from those in a single shell.

From Kuo–Brown to today's realistic shell-model calculations

This paper is an homage to the seminal work of Gerry Brown and Tom Kuo, where shell model calculations were performed for 18O and 18F using an effective interaction derived from the Hamada-Johnston nucleon-nucleon potential. That work has been the first successful attempt to provide a description of nuclear structure properties starting from the free nucleon-nucleon potential. We shall compare the approach employed in the 1966 paper with the derivation of a modern realistic shell-model interaction for sd-shell nuclei, evidencing the progress that has been achieved during the last decades.

Spectroscopic study of neutron-rich calcium isotopes with a realistic shell-model interaction

We have studied neutron-rich calcium isotopes in terms of the shell model, employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. The short-range repulsion of the potential is renormalized by way of the ${V}_{\mathrm{low}\ensuremath{-}\mathrm{k}}$ approach. The calculated results are in very good agreement with the available experimental data, thus supporting our predictions for the hitherto unknown spectra of $^{53\ensuremath{-}56}\mathrm{Ca}$ nuclei. In this context, the possible existence of an $N=34$ shell closure is discussed.

Interacting boson model for exotic nuclei at low isospin

With Wigner's SU(4) supermultiplet symmetry [and its generalization to pseudo-SU(4)] as a starting point, a boson-model space is constructed that includes $T=0$ as well as $T=1$ bosons (interacting boson model-4). The boson Hamiltonian is derived microscopically from a realistic shell-model interaction through a mapping that relies on the existence of approximate shell-model symmetries. Applications are presented for odd-odd $N=Z$ nuclei from ${}_{29}^{58}{\mathrm{Cu}}_{29}$ to ${}_{35}^{70}{\mathrm{Br}}_{35}.$

Sum rules regarding the sign problem in Monte Carlo shell model calculations

The Monte Carlo shell model is a powerful technique for computational nuclear structure. Only a certain class of nuclear interactions, however, such as pairing and quadrupole, are free of the numerical noise known as the sign problem.This paper presents sum rules that relate the sign problem to the J=0 pairing matrix elements, thus illuminating the extrapolation procedure routinely used for realistic shell-model interactions.

Estimating the nuclear level density with the Monte Carlo shell model

A method for making realistic estimates of the density of levels in even-even nuclei is presented making use of the Monte Carlo shell model (MCSM). The procedure follows three basic steps: (1) computation of the thermal energy with the MCSM, (2) evaluation of the partition function by integrating the thermal energy, and (3) evaluating the level density by performing the inverse Laplace transform of the partition function using maximum entropy reconstruction techniques. It is found that results obtained with schematic interactions, which do not have a sign problem in the MCSM, compare well with realistic shell-model interactions provided an important isospin dependence is accounted for.

Spin-tensor analysis of realistic shell model interactions.

In this paper various realistic shell model effective interactions are analyzed in terms of their central, vector, and tensor components. The effective forces were obtained from phenomenological (Hamada-Johnston) as well as from modern meson-exchange (Bonn-Juelich and Paris) nucleon-nucleon potentials and were calculated to various approximations within the framework of perturbation theory. For all forces examined, the dominant contribution comes from the central part. The vector component is small for the bare {ital G}-matrix interaction, especially for {ital T}=0, but is considerably modified by renormalization. The tensor component is somewhat larger than the vector component and is relatively larger for the Hamada-Johnston potential than for the Bonn-Juelich and Paris potentials. Centroids in {ital j}-{ital j} and SU(3) coupling were obtained with and without noncentral contributions; considerable sensitivity was observed in the SU(3) basis.

Core polarization effects on spin-dipole and first-forbidden beta -decay operators in the lead region.

The effect of two-particle--two-hole ground-state correlations on spin-dipole transitions and the similar first-forbidden \ensuremath{\beta}-decay transitions is studied for nuclei in the lead region with realistic shell-model interactions. Transitions are considered between states for which one is a particle-hole excitation of the other. It is found that the tensor component of the residual interaction is quite important for the ${0}^{\mathrm{\ensuremath{-}}}$ and ${1}^{\mathrm{\ensuremath{-}}}$ spin-dipole transitions and the analogous \ensuremath{\beta}-decay matrix elements. It is destructive for ${0}^{\mathrm{\ensuremath{-}}}$ and constructive for ${1}^{\mathrm{\ensuremath{-}}}$ so that the quenching of the two modes is quite different. The atypical 1${\mathit{g}}_{9/2}$\ensuremath{\rightarrow}0${\mathit{h}}_{9/2}$ transition is described. The results are compared to previous determinations.