Exact sum rules with approximate ground states

Johnson, Calvin W.; Luu, Ken; Lu, Yi

doi:10.1088/1361-6471/abacda

Cited by 8 publications

(7 citation statements)

References 55 publications

(96 reference statements)

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“…Note that the validity of the usual sum rule depends on the structure of the subspace (see Appendix A). This fact is known numerically [37], and it can be seen also with the DGCM and the GCM. table are the ratios of the left-hand side to the right-hand side of Eqs.…”

Section: B Resultsmentioning

confidence: 64%

Applications of the dynamical generator coordinate method to quadrupole excitations

Hizawa,

Hagino,

Yoshida

2022

Preprint

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We apply the dynamical generator coordinate method (DGCM) with a conjugate momentum to a nuclear collective excitation. To this end, we first discuss how to construct a numerically workable scheme of the DGCM for a general one-body operator. We then apply the DGCM to the quadrupole vibration of 16 O using the Gogny D1S interaction. We show that both the ground state energy and the excitation energies are lowered as compared to the conventional GCM with the same number of basis functions. We also compute the sum rule values for the quadrupole and monopole operators, and show that the DGCM yields more consistent results than the conventional GCM to the values from the double commutator. These results imply that the conjugate momentum is an important and relevant degree of freedom in collective motions.

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Section: B Resultsmentioning

confidence: 64%

Applications of the dynamical generator coordinate method to quadrupole excitations

Hizawa,

Hagino,

Yoshida

2022

Preprint

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“…is more than 5 MeV. For example, 32 S is a rotational nucleus, while the Hartree-Fock minimum generates a spherical shape for it, therefore only a 0 + is projected out, as is also pointed out in [47]. PVPC is rather accurate for ground states of semi-magic nuclei, with ∆E PVPC g.s.…”

Section: A Even-even Nuclei In 1s0d Shellmentioning

confidence: 78%

Nuclear states projected from a pair condensate

Lu,

Lei,

Johnson

et al. 2021

Preprint

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Atomic nuclei exhibit deformation, pairing correlations, and rotational symmetries. To meet these competing demands in a computationally tractable formalism, we revisit the use of general pair condensates with good particle number as a trial wave function for even-even nuclei. After minimizing the energy of the condensate, we project out states with good angular momentum with a fast projection technique, allowing for general triaxial deformations. To show applicability, we present example calculations from pair condensates in several model spaces, and compare against projected Hartree-Fock and full configuration-interaction shell model calculations. This approach successfully generates spherical, vibrational and rotational spectra, demonstrating potential for modeling medium-to heavy-mass nuclei.

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“…Nuclear approaches to reactions and scattering face several challenges, especially since nuclear probes are often peripheral and, hence, require a correct asymptotic treatment. Major challenges include: the long-range Coulomb force, and in particular in the case of large projectile and/or target charges where the asymptotics may not be analytically known; the high sensitivity of reaction observables to the reaction thresholds (Q-values); the importance of the non-resonant continuum when nuclei break up into the continuum; and the difficulties in describing scattering states asymptotics with single-particle bound-state bases typically used in many-body methods (31).…”

Section: Rare Isotope Beam Facilities and Needs For Theorymentioning

confidence: 99%

“…Thus, for example, experiments can provide precise thresholds, whereas theory can pinpoint critical collective and clustering correlations in wave functions to achieve the best estimates for reaction rates for astrophysics. Indeed, to analyze and interpret experimental data, theory with uncertainties lower than 10% is needed (31).…”

Section: Rare Isotope Beam Facilities and Needs For Theorymentioning

confidence: 99%

“…4.2.2), An important outcome of the RGM and multiple scattering approaches is an ab initio nucleon-nucleus effective potential. An alternative approach has employed the Green's function framework and applied to low energies ( 20 MeV per nucleon) using the selfconsistent Green's function method (68) and coupled-cluster method (69) (see also 31). These studies have built upon earlier theoretical frameworks, such as the one introduced by Feshbach, leading to the Green's function formulation (139), and the one pioneered by Watson (140,141) for elastic scattering of a nucleon from a nucleus, leading to the spectator expansion of the multiple scattering theory (142).…”

Section: Scattering and Reactions For A Single-nucleon Projectilementioning

confidence: 99%

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Nuclear Dynamics and Reactions in the Ab Initio Symmetry-Adapted Framework

Launey,

Mercenne,

Dytrych

2021

Preprint

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We review the ab initio symmetry-adapted (SA) framework for determining the structure of stable and unstable nuclei, along with related electroweak, decay and reaction processes. This framework utilizes the dominant symmetry of nuclear dynamics, the shape-related symplectic Sp(3, R) symmetry, which has been shown to emerge from first principles and to expose dominant degrees of freedom that are collective in nature, even in the lightest species or seemingly spherical states. This feature is illustrated for a broad scope of nuclei ranging from helium to titanium isotopes, enabled by recent developments of the ab initio symmetry-adapted no-core shell model expanded to the continuum through the use of the SA basis and that of the resonating group method. The review focuses on energies, electromagnetic transitions, quadrupole and magnetic moments, radii, form factors, and response function moments, for ground-state rotational bands and giant resonances. The method also determines the structure of reaction fragments that is used to calculate decay widths and alpha-capture reactions for simulated x-ray burst abundance patterns, as well as nucleon-nucleus interactions for cross sections and other reaction observables.

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Exact sum rules with approximate ground states

Cited by 8 publications

References 55 publications

Applications of the dynamical generator coordinate method to quadrupole excitations

Applications of the dynamical generator coordinate method to quadrupole excitations

Nuclear states projected from a pair condensate

Nuclear Dynamics and Reactions in the Ab Initio Symmetry-Adapted Framework

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