A review is presented of the development and current status of nuclear shell-model calculations in which the two-body effective interaction is derived from the free nucleon-nucleon potential. The significant progress made in this field within the last decade is emphasized, in particular as regards the so-called V-low-k approach to the renormalization of the bare nucleon-nucleon interaction. In the last part of the review we first give a survey of realistic shell-model calculations from early to present days. Then, we report recent results for neutron-rich nuclei near doubly magic 132Sn and for the whole even-mass N=82 isotonic chain. These illustrate how shell-model effective interactions derived from modern nucleon-nucleon potentials are able to provide an accurate description of nuclear structure properties.
We propose a unified realistic shell-model Hamiltonian employing the pairing plus multipole Hamiltonian combined with the monopole interaction constructed starting from the monopole-based universal force by Otsuka it et al. (Phys. Rev. Lett. 104, 012501 (2010)). It is demonstrated that the proposed PMMU model can consistently describe a large amount of spectroscopic data as well as binding energies in the pf and pf5/2g9/2 shell spaces, and could serve as a practical shell model for even heavier mass regions.
The main steps involved in realistic shell-model calculations employing two-body low-momentum interactions are briefly reviewed. The practical value of this approach is exemplified by the results of recent calculations and some remaining open questions and directions for future research are discussed.
We report on the calculation of the neutrinoless double-beta decay nuclear matrix element for 76Ge within the framework of the realistic shell model. The effective shell-model Hamiltonian and the two-body transition operator describing the decay are derived by way of many-body perturbation theory. Particular attention is focused on the role played by the so-called Pauli blocking effect in the derivation of the effective operator.
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-low-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 53-56Ca nuclei. In this context, the possible existence of an N=34 shell closure is discussed.
This paper starts with a brief historical overview of pairing in nuclei, which fulfills the purpose of properly framing the main subject. This concerns the pairing properties of a realistic shell-model effective interaction which has proved very successful in describing nuclei around doubly magic 132Sn. We focus attention on the two nuclei 134Te and 134Sn with two valence protons and neutrons, respectively. Our study brings out the key role of one particle-one hole excitations in producing a significant difference between proton and neutron pairing in this region.
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.
The generalized seniority scheme has long been proposed as a means of dramatically reducing the dimensionality of nuclear shell model calculations, when strong pairing correlations are present. However, systematic benchmark calculations, comparing results obtained in a model space truncated according to generalized seniority with those obtained in the full shell model space, are required to assess the viability of this scheme. Here, a detailed comparison is carried out, for semimagic nuclei taken in a full major shell and with realistic interactions. The even-mass and odd-mass Ca isotopes are …
Based on the realistic nuclear force of the high-precision CD-Bonn potential, we have performed comprehensive calculations for neutron-rich calcium isotopes using the Gamow shell model (GSM) which includes resonance and continuum. The realistic GSM calculations produce well binding energies, one- and two-neutron separation energies, predicting that $^{57}$Ca is the heaviest bound odd isotope and $^{70}$Ca is the dripline nucleus. Resonant states are predicted, which provides useful information for future experiments on particle emissions in neutron-rich calcium isotopes. Shell evolutions in th…
We perform analysis of realistic nucleon-nucleon interactions, as well as of empirically-corrected interactions, fitted to reproduce in detail the spectroscopic data in p and sd shells. We focus on the multipole part of the interactions, contrary to previous studies of that type which focused on monopole parts. We analyze how the different parts of the NN force (tensor, spin-orbit and central) contribute to the leading multipoles of the interaction and how do they renormalize in medium. We show that the leading coherent terms of the realistic and effective interactions are dominated by the cen…
Generalized seniority provides a truncation scheme for the nuclear shell model, based on pairing correlations, which offers the possibility of dramatically reducing the dimensionality of the nuclear shell-model problem. Systematic comparisons against results obtained in the full shell-model space are required to assess the viability of this scheme. Here, we extend recent generalized seniority calculations for semimagic nuclei, the Ca isotopes, to open-shell nuclei, with both valence protons and valence neutrons. The even-mass Ti and Cr isotopes are treated in a full major shell and with realis…
We approach the calculation of the nuclear matrix element of the neutrinoless double-beta decay process, considering the light-neutrino-exchange channel, by way of the realistic shell model. To this end, we start from a realistic nucleon-nucleon potential and then derive the effective shell-model Hamiltonian and neutrinoless double-beta decay operator within the many-body perturbation theory. We focus on investigating the perturbative properties of the effective shell-model operator of such a decay process, aiming to establish the degree of reliability of our predictions. The contributions of …
This paper presents a short overview of the shell-model approach with realistic effective interactions to the study of exotic nuclei. We first give a sketch of the current state of the art of the theoretical framework of this approach, focusing on the main ingredients and most relevant recent advances. Then, we present some selected results for neutron-rich nuclei in various mass regions, namely oxygen isotopes, $N=40$ isotones, and nuclei around $^{132}$Sn, to show the merit as well as the limits of these calculations.
This paper discusses the derivation of an effective shell-model hamiltonian starting from a realistic nucleon-nucleon potential by way of perturbation theory. More precisely, we present the state of the art of this approach when the starting point is the perturbative expansion of the Q-box vertex function. Questions arising from diagrammatics, intermediate-states and order-by-order convergences, and their dependence on the chosen nucleon-nucleon potential, are discussed in detail, and the results of numerical applications for the p-shell model space starting from chiral next-to-next-to-next-to…
Background: Collective excitations of nuclei and their theoretical descriptions provide an insight into the structure of nuclei. Replacing traditional phenomenological interactions with unitarily transformed realistic nucleon-nucleon interactions increases the predictive power of the theoretical calculations for exotic or deformed nuclei. Purpose: Extend the application of realistic interactions to deformed nuclei and compare the performance of different interactions, including phenomenological interactions, for collective excitations in the sd-shell. Method: Ground-state energies and charge r…
Shell structure in the neutron-rich Ca and Ni nuclei is investigated by the spherical Hartree-Fock calculations with the semi-realistic $NN$ interactions. Specific ingredients of the effective interaction, particularly the tensor force, often play a key role in the $Z$ dependence of the neutron shell structure. Such examples are found in N=32 and N=40; N=32 becomes magic or submagic in $^{52}$Ca while its magicity is broken in $^{60}$Ni, and N=40 is submagic (though not magic) in $^{68}$Ni but not in $^{60}$Ca. Comments are given on the doubly magic nature of $^{78}$Ni. We point out that the l…
Realistic shell model calculation of $2νββ$ nuclear matrix elements and role of shell structure in intermediate states
We discuss two conditions needed for correct computation of $2νββ$ nuclear matrix-elements within the realistic shell-model framework. An algorithm in which intermediate states are treated based on Whitehead's moment method is inspected, by taking examples of the double GT $^+$ transitions $\mbox{$ ^{36} $Ar}\rightarrow\mbox{$ ^{36} $S}$ , $\mbox{$ ^{54} $Fe}\rightarrow\mbox{$ ^{54} $Cr}$ and $\mbox{$ ^{58} $Ni} \rightarrow\mbox{$ ^{58} $Fe}$ . This algorithm yields rapid convergence on the $2νββ$ matrix-elements, even when neither relevant GT $^+$ nor GT $^-$ strength distribution is converge…
We report on a shell-model study of Sn isotopes beyond N=82 employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential renormalized through use of the V-low-k approach. At present, the most exotic Sn isotope for which some experimental information exists is 134Sn with an N/Z ratio of 1.68. It is the aim of our study to compare the results of our calculations with the available experimental data and to make predictions for the neighboring heavier isotopes which may be within reach of the next generation of radioactive ion beam facilities. The very good agreem…
We perform realistic shell-model calculations for nuclei with valence nucleons outside 48Ca, employing two different model spaces. The matrix elements of the effective two-body interaction and electromagnetic multipole operators have been calculated within the framework of the many-body perturbation theory, starting from a low-momentum potential derived from the high-precision CD-Bonn free nucleon-nucleon potential. The role played by the neutron orbital 1d5/2 has been investigated by comparing experimental data on yrast quadrupole excitations of isotopic chains north-east of 48Ca with the res…
We have performed shell-model calculations for the even- and odd-mass N=82 isotones, focusing attention on low-energy states. The single-particle energies and effective two-body interaction have been both determined within the framework of the time-dependent degenerate linked-diagram perturbation theory, starting from a low-momentum interaction derived from the CD-Bonn nucleon-nucleon potential. In this way, no phenomenological input enters our effective Hamiltonian, whose reliability is evidenced by the good agreement between theory and experiment.
The advent of nucleon-nucleon potentials derived from chiral perturbation theory, as well as the so-called V-low-k approach to the renormalization of the strong short-range repulsion contained in the potentials, have brought renewed interest in realistic shell-model calculations. Here we focus on calculations where a fully microscopic approach is adopted. No phenomenological input is needed in these calculations, because single-particle energies, matrix elements of the two-body interaction, and matrix elements of the electromagnetic multipole operators are derived theoretically. This has been …
In nuclear structure calculations, the choice of a limited model space, due to computational needs, leads to the necessity to renormalize the Hamiltonian as well as any transition operator. Here, we present a study of the renormalization procedure and effects of the Gamow-Teller operator within the framework of the realistic shell model. Our effective shell-model operators are obtained, starting from a realistic nucleon-nucleon potential, by way of the many-body perturbation theory in order to take into account the degrees of freedom that are not explicitly included in the chosen model space. …
We present calculations for the $c$-coefficients of the isobaric mass multiplet equation for nuclei from $A=42$ to $A=54$ based on input from three realistic nucleon-nucleon interactions. We demonstrate that there is a clear dependence on the short-ranged charge-symmetry breaking (CSB) part of the strong interaction and that there is significant disagreement in the CSB part between the commonly used CD-Bonn, N$^3$LO, and Argonne V18 nucleon-nucleon interactions. In addition, we show that all three interactions give a CSB contribution to the $c$-coefficient that is too large when compared to ex…
No-Core Gamow Shell Model (NCGSM) is applied for the first time to study selected well-bound and unbound states of helium isotopes. This model is formulated on the complex energy plane and, by using a complete Berggren ensemble, treats bound, resonant, and scattering states on equal footing. We use the Density Matrix Renormalization Group method to solve the many-body Schrödinger equation. To test the validity of our approach, we benchmarked the NCGSM results against Faddeev and Faddeev-Yakubovsky exact calculations for $^3$H and $^4$He nuclei. We also performed {\textit ab initio} NCGSM calcu…
We study the neutron-rich calcium isotopes performing shell-model calculations with a realistic effective interaction. This is derived from the CD-Bonn nucleon-nucleon potential renormalized by way of the V-low-k approach, considering 48Ca as an inert core and including the neutron 0g9/2 orbital. We compare our results with experiment and with the results of a previous study where 40Ca was assumed as a closed core and the standard 1p0f model space was employed. The calculated spectroscopic properties are in both cases in very good agreement with the available experimental data and enable a dis…
Shell evolution in exotic nuclei is investigated with large-scale shell-model calculations. After presenting that the central and tensor forces produce distinctive ways of shell evolution, we show several recent results: (i) evolution of single-particle-like levels in antimony and cupper isotopes, (ii) shape coexistence in nickel isotopes understood in terms of configuration-dependent shell structure, and (iii) prediction of the evolution of the recently established $N=34$ magic number towards smaller proton numbers. In any case, large-scale shell-model calculations play indispensable roles in…
In this paper we present an evolution of our derivation of the shell-model effective Hamiltonian, namely introducing effects of three-body contributions. More precisely, we consider a three-body potential at next-to-next-to-leading order in chiral perturbation theory, and the induced three-body forces that arise from many-body correlations among valence nucleons. The first one is included, in the derivation of the effective Hamiltonian for one- and two-valence nucleon-systems, at first order in the many-body perturbation theory. Namely, we include only the three-body interaction between one or…
We note that in large space shell model calculaiotns and experiment one sometimes get results, the form of which also appear in smaller space calculations. On the other hand there are some results which demand the large space approach.
We review the latest variational calculations of the ground state properties of doubly closed shell nuclei, from $^{12}$C to $^{208}$Pb, with semirealistic and realistic two- and three-nucleon interactions. The studies are carried on within the framework of the correlated basis function theory and integral equations technique, with state dependent correlations having central and tensor components. We report results for the ground state energy, one- and two-body densities and static structure functions. For $^{16}$O and $^{40}$Ca we use modern interactions and find that the accuracy of the meth…
Shell-model calculation with density-dependent interaction for $pf$-shell nuclei
Graduate School of Science and Technology, University of Tsukuba（筑波大学科学技术研究院）；Center for Computational Sciences and Institute of Pure and Applied Sciences, University of Tsukuba（筑波大学计算科学中心及纯应用科学研究所）；RIKEN Nishina Center（理化学研究所仁科研究中心）
We present recent shell-model calculations of the gamma-decay in sd-pf and pf-shell nuclei. We focus on the M1 part of the dipole strength which was shown to exhibit interesting low-energy effects, in particular a low-energy enhancement which can have a considerable impact on the radiative neutron capture. We discuss the persistence of the shell effects in the nuclear quasi-continuum and the relation between the shape of the strength function at low energy and nuclear deformation.
A recursive calculational scheme is developed for matrix elements in the generalized seniority scheme for the nuclear shell model. Recurrence relations are derived which permit straightforward and efficient computation of matrix elements of one-body and two-body operators and basis state overlaps.
