Transition sum rules in the shell model

Lü, Yi; Johnson, Calvin W.

doi:10.1103/physrevc.97.034330

Cited by 12 publications

(21 citation statements)

References 54 publications

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“…However, compared * E-mail: toishi@phy.hr † E-mail: npaar@phy.hr with the electric dipole (E1) and quadrupole (E2) modes [28][29][30][31][32][33][34], the knowledge on the pairing effect on magnetic modes, as well as on unnatural-parity states, is rather limited [10][11][12]20]. In studies of nuclear modes of excitation, the sum rules associated to the transition strength and energyweighted sum rules, represent an essential tool for the analyses of the excitations, not only as benchmark tests of the theoretical frameworks involved, but also to inspect the completeness of the experimental data [35][36][37][38][39][40][41][42][43][44][45][46][47][48]. Over the past decades, the analyses of the sum rules have been mandatory to validate theoretical approaches to describe various modes of excitation.…”

Section: Introductionmentioning

confidence: 99%

Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons

Oishi

Paar

2019

Phys. Rev. C

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Background: Magnetic dipole (M1) excitation is the leading mode of nuclear excitation by the magnetic field, which couples unnatural-parity states. Since the M1 excitation occurs mainly for open-shell nuclei, the nuclear pairing effect is expected to play a role. As expected from the form of operator, this mode may provide the information on the spin-related properties, including the spin component of dineutron and diproton correlations. In general, the sum rule for M1 transition strength has not been derived yet. Purpose: To investigate the M1 excitation of the systems with two valence nucleons above the closed-shell core, with pairing correlation included, and to establish the M1 sum rule that could be used to validate theoretical and experimental approaches. Possibility to utilize the M1 excitation as a tool to investigate the pairing correlation in medium is also discussed. Method: Three-body model, which consists of a rigid spherical core and two valence nucleons, is employed. Interactions for its two-body subsystems are phenomenologically determined in order to reproduce the two-body and three-body energies. We also derive the M1 sum rule within this three-body picture. Conclusion: The introduced M1 sum rule can be utilized as a benchmark for model calculations of M1 transitions in the systems with two valence nucleons. The total sum of the M1 transition strength is related with the coupled spin of valence nucleons in the open shell, where the pairing correlation is unnegligible. The three-body-model calculations for 18 O, 18 Ne, and 42 Ca nuclei demonstrate a significant effect of the pairing correlations on the low-lying M1 transitions. Therefore, further experimental studies of M1 transitions in those systems are on demand, in order to validate proposed sum rule, provide a suitable probe for the nuclear pairing in medium, as well as to optimize the pairing models.

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Section: Introductionmentioning

confidence: 99%

Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons

Oishi

Paar

2019

Phys. Rev. C

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“…Yet, by going up to systematically higher initial energies, recent work on several transition operators (electric quadrupole, magnetic dipole, and Gamow-Teller) has provided both numerical evidence and mathematical arguments that the sum rules are not and cannot be independent of energy. However, it is crucial to note that the sum rules evolve smoothly with energy, exhibiting robust fluctuations, by which we mean that the fluctuations calculated in an energy bin are insensitive to the bin size [21,32]. This observation leads to a modification of the Brink-Axel hypothesis, as we discuss in the next section.…”

Section: A Strength Functions and The Brink-axel Hypothesismentioning

confidence: 91%

“…As a test of the Brink-Axel hypothesis in calculations, one can consider moments or sum rules of the strength function, specifically the non-energy-weighted sum rule or total strength, S 0 (E i ) = B(E i , E tr ) dE tr , and the energyweighted sum rule, S 1 (E i ) = E tr B(E i , E tr ) dE tr . Both are convenient to write as expectation values and so one can efficiently evaluate the sum rules for many states [21,32]. If the Brink-Axel hypothesis were true, the sum rules would be independent of the initial energy E i .…”

Section: A Strength Functions and The Brink-axel Hypothesismentioning

confidence: 99%

A modified Brink-Axel hypothesis for astrophysical Gamow-Teller transitions

Herrera,

Johnson,

Fuller

2021

Preprint

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Weak interaction charged current transition strengths from highly excited nuclear states are fundamental ingredients for accurate modeling of compact object composition and dynamics, but are difficult to obtain either from experiment or theory. For lack of alternatives, calculations have often fallen back upon a generalized Brink-Axel hypothesis, that is, assuming the strength function (transition probability) is independent of the initial nuclear state but depends only upon the transition energy and the weak interaction properties of the parent nucleus ground state. Here we present numerical evidence for a modified 'local' Brink-Axel hypothesis for Gamow-Teller transitions for pf -shell nuclei relevant to astrophysical applications. Specifically, while the original Brink-Axel hypothesis does not hold globally, strength functions from initial states nearby in energy are similar within statistical fluctuations. This agrees with previous work on strength function moments. Using this modified hypothesis, we can tackle strength functions at previously intractable initial energies, using semi-converged initial states at arbitrary excitation energy. Our work provides a well-founded method for computing accurate thermal weak transition rates for medium-mass nuclei at temperatures occurring in stellar cores near collapse. We finish by comparing to previous calculations of astrophysical rates.

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“…One can get around this limitation by using sum rules [11,12,13]. Let Ô be some transition operator, and let {|n } be eigenstates of a Hamiltonian Ĥ with energies E n .…”

Section: Introductionmentioning

confidence: 99%

“…Ô † , Ĥ , Ô for general one-body transition operators, including nonscalar operators with nonzero angular momentum rank, and general 1+2-body Hamiltonians [13]. This allows one to efficiently compute the NEWSR and EWSR for many nuclei for arbitrary one-body transitions.…”

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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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Transition sum rules in the shell model

Cited by 12 publications

References 54 publications

Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons

Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons

A modified Brink-Axel hypothesis for astrophysical Gamow-Teller transitions

Exact sum rules with approximate ground states

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