Anderson-Bogoliubov phonons in the inner crust of neutron stars: Dipole excitation in a spherical Wigner-Seitz cell

Inakura, Tsunenori

doi:10.1103/physrevc.96.025806

Cited by 10 publications

(25 citation statements)

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“…This suggests that one is dealing here with the Anderson-Bogolyubov mode of neutron matter modified by the existence of a nuclear cluster in the center of the WS cell. The presence of the dipole Anderson-Bogolyubov mode was confirmed in a later study [410], which finds that this mode is present outside the cluster and is strongly suppressed inside it. That this mode shows up only for neutrons is consistent with the fact that these are continuum modes associated with the dripped neutron fluid.…”

Section: Collective Modes and Entrainmentmentioning

confidence: 65%

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Superfluidity in nuclear systems and neutron stars

2019

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Nuclear matter and finite nuclei exhibit the property of superfluidity by forming Cooper pairs. We review the microscopic theories and methods that are being employed to understand the basic properties of superfluid nuclear systems, with emphasis on the spatially extended matter encountered in neutron stars, supernova envelopes, and nuclear collisions. Our survey of quantum many-body methods includes techniques that employ Green functions, correlated basis functions, and Monte Carlo sampling of quantum states. With respect to empirical realizations of nucleonic and hadronic superfluids, this review is focused on progress that has been made toward quantitative understanding of their properties at the level of microscopic theories of pairing, with emphasis on the condensates that exist under conditions prevailing in neutron-star interiors. These include singlet S-wave pairing of neutrons in the inner crust, and, in the quantum fluid interior, singlet-S proton pairing and triplet coupled P -F -wave neutron pairing. Additionally, calculations of weak-interaction rates in neutron-star superfluids within the Green function formalism are examined in detail. We close with a discussion of quantum vortex states in nuclear systems and their dynamics in neutron-star superfluid interiors. PACS. 97.60.Jd Neutron stars -21.65.+f Nuclear matter -47.37.+q Hydrodynamic aspects of superfluidity; quantum fluids -67.85.+d Ultracold gases, trapped gases -74.25.Dw Superconductivity phase diagrams Contents arXiv:1802.00017v4 [nucl-th] 26 Sep 2019 emerge in the interaction part of the Hamiltonian when evaluating Eq. (5) in terms of Bogolyubov operators vanish. Such terms would account for fluctuations in the system, but are beyond the scope of the present mean-field treatment. 4 Note that the variation δ(E − µN )/δn p,↑ , with up and vp held constant, yields the quantity Ep, confirming its interpretation. Armen Sedrakian, John W. Clark: Superfluidity in nuclear systems and neutron stars 5

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Section: Collective Modes and Entrainmentmentioning

confidence: 65%

“…An additional mode was found at zero energy, which arises from the displacements of the cluster as whole, the corresponding quanta being the lattice phonons. The coupling of these two modes was found to be weak [410].…”

Section: Collective Modes and Entrainmentmentioning

confidence: 93%

Superfluidity in nuclear systems and neutron stars

2019

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“…We employ the HFB model and the QRPA theory. The calculation framework and the model parameters are the same as those in Part I [26]. Here we recapitulate the adopted HFB+QRPA formalism briefly.…”

Section: Modelmentioning

confidence: 99%

“…In the following we call the superfluid phonon mode of neutron superfluid the Anderson-Bogoliubov phonon mode (abbreviated as AB phonon) to keep the same nomenclature as in Part I [26]. The paper is organized as follows: In Sec.…”

Section: Introductionmentioning

confidence: 99%

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Coexistence of Anderson-Bogoliubov phonon and quadrupole cluster vibration in the inner crust of neutron stars

Inakura

2019

Phys. Rev. C

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Background: Low-lying collective excitations of inner crust matter in neutron stars are expected to have impact on observables such as the quasi-periodic oscillation in giant flares and the cooling of inner crust in transient phenomena. Coupling between Anderson-Bogoliubov superfluid phonon (AB phonon) in superfluid neutron gas and collective excitations of nuclear clusters is a key issue. Purpose: We intend to predict the nature of low-lying excitation modes of superfluid inner crust matter with focus on quadrupole excitations around a spherical nuclear cluster. We study how the AB phonon of neutron superfluid and possible quadrupole shape vibration of clusters are affected by the inhomogeneous structure of inner crust matter. Methods: The coordinate-space Hartree-Fock-Bogoliubov method and the quasiparticle randomphase approximation formulated in a spherical Wigner-Seitz cell are adopted to describe neutron superfluidity and low-lying collective excitations. We perform systematic numerical calculations for quadrupole excitations by varying the neutron chemical potential and the number of protons in a cell. Results: The calculated results indicate emergence of both AB phonon and quadrupole shape vibration of the cluster with small mixing between the two collective modes. The quadruple AB phonon is similar to that in uniform superfluid apart from small admixture of the shape vibration of cluster. The excitation energy and the collectivity of the cluster vibration mode shows strong and oscillatory dependence on the neutron chemical potential (the neutron gas density), leading to softening and instability in certain situations. This is caused by the resonance shell effect where unbound but resonant single-particle states of neutrons play a central role. Conclusions: The AB phonon of superfluid neutron gas and the quadrupole shape vibration of nuclear cluster coexist in inner crust. The coupling between the AB phonon and the quadrupole shape vibration is weak. The collectivity of the quadrupole shape vibration is governed by the resonance shell effect, and it suggests that emergence of deformed nuclear clusters is possible at any layer of inner crust.

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Proximity effect of pair correlation in the inner crust of neutron stars

Okihashi

2020

Progress of Theoretical and Experimental Physics

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We study proximity effect of pair correlation in the inner crust of neutron stars by means of the Skyrme-Hartree-Fock-Bogoliubov theory formulated in the coordinate space. We describe a system composed of a nuclear cluster immersed in neutron superuid, which is confined in a spherical box. Using a density-dependent effective pairing interaction which reproduces both the pair gap of neutron matter obtained in ab initio calculations and that of finite nuclei, we analyze how the pair condensate in neutron superuid is affected by the presence of the nuclear cluster. It is found that the proximity effect is characterized by the coherence length of neutron superuid measured from the edge position of the nuclear cluster. The calculation predicts that the proximity effect has a strong density dependence. In the middle layers of the inner crust with baryon density 5 × 10-4 fm-3 ≲ ρb ≲ 2 × 10-2 fm-3, the proximity effect is well limited in the vicinity of the nuclear cluster, i.e. in a sufficiently smaller area than the Wigner-Seitz cell. On the contrary, the proximity effect is predicted to extend to the whole volume of the Wigner-Seitz cell in shallow layers of the inner crust with ρb ≲ 2 × 10-4 fm-3, and in deep layers with ρb ≲ 5 × 10-2 fm-3.

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Anderson-Bogoliubov phonons in the inner crust of neutron stars: Dipole excitation in a spherical Wigner-Seitz cell

Cited by 10 publications

References 58 publications

Superfluidity in nuclear systems and neutron stars

Superfluidity in nuclear systems and neutron stars

Coexistence of Anderson-Bogoliubov phonon and quadrupole cluster vibration in the inner crust of neutron stars

Proximity effect of pair correlation in the inner crust of neutron stars

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