Nucleon pair shell model in 
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 scheme

He, B. C.; Li, Lei; Luo, Yan-An; Zhang, Y.; Pan, Feng; Draayer, J. P.

doi:10.1103/physrevc.102.024304

Cited by 23 publications

(29 citation statements)

References 27 publications

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“…However, such formalism enables only one type of collective pair in the many-body configuration, because it is specified for variational calculations. Later, the present authors and collaborator [7] also noted that the matrix representation works for the M -scheme NPA [8]. We suggested that the commutators between pair operators and one-body operators can be expressed as general matrix products, and thus a recursive formalism was obtained based on the trace calculations of these products.…”

Section: Introductionmentioning

confidence: 77%

OMR-NPA: Optimized Matrix Representation of Nucleon Pair Approximation

Lei¹,

Lu²

2022

Preprint

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We optimize the matrix representation of the nucleon-pair approximation (NPA) of the nuclear shell model. The NPA is a widely adopted truncation approach of the nuclear shell model and proves to be effective in describing low-lying states of medium-heavy and heavy nuclei. Due to simplified (yet flexible) commutators and absolute elimination of angular momentum coupling, the matrix representation provides a formalism for the M -scheme NPA more efficient than others as far as we know. It also enables the practicable organization and storage design for intermediate results, including generated collective pairs, matrix products, and matrix traces, so that further optimization is achieved by reducing repetitive matrix operations, which are the most time-consuming procedures in the matrix-represented M -scheme NPA. We also describe optimizations specified for the M -scheme NPA, realized by invoking the Wigner-Eckart theorem, timereversal symmetry, and conjugate operation of spherical tensors. Our optimization makes the combination of matrix representation and NPA more profitable. Such an implementation denoted by optimized matrix representation of NPA (OMR-NPA) is publicly released with open source. Its performance is analyzed and compared against unoptimized NPA codes.

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Section: Introductionmentioning

confidence: 77%

OMR-NPA: Optimized Matrix Representation of Nucleon Pair Approximation

Lei¹,

Lu²

2022

Preprint

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“…One must restrict the singleparticle states, which leads to a finite many-body basis which can nonetheless be very large. We use two valence spaces: the 1s 1/2 -0d 3/2 -0d 5/2 space, of sd-shell, with a frozen 16 O core, and the 1p 1/2 -1p 3/2 -0f 5/2 -0f 7/2 , or pf -shell, with a frozen 40 Ca core. In the sd shell we use the universal sd-shell interaction version B, or USDB [19], and in the pf shell we use a modified G-matrix interaction version 1A, or GX1A [20,21].…”

Section: Methodsmentioning

confidence: 99%

“…While previous implementations of the nucleon pair approximation utilized the natural J-scheme formalism [39,35], recent efforts have recast the NPA efficiently into the M -scheme [40]. Although the dimensionality of the M -scheme Hamilonian is 1-2 orders of magnitude larger than in the J-scheme, the matrix elements themselves take considerably more time to compute in the latter due to a proliferation of recursion branches arising from angular momentum recoupling.…”

Section: Nucleon Pair Approximationmentioning

confidence: 99%

Exact sum rules with approximate ground states

Johnson,

Luu,

2020

Preprint

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Electromagnetic and weak transitions tell us a great deal about the structure of atomic nuclei. Yet modeling transitions can be difficult: it is often easier to compute the ground state, if only as an approximation, than excited states. One alternative is through transition sum rules, in particular the non-energy-weighted and energy-weighted sum rules, which can be computed as expectation values of operators. We investigate by computing sum rules for a variety of nuclei, comparing the numerically exact full configuration-interaction shell model, as a reference, to Hartree-Fock, projected Hartree-Fock, and the nucleon pair approximation. These approximations yield reasonable agreement, which we explain by prior work on the systematics of transition moments.

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“…For a comprehensive review, see Reference [45]. In recent years, the NPA with isospin symmetry [46], the version with particle-hole excitations [27], and the versions considering pairs in the M-scheme [47,48] have been developed. In the NPA with particle-hole excitations [27], a particle-hole "mixed" representation is adopted, where the particle-hole conjugate transformation is applied to the operators of the lower major shell while the operators of the upper major shell remain unchanged, so that three types of collective pairs, i.e., particle-particle, hole-hole, and particle-hole pairs, are equally treated in technique.…”

Section: Introductionmentioning

confidence: 99%

Description for N = 126 Isotones 210Po and 212Rn with Particle-Hole Excited Nucleon-Pair Approximation and Realistic Effective Interaction

2022

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In this paper, we study yrast states of two N = 126 isotones 210Po and 212Rn using the nucleon-pair approximation with particle–hole excitations and using a low-momentum interaction Vlow−k renormalized from the free CD-Bonn NN potential. An overall good agreement with experimental level structures, B(E2)s, and B(E3)s, is achieved. We also calculate the probabilities of neutron particle–hole excitations in these yrast states, with a focus on negative-parity states, which reflect the roles played by the neutron negative-parity configurations of one-particle-one-hole excitations across the N = 126 shell gap and the negative-parity configurations of valence proton particles involving the 0i13/2 orbit. The N = 126 shell gap is discussed in terms of energies of neutron one-particle-one-hole excitations.

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Nucleon pair shell model in M scheme

Cited by 23 publications

References 27 publications

OMR-NPA: Optimized Matrix Representation of Nucleon Pair Approximation

OMR-NPA: Optimized Matrix Representation of Nucleon Pair Approximation

Exact sum rules with approximate ground states

Description for N = 126 Isotones 210Po and 212Rn with Particle-Hole Excited Nucleon-Pair Approximation and Realistic Effective Interaction

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