Microscopic approaches to nuclear structure: Configuration interaction

Nuclear recoil from scattering with weakly interacting massive particles (WIMPs) is a signature searched for in direct detection of dark matter. The underlying WIMP-nucleon interactions could be spin and/or orbital angular momentum (in)dependent. Evaluation of nuclear recoil rates through these interactions requires accounting for nuclear structure, e.g., through shell model calculations. We evaluate nuclear response functions induced by these interactions for F19, Na23, Si28,29,30, Ar40, Ge70,72,73,74,76, I127, and Xe128,129,130,131,132,134,136 nuclei that are relevant to current direct detection experiments, and estimate their sensitivity to shell model interactions. Shell model calculations are performed with the NuShellX solver. Nuclear response functions from nonrelativistic effective field theory are evaluated and integrated over transferred momentum for quantitative comparisons. We show that although the standard spin-independent response is barely sensitive to the structure of the nuclei, large variations with the shell model interaction are often observed for the other channels. Significant uncertainties may arise from the nuclear components of WIMP-nucleus scattering amplitudes due to nuclear structure theory and modeling. These uncertainties should be accounted for in analyses of direct detection experiments. Published by the American Physical Society 2024

Journal of Physics G: Nuclear and Particle Physics is committed to bringing its readers timely reviews in topics of interest to the nuclear and particle physics community, and an active programme of Topical Reviews is scheduled for future issues. Appropriate topics and authors are identified by the Editorial Board prior to invitation and commissioning of reviews, but any suggestions of suitable topics or offers of review contributions will be welcomed by the Board.

Shell model calculations based on large basis has been conducted to study the nuclear structure of $^{20}Ne$, $^{22}Ne$ and $^{24}Mg$ nuclei. The energy levels, inelastic electron scattering form factors and transition probabilities are discussed by considering the contribution of configurations with high-energy beyond the model space of sd-shell model space which is denoted as the core polarization (CP) effects.~The Core polarization is considered by taking the excitations of nucleus from the $1s$ and $1p$ core orbits and also from the valence $2s$ $1d$ shell orbit in to higher shells with $4\hbar\omega$. The effective interactions $USDA$ and $USDB$ are employed with $sd$ shell model space to perform the calculation and the core polarization are calculated with $MSDI$ as residual interaction.~The calculated energy level schemes, form factors and transition probabilities were compared with the corresponding experimental data. The effect of core polarization is found very important for the calculation of $B(C2)$, $B(C4)$ and form factors, and gives excellent results in comparison with the experimental data without including any adjustable parameters.

The nuclear shell model has perhaps been the most important conceptual and computational paradigm for the understanding of the structure of atomic nuclei. While the shell model has been used predominantly in a phenomenological context, there have been efforts stretching back more than half a century to derive shell model parameters based on a realistic interaction between nucleons. More recently, several ab initio many-body methods—in particular, many-body perturbation theory, the no-core shell model, the in-medium similarity renormalization group, and coupled-cluster theory—have developed the capability to provide effective shell model Hamiltonians. We provide an update on the status of these methods and investigate the connections between them and their potential strengths and weaknesses, with a particular focus on the in-medium similarity renormalization group approach. Three-body forces are demonstrated to be important for understanding the modifications needed in phenomenological treatments. We then review some applications of these methods to comparisons with recent experimental measurements, and conclude with some remaining challenges in ab initio shell model theory.

We propose a new approach employing the Brueckner-AMD in which the G-matrix is calculated using the antisymmetrized molecular dynamics (AMD). Its applications to some light nuclei are demonstrated, and the high reliability of the description of the shell and cluster structures is discussed. In the conventional approach employing the G-matrix for the study of nuclear matter or the shell model, the constructed G-matrix is used to reproduce effective interactions. Therefore, the effective interactions are valid only in the model space. It is desirable for the model space to be as large as possible, but for practical reasons, a finite dimensional space is used. For this reason, the effective interaction is model dependent, 1) and one must accept the limits of its applicability. The conventional shell model calculations have failed in the description of nuclear cluster states, which are observed in the excited states around cluster thresholds. By contrast, the cluster model has been shown to provide a successful description of these states. Recent developments of the cluster model based on the antisymmetrized molecular dynamics (AMD) 2) have led to success in reproducing the various kinds of cluster structures of excited states, in addition to the shell model structure of the ground and low-lying states, without any assumption concerning cluster configurations. This result indicates that the functional space of AMD is very large; the wave functions of AMD can describe not only shell model configurations but also cluster configurations. However, to this time studies of AMD have been carried out without detailed investigations of the effective interactions. It is important to construct a framework of the G-matrix for AMD. In this letter, we propose a framework of the Brueckner-AMD to calculate the G-matrix for AMD. Since the pioneering cluster study of α + α, 3) there has been much interest in elucidating the role of the tensor force component resulting from the one-pion exchange potential (OPEP) in the α-cluster formation and the binding mechanism of the α-particle. 4) – 8) Study of the G-matrix has been carried out in association with the appearance of α-clustering and the cluster structures in the low-excitation [ (

The effective InteractionU for a shell model with hamiltonianHm is investigated by means of a “mixed” model with hamiltonianHm. For this model the Bornv. Neumann expansion of the effective interactionŨ reduces to its first two terms. Within the finite dimensional function space ℜn used in the shell model calculation the operatorsU andŨ are exactly equivalent. This is used to show that an energy independent approximation forU- if it is possible at all-is necessarily equal to the residual interaction, i.e. to the difference between nucleon-nucleon interaction and shell model interaction.

The Brueckner $G$ matrix from the Reid soft-core potential is taken for the leading contribution to the effective two-neutron hole interaction in the $^{208}\mathrm{Pb}$ region. To accomodate the corrections expected from core polarization and other higher order effects, including truncation of the model space, we add phenomenological two-body pairing and multipole forces whose strengths are determined by fitting the $^{206}\mathrm{Pb}$ spectrum. A satisfactory fit is obtained with an interaction where the average total contribution of the added terms is less than 45% of the interaction. The same total effective interaction is then shown to yield a satisfactory spectrum for $^{204}\mathrm{Pb}$ which may indicate the neglected effective many-body forces are not important. A comparison with the results of McGrory and Kuo is presented to examine the impact on the effective interaction of limiting the model space. We conclude the prospects are good for extending this approach to other nuclei below $^{208}\mathrm{Pb}$ viewed as shell-model systems of valence holes in $^{208}\mathrm{Pb}$.NUCLEAR STRUCTURE Shell-model structure of Pb isotopes; theory of shell-model effective interaction with phenomenological corrections; multipole potentials added to Brueckner reaction matrix.

Shell model calculation has been performed for even–even [Formula: see text]Zn using NuShellX code in [Formula: see text] model space with two different effective Hamiltonians, viz. JUN45 and jj44b. The low-lying structure is studied up to angular momentum, [Formula: see text] = 10[Formula: see text] by calculating level energies, reduced transition probabilities, occupation numbers, lifetimes, and quadrupole moments. The results of the calculations are compared with the available experimental data. It is observed that the inclusion of 1[Formula: see text] orbital in the model space is essential to understand nuclear structure in these isotopes. Shell model calculation with an improved set of effective Hamiltonian parameters and inclusion of [Formula: see text] orbital in the model space are necessary in order to produce finer agreement with the experimental observations.

Shell model calculations using optimized effective interactions are becoming the standard model of nuclear structure physics. While earlier effective interactions were optimized for nuclei near the valley of stability, radioactive beam facilities have allowed the study of nuclei much farther from stability. These results suggest that with increasing proton-neutron imbalance significant modifications are needed to the interactions. For example, evidence is mounting that the filling of proton shells modifies the neutron shell structure and vice-versa. The s-d shell provides an excellent testing ground for confronting theory with experiment where intruder structures from higher orbitals have already been recognized, especially in the region where N ~ 2*Z called the “Island of Inversion.” The approach to this region is critical to understanding how the shell structure changes towards inversion. The nucleus 34P with Z = 15 and N = 19 is a key one along this approach. The known level scheme of 34P was doubled in a recent experimental study using the GAMMASPHERE gamma detector array with the reaction 18O + 18O at 24 MeV using the ATLAS accelerator facility at Argonne National Laboratory. Comparison of the observed nuclear structure with shell model calculations using both the WBP-a and SDPF-NR interactions shows relatively good agreement for the pure 1s-0d shell states and for those involving the promotion of one particle to the 0f7/2 and 1p3/2 orbitals. However, both calculations badly overpredict the energies of states involving two or more particles in the f-p shell. It remains to be seen whether adjustments to these interactions can substantially improve the agreement for the latter states while not worsening the fit to the states with fewer intruders.

We perform the particle-number-projected mean-field study using the recently developed symmetry-projected Hartree–Fock–Bogoliubov (HFB) equations. Realistic calculations have been performed in sd- and fp-shell nuclei using the shell model empirical interactions, USD and GXPFIA. It is demonstrated that the mean-field results for energy surfaces, obtained with these shell model interactions, are quite similar to those obtained using the density functional approaches. Further, it is shown that particle-number-projected results, for neutron-rich isotopes, can lead to different ground-state shapes in comparison to bare HFB calculations.

This work is devoted to new investigations of the 12Be spectrum with No‐core Shell Model (NCSM) calculations and with the Generator Coordinate Method (GCM). The NCSM calculations do not reproduce the breaking of the N = 8 shell closure. The NCSM and the GCM calculations do not support the existence of a band based on the ground state. The GCM calculations lead to a good description of the molecular band of Freer et al. and Saito et al.. The 02+ isomeric state and the 22+ state are also well described by the GCM. New bands of positive and negative parities are proposed.

We present the framework for the ab initio no-core nuclear shell model and apply it to obtain properties of ${}^{12}\mathrm{C}.$ We derive two-body effective interactions microscopically for specific model spaces from the realistic CD-Bonn and the Argonne V8' nucleon-nucleon $(\mathrm{NN})$ potentials. We then evaluate binding energies, excitation spectra, radii, and electromagnetic transitions in the $0\ensuremath{\Elzxh}\ensuremath{\Omega},$ $2\ensuremath{\Elzxh}\ensuremath{\Omega},$ and $4\ensuremath{\Elzxh}\ensuremath{\Omega}$ model spaces for the positive-parity states and the $1\ensuremath{\Elzxh}\ensuremath{\Omega},$ $3\ensuremath{\Elzxh}\ensuremath{\Omega},$ and $5\ensuremath{\Elzxh}\ensuremath{\Omega}$ model spaces for the negative-parity states. Dependence on the model-space size, on the harmonic-oscillator frequency, and on the type of the $\mathrm{NN}$ potential, used for the effective interaction derivation, are studied. In addition, electromagnetic and weak neutral elastic charge form factors are calculated in the impulse approximation. Sensitivity of the form-factor ratios to the strangeness one-body form-factor parameters and to the influence of isospin-symmetry violation is evaluated and discussed. Agreement between theory and experiment is favorable for many observables, while others require yet larger model spaces and/or three-body forces. The limitations of the present results are easily understood by virtue of the trends established and previous phenomenological results.

Nuclear shell model and interacting boson fermion approximation

There has been significant progress in the ab initio approaches to the structure of light nuclei. One such method is the ab initio no-core shell model (NCSM). Starting from the realistic two- and three-nucleon interactions, this method can predict the low-lying levels in p-shell nuclei. It is a challenging task to extend the ab initio methods to describe nuclear reactions. In this contribution, we present a brief overview of the NCSM with examples of recent applications as well as the first steps taken toward nuclear reaction applications.

Nuclear structure properties of Si and P isotopes with the microscopic effective interactions