Jost function formalism based on the Hartree-Fock-Bogoliubov formalism

Mizuyama, Kazuhito; Le, N. Nhu; Thuy, T. Dieu; Hao, T. V. Nhan

doi:10.1103/physrevc.99.054607

Cited by 9 publications

(12 citation statements)

References 68 publications

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“…U lj (r) and ∆(r) are the HF mean field and the pair potential, respectively. We adopt the same Woods-Saxon form and their parameters as [13] for the numerical calculation. ϕ r 0,lj (r; k 1 (E)) is the regular solution of the HF equation.…”

Section: A Gell-mann-goldberger Relation In Hfbmentioning

confidence: 99%

“…where ψ (±) 0,lj (r; k 1 (E)) = ϕ r 0,lj (r; k 1 (E))/J (±) 0,lj (k 1 (E)) and ψ (+) 2,lj (r; E) is the lower component of the HFB scattering wave function [13].…”

Section: A Gell-mann-goldberger Relation In Hfbmentioning

confidence: 99%

“…Since it has been proved that S 11 lj (E) satisfies the unitarity on the scattering states defined on the real axis of E above the Fermi energy −λ in [13], S 11 lj (E) can be expressed as S 11 lj (E) = e 2iδ lj (E) . (The quasiparticle energy E is hereafter supposed to be on the scattering states.)…”

Section: A Gell-mann-goldberger Relation In Hfbmentioning

confidence: 99%

“…In this paper, we analyze the pairing effect on the partial cross sections of p 1/2 with λ = −8.0 MeV and d 3/2 with λ = −1.0 MeV by using the same Woods-Saxon parameters for the numerical calculation as in Ref. [13]. Both resonances are the so-called hole-type resonances originated from the hole state resulting from the particle-hole (p-h) configuration mixing due to the pairing.…”

Section: B Fano Parametersmentioning

confidence: 99%

“…The aim of this study is to organize the Fano formula for the neutron elastic scattering on the open shell nuclei with the help of the Jost function formalism [12] based on the HFB [13], and we shall discuss the role of the Fano parameters for the quasiparticle resonances seen in the partial cross section of the neutron elastic scattering. Because characteristic asymmetric shapes of the cross sections have been shown as the numerical results obtained by the HFB framework [13]. * corresponding author: T. V. Nhan Hao (tvnhao@hueuni.edu.vn) Firstly, we divide the Jost function into two parts: the scattering part and the pairing part.…”

Section: Introductionmentioning

confidence: 99%

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Fano effect on neutron elastic scattering by open-shell nuclei

Mizuyama

Hao

2020

Phys. Rev. C

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By focusing on the asymmetric shape of cross section, we analyze the pairing effect on the partial wave components of cross section for neutron elastic scattering off stable and unstable nuclei within the Hartree-Fock-Bogoliubov (HFB) framework. Explicit expressions for Fano parameters q lj and ǫ lj have been derived and the pairing effects have been analyzed in term of these parameters, and the Fano effect was found on the neutron elastic scattering off the stable nucleus in terms of the pairing correlation. Fano effect was appeared as the asymmetric line-shape of the cross section caused by the small absolute value of q lj due to the small pairing effect on the deep-lying hole state of the stable nucleus. In the case of the unstable nuclei, the large q lj value is expected because of the small absolute value of the Fermi energy. The quasiparticle resonance with the large q lj forms the Breit-Wigner type shape in the elastic scattering cross section.

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Section: A Gell-mann-goldberger Relation In Hfbmentioning

confidence: 99%

“…where ψ (±) 0,lj (r; k 1 (E)) = ϕ r 0,lj (r; k 1 (E))/J (±) 0,lj (k 1 (E)) and ψ (+) 2,lj (r; E) is the lower component of the HFB scattering wave function [13].…”

Section: A Gell-mann-goldberger Relation In Hfbmentioning

confidence: 99%

Section: A Gell-mann-goldberger Relation In Hfbmentioning

confidence: 99%

Section: B Fano Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fano effect on neutron elastic scattering by open-shell nuclei

Mizuyama

Hao

2020

Phys. Rev. C

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Optical potentials for the rare-isotope beam era

Hebborn

Nunes

Potel

et al. 2023

J. Phys. G: Nucl. Part. Phys.

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We review recent progress and motivate the need for further developments in nuclear optical potentials that are widely used in the theoretical analysis of nucleon elastic scattering and reaction cross sections. In regions of the nuclear chart away from stability, which represent a frontier in nuclear science over the coming decade and which will be probed at new rare-isotope beam facilities worldwide, there is a targeted need to quantify and reduce theoretical reaction model uncertainties, especially with respect to nuclear optical potentials. We first describe the primary physics motivations for an improved description of nuclear reactions involving short-lived isotopes, focusing on its benefits for fundamental science discoveries and applications to medicine, energy, and security. We then outline the various methods in use today to build optical potentials starting from phenomenological, microscopic, and ab initio methods, highlighting in particular the strengths and weaknesses of each approach. We then discuss publicly-available tools and resources facilitating the propagation of recent progresses in the field to practitioners. Finally, we provide a set of open challenges and recommendations for the field to advance the fundamental science goals of nuclear reaction studies in the rare-isotope beam era.

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s-wave quasiparticle resonance in neutron-rich drip-line nuclei

Kobayashi

2020

Progress of Theoretical and Experimental Physics

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We investigate unbound single-particle states in pair-correlated drip-line nuclei by describing a low-energy elastic scattering of a neutron in the $s$-wave within the framework of the coordinate space Hartree–Fock–Bogoliubov (Bogoliubov–de Genne) equation. A numerical study is performed for a neutron drip-line carbon isotope where the neutron $2s_{1/2}$ orbit is located close to zero energy. Analyzing the S-matrix poles of the elastic scattering, we discuss properties of the $s$-wave quasiparticle resonance and, in particular, behaviors characteristic to drip-line nuclei. It is found that the S-matrix has two pairs of poles; one pair appears as either a weakly bound state, a virtual state or a resonance while the other pair makes a contribution analogous to a bound single-particle state. The $s$-wave quasiparticle resonance emerges with a large variation depending on the pairing gap and the single-particle energy of the $s$-orbit.

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Jost function formalism based on the Hartree-Fock-Bogoliubov formalism

Cited by 9 publications

References 68 publications

Fano effect on neutron elastic scattering by open-shell nuclei

Fano effect on neutron elastic scattering by open-shell nuclei

Optical potentials for the rare-isotope beam era

s-wave quasiparticle resonance in neutron-rich drip-line nuclei

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