Heavy Deformed Nuclei in the Shell Model Monte Carlo Method

Alhassid, Y.; Fang, L.; Nakada, H.

doi:10.1103/physrevlett.101.082501

Cited by 72 publications

(138 citation statements)

References 15 publications

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“…Here we describe a practical method that allows us to determine the ground-state energy using a single-parameter fit to experimental data. We use this method to calculate the SMMC state density of odd-even rare-earth isotopes 149−155 Sm and 143−149 Nd with the same Hamiltonian we used to calculate the state densities of even-even rareearth nuclei [15,16]. We find close agreement with the state densities that are extracted from experimental data.…”

Section: Introductionsupporting

confidence: 74%

“…(1), : : denotes normal ordering and V WS represents the Woods-Saxon potential. The pairing strengths is expressed as g ν = γḡ ν , where γ is a renormalization factor andḡ p = 10.9/Z, g n = 10.9/N are parametrized to reproduce the experimental odd-even mass differences for nearby spherical nuclei in the number-projected BCS approximation [15]. The quadrupole, octupole and hexadecupole interaction terms have strengths given by χ λ = k λ χ for λ = 2, 3, 4 respectively.…”

Section: Choice Of Model Space and Interactionmentioning

confidence: 99%

“…[15,16] spanned by the single-particle orbitals 0g 7/2 , 1d 5/2 , 1d 3/2 , 2s 1/2 , 0h 11/2 and 1f 7/2 for protons, and 0h 11/2 , 0h 9/2 , 1f 7/2 , 1f 5/2 , 2p 3/2 , 2p 1/2 , 0i 13/2 , and 1g 9/2 for neutrons. We have chosen these orbitals by the requirement that their occupation probabilities in well-deformed nuclei be between 0.9 and 0.1.…”

Section: Choice Of Model Space and Interactionmentioning

confidence: 99%

“…The bare single-particle energies in the shellmodel Hamiltonian are determined so as to reproduce the Woods-Saxon single-particle energies in the spherical Hartree-Fock approximation. The effective interaction consists of monopole pairing and multipole-multipole terms [15] …”

Section: Choice Of Model Space and Interactionmentioning

confidence: 99%

“…For β 3 MeV −1 , the dependence of E(β) on ∆β is weaker and an average value is taken instead. The calculations for β > 2 MeV −1 were carried out using a stabilization method of the one-body canonical propagator for each configuration of the auxiliary fields [15].…”

Section: Ground-state Energymentioning

confidence: 99%

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Nuclear state densities of odd-mass heavy nuclei in the shell model Monte Carlo approach

2015

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The shell model Monte Carlo (SMMC) approach enables the microscopic calculation of nuclear state densities in model spaces that are many orders of magnitude larger than those that can be treated by conventional diagonalization techniques. However, it has been difficult to calculate accurate state densities of odd-mass heavy nuclei as a function of excitation energy. This is because of a sign problem that arises from the projection on an odd number of particles at low temperatures, making it difficult to calculate accurate ground-state energies of odd-mass nuclei in direct Monte Carlo calculations. Here we extract the ground-state energy from a one-parameter fit of the SMMC thermal energy to the thermal energy that is determined from experimental data. This enables us to calculate the state densities of the odd-even isotopes 149−155 Sm and 143−149 Nd as a function of excitation energy. We find close agreement with state densities extracted from experimental data. Our results demonstrate that the state densities of the odd-mass samarium and neodymium isotopes can be consistently reproduced using the same Hamiltonian of the neighboring even-mass isotopes within the configuration-interaction shell model approach.

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Section: Introductionsupporting

confidence: 74%

Section: Choice Of Model Space and Interactionmentioning

confidence: 99%

Section: Choice Of Model Space and Interactionmentioning

confidence: 99%

Section: Choice Of Model Space and Interactionmentioning

confidence: 99%

Section: Ground-state Energymentioning

confidence: 99%

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Nuclear state densities of odd-mass heavy nuclei in the shell model Monte Carlo approach

2015

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Matrix‐Product State Approach to the Generalized Nuclear Pairing Hamiltonian

Rausch,

Plorin,

Peschke

et al. 2024

Annalen der Physik

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It is shown that from the point of view of the generalized pairing Hamiltonian, the atomic nucleus is a system with small entanglement and can thus be described efficiently using a 1D tensor network (matrix‐product state) despite the presence of long‐range interactions. The ground state can be obtained using the density‐matrix renormalization group (DMRG) algorithm, which is accurate up to machine precision even for large nuclei, is numerically as cheap as the widely used Bardeen‐Cooper‐Schrieffer (BCS) approach, and does not suffer from any mean‐field artifacts. This framework is applied to compute the even‐odd mass differences of all known lead isotopes from to in a very large configuration space of 13 shells between the neutron magic numbers 82 and 184 (i.e., two major shells) and find good agreement with the experiment. Pairing with non‐zero angular momentum is also considered and the lowest excited states in the full configuration space of one major shell is determined, which is demonstrated for the , isotones. To demonstrate the capabilities of the method beyond low‐lying excitations, the first 100 excited states of with singlet pairing and the two‐neutron removal spectral function of are calculated, which relate to a two‐neutron pickup experiment.

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Ab initio computations of molecular systems by the auxiliary‐field quantum Monte Carlo method

Motta

Zhang

2018

WIREs Comput Mol Sci

133

215

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The auxiliary-field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time-independent Schrödinger equation in atoms, molecules, solids, and a variety of model systems. AFQMC has recently witnessed remarkable growth, especially as a tool for electronic structure computations in real materials. The method has demonstrated excellent accuracy across a variety of correlated electron systems. Taking the form of stochastic evolution in a manifold of nonorthogonal Slater determinants, the method resembles an ensemble of density-functional theory (DFT) calculations in the presence of fluctuating external potentials. Its computational cost scales as a low-power of system size, similar to the corresponding independentelectron calculations. Highly efficient and intrinsically parallel, AFQMC is able to take full advantage of contemporary high-performance computing platforms and numerical libraries. In this review, we provide a self-contained introduction to the exact and constrained variants of AFQMC, with emphasis on its applications to the electronic structure of molecular systems. Representative results are presented, and theoretical foundations and implementation details of the method are discussed. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Structure and Mechanism > Computational Materials Science Computer and Information Science > Computer Algorithms and Programming K E Y W O R D S ab initio methods, auxiliary-field quantum Monte Carlo, back-propagation, computational quantum chemistry, constrained path approximation, electronic structure, importance sampling, phase problem, phaseless approximation, quantum many-body computation, quantum Monte Carlo methods, sign problem 1 | INTRODUCTIONA central challenge in the fields of condensed matter physics, quantum chemistry (QC), and materials science is to determine the quantum mechanical behavior of many interacting electrons and nuclei. Often relativistic effects and the coupling between the dynamics of electrons and nuclei can be neglected, or treated separately. Within this approximation, the many-electron wave function can be found by solving the time-independent Schrödinger equation for the Born-Oppenheimer Hamiltonian

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Heavy Deformed Nuclei in the Shell Model Monte Carlo Method

Cited by 72 publications

References 15 publications

Nuclear state densities of odd-mass heavy nuclei in the shell model Monte Carlo approach

Nuclear state densities of odd-mass heavy nuclei in the shell model Monte Carlo approach

Matrix‐Product State Approach to the Generalized Nuclear Pairing Hamiltonian

Ab initio computations of molecular systems by the auxiliary‐field quantum Monte Carlo method

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