Large-scale Shell Model Research Articles

Gamma-ray spectroscopy of 55Sc

The N = 34 isotope 55Sc has been investigated using in-beam γ-ray spectroscopy at the RIKEN Radioactive Isotope Beam Factory. Spectra from the direct (p, pn) reaction as well as indirect reaction channels have been investigated. γ rays with energies 496(10), 570(12), 682(14), 1510(30), 1780(36), 2345(57) and 2470(50) keV have been observed. A level scheme was constructed based on γ γ coincidence analysis and relative intensities. The results have been compared to the level scheme already reported in literature, as well as to large-scale shell model calculations in the sd − pf model space. A new level at 1510keV, decaying directly to the ground state, has been proposed and spin-parity J π = 7/2− was tentatively assigned. The effect of including the ν g 9/2 orbital is discussed. It can be concluded that the main low-energy properties of 55Sc seem to be included in the original sd − pf model space.

Excited-State Half-Lives in ^{130}Cd and the Isospin Dependence of Effective Charges.

The known I^{π}=8_{1}^{+}, E_{x}=2129-keV isomer in the semimagic nucleus ^{130}Cd_{82} was populated in the projectile fission of a ^{238}U beam at the Radioactive Isotope Beam Factory at RIKEN. The high counting statistics of the accumulated data allowed us to determine the excitation energy, E_{x}=2001.2(7) keV, and half-life, T_{1/2}=57(3) ns, of the I^{π}=6_{1}^{+} state based on γγ coincidence information. Furthermore, the half-life of the 8_{1}^{+} state, T_{1/2}=224(4) ns, was remeasured with high precision. The new experimental information, combined with available data for ^{134}Sn and large-scale shell model calculations, allowed us to extract proton and neutron effective charges for ^{132}Sn, a doubly magic nucleus far-off stability. A comparison to analogous information for ^{100}Sn provides first reliable information regarding the isospin dependence of the isoscalar and isovector effective charges in heavy nuclei.

PROBING THE NUCLEAR STRUCTURE OF EXOTIC 33Mg ISOTOPE

Research on the nuclear structure of exotic isotopes, such as 33Mg, is an exciting and cuttingedge field of nuclear physics. Exotic isotopes are typically those that are far from the stable region of the nuclear chart and often exhibit unique properties that can help us better understand the fundamental forces and structure of atomic nuclei. In this paper the largescale shell model calculations are performed within the model spaces SDPFMU, to study the positive- and negative-parity energy levels and electromagnetic transitions in the exotic 33Mg isotope. Core-polarization effects on reduced transition probability are introduced through first order perturbation theory, which allows for higher energy configurations through excitations of nucleons from core orbits to that outside model space up to . The corepolarization effects have been improved the agreement of B(E2) with their corresponding experimental data, and have ignorable effect on B(M1)

Neutrinos from pre-supernova in the framework of TQRPA method

Abstract We propose a new method for calculating spectra and luminosities for (anti)neutrinos produced in the pre-supernova environment by weak processes with hot nuclei. It is based on the thermal quasiparticle random phase approximation (TQRPA), that allows microscopic thermodynamically consistent calculations of the weak-interaction response of nuclei at finite temperatures. For realistic representative pre-supernova conditions from the stellar evolution code MESA, we compute (anti)neutrino luminosities and spectra arising from neutral- and charged-current weak reactions with hot 56Fe and compare them with the contribution of thermal processes. We find that the TQRPA approach produces not only a higher total luminosity of electron neutrinos (mainly born in the electron capture reaction), compared to the standard technique based on the large-scale shell model (LSSM) weak-interaction rates, but also a harder neutrino spectrum. Besides, applying the TQRPA and LSSM, we find that in the context of electron antineutrino generation, the neutral-current nuclear de-excitation (ND) process via neutrino-antineutrino pair emission is at least as important as the electron-positron pair annihilation process. We also show that flavor oscillations enhance the high-energy contribution of the ND process to the electron antineutrino flux. This could potentially be important for pre-supernova antineutrino registration by the Earth’s detectors.

Nuclear chiral rotation within Relativistic Configuration-interaction Density functional theory

The Relativistic Configuration-interaction Density functional (ReCD) theory that combines the advantages of large-scale configuration-interaction shell model and relativistic density functional theory is extended to study nuclear chiral rotation. The energy spectra and transition probabilities of the chiral doublet bands are reproduced satisfactorily without any free parameters. By analyzing the probability amplitudes of the wavefunctions, the significant roles of configuration mixing and four quasiparticle states to the chiral doublets are revealed. The evolution from chiral vibration to static chirality is clearly illustrated by the K plot and azimuthal plot. The present investigation provides both microscopic and quantal descriptions for nuclear chirality for the first time and demonstrates the robustness of chiral geometry against the configuration mixing as well as the four quasiparticle states.

PANDORA Project for the study of photonuclear reactions below A=60

Photonuclear reactions of light nuclei below a mass of A=60 are planned to be studied experimentally and theoretically with the PANDORA (Photo-Absorption of Nuclei and Decay Observation for Reactions in Astrophysics) project. Two experimental methods, virtual photon excitation by proton scattering and real photo absorption by a high-brilliance gamma -ray beam produced by laser Compton scattering, will be applied to measure the photoabsorption cross sections and decay branching ratio of each decay channel as a function of the photon energy. Several nuclear models, e.g. anti-symmetrized molecular dynamics, mean-field and beyond-mean-field models, a large-scale shell model, and ab initio models, will be employed to predict the photonuclear reactions. The uncertainty in the model predictions will be evaluated based on the discrepancies between the model predictions and experimental data. The data and predictions will be implemented in the general reaction calculation code, TALYS. The results will be applied to the simulation of the photo-disintegration process of ultra-high-energy cosmic rays in inter-galactic propagation.

Shell evolution and emerging paradigm changes

The shell structure conceived by Mayer and Jensen in 1949 has been shown to be quite appropriate for stable and near-stable nuclei, but substantial deviations from it have also been observed more recently for exotic nuclei with notable neutron excess. Such changes of the basic picture of the nuclear shell structure, called the shell evolution, seem to be the subject studied most extensively and most elaborately by RI beam experiments worldwide. An overview of the shell evolution is presented in this talk, from both theoretical and experimental perspectives. The shell structure is shown to be varied, for instance, from the one presented by Mayer and Jensen, by particular types of the monopole components of the effective nucleon-nucleon interaction in nuclei. Among various contributions, the importance of the tensor force is illuminated here, with an outstanding example: the emergence of new neutron magic number 34 in neutron-rich Ca isotopes. The mechanism of the shell evolution produces significant impacts also on the nuclear shapes. Type II shell evolution shifts the excitation energies of intruder deformed bands, for instance, in some Ni isotopes. In other more general cases, the monopole interaction is shown to produce unexpected crucial effects on the patters of rotational bands of heavy deformed nuclei. In fact, the shape of the ellipsoidal deformation is investigated by large-scale shell model calculations, which is nothing but the Monte Carlo Shell Model. The unique role of the monopole component of the tensor force is clarified: the interplay between this monopole interaction and the quadrupole interaction provides us with various patterns of triaxial shapes for many nuclei, such as 166Er, one of the traditional prolate deformed heavy nuclei. Thus, the prolate preponderance hypothesis by Aage Bohr is investigated for its microscopic validity. Some of the nuclear paradigms are changing now in this way, due to emerging aspects of nuclear-force effects.

Energy rates due to Fe isotopes during presupernova evolution of massive stars

This work presents the microscopic calculation of energy rates (γ-ray heating and (anti)neutrino cooling rates) due to weak decay of selected Fe Isotopes. The isotopes have astrophysical significance during the presupernova evolution of massive stars. The energy rates are calculated using the pn-QRPA model and compared with the independent particle model (IPM), large scale shell model (LSSM) and recent shell model calculation (GXPF1J). The reported (anti)neutrino cooling rates are smaller by up to two orders of magnitude at low core temperature values than the IPM rates. The two calculations compare well at T = 30 GK. The comparison of cooling rates with the LSSM is interesting. The pn-QRPA cooling rates due to even-even Fe isotopes are smaller (up to 2 orders of magnitude). For the odd-A isotopes, the reported rates are bigger up to an order of magnitude. The pn-QRPA computed cooling rates are, up to 2 orders of magnitude, bigger when compared with the GXPF1J calculation. The γ-ray heating rates due to electron capture rates rise with the temperature and density values of the stellar core. On the other hand, the γ-ray heating due to β-decay increases with the core temperature values but decreases by orders of magnitude when the stellar core stiffens. The pn-QRPA computed γ heating rates are bigger (up to 3 orders of magnitude) at high temperatures and densities (for the case of 55,56Fe) when compared with the recent shell model results. Owing to the importance of energy rates, this study may contribute to a realistic simulation of presupernova evolution of massive stars.

Electroexcitation Form Factors for Positive- and Negative-Parity States in Some Si Isotopes Using Truncated Large-Scale Shell Model With Skyrme–Hartree–Fock Method

Electroexcitation Form Factors for Positive- and Negative-Parity States in Some Si Isotopes Using Truncated Large-Scale Shell Model With Skyrme–Hartree–Fock Method

^{133}In: A Rosetta Stone for Decays of r-Process Nuclei.

The β decays from both the ground state and a long-lived isomer of ^{133}In were studied at the ISOLDE Decay Station (IDS). With a hybrid detection system sensitive to β, γ, and neutron spectroscopy, the comparative partial half-lives (logft) have been measured for all their dominant β-decay channels for the first time, including a low-energy Gamow-Teller transition and several first-forbidden (FF) transitions. Uniquely for such a heavy neutron-rich nucleus, their β decays selectively populate only a few isolated neutron unbound states in ^{133}Sn. Precise energy and branching-ratio measurements of those resonances allow us to benchmark β-decay theories at an unprecedented level in this region of the nuclear chart. The results show good agreement with the newly developed large-scale shell model (LSSM) calculations. The experimental findings establish an archetype for the β decay of neutron-rich nuclei southeast of ^{132}Sn and will serve as a guide for future theoretical development aiming to describe accurately the key β decays in the rapid-neutron capture (r-) process.

Isomeric Excitation Energy for ^{99}In^{m} from Mass Spectrometry Reveals Constant Trend Next to Doubly Magic ^{100}Sn.

The excitation energy of the 1/2^{-} isomer in ^{99}In at N=50 is measured to be 671(37)keV and the mass uncertainty of the 9/2^{+} ground state is significantly reduced using the ISOLTRAP mass spectrometer at ISOLDE/CERN. The measurements exploit a major improvement in the resolution of the multireflection time-of-flight mass spectrometer. The results reveal an intriguing constancy of the 1/2^{-} isomer excitation energies in neutron-deficient indium that persists down to the N=50 shell closure, even when all neutrons are removed from the valence shell. This trend is used to test large-scale shell model, abinitio, and density functional theory calculations. The models have difficulties describing both the isomer excitation energies and ground-state electromagnetic moments along the indium chain.

Occupancy of orbitals and the quadrupole collectivity in 45Sc nucleus.

In the present work, the Doppler Shift Attenuation method (DSAM) was used to analyze the observed lineshapes of transitions from excited states in 45Sc, populated in the reaction 36Ar + 12C at a beam energy of 145 MeV. The interpretation and comparison of the experimental results have been performed with large-scale shell model calculations, involving different interactions like: GX1A, GX1J, FPD6, KB3 and ZBM2. KB3 and FPD6 (present work) interactions in the negative parity states, and in positive parity states ZBM2 are most pre-eminent in reproducing the results, due to the large configuration space describing strong collective effects. Furthermore, the present work also looks at the details of the shell model helping in improving the understanding for the occupancy of orbitals. The present investigation suggests the observation of stronger collectivity for positive parity states over negative parity states with predicted enhanced collectivity of states in 45Sc nucleus.

Correlations between nuclear Schiff moment and electromagnetic measurements

We study the nuclear Schiff moments of 129Xe and 199Hg induced by the nucleon electric dipole moment using large-scale shell model calculations. For 129Xe, we find a linear relation between the leading-order contribution and magnetic moment, which would be useful in reducing the theoretical uncertainty. The conventional model space does not contain the 0g9/2 and 0h9/2 orbitals, which are connected to the spin-orbit partners by large matrix elements. Thus, to evaluate the influence of the relevant single-particle orbitals outside the conventional model space, we apply the quasiparticle vacua shell model method. Moreover, the next-to-leading-order contribution arises from parity and time-reversal violation in the nucleus. We demonstrate that these secondary effects do not induce any significant disturbance to the correlation. Additionally, we report the shell model results for the nuclear Schiff moment coefficients of 199Hg. Compared to previous studies, the results obtained in this study are rather large, indicating a higher sensitivity to the neutron electric dipole moment.

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.

Lifetime measurements in the yrast band of Po212 with a shell-model investigation

The lifetimes of the first excited ${4}^{+}$ and ${6}^{+}$ states in $^{212}\mathrm{Po}$ were measured using the recoil-distance Doppler shift method. The nucleus of interest was populated in the $^{208}\mathrm{Pb}(^{18}\mathrm{O},^{14}\mathrm{C})^{212}\mathrm{Po}$ reaction. The experimental results are compared to large-scale shell model calculations performed using the recently developed H208 effective interaction. The calculations describe well the low-lying structure of $^{212}\mathrm{Po}$ with an exception of the ${2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+}$ transition rate which is strongly overestimated. This has been attributed to additional components in the wave function of the ground state.

Nuclear level density and γ -ray strength function of Ni63

The nuclear level density (NLD) and $\gamma$-ray strength function ($\gamma$SF) of $^{63}\mathrm{Ni}$ have been investigated using the Oslo method. The extracted NLD is compared with previous measurements using particle evaporation and those found from neutron resonance spacing. The $\gamma$SF was found to feature a strong low energy enhancement that could be explained as M1 strength based on large scale shell model calculations. Comparison of $\gamma$SFs measured with the Oslo method for various $\mathrm{Ni}$ isotopes reveals systematic changes to the strength below $5$ MeV with increasing mass.

Nucleon-pair truncation of the shell model for medium-heavy nuclei

Background: Establishing computationally tractable models of atomic nuclei is a long-time goal of nuclear structure physics. A flexible framework which easily includes excited states and many-body correlations is the configuration-interaction shell model (SM), but the exponential growth of the basis means one needs an efficient truncation scheme, ideally one that includes both deformation and pairing correlations.Purpose: We propose an efficient truncation scheme of the SM: starting from a pair condensate variationally defined by Hartree-Fock single-particle states and the particle-number conserved Bardeen-Cooper-Schrieffer (NBCS) approximation, we carry out projection of states with good angular momentum.Methods: After generating Hartree-Fock single-particle states with Kramers degeneracy in a SM space, we optimize the pair amplitudes in the NBCS by minimizing the energy, and then use linear algebra projection (LAP) of states with good angular momentum. Both NBCS and LAP are computationally fast.Results: Our calculations yield good agreement with full configuration-interaction SM calculations for low-lying states of transitional and rotational nuclei with axially symmetric and triaxial deformation in medium- and heavy-mass regions: $^{44,46,48}\mathrm{Ti}$, $^{48,50}\mathrm{Cr}$, $^{52}\mathrm{Fe}$, $^{60,62,64}\mathrm{Zn}$, $^{66,68}\mathrm{Ge}$, $^{68}\mathrm{Se}$, and $^{108,110}\mathrm{Xe}$. We predict low-lying states of $^{112--114}\mathrm{Ba}$ and $^{116--120}\mathrm{Ce}$, nuclei difficult to reach by large-scale SM calculations.Conclusions: Both pair correlation and the configuration mixing between different intrinsic states play a key role in reproducing collectivity and shape coexistence, demonstrating the utility of this truncation scheme of the SM to study transitional and deformed nuclei.

Beta decay and electron capture rates of manganese isotopes in astrophysical environments

The isotopes of manganese in the mass range of A=53−63 are abundant in the core materials of high-mass stars and they are considered to be of prime importance in the progression of the pre-collapse phases. During these late evolutionary phases, nuclear processes associated with weak interactions, including β−-decay and electron capture (EC) of these isotopes, significantly alter the lepton to baryon ratio (Ye) in the core’s composition. The temporal change in this parameter is one of the basic elements used to simulate a successful explosion. Hence, the β−-decay and EC rates of manganese (Mn) nuclides may serve as important inputs in the simulation codes for core-collapse supernova. In this study, we investigated the weak decay characteristics of 55−63Mn nuclides. The strength distributions of Gamow–Teller transitions in the directions of β−-decay and EC were calculated for these isotopes using the proton–neutron quasi-particle random-phase approximation (pn-QRPA) model. The β-decay half-life values of Mn isotopes under terrestrial conditions were computed and compared with measured data and previous calculations. The pn-QRPA estimated half-lives were in good agreement with the experimental values. The β− and EC rates were then calculated over a large range of stellar temperatures (0.01−30)×109K and densities (10−1011) g/cm3. The computed rates were compared with previous calculations performed using the large-scale shell model (LSSM) and independent particle model (IPM). For most of the isotopes, in high temperature and density regimes, the pn-QRPA calculated β−-decay rates were smaller than the LSSM and IPM rates by up to an order of magnitude. By contrast, the EC rates were larger by up to an order of magnitude (factor of 3−10) at high temperature compared with the LSSM (IPM) results.

Density matrix renormalization group description of the island of inversion isotopes F28–33

Recent experiments have confirmed that the neutron-rich isotopes $^{28,29}$F belong to the so-called island of inversion (IOI), a region of the nuclear chart around $Z=10$ and $N=20$ where nuclear structure deviates from the standard shell model predictions due to deformation and continuum effects. However, while the general principles leading to the IOI are relatively well understood, the details of the low-lying structure of the exotic fluorine isotopes $^{28-33}$F are basically unknown. In this work, we perform large-scale shell model calculations including continuum states to investigate the properties of the neutron-rich isotopes $^{25-33}$F, using a core of $^{24}$O and an effective two-body interaction with only three adjustable parameters. We adjust the core potential and interaction on experimentally confirmed states in $^{25,26}$O and $^{25-27}$F and solve the many-body problem using the density matrix renormalization group method for open quantum systems in a $sd$-$fp$ model space. We obtain the first detailed spectroscopy of $^{25-33}$F in the continuum and show how the interplay between continuum effects and deformation explains the recent data on $^{28,29}$F, and produces an inversion of the ${5/2}^+$ and ${1/2}^+$ states in $^{29,31,33}$F. Several deformed one- and two-neutron halo states are predicted in $^{29,31}$F, and we predict the ground state of $^{30}$F to have a structure similar to that of the first ${5/2}^+$ state of $^{29}$F. We also suggest several experimental studies to constraint models and test the present predictions. The complex structure of neutron-rich fluorine isotopes offers a trove of information about the formation of the southern shore of the IOI through a subtle interplay of deformation and continuum couplings driven by the occupation of the quasi-degenerate neutron shells $0d_{3/2}$ and $1p_{3/2}$.