Renormalization of the Hartree-Fock-Bogoliubov Equations in the Case of a Zero Range Pairing Interaction

Bulgac, Aurel; Yu, Yongle

doi:10.1103/physrevlett.88.042504

Cited by 191 publications

(272 citation statements)

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“…The reason is that the δ-function interaction is singular in the pairing channel and so must be regularized (see, e. g. Ref. [56]). Here we do so by cutting off the single-quasiparticle spectrum.…”

Section: B N -And Z-dependencementioning

confidence: 99%

Testing Skyrme energy-density functionals with the quasiparticle random-phase approximation in low-lying vibrational states of rare-earth nuclei

Terasaki

Engel

2011

Phys. Rev. C

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Although nuclear energy density functionals are determined primarily by fitting to ground state properties, they are often applied in nuclear astrophysics to excited states, usually through the quasiparticle random phase approximation (QRPA). Here we test the Skyrme functionals SkM * and SLy4 along with the self-consistent QRPA by calculating properties of low-lying vibrational states in a large number of well-deformed even-even rare-earth nuclei. We reproduce trends in energies and transition probabilities associated with γ-vibrational states, but our results are not perfect and indicate the presences of multi-particle-hole correlations that are not included in the QRPA. The Skyrme functional SkM * performs noticeably better than SLy4. In a few nuclei, changes in the treatment of the pairing energy functional have a significant effect. The QRPA is less successful with "β-vibrational" states than with the γ-vibrational states.

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Section: B N -And Z-dependencementioning

confidence: 99%

Testing Skyrme energy-density functionals with the quasiparticle random-phase approximation in low-lying vibrational states of rare-earth nuclei

Terasaki

Engel

2011

Phys. Rev. C

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“…Whereas vortices are well understood both in the BEC and the BCS limits, it is not clear how the characteristics of the vortex (such as the core size) behave in the crossover regime. Bulgac and Yu have extended density functional theory to superfluid fermion systems [4], and studied vortex states in the BCS regime within their superfluid local density approximation (SLDA) [5]. They found that in the BCS regime vortices give rise to a depletion in the fermion density.…”

Section: Introductionmentioning

confidence: 99%

Path-integral mean-field description of the vortex state in the BEC-to-BCS crossover

2005

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We derive a path-integral description of the vortex state of a fermionic superfluid in the crossover region between the molecular condensate (BEC) regime and the Cooper pairing (BCS) regime.This path-integral formalism, supplemented by a suitable choice for the saddle point value of the pairing field in the presence of a vortex, offers a unified description that encompasses both the BEC and BCS limits. The vortex core size is studied as a function of the tunable interaction strength between the fermionic atoms. We find that in the BEC regime, the core size is determined by the molecular healing length, whereas in the BCS regime, the core size is proportional only to the Fermi wave length. The observation of such quantized vortices in dilute Fermi gases would provide an unambiguous proof of the realization of superfluidity in these gases.

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“…Firstly, the bare coupling constant in the pairing channel could in principle have some intrinsic density dependence and such dependence has been considered by various authors during the years [2,[6][7][8][9]13]. Secondly, the renormalization of the pairing interaction, as described in our recent work [3][4][5], leads to position dependence as well. The equations for the quasi-particle wave functions u i (r) and v i (r) and related quantities are…”

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confidence: 99%

“…The argument that nuclear forces have a finite-range is superfluous, see Refs. [3][4][5], since nuclear pairing phenomena are manifest at small energies and distances of the order of the coherence length, which is larger than nuclear radii.We shall consider local nuclear EDFs only (which depend on various densities, as opposed to an explicit dependence on the full density matrix), as they proved overwhelmingly successful in describing normal nuclear properties. It is natural to expect that the same should apply to pairing properties.…”

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Energy Density Functional Approach to Superfluid Nuclei

Bulgac

2003

Phys. Rev. Lett.

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153

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We show that within the framework of a simple local nuclear energy density functional (EDF), one can describe accurately the one-and two-nucleon separation energies of semimagic nuclei. While for the normal part of the EDF we use previously suggested parameterizations, for the superfluid part of the EDF we use the simplest possible local form compatible with known nuclear symmetries.PACS numbers: 21.60. Jz, 21.30.Fe A steady transition is taking place during the last several years from the mean-field description of nuclear properties in terms of effective forces to an energy density functional approach (EDF). A significant role is played in this transition process by the fact that an EDF approach has a strong theoretical underpinning [1]. The effective forces used to derive the EDF are nothing else but a vehicle, since in themselves they have no well-defined physical meaning. For example, the effective Skyrme two-particle interaction is neither a particle-hole nor a particle-particle interaction. The particle-hole interaction (or the Landau parameters) is defined only as the second order functional derivative of the total EDF with respect to various densities, while the particle-particle interaction responsible for the pairing correlations in nuclei has to be supplied independently and with no logical connection to the Skyrme parameters.We shall not attempt to even mention various meanfield approaches suggested so far, in this respect see Refs.[2], but we shall concentrate instead on a single aspect of the nuclear EDF, namely its pairing properties. Only recently it became clear that a theoretically consistent local EDF formulation of the nuclear pairing properties is indeed possible [3][4][5]. Even though the crucial role of the pairing phenomena in nuclei has been established firmly, it is surprising to realize how poor the quality of our knowledge still is. Phenomenologically, one cannot unambiguously decide whether the pairing correlations in nuclei have a volume or/and a surface character [6][7][8][9][10][11][12][13]. The isospin character of the nuclear pairing correlations requires further clarification as well. These questions become even sharper in the language of a local EDF.There is also the largely practical issue of whether one should use a zero-range or a finite-range effective pairing interaction. The only reason for the introduction of a finite-range was to resolve the formal difficulty with divergences in calculating the anomalous densities [10]. The majority of practitioners favor a much simpler approach, which embodies essentially the same physics, the introduction of an explicit energy cut-off. The best example are perhaps the works of the group [11,12], which so far is the leader in describing all known nuclear masses. An explicit finite-range of the pairing interaction r 0 (which can be translated into an energy cut-off E c ≈h 2 /mr 2 0 ) and a zero-range with an explicit energy cut-off E c in the final analysis are equivalent. Both approaches, however, are a poor's man solution to the r...

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Renormalization of the Hartree-Fock-Bogoliubov Equations in the Case of a Zero Range Pairing Interaction

Abstract: We introduce a natural and simple way to implement the regularization scheme of the Hartree-Fock-Bogoliubov equations with zero range pairing interaction. The renormalization scheme proves to be equivalent to a simple energy cutoff with a position dependent running coupling constant.

Cited by 191 publications

References 22 publications

Testing Skyrme energy-density functionals with the quasiparticle random-phase approximation in low-lying vibrational states of rare-earth nuclei

Testing Skyrme energy-density functionals with the quasiparticle random-phase approximation in low-lying vibrational states of rare-earth nuclei

Path-integral mean-field description of the vortex state in the BEC-to-BCS crossover

Energy Density Functional Approach to Superfluid Nuclei

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