On the validity of the mean field approach for the description of pairing collapse in finite nuclei

Egido, J.L.; Ring, P.; Iwasaki, S.; Mang, H.J.

doi:10.1016/0370-2693(85)91555-2

Cited by 77 publications

(28 citation statements)

References 20 publications

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“…All these methods tried to solve the problem of the particlenumber nonconservation. However, when it is achieved, no pairing phase transition was found [16,17]. This proves that the occurrence of nuclear pairing collapsing originates from particle-number non-conservation.…”

Section: Introductionmentioning

confidence: 86%

“…However, earlier studies showed that the LN method broke down in the weak pairing limit [14,15]. At the same time, various particle-number projection approaches of pairing interaction in BCS or HFB formalism have been developed [16][17][18][19]. In these approaches, the ideal treatment is variation after projection, but when spin goes higher, this method becomes very complicated and computational expensive.…”

Section: Introductionmentioning

confidence: 99%

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Nuclear pairing reduction due to rotation and blocking

et al. 2011

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Nuclear pairing gaps of normally deformed and superdeformed nuclei are investigated using the particle-number conserving (PNC) formalism for the cranked shell model, in which the blocking effects are treated exactly. Both rotational frequency ω-dependence and seniority (number of unpaired particles) ν-dependence of the pairing gap∆ are investigated. For the ground-state bands of even-even nuclei, PNC calculations show that in general∆ decreases with increasing ω, but the ω-dependence is much weaker than that calculated by the number-projected Hartree-FockBogolyubov approach. For the multiquasiparticle bands (seniority ν > 2), the pairing gaps keep almost ω-independent. As a function of the seniority ν, the bandhead pairing gaps∆(ν, ω = 0) decrease slowly with increasing ν. Even for the highest seniority ν bands identified so far,∆(ν, ω = 0) remains greater than 70% of∆(ν = 0, ω = 0).

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Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Nuclear pairing reduction due to rotation and blocking

et al. 2011

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Section: Resultsmentioning

confidence: 99%

“…Furthermore, the discordant point of a "sharp" transition for a small system, like the nucleus, predicted by both approaches requires further investigation. Earlier calculations with the Pairing plus Quadrupole Hamiltonian [11,20] have pointed out the relevance of including fluctuations in mean field approaches at finite temperature as a step forward to clarify 2 some aspects of these problems. It is the aim of this paper to investigate the problems just mentioned as well as other related high excitation energy topics, level densities, etc., within a beyond mean field theory.…”

Section: Introductionmentioning

confidence: 99%

“…Thermal shape fluctuations, as expected in the low temperature regime, have little effect on the pairing correlations. Pairing fluctuations which would be more relevant [20] are not considered in this work.It is interesting to take a look at the internal excitation energy, E * , and also analyze it through the behavior of its derivative, the specific heat C V (T ) = ∂E * /∂T , since the appearance of peaks in this quantity is customarily interpreted as a signature in the search for phase transitions.The evolution of E * with temperature for both the FTHFB, E * , and the average, E * , calculations, is presented in panels e) (Gogny force) and f) (PPQ force) of Fig. 2.…”

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confidence: 99%

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Thermal shape fluctuation effects in the description of hot nuclei

2003

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The behavior of several nuclear properties with temperature is analyzed within the framework of the Finite Temperature Hartree-Fock-Bogoliubov (FTHFB) theory with the Gogny force and large configuration spaces. Thermal shape fluctuations in the quadrupole degree of freedom, around the mean field solution, are taken into account with the Landau prescription. As representative examples the nuclei 164 Er, 152 Dy and 192 Hg are studied. Numerical results for the superfluid to normal and deformed to spherical shape transitions are presented. We found a substantial effect of the fluctuations on the average value of several observables. In particular, we get a decrease in the critical temperature (Tc) for the shape transition as compared with the plain FTHFB prediction as well as a washing out of the shape transition signatures. The new values of Tc are closer to the ones found in Strutinsky calculations and with the Pairing Plus Quadrupole model Hamiltonian. IntroductionSince the advent of the new generation of 4π gamma ray detectors and the improved accuracy in the channel selection new possibilities have opened up in the study of nuclear structure. Besides this, the availability of faster computers has made possible to perform realistic theoretical investigations with large configuration spaces. The high excitation energy is specially interesting since new features may take place. For example, in the quasicontinuum, the high level density gives rise to the unexpected phenomenon of the damping of the rotational motion. In the limit of high excitation energies (or temperature T ) quantum effects become less relevant or may even disappear. Thus one expects that in a heated nucleus physical effects like superfluidity or shape deformations are washed out when T increases. This expectation can be easily understood in terms of the shell model since, by increasing T , one promotes particles from levels below the Fermi surface to levels above it. In the case of pairing correlations, blocking levels amounts to destroying Cooper pairs. In the case of shape deformation, by depopulating the deformation driving levels (intruders) one gets on the average less deformation. Experimental information about nuclear shape changes can be obtained by means of the Giant Dipole Resonance (GDR) built on excited states. Exclusive experiments studying the GDR strength at a given excitation energy (or T ) of the nucleus have been carried out in refs. [1,2,3,4]. The understanding of these phenomena is relevant because it affects important features like the fission barriers and the stability of the nucleus itself. For a recent review on hot nuclei see ref. [5].The shape transitions have been object of many studies, most of them with schematic models, separable forces, and small configuration spaces [6,7,8,9,10]. The theoretical approaches used in the calculations are based on the mean field approximation, mainly the Finite Temperature Hartree-Fock-Bogoliubov theory (FTHFB). The mean field approximations predict sharp shape transitions, wherea...

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Phase Transitions in Nuclei at Low Temperatures

Goodman

1990

Phase Structure of Strongly Interacting Matter

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On the validity of the mean field approach for the description of pairing collapse in finite nuclei

Cited by 77 publications

References 20 publications

Nuclear pairing reduction due to rotation and blocking

Nuclear pairing reduction due to rotation and blocking

Thermal shape fluctuation effects in the description of hot nuclei

Phase Transitions in Nuclei at Low Temperatures

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