Shell-model Calculations Research Articles

Merging of the island of inversion at N = 40 and N = 50

We performed a quantitative study of the nuclei with proton numbers from Z=20 (Ca) to Z=28 (Ni) and neutron numbers ranging from N=38 to 52 using the realistic shell model, which merged the descriptions of nuclei around N=40 and N=50 within an extended model space. The 21+ excitation energy (E(21+)) is calculated for neutron-rich Cr, Fe, and Ni isotopes. The results suggest that the islands of inversion at N=40 and N=50 merge around the Cr chain, and the N=50island of inversion is located below 78Ni. To demonstrate the prediction of the N=50island of inversion, we calculated and compared the E(21+), B(E2;01+→21+), effective single-particle energies (ESPEs), the probability of particle-hole excitation, and the average occupations in the N=40 and N=50 isotones. Similar parabolic trends of E(21+) and B(E2;01+→21+) in the N=40 and 50 isotones are obtained. The calculated ESPEs give that the N=40 and N=50 shell gaps both increase with the variation of proton number from Z=20 (Ca) to Z=28 (Ni). However, our calculations indicate that different particle-hole excitations dominate in the ground states of the N=40 and N=50islands of inversion, with 2p2h and 4p4h configurations being prominent in N=40 isotones, whereas 2p2h excitations are most important in the N=50 isotones. Furthermore, large occupations of the intruder quadrupole partner orbitals are also obtained in N=40 and N=50 isotones in our realistic shell model calculations.

First spectroscopic study of odd-odd Cu78

Nuclei in the vicinity of Ni78 are important benchmarks for nuclear structure, which can reveal changes in the shell structure far from stability. Spectroscopy of the odd-odd isotope Cu78 was performed for the first time in an experiment with the EURICA setup at the Radioactive Isotope Beam Factory at RIKEN Nishina Center. Excited states in the neutron-rich isotope were populated following the β decay of Ni78 produced by in-flight fission and separated by the BigRIPS separator. A level scheme based on the analysis of γ−γ coincidences is presented. Tentative spin and parity assignments were made when possible based on the β-decay feeding intensities and γ-decay properties of the excited states. Time correlations between β and γ decay show clear indications of an isomeric state with a half-life of 3.8(4) ms. Large-scale Monte Carlo shell-model calculations were performed using the A3DA-m interaction and a valence space comprising the full fp shell and the 1g9/2 and 2d5/2 orbitals for both protons and neutrons. The comparison of the experimental results with the shell-model calculations allows interpreting the excited states in terms of spin multiplets arising from the proton-neutron interaction. The results provide further insight into the evolution of the proton single-particle orbitals as a function of neutron number, and quantitative information about the proton-neutron interaction outside the doubly magic Ni78 core.Received 6 October 2022Revised 3 January 2023Accepted 9 January 2023DOI:https://doi.org/10.1103/PhysRevC.107.044301©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBeta decayEnergy levels & level densitiesIsomer decaysNuclear spin & parityNuclear structure & decaysNucleon-nucleon interactionsShell modelProperties59 ≤ A ≤ 89Nuclear Physics

Hamiltonian sensitivity in calculating the electromagnetic moments and electroexcitation form factor for the sd nuclei using shell model with Skyrme–Hartree–Fock

In this work, the nuclear electromagnetic moments for the ground and low-lying excited states for sd shell nuclei have been calculated, resulting in a revised database with 56 magnetic dipole moments and 41 electric quadrupole moments. The shell model calculations are performed for each sd isotope chain, considering the sensitivity of changing the sd two-body effective interactions USDA, USDE, CWH and HBMUSD in the calculation of the one-body transition density matrix elements. The calculations incorporate the single-particle wave functions of the Skyrme interaction to generate a one-body potential in Hartree–Fock theory to calculate the single-particle matrix elements. For most sd shell nuclei, the experimental data are well reproduced, except for those spans near the island of inversion. In order to interpret the structure of low-lying excited states, the electric quadrupole and magnetic dipole transition form factors and the corresponding reduced transition probabilities in the sd shell nuclei have also been calculated, for which the experimental data are available. The present results demonstrate the nuclear electromagnetic moments’ sensitivity to many forms of the understanding of nucleon–nucleon interactions and provide a crucial baseline for future improvements in conceptual calculations.

Direct Measurement of Hexacontatetrapole, E6 γ Decay from Fe53m

The only proposed observation of a discrete, hexacontatetrapole (E6) transition in nature occurs from the T_{1/2}=2.54(2)-min decay of ^{53m}Fe. However, there are conflicting claims concerning its γ-decay branching ratio, and a rigorous interrogation of γ-ray sum contributions is lacking. Experiments performed at the Australian Heavy Ion Accelerator Facility were used to study the decay of ^{53m}Fe. For the first time, sum-coincidence contributions to the weak E6 and M5 decay branches have been firmly quantified using complementary experimental and computational methods. Agreement across the different approaches confirms the existence of the real E6 transition; the M5 branching ratio and transition rate have also been revised. Shell model calculations performed in the full fp model space suggest that the effective proton charge for high-multipole, E4 and E6, transitions is quenched to approximately two-thirds of the collective E2 value. Correlations between nucleons may offer an explanation of this unexpected phenomenon, which is in stark contrast to the collective nature of lower-multipole, electric transitions observed in atomic nuclei.

First Evidence of Axial Shape Asymmetry and Configuration Coexistence in Zn74 : Suggestion for a Northern Extension of the N=40 Island of Inversion

The excited states of N=44 ^{74}Zn were investigated via γ-ray spectroscopy following ^{74}Cu β decay. By exploiting γ-γ angular correlation analysis, the 2_{2}^{+}, 3_{1}^{+}, 0_{2}^{+}, and 2_{3}^{+} states in ^{74}Zn were firmly established. The γ-ray branching and E2/M1 mixing ratios for transitions deexciting the 2_{2}^{+}, 3_{1}^{+}, and 2_{3}^{+} states were measured, allowing for the extraction of relative B(E2) values. In particular, the 2_{3}^{+}→0_{2}^{+} and 2_{3}^{+}→4_{1}^{+} transitions were observed for the first time. The results show excellent agreement with new microscopic large-scale shell-model calculations, and are discussed in terms of underlying shapes, as well as the role of neutron excitations across the N=40 gap. Enhanced axial shape asymmetry (triaxiality) is suggested to characterize ^{74}Zn in its ground state. Furthermore, an excited K=0 band with a significantly larger softness in its shape is identified. A shore of the N=40 "island of inversion" appears to manifest above Z=26, previously thought as its northern limit in the chart of the nuclides.

In-beam gamma -ray spectroscopy of ^{94}Ag

A recoil-beta-tagging experiment has been performed to study the excited T=0 and T=1 states in the odd–odd N=Z nucleus ^{94}Ag, populated via the ^{40}Ca(^{58}Ni,1p3n)^{94}Ag reaction. The experiment was conducted using the MARA recoil separator and JUROGAM3 array at the Accelerator Laboratory of the University of Jyväskylä. Through correlating fast, high-energy beta decays at the MARA focal plane with prompt gamma rays emitted at the reaction target, a number of transitions between excited states in ^{94}Ag have been identified. The timing characteristics of these transitions confirm that they fall within decay sequences that feed the short-lived T=1 ground state of ^{94}Ag. The transitions are proposed to proceed within and between the sets of states with T=0 and T=1. Possible correspondence between some of these transitions from analog states in ^{94}Pd has been discussed, and shell-model calculations including multipole and monopole electromagnetic effects have been presented, in order to enable predictions of the decay patterns between the T=0 and T=1 states and to allow a theoretical set of Coulomb energy differences to be calculated for the A = 94T=1 analog states.

Studying Gamow-Teller transitions and the assignment of isomeric and ground states at N = 50

Direct mass measurements of neutron-deficient nuclides around the N=50 shell closure below 100Sn were performed at the FRS Ion Catcher (FRS-IC) at GSI, Germany. The nuclei were produced by projectile fragmentation of 124Xe, separated in the fragment separator FRS and delivered to the FRS-IC. The masses of 14 ground states and two isomers were measured with relative mass uncertainties down to 1×10−7 using the multiple-reflection time-of-flight mass spectrometer of the FRS-IC, including the first direct mass measurements of 98Cd and 97Rh. A new QEC=5437±67 keV was obtained for 98Cd, resulting in a summed Gamow-Teller (GT) strength for the five observed transitions (0+⟶1+) as B(GT)=2.94−0.28+0.32. Investigation of this result in state-of-the-art shell model approaches accounting for the first time experimentally observed spectrum of GT transitions points to a perfect agreement for N=50 isotones. The excitation energy of the long-lived isomeric state in 94Rh was determined for the first time to be 293±21 keV. This, together with the shell model calculations, allows the level ordering in 94Rh to be understood.

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

In the present work, we have reported comprehensive study of the sd-shell nuclei Si and P with neutron number varying from N=9 to N=20 using the microscopic effective valence shell interactions, namely, N3LO, JISP16 and DJ16A. These effective sd-shell interactions are developed using the ab initio no-core shell model wave functions and the Okubo-Lee-Suzuki transformation method. For comparison, we have also performed shell model calculations with the empirical USDB interaction. Energy spectra and electromagnetic properties of these isotopic chains have been studied. Theoretically calculated shell model results are compared with the available experimental data, to check the predictive strength of these microscopic interactions. It is found that the binding energies of the ground states are better reproduced with the DJ16A interaction as compared to other microscopic interactions and a proton subshell closure at Z=14 is obtained in Si. Spin-tensor decomposition of two-body interaction is presented to understand the contributions from central, vector and tensor components into these interactions. Spectroscopic strengths of 23Al(d,n)24Si are examined for the newly performed experiment at NSCL.

Nuclear Energy Levels in 44Ca using FPD6pn Interaction

Nuclear energy levels; total angular moment, even-even parity, and even odd parities for nucleons that were present outside closed core for the isobars 44Ca nuclei, which occupied low levels fp-LS shell (1f7/2,1f5/2, 2p3/2,2p1/2), within shell model calculations had been studied. The interaction has been used to calculate the nuclear energy levels which are fpd6pnwith fp shell model space. The results are compared with each other and with available experimental data, its agreement with some results is clear. All inscriptions are given in diagrammatic notation., the wave vectors and analysis are modeled in the so-called diagrammatic notation. The potential of the oscillator is utilized to construct a single particle vector, considered as a core. The OXFORD BEUNES AIRES SHELL MODEL CODE (OXBASH) is utilized to accomplish the results for all tested nuclei, the results as illustrated in figure (1) revealing that the levels have somehow consisted especially below 4 MeV, and the order are arranged similarly to the experimental scheme. All the states inherent above 4MeV are shifted especially for the odd values of total spin (J), so the model and interaction need to be modified.

FP Shell Effective Interactions and Nuclear Shell Structure of 44Sc

Abstract: Nuclear energy levels in 44Sc isotope, with fp shell model space occupation low levels fp-LS shell within shell model calculations had been investigated. The interactions has been used to calculate the nuclear energy levels which are fpd6, hw, fpy, with fp shell model space, d3f7cospn for 1d3/21f7/2 model space. The results are compared with each other and with available experimental data, its agreement with some results are clear. The used of model space interactions is the best fitted two body matrix elements in fp shell model space beside the good agreements in the reproduced values of energy levels scheme. The general estimation of the reproduced data are good especially below 3MeV. All inscriptions are given in diagrammatic notation, the wave vectors and analysis are modeled in the so called diagrammatic notation. The potential of oscillator is utilized to construct single particle vector, considering (_20^40)〖Ca〗_20 as a core for fp shell model space and (_16^32)S_(16 ) as an inert core for the model space d3f7. The OXFORD BEUNES AIRES SHELL MODEL CODE is utilized to accomplish the results for all tested nuclei.

Shell-Model Study of Nuclear Weak Rates relevant to Astrophysical Processes in Stars

New shell-model Hamiltonians which can successfully describe spin responses in nuclei are used to evaluate nuclear weak rates in stellar environments. The e-capture and β-decay rates for the nuclear pair with 31Mg-31Al, in the island of inversion, which have been pointed out to be important for the cooling of neutron star crusts, are studied by shell-model calculations with the effective interaction in sd-pf shell obtained by the extended Kuo-Krenciglowa (EKK) method. The weak rates induced by the Gamow-Teller transitions between the low-lying states in the nuclear pair lead to a nuclear Urca process. The spin-dipole strengths and e-capture rates for 78Ni are evaluated by shell-model with full pf-sdg shells including up to 5p-5h excitations outside filling configurations of 78Ni. The e-capture rates obtained are compared with RPA calculations and the effective rate formula. Weak rates for the second-forbidden transition in 20Ne are evaluated by the multipole expansion method of Walecka as well as the Behrens-Bühring method within sd-shell. Difference in the rates between the two methods is found to be rather small as far as the conserved-vector-current (CVC) relation is satisfied. Possible important contributions of the forbidden transition to the heating of the ONeMg core by double e-captures on 20Ne in a late stage of the evolution of the core and implications on the final fate of the core, whether core-collapse or thermonuclear explosion, are discussed.

Nuclear structure studies in mirror nuclei

The nuclear structure of the A=31 and A=47 mirror couples produced by two fusion evaporation reactions has been elaborated, utilizing the Doppler-shift attenuation method. Excited states in 31P and 31S were populated using the 1p and 1n exit channels, respectively, of the reaction 20Ne + 12C, while in 47Cr and 47V couple excited states were populated based on 28Si + 28Si reaction, as products of 2αn and 2αp exit channels. The A=31 mirror couple was studied utilizing Piave-Alpi accelerator of the Laboratori Nazionali di Legnaro with GASP multidetector array and for A=47 one - with the EUROBALL array using XTU Tandem also in Legnaro. In both cases the lifetime measurements in mirror couples at the same experiment open possibilities for investigations of isospin symmetry. Determined B(E1) strengths in the mirror nuclei 31P and 31S allow to extract the isoscalar component, which can reach up to 24% of the isovector one. The B(E1) values can be modeled by the Equation of motion method. In the case of A=47 mirror couple, the quadrupole moments can be described by shell-model calculations.

Analysis of two-particle transfer reaction in the 18O+40Ca and 20Ne+116Cd collisions

Two-neutron and two-proton transfer reactions have been analyzed in the present work. These kind of transfer reactions is an excellent tool to get insights into the short-range correlations on nucleons in a nuclear state. The direct and sequential two-particle transfer mechanisms, for which the valence particles can be transferred, were compared one with other to probe the populated nuclear states. Large-scale shell model calculations were performed to obtained the spectroscopic amplitudes for one and two valence particles.

Study of the one-neutron transfer reaction in 18O + 76Se collision at 275 MeV in the context of the NUMEN project

Heavy-ion one-nucleon transfer reactions are promising tools to investigate single-particle configurations in nuclear states, with and without the excitation of the core degrees of freedom. An accurate determination of the spectroscopic amplitudes of these configurations is essential for the study of other direct reactions as well as beta-decays. In this context, the 76Se(18O,17O)77Se one-neutron transfer reaction gives a quantitative access to the relevant single particle orbitals and core polarization transitions built on 76Se. This is particularly relevant, since it provides data-driven information to constrain nuclear structure models for the 76Se nucleus.The excitation energy spectrum and the differential cross section angular distributions of this nucleon transfer reaction was measured at 275 MeV incident energy for the first time using the MAGNEX large acceptance magnetic spectrometer. The data are compared with calculations based on distorted wave Born approximation and coupled channel Born approximation adopting spectroscopic amplitudes for the projectile and target overlaps derived by large-scale shell model calculations and interacting boson-fermion model.These reactions are studied in the frame of the NUMEN project. The NUMEN (NUclear Matrix Elements for Neutrinoless double beta decay) project was conceived at the Istituto Nazionale di Fisica Nucleare–Laboratori Nazionali del Sud (INFN-LNS) in Catania, Italy, aiming at accessing information about the nuclear matrix elements (NME) of neutrinoless double beta decay (0νββ) through the study of the heavy-ion induced double charge exchange (DCE) reactions on various 0νββ decay candidate targets. Among these, the 76Se nucleus is under investigation since it is the daughter nucleus of 76Ge in the 0νββ decay process.

Core-proton coupled nature of the 11/2+ state in 131 Sb probed by lifetime measurements

The structure of the state in 131Sb was investigated at the LOHENGRIN spectrometer of Institut Laue-Langevin via neutron-induced fission of 235U and lifetime measurements, yielding , at the edge of the sensitivity of the experimental method. This first result for the state half-life in neutron-rich Sb isotopes provides a quadrupole reduced transition probability to the ground state of W.u., very close to the in 130Sn. Realistic shell-model calculations reproduce well both the experimental level scheme of 131Sb and the value, indicting a dominant core-proton coupled configuration for the state.

First application of Markov chain Monte Carlo-based Bayesian data analysis to the Doppler-shift attenuation method

Motivated primarily by the large uncertainties in the thermonuclear rate of the 30P(p,γ)31S reaction that limit our understanding of classical novae, we carried out lifetime measurements of 31S excited states using the Doppler Shift Lifetimes (DSL2) facility at the TRIUMF Isotope Separator and Accelerator (ISAC-II) facility. The 31S excited states were populated by the 3He(32S,α)31S reaction. The deexcitation γ rays were detected by a clover-type high-purity germanium detector in coincidence with the α particles detected by a silicon detector telescope. We have applied modern Markov chain Monte Carlo-based Bayesian statistical techniques to perform lineshape analyses of Doppler-shift attenuation method γ-ray data for the first time. We have determined the lifetimes of the two lowest-lying 31S excited states. First experimental upper limits on the lifetimes of four higher-lying states have been obtained. The experimental results were compared to shell-model calculations using five universal sd-shell Hamiltonians. Evidence for γ rays originating from the astrophysically important Jπ=3/2+, 260-keV 30P(p,γ)31S resonance with an excitation energy of Ex=6390.2(7) keV in 31S has also been observed, although strong constraints on the lifetime will require better statistics.

Single-particle configurations of low- and medium-spin states in Cu63

The excitation scheme of the $^{63}\mathrm{Cu}$ nucleus has been probed following its population in a light-ion induced fusion-evaporation reaction and using an array of Compton suppressed HPGe clover detectors as the detection system. Apart from ascribing $\ensuremath{\gamma}$-ray transitions to the level scheme of the nucleus, through $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence measurements, and identifying the new transitions in the process, measurements of angular correlation and linear polarization of the $\ensuremath{\gamma}$ rays have also been carried out towards assigning their multipolarities and electric and magnetic characters. The observed level scheme has been interpreted through shell model calculations in two different model spaces. One of these was the $f5pg9$ space outside the $^{56}\mathrm{Ni}$ core while the other included the ${f}_{7/2}$ orbital for the protons outside the $^{48}\mathrm{Ca}$ core and was directed at probing the influence of the ${f}_{7/2}$ excitations in the regime of spins being investigated. The latter has been found to be of rather modest impact, in general, and the observed level structure can largely be interpreted through particle excitations in the $f5pg9$ model space.

Machine learning for the prediction of converged energies from ab initio nuclear structure calculations

The prediction of nuclear observables beyond the finite model spaces that are accessible through modern ab initio methods, such as the no-core shell model, poses a challenging task in nuclear structure theory. It requires reliable tools for the extrapolation of observables to infinite many-body Hilbert spaces along with reliable uncertainty estimates. In this work we present a universal machine learning tool capable of capturing observable-specific convergence patterns independent of nucleus and interaction. We show that, once trained on few-body systems, artificial neural networks can produce accurate predictions for a broad range of light nuclei. In particular, we discuss neural-network predictions of ground-state energies from no-core shell model calculations for ▪, ▪ and ▪ based on training data for ▪, ▪ and ▪ and compare them to classical extrapolations.

Machine learning light hypernuclei

We employ a feed-forward artificial neural network to extrapolate at large model spaces the results of ab-initio hypernuclear No-Core Shell Model calculations for the Λ separation energy BΛ of the lightest hypernuclei, Λ3H, Λ4H and Λ4He, obtained in computationally accessible harmonic oscillator basis spaces using chiral nucleon-nucleon, nucleon-nucleon-nucleon and hyperon-nucleon interactions. The overfitting problem is avoided by enlarging the size of the input dataset and by introducing a Gaussian noise during the training process of the neural network. We find that a network with a single hidden layer of eight neurons is sufficient to extrapolate correctly the value of the Λ separation energy to model spaces of size Nmax=100. The results obtained are in agreement with the experimental data in the case of Λ3H and the 0+ state of Λ4He, although they are off of the experiment by about 0.3 MeV for both the 0+ and 1+states of Λ4H and the 1+ state of Λ4He. We find that our results are in excellent agreement with those obtained using other extrapolation schemes of the No-Core Shell Model calculations, showing this that an ANN is a reliable method to extrapolate the results of hypernuclear No-Core Shell Model calculations to large model spaces.

Nuclear magnetic moment of the neutron-rich nucleus O21

The ground-state magnetic dipole moment of the neutron-rich $^{21}\mathrm{O}$ isotope has been measured via $\ensuremath{\beta}$-ray-detected nuclear magnetic resonance ($\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{NMR}$) spectroscopy by using a spin-polarized secondary beam of $^{21}\mathrm{O}$ produced from the $^{22}\mathrm{Ne}$ primary beam. From the present measurement, the $g$ factor $|{g}_{\mathrm{exp}}(^{21}\mathrm{O}_{\mathrm{g}.\mathrm{s}.})|=0.6036(14)$ has been determined. Based on the comparison of this value with Schmidt values, we unambiguously confirm the $\ensuremath{\nu}{d}_{5/2}$ configuration with spin and parity assignments ${I}^{\ensuremath{\pi}}=5/{2}^{+}$ for the $^{21}\mathrm{O}$ ground state, suggested by previously reported studies. Consequently, the magnetic moment has been determined as ${\ensuremath{\mu}}_{\mathrm{exp}}(^{21}\mathrm{O}_{\mathrm{g}.\mathrm{s}.})=(\ensuremath{-})1.5090(35){\ensuremath{\mu}}_{N}$. The obtained experimental magnetic moment is in good agreement with the predictions of the shell-model calculations using the USD, YSOX, and SDPF-M interactions as well as random phase approximation (RPA) calculations. This observation indicates that the $^{21}\mathrm{O}$ nucleus in its ground state does not manifest any anomalous structure and is not influenced by the proximity of the drip line.