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We introduce a simple model to calculate the nuclear moment of inertia at finite temperature. This moment of inertia describes the spin distribution of nuclear levels in the framework of the spincutoff model. Our model is based on a deformed single-particle Hamiltonian with pairing interaction and takes into account fluctuations in the pairing gap. We derive a formula for the moment of inertia at finite temperature that generalizes the Belyaev formula for zero temperature. We show that a number-parity projection explains the strong odd-even effects observed in shell model Monte Carlo studies of the nuclear moment of inertia in the iron region.

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“…In general, the SMMC method [24,25] can be used to calculate thermal expectation values of observables O…”

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confidence: 99%

Nuclear moment of inertia and spin distribution of nuclear levels

et al. 2005

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“…Correlation effects can be taken into account in the context of the configuration-interaction (CI) shell model approach, but the size of the required model space in heavy nuclei is prohibitively large for direct diagonalization of the CI shell model Hamiltonian. This limitation can be overcome in part by using the shell model Monte Carlo (SMMC) method [1][2][3][4][5]. The SMMC method enables the calculation of statistical nuclear properties, and in particular of level densities, in very large model spaces [6][7][8][9][10].…”

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confidence: 99%

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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“…Since the strengths of the individual pairing modes and even the total isovector pairing strength are hard to extract from the limited data available, we again turn to a large-scale shell model Monte Carlo (SMMC) calculation in the full f p shell to see if the physics plays out in the same way. Unfortunately in odd-A and oddodd (excepting N = Z) nuclei the notorious sign-problem [4] inherent in SMMC studies with realistic interactions cannot be circumvented at low temperatures (T ≤ 0.8 MeV) by "g-extrapolation" [5]. We in large part avoid the problem, however, by using "pairing plus multipole-multipole" interaction of the kind used in Ref.…”

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Isovector pairing in odd-A proton-rich nuclei

1998

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A simple model based on the group SO(5) suggests that both the likeparticle and neutron-proton components of isovector pairing correlations in odd-A nuclei are Pauli blocked. The same effect emerges from Monte Carlo Shell-model calculations of proton-rich nuclei in the full f p shell. There are small differences between the two models in their representation of the effects of an odd nucleon on the competition between like-particle and neutron-proton pairing, but they can be understood and reduced by using a two-level version of the SO(5) model. On the other hand, in odd-odd nuclei with N = Z, SO(5) disagrees more severely with the shell model because it incorrectly predicts ground-state isospins. The shell model calculations for any f p-shell nuclei can be extended to finite temperature, where they show a decrease in blocking.

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Practical solution to the Monte Carlo sign problem: Realistic calculations ofFe54

Cited by 161 publications

References 13 publications

Nuclear moment of inertia and spin distribution of nuclear levels

Nuclear moment of inertia and spin distribution of nuclear levels

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

Isovector pairing in odd-A proton-rich nuclei

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