Kinetic equation for finite systems of fermions with pairing

Abrosimov, V. I.; Brink, D.M.; Dellafiore, A.; Matera, F.

doi:10.1016/j.nuclphysa.2007.11.009

Cited by 10 publications

(26 citation statements)

References 13 publications

(35 reference statements)

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“…Then, at some excitation energy ~ or temperature a sharp second-order phase transition occurs to a normal-heated Fermi liquid where the pairing effects are usually neglected [63]. The thermodynamically properties [44][45][46][47][48][49][50], entropy [51][52][53][54][55] and etc have been studied by different authors. The statistical properties of energy levels can be used for investigating the pairing effect on nuclear structures, too.…”

Section: Pairing Hamiltonianmentioning

confidence: 99%

“…As it was mentioned in introduction, our investigations have carried out with pure experimental data but we review the role of pairing Hamiltonian briefly in order to clarify theoretical aspects of pairing (complete descriptions are presented in [42][43][44][45][46][47][48][49][50][51][52][53][54][55]). To study obvious pairing effect in Hamiltonian, some authors use the following Hamiltonian [59], Where is a realistic Hamiltonian and [59] To investigate the pairing effect in nuclear spectra, they have carried their calculation with different values of G. Their results obviously display important effect of pairing in low-lying region of energy spectra, on the other hand, when they have assumed the exotic states in their calculation, broken pairs and phase transitions caused to neglecting the pairing effects [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59].On the other hand, pairing force in addition to quadrupole interaction has been regarded as the main reason in constructing bosons in the interaction Boson Model (IBM) framework.. The IBM [25][26][27][28][29][30] is expressed in terms of a U(6) Lie algebra spanned by the bilinear combinations of five pairs of (...…”

Section: Pairing Hamiltonianmentioning

confidence: 99%

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A non-parametric estimation approach in the investigation of spectral statistics

et al. 2013

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In this paper, Kernel Density Estimation (KDE) as a non-parametric estimation method is used to investigate statistical properties of nuclear spectra. The deviation to regular or chaotic dynamics, is exhibited by closer distances to Poisson or Wigner limits respectively which evaluated by Kullback-Leibler Divergence (KLD) measure. Spectral statistics of different sequences prepared by nuclei corresponds to three dynamical symmetry limits of Interaction Boson Model(IBM), oblate and prolate nuclei and also the pairing effect on nuclear level statistics are analyzed (with pure experimental data). KD-based estimated density function, confirm previous predictions with minimum uncertainty (evaluated with Integrate Absolute Error (IAE)) in compare to Maximum Likelihood (ML)-based method. Also, the increasing of regularity degrees of spectra due to pairing effect is reveal.

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Section: Pairing Hamiltonianmentioning

confidence: 99%

Section: Pairing Hamiltonianmentioning

confidence: 99%

A non-parametric estimation approach in the investigation of spectral statistics

et al. 2013

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“…Like in [4,5], we approximate the static nuclear mean field with a spherical square-well potential of radius R, this choice allows us to take into account finite-size effects and, at the same time, to recover the simplicity of homogeneous systems. In the following, we also approximate the equilibrium pairing field  0 (r,p) with the phenomenological parameter  which, in heavy nuclei takes values between 1 and 1.5 MeV [8].…”

Section: Dynamical Equations With Pairingmentioning

confidence: 99%

“…The equations of motion (1)- (3) together with the selfconsistency relations (18)-(19) can be solved for finite systems with the method of action-angle variables [4,10]. By using these solutions we study the effects of a selfconsistent pairing interaction on the normal density response function and pairing collective modes.…”

Section: Solution Of Dynamical Equationsmentioning

confidence: 99%

“…This is equivalent to the condition that ħ 0 << F , where  0 is a frequency characteristic of the classical orbits and  F is the Fermi energy. Since in heavy nuclei the condition p F R/ħ>>1 is well satisfied, in [4,5] we have used an approach similar to that of Ref. [6] to study the linear response of (heavy) nuclei, with the aim of developing a simplified tool for the study of pairing effects in collective nuclear excitations.…”

Section: Introductionmentioning

confidence: 99%

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Self-consistent pairing interaction and collective motion in nuclei: a semiclassical approach

Abrosimov

Brink

Dellafiore

et al. 2012

EPJ Web of Conferences

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Abstract. The solutions of the semiclassical time-dependent Hartree-Fock-Bogoliubov equations of motion are studied in a linear approximation in which the pairing field is allowed to oscillate and to become complex. The pairing field fluctuations are derived from the self-consistent relation (the gap equation of the BCS type), while the static pairing field is approximated with a phenomenological constant . The self-consistent pairingfield fluctuations introduce possibility of new collective modes of the system. We have found out the dispersion relation which determines possible collective modes of the system generated by the pairing interaction. The obvious solution of our dispersion relation at =0 corresponds to the Anderson-GoldstoneNambu mode and is related to gauge symmetry. The solutions of dispersion relation have been studied in a simple model, in which nuclei are represented as homogeneous spheres of symmetric nuclear matter characterized by parameters (size, density, pairing gap) typical of heavy nuclei. We have found that the dispersion relation has approximate solution at ħ2 for the monopole channel. Our semiclassical approach is valid for both weak and strong pairing. Here we focus on weak pairing which is suitable for systems with size and pairing parameter appropriated to nuclei.

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Self-consistency and search for collective effects in semiclassical pairing theory

Abrosimov¹,

Brink²,

Dellafiore³

et al. 2011

Nuclear Physics A

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A simple model, in which nuclei are represented as homogeneous spheres of symmetric nuclear matter, is used to study the effects of a self-consistent pairing interaction on the nuclear response. Effects due to the finite size of nuclei are suitably taken into account. The semiclassical equations of motion derived in a previous paper for the time-dependent Hartree-Fock-Bogoliubov problem are solved in an improved (linear) approximation in which the pairing field is allowed to oscillate and to become complex. The new solutions are in good agreement with the old ones and also with the result of well-known quantum approaches. The role of the Pauli principle in eliminating one possible set of solutions is also discussed. The pairing-field fluctuations have two main effects: they restore the particle-number symmetry which is broken in the constant-∆ approximation and introduce the possibility of collective eigenfrequencies of the system due to the pairing interaction. A numerical study with values of parameters appropriate for nuclei, shows an enhancement of the density-density strength function in the region of the low-energy giant octupole resonance, while no similar effect is present in the region of the high-energy octupole resonance and for the giant monopole and quadrupole resonances.

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Kinetic equation for finite systems of fermions with pairing

Cited by 10 publications

References 13 publications

A non-parametric estimation approach in the investigation of spectral statistics

A non-parametric estimation approach in the investigation of spectral statistics

Self-consistent pairing interaction and collective motion in nuclei: a semiclassical approach

Self-consistency and search for collective effects in semiclassical pairing theory

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