Monte Carlo Shell Model Calculations Research Articles

Spin distribution in low-energy nuclear level schemes

The spin-cutoff parameter \ensuremath{\sigma} has been determined for experimental spin distributions at low excitation energies of 310 nuclei between $^{18}\mathrm{F}$ and $^{251}\mathrm{Cf}$ (more than 8000 levels with their spin). The results indicate a weak dependence on the mass number $A$ of the spin-cutoff parameter ${\ensuremath{\sigma}}^{2}~{A}^{0.28}$, and an even-odd spin staggering in the spin distribution of the even-even nuclei, with a strong enhancement of the number of states with spin zero. A modification of the spin-cutoff distribution formula is proposed in order to describe the even-even nuclei data. These findings are in good agreement with recent predictions of shell-model Monte Carlo calculations.

Excited intruder states inMg32

The low energy level structure of $N=20$ $^{32}\mathrm{Mg}$ obtained via \ensuremath{\beta}-delayed \ensuremath{\gamma} spectroscopy is reported. The level structure of $^{32}\mathrm{Mg}$ is found to be completely dominated by intruders. An inversion between the 1p-1h and 3p-3h states is observed for the negative parity states, similar to the 0p-0h and 2p-2h inversion for the positive parity states in these $N~20$ nuclei. The intruder excited states, both positive and negative parity, are reasonably explained by Monte Carlo shell model calculations, which suggest a shrinking $N=20$ shell gap with decreasing $Z$.

Spin- and Parity-Resolved Level Densities from the Fine Structure of Giant Resonances

Level densities of J pi=2+ and 2- states extracted from high-resolution studies of E2 and M2 giant resonances in 58Ni and 90Zr are used to test recent predictions of a possible parity dependence. The experimental results are compared to a combinatorial approach based on the Hartree-Fock-Bogoliubov model and to shell-model Monte Carlo calculations including both spin and parity projection. No parity dependence is observed experimentally, which is in agreement for 90Zr but in contrast with the model predictions for 58Ni.

Spectroscopy ofMg36: Interplay of Normal and Intruder Configurations at the Neutron-Rich Boundary of the “Island of Inversion”

We report on the first spectroscopy study of the very neutron-rich nucleus (36)(12)Mg24 using the direct two-proton knockout reaction 9Be(38Si,36Mg+gamma)X at 83 MeV/nucleon. The energy of the first excited 2+ state of 36Mg, E(2+(1)=660(6) keV, was measured. The magnitude of the partial cross sections to the ground state and the 2+(1) state is indicative of strong intruder admixtures in the lowest-lying states as suggested by Monte Carlo shell-model calculations.

Competition between normal and intruder states inside the “island of inversion”

The beta decay of the exotic 30Ne (N=20) is reported. For the first time, the low-energy level structure of the N=19, 30Na (Tz = 4), is obtained from beta-delayed gamma spectroscopy using fragment-beta-gamma-gamma coincidences. The level structure clearly displays "inversion", i.e., intruder states with mainly 2p2h configurations displacing the normal states to higher excitation energies. The good agreement in excitation energies and the weak and electromagnetic decay patterns with Monte Carlo Shell Model calculations with the SDPF-M interaction in the sdpf valence space illustrates the small d3/2 - f7/2 shell gap. The relative position of the "normal dominant" and "intruder dominant" excited states provides valuable information to understand better the N=20 shell gap.

Spectroscopic Study of Neutron Shell Closures via Nucleon Transfer in the Near-Dripline NucleusO23

Neutron single particle energies have been measured in 23O using the 22O(d,p)23O*-->22O+n process. The energies of the resonant states have been deduced to be 4.00(2) MeV and 5.30(4) MeV. The first excited state can be assigned to the nu d3/2 single particle state from a comparison with shell model calculations. The measured 4.0 MeV energy difference between the nu s1/2 and nu d3/2 states gives the size of the N=16 shell gap which is in agreement with the recent USD05 ("universal" sd from 2005) shell model calculation, and is large enough to explain the unbound nature of the oxygen isotopes heavier than A=24. The resonance detected at 5.3 MeV can be assigned to a state out of the sd shell model space. Its energy corresponds to a approximately 1.3 MeV sized N=20 shell gap, therefore, the N=20 shell closure disappears at Z=8 in agreement with Monte Carlo shell model calculations using SDPF-M interaction.

Evolution of the N = 20 shell gap

Stucture of N = 17,18 nuclei has been investigated via proton inelastic scattering and neutron removal reactions up to the neutron dripline in inverse kinematics by use of radioctive ion beams provided by the RIKEN isotope separator, RIPS. Low energy excited states have been found in all the 26,27F and 27Ne nuclei, which are out of the neutron sd shell configuration space and are considered as intruder states arisng from cross shell excitations. Monte-Carlo shell model calculations with the sdpf-m interaction predict low energy negative parity excited states from neutron cross shell excitation at N = 17,18, which is in agreement with our experimental results. Observation of intruder states even at N = 17, especially the p3/2 state in 27Ne at 765 keV is a clear indication of a vanishing N = 20 shell gap at Z = 8 as predicted by the sdpf-m shell model calculations.

Direct evidence for the onset of intruder configurations in neutron-rich Ne isotopes

Abstract We report on direct experimental evidence of the population of the 3 / 2 − intruder state in 27Ne in the knockout of a single neutron from the ground state of 28Ne. This low-lying negative parity state is consistent with a narrower shell gap for exotic nuclei with Z ≪ N and N ≈ 20 . Monte Carlo shell-model calculations with the modern SDPF-M interaction successfully describe neutron-rich nuclei in the vicinity of N = 20 where normal and intruder configurations coexist at low excitation energy. This observation demonstrates the importance of direct reactions for the study of exotic nuclei and the predictive power of these large-scale shell-model calculations.

Quadrupole Deformation of the Self-Conjugate NucleusKr72

We report on the first determination of the absolute B(E2;0+(1)-->2+(1)) excitation strength in the N=Z nucleus 72Kr. 72Kr is the heaviest N=Z nucleus for which this quantity has been measured and provides a benchmark in a region of the nuclear chart dominated by rapidly changing deformations and shapes mediated by the interplay of strongly oblate and prolate-driving orbitals. The deduced quadrupole deformation strength is in agreement with a variety of self-consistent models that predict an oblate shape for the ground state of 72Kr. Large-scale shell-model Monte Carlo calculations reproduce the experimental B(E2) value and link the result to the occupation of the deformation-driving g9/2 orbit.

Shape coexistence and mixing in N ∼ 20 region

Spherical-deformed shape coexistence in the N ∼ 20 region is studied with the Monte Carlo shell model calculation. We focused upon the role of the configuration mixing in its description, and found that the deformed state is not correctly positioned until the mixing is treated in a proper way. It is also mentioned that the intruder component in 33Al is accessible through the measurement of the magnetic moment.

Monte-Carlo shell model calculations of triaxially deformed states around 134Ba

The nuclear structure of ground states and low-lying excited states of even-even isotopes around 134Ba is described using the nuclear shell model microscopically. These structures are revealed to show various phenomena of quadrupole collective states, including the transition of spherical, axially symmetric deformed and triaxially deformed shapes and the realization of the critical point symmetry, E(5).

Shell model Monte Carlo studies of nuclei in the A∼80 mass region

We perform shell model Monte Carlo calculations for proton-rich Kr, Sr, and Zr isotopes in the mass range A=72–84. We employ a complete 1 p0 f–0 g1 d2 s configuration space and an effective quadrupole-plus-pairing residual interaction. Our calculation reproduces the large B( E2) values observed in these nuclei. We relate these values to the gain in correlation energy obtained by moving nucleons across the N=40 subshell closure into g 9/2 orbitals.

Electron capture rates for core collapse supernovae

Electron capture rates on neutron-rich nuclei (A>65) were calculated within the Random Phase Approximation with partial number formalism, including allowed and forbidden transitions. The partial occupation numbers were provided as a function of temperature by Shell-Model Monte Carlo calculations, including an pairing+quadrupole interaction. Capture rates on relevent nuclei were calculated for density and temperature conditions during the core collapse of a massive star. It was found that electron captures on nuclei can compete with electron captures on free protons. Furthermore, they produce neutrinos with average energies lower than neutrinos emitted from captures on free protons, with possible consequences on the cooling of the core.

Monte Carlo shell model calculation for unstable nuclei around N=20

Monte Carlo shell model calculation for unstable nuclei around N=20

MONTE CARLO SHELL MODEL CALCULATIONS FOR ATOMIC NUCLEI

The formulation and recent applications of the Quantum Monte Carlo diagonalization (QMCD) method are reported. The QMCD has been proposed for solving the quantum many-body inteacting systems, providing us with energy eigenvalues, transition matrix elements and wave functions. Its application to the nuclear shell model is referred to as the Monte Carlo Shell Model. By the Monte Carlo Shell Model calculations, the level structure of low-lying states can be studied with realistic interactions, providing a useful tool for nuclear spectroscopy. The Monte Carlo Shell Model has been applied to the study of a variety of nuclei, and can be characterized as the importance truncation scheme to the full diagonalization which is infeasible in many cases due to extremely large dimensions.

Exotic nuclei in the Monte Carlo shell model calculations

Exotic nuclei in the Monte Carlo shell model calculations

Striking harmony between the nuclear shell model and new experimentalgfactors andB(E2)values of even Ni isotopes

High precision g factors and $B(E2)$ values were obtained in measurements of the first ${2}^{+}$ states of ${}^{58\ensuremath{-}64}\mathrm{Ni}$ using the technique of projectile Coulomb excitation in combination with transient magnetic fields. The new results are well explained by large-scale shell model calculations in which, for ${}^{58\ensuremath{-}62}\mathrm{Ni},$ up to $t=5$ nucleons are excited from the ${f}_{7/2}$ shell into the remaining $\mathrm{fp}$ shell orbits. A complete calculation was carried out for ${}^{64}\mathrm{Ni}.$ The g factor of ${}^{58}\mathrm{Ni}$ is particularly surprising as it is small but definitely positive, a result which was not expected and therefore not considered in several earlier calculations. This observation can be explained by strong coupling of valence particles to an excited ${}^{56}\mathrm{Ni}$ core in accordance with recent Monte Carlo shell model calculations.

Parity dependence of nuclear level densities

A simple formula for the ratio of the number of odd- and even-parity states as a function of temperature is derived. This formula is used to calculate the ratio of level densities of opposite parities as a function of excitation energy. We test the formula with quantum Monte Carlo shell model calculations in the (pf+g(9/2)) shell. The formula describes well the transition from low excitation energies where a single parity dominates to high excitations where the two densities are equal.

Sum rules regarding the sign problem in Monte Carlo shell model calculations

The Monte Carlo shell model is a powerful technique for computational nuclear structure. Only a certain class of nuclear interactions, however, such as pairing and quadrupole, are free of the numerical noise known as the sign problem.This paper presents sum rules that relate the sign problem to the J=0 pairing matrix elements, thus illuminating the extrapolation procedure routinely used for realistic shell-model interactions.

Monte Carlo Shell Model Calculations for Atomic Nuclei and Their Parallel Computing

The Quantum Monte Carlo Diagonalization methodfor solving quantum many-bod y problems has been proposed, and its applications to the nuclear shell model have been extensively developed. This application is called Monte Carlo Shell Model. The actual numerical calculations of Monte Carlo Shell Model can be carried out very efficiently by a massive parallel computer, and indeed we have introduced one called Alphleet to RIKEN recently. A brief sketch of the Monte Carlo Shell Model and its parallel computing are presented.