Shell-model Interaction Research Articles

Theoretical analysis and predictions for the two-neutrino double electron capture of 124Xe

Abstract We provide a complete theoretical description of the two-neutrino electron capture in 124Xe improving both the nuclear and the atomic structure calculations. We improve the general formalism through the use of the Taylor expansion method, leading to higher order terms in the decay rate of the process. The nuclear part is treated with pn-QRPA and interacting shell model (ISM) methods. The nuclear matrix elements (NMEs) are calculated with the pn-QRPA method with isospin restoration by fixing the input parameters so that the experimental decay rate is reproduced, resulting in values significantly lower than in previous calculations. The validity of the pn-QRPA NMEs is tested by showing their values to be comparable with the ones for double-beta decay with emission of two electrons of 128,130Te, which have similar pairing features. Within the ISM, we reproduce the total experimental half-life within a factor of two and predict the capture fraction to the KK channel of about 74%. We also predict the capture fractions to other decay channels and show that for the cumulative decay to the KL1-KO1 channels, a capture fraction of about 24% could be observed experimentally. On the atomic side, calculations are improved by accounting for the Pauli blocking of the decay of innermost nucleon states and by considering all s-wave electrons available for capture, expanding beyond the K and L1 orbitals considered in previous studies. We also provide improved atomic relaxation energies of the final atomic states of 124Te, which may be used as input for background modeling in liquid Xenon experiments.

Simultaneous Measurement of the Half-Life and Spectral Shape of ^{115}In β Decay with an Indium Iodide Cryogenic Calorimeter.

Current bounds on the neutrino Majorana mass are affected by significant uncertainties in the nuclear calculations for neutrinoless double-beta decay. A key issue for a data-driven improvement of the nuclear theory is the actual value of the axial coupling constant g_{A}, which can be investigated through forbidden β decays. We present the first measurement of the 4th-forbidden β decay of ^{115}In with a cryogenic calorimeter based on indium iodide. Exploiting the enhanced spectrum-shape method for the first time to this isotope, our study accurately determines simultaneously spectral shape, g_{A}, and half-life. The interacting shell model, which best fits our data, indicates a half-life for this decay at T_{1/2}=(5.26±0.06)×10^{14} yr.

Impact of shell model interactions on nuclear responses to WIMP elastic scattering

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

Indispensability of cross-shell contributions in neutron resonance spacing

Spin- and parity-dependent nuclear level densities (NLDs) are obtained for a configuration interaction shell model using a numerically efficient spectral distribution method. The calculations are performed for 24Na and 25,26,27Mg nuclei using full sd-pf model space that incorporates the cross-shell excitations from the sd to the pf-shell. The obtained NLDs are then employed to determine the s-wave neutron resonance spacing (D0), which is one of the crucial inputs for the predictions of astrophysical reaction rates. Although the considered nuclei are not neutron-rich, the contributions from cross-shell excitations to the pf-shell are indispensable for explaining the experimental data for D0, which otherwise are significantly overestimated.

Nuclear structure studies within the realistic shell model

The role of three-nucleon forces on structure properties of nuclei is discussed within the realistic shell model. Calculations are performed by employing effective shell-model Hamiltonians derived by way of many-perturbation theory from chiral potentials including the nucleon-nucleon and three-nucleon components. A sketch of the formalism in treating the three-nucleon force is given and some selected results for f p- and p-shell nuclei are shown. Particular attention is devoted to the effects of the three-nucleon force on the monopole component of the effective shell-model interaction by showing how relevant they are in correcting the monopole interaction derived from the nucleon-nucleon force only and correctly describing the formation of shell structure as well as the enhancement in the spin-orbit splitting. A decomposition scheme based on the rank of irreducible tensors forming the three-nucleon force at the next-to-next-to-leading order is also presented to recognize their impact on the spin-orbit enhancement.

Recent progress in configuration–interaction shell model

Since Mayer and Jensen employed the single-particle shell model to interpret the magic numbers, various microscopic nuclear models have been developed to study the nuclear force and structure. The configuration–interaction shell model (CISM), performed in truncated model space with the inclusion of the residual interaction, is one widely-used nuclear structure model. In the last decade, CISM has progressed in investigating the cross-shell excitation in exotic light nuclei, the similarity and difference in mirror nuclei, and the isomerism and seniority conservation in medium and heavy nuclei. Additionally, researchers have attempted to construct effective Hamiltonians for nuclei near [Formula: see text]Sn and [Formula: see text]Pb through a unified way in the CISM framework. In parallel, related models, including the nucleon-pair approximation (NPA) approach, the Monte Carlo shell model (MCSM), the projected shell model (PSM), the Gamow shell model (GSM), etc., have also been extensively developed and validated in the last decade. This paper reviews the recent progress in CISM and some related models.

Systematic shell-model study of 98−130Cd isotopes and 8+ isomeric states

We present systematic shell-model studies of even-even 98−130Cd isotopes using a realistic effective shell-model interaction derived from the G-matrix approach with an inert core 88Sr. Our calculated low-lying excited energy spectra and electromagnetic properties are compared with the experimental data. On the basis of recently available experimental data, we predict spins and parities corresponding to unconfirmed states. We also discuss the properties of 8+ isomeric states in 98−104,130Cd isotopes.

Ordinary Muon Capture on 136Ba: Comparative Study Using the Shell Model and pnQRPA

In this work, we present a study of ordinary muon capture (OMC) on 136Ba, the daughter nucleus of 136Xe double beta decay (DBD). The OMC rates at low-lying nuclear states (below 1 MeV of excitation energy) in 136Cs are assessed by using both the interacting shell model (ISM) and proton–neutron quasiparticle random-phase approximation (pnQRPA). We also add chiral two-body (2BC) meson-exchange currents and use an exact Dirac wave function for the captured s-orbital muon. OMC can be viewed as a complementary probe of the wave functions in 136Cs, the intermediate nucleus of the 136Xe DBD. At the same time, OMC can be considered a powerful probe of the effective values of weak axial-type couplings in a 100 MeV momentum exchange region, which is relevant for neutrinoless DBD. The present work represents the first attempt to compare the ISM and pnQRPA results for OMC on a heavy nucleus while also including the exact muon wave function and the 2BC. The sensitivity estimates of the current and future neutrinoless DBD experiments will clearly benefit from future OMC measurements taken using OMC calculations similar to the one presented here.

Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in case of CI calculations reaches about 20 billion terms. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. The canonical wave functions/natural orbitals and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex non-equilibrium time-dependent process, induced nuclear fission described within a real-time Density Functional Theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short range correlations between fermions.

Predicting the neutrinoless double- β -decay matrix element of Xe136 using a statistical approach

Calculation of the nuclear matrix elements (NMEs) for double-beta decay is of paramount importance for guiding experiments and for analyzing and interpreting the experimental data, especially for the search of the neutrinoless double beta decay mode ($0\nu\beta\beta$). However, there are currently still large differences between the NME values calculated by different methods, hence a quantification of their uncertainties is very much required. In this paper we propose a statistical analysis of $0\nu\beta\beta$ NME for the $^{136}Xe$ isotope, based on the interacting shell model, but using three independent effective Hamiltonians, emphasizing the range of the NMEs' most probable values and its correlations with observables that can be obtained from the existing nuclear data. Consequently, we propose a common probability distribution function for the $0\nu\beta\beta$ NME, which has a range of (1.55 - 2.65) at 90\% confidence level, with a mean value of 1.99 and a standard deviation of 0.37.

Excited Energy Spectra for He and Be Isotopes from Different Shell Model Interactions

Excited Energy Spectra for He and Be Isotopes from Different Shell Model Interactions

Robustness of pair structures for nuclear yrast states* *Supported by the National Natural Science Foundation of China (11875134, 11875188, 12175071, 11975151, 11961141003), and the Shanghai Key Laboratory of Particle Physics and Cosmology (21DZ2271500-2)

In this study, we investigate the robustness of pair structures for nuclear yrast states, that is, whether the structures of relevant collective pairs as building blocks of different yrast states are the same. We focus on deformed and transitional nuclei and study the yrast states of Si, Cr, and Xe, whose experimental values are 2.60, 2.40, and 2.16, respectively, using the nucleon-pair approximation (NPA) and shell-model effective interactions. For each yrast state, we consider optimized pair structures to be those providing the energy minimum for this state. To find the minimum, many full NPA calculations are performed with varying pair structures, and the numerical optimization procedure of the conjugate gradient method is implemented. Our results suggest that optimized pair structures remain the same for all states within a rotational band of a deformed nucleus. Our results also suggest that after backbending, that is, changing of the intrinsic state, the structure of the S pair, which is essential to build the monopole pairing correlation, remains approximately unchanged, whereas the structures of the non-S pairs, which are essential to build the quadrupole correlation, change significantly.

Unbound states in 17C and p-sd shell-model interactions

Unbound states in C17 were investigated via one-neutron removal from a C18 beam at an energy of 245 MeV/nucleon on a carbon target. The energy spectrum of C17, above the single-neutron decay threshold, was reconstructed using invariant mass spectroscopy from the measured momenta of the C16 fragment and neutron, and was found to exhibit resonances at Er=0.52(2), 0.77(2), 1.36(1), 1.91(1), 2.22(3) and 3.20(1) MeV. The resonance at Er=0.77(2) MeV [Ex=1.51(3) MeV] was provisionally assigned as the second 5/2+ state. The two resonances at Er=1.91(1) and 3.20(1) MeV [Ex=2.65(2) and 3.94(2) MeV] were identified, through comparison of the energies, cross sections and momentum distributions with shell-model and eikonal reaction calculations, as p-shell hole states with spin-parities 1/21− and 3/21−, respectively. A detailed comparison was made with the results obtained using a range of shell-model interactions. The YSOX shell-model Hamiltonian, the cross-shell part of which is based on the monopole-based universal interaction, was found to provide a very good description of the present results and those for the neighbouring odd-A carbon isotopes – in particular for the negative parity cross-shell states.

Exotic Structure of 17Ne-17N and 23Al-23Ne Mirror Nuclei

In terms of the core nucleus plus valence nucleon, shell-model calculations using two model spaces and interactions, the relationship between a nucleus' proton skin, and the difference in proton radii of mirror pairs of nuclei with the same mass number are investigated. In this work, two pairs of mirror nuclei will be studied: 17Ne-17N and 23Al-23Ne. For 17Ne-17N nuclei, p-shell and mixing of psd orbits are adopted with Cohen-Kurath (ckii) and psdsu3 interactions. While for 23Al-23Ne, the sd-shell and sdpf shell are adopted with the universal shell model (USD) and sdpfwa interactions. Also, the ground state density distributions, elastic form factors, and root mean square radii of these pairs' nuclei are studied and compared with available experimental data. . In general, it was found that the rms radius of the valence proton(s) is larger than that of the valence neutron(s) in its mirror nucleus. The results show that these nuclei have the exotic structure of a halo or skin.

Determining gA/gV with High-Resolution Spectral Measurements Using a LiInSe2 Bolometer

Neutrinoless double beta decay (0νββ) processes sample a wide range of intermediate forbidden nuclear transitions, which may be impacted by quenching of the axial vector coupling constant (g_{A}/g_{V}), the uncertainty of which plays a pivotal role in determining the sensitivity reach of 0νββ experiments. In this Letter, we present measurements performed on a high-resolution LiInSe_{2} bolometer in a "source=detector" configuration to measure the spectral shape of the fourfold forbidden β decay of ^{115}In. The value of g_{A}/g_{V} is determined by comparing the spectral shape of theoretical predictions to the experimental β spectrum taking into account various simulated background components as well as a variety of detector effects. We find evidence of quenching of g_{A}/g_{V} at >5σ with a model-dependent quenching factor of 0.655±0.002 as compared to the free-nucleon value for the interacting shell model. We also measured the ^{115}In half-life to be [5.18±0.06(stat)_{-0.015}^{+0.005}(sys)]×10^{14} yr within the interacting shell model framework. This Letter demonstrates the power of the bolometeric technique to perform precision nuclear physics single-β decay measurements, which along with improved nuclear modeling can help reduce the uncertainties in the calculation of several decay nuclear matrix elements including those used in 0νββ sensitivity calculations.

Statistical analysis for the neutrinoless double- β -decay matrix element of Ca48

Neutrinoless double beta decay ($0\nu\beta\beta$) nuclear matrix elements (NME) are the object of many theoretical calculation methods, and are very important for analysis and guidance of a large number of experimental efforts. However, there are large discrepancies between the NME values provided by different methods. In this paper we propose a statistical analysis of the $^{48}$Ca $0\nu\beta\beta$ NME using the interacting shell model, emphasizing the range of the NME probable values and its correlations with observables that can be obtained from the existing nuclear data. Based on this statistical analysis with three independent effective Hamiltonians we propose a common probability distribution function for the $0\nu\beta\beta$ NME, which has a range of (0.45 - 0.95) at 90\% confidence level of, and a mean value of 0.68.

Atomistically-informed continuum modeling and isogeometric analysis of 2D materials over holey substrates

This work develops, discretizes, and validates a continuum model of a molybdenum disulfide (MoS2) monolayer interacting with a periodic holey silicon nitride (Si3N4) substrate via van der Waals (vdW) forces. The MoS2 layer is modeled as a geometrically nonlinear Kirchhoff–Love shell, and vdW forces are modeled by a Lennard-Jones (LJ) potential, simplified using approximations for a smooth substrate topography. Both the shell model and LJ interactions include novel extensions informed by close comparison with fully-atomistic calculations. The material parameters of the shell model are calibrated by comparing small-strain tensile and bending tests with atomistic simulations. This model is efficiently discretized using isogeometric analysis (IGA) for the shell structure and a pseudo-time continuation method for energy minimization. The IGA shell model is validated against fully-atomistic calculations for several benchmark problems with different substrate geometries. Agreement with atomistic results depends on geometric nonlinearity in some cases, but a simple isotropic St.Venant–Kirchhoff model is found to be sufficient to represent material behavior. We find that the IGA discretization of the continuum model has a much lower computational cost than atomistic simulations, and expect that it will enable efficient design space exploration in strain engineering applications. This is demonstrated by studying the dependence of strain and curvature in MoS2 over a holey substrate as a function of the hole spacing on scales inaccessible to atomistic calculations. The results show an unexpected qualitative change in the deformation pattern below a critical hole separation.

Investigation of electrical and magnetical multipoles contributions to the total longitudinal and transverse form factors in some positive and negative 27Al states using different interactions

The shell model and Skyrme interaction calculations were used to study the nuclear structure of the 27Al nucleus. In particular, inelastic electron scattering form factors, energy levels, and transition probabilities for positive and some negative parity low energy states have been calculated. The sd shell model was used with SKX parameters for positive parity cases. The calculations were performed on sd space interactions and the best results were obtained from HBUMSD, HBUSD, CWH, PW, and W interactions. For negative parity cases, the zbm model space with SKXcsb parameters has been used with zwm interactions. The excitation energies and transitions probabilities to the ground state 5/2+ for positive parity states have been also calculated. The calculated form factors, energy level diagrams, and transition probabilities were compared with the available experimental data. It was confirmed that the Skyrme interaction is suitable with the shell model to study the nuclear structure.

Multiparticle-hole excitations in nuclei near N = Z = 20: $$^{41}$$K

This experimental study of high-spin structure near \(N = Z = 20\) nuclei was focused on \(^{41}\)K, but will also mention three newly observed \(\gamma \) transitions in \(^{41}\)Ca observed in the same reaction. High-spin states were populated using the \(^{26}\)Mg(\(^{18}\)O, \(p2n\gamma \))\(^{41}\)K and \(^{26}\)Mg(\(^{18}\)O, \(3n\gamma \))\(^{41}\)Ca reactions. The experiment was carried out at an incident beam energy of 50 MeV at the Florida State University (FSU) John D. Fox Superconducting Linear Accelerator Laboratory and used the FSU high-purity germanium detector array. The \(^{41}\)K level scheme was extended to 12325 keV, possibly with J\(^{\pi }\) = 25/2\(^-\) or 27/2\(^+\), by means of 25 new transitions and that of \(^{41}\)Ca to 9916 keV. Linear polarization and a measure of angular distribution results are also reported and used to provide information on the spins and parities of several states in the \(^{41}\)K level scheme. The results have been compared to the spsdpf cross-shell FSU shell model interaction calculations. The theoretical results from configurations involving no or one additional nucleon promoted from the sd to the fp shell agree relatively well with the energies of known states, while those that involve multi-particle excitations paint an interesting and complex picture of interplay between single-particle excitations, collective pairing, and deformation. This presents an interesting challenge for future theory.

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.