Effects of particle-number conservation on heat capacity of nuclei

Esashika, Keiko; Nakada, H.; Tanabe, K.

doi:10.1103/physrevc.72.044303

Cited by 25 publications

(23 citation statements)

References 16 publications

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“…Therefore the signature of a transition from a 'paired phase' to an 'unpaired phase' when approaching a major shell gap becomes less and less pronounced. We should note that very recently an alternative interpretation has been given [51]. These authors find that the S-shape can be accounted for as an effect of the particle-number conservation, and it occurs even when assuming a constant gap in the BCS theory.…”

Section: B Comparison With Experimental Datamentioning

confidence: 95%

Level densities and thermodynamical quantities of heatedMo93−98isotopes

et al. 2006

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Level densities for93−98 Mo have been extracted using the ( 3 He,αγ) and ( 3 He, 3 He'γ) reactions. From the level densities thermodynamical quantities such as temperature and heat capacity can be deduced. Data have been analyzed by utilizing both the microcanonical and the canonical ensemble. Structures in the microcanonical temperature are consistent with the breaking of nucleon Cooper pairs. The S-shape of the heat capacity curves found within the canonical ensemble is interpreted as consistent with a pairing phase transition with a critical temperature for the quenching of pairing correlations at Tc ∼ 0.7 − 1.0 MeV.

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Section: B Comparison With Experimental Datamentioning

confidence: 95%

Level densities and thermodynamical quantities of heatedMo93−98isotopes

et al. 2006

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“…For the pairing phase transition, within the mean-field theories, the particle number conservation is violated in the superfluid phase while preserved in the normal-fluid phase. The number conservation effects on the nuclear heat capacity has been investigated through the particlenumber projection methods based on the finite-temperature BCS or HFB approaches [18,21,22]. Due to the restoration of particle number conservation, the calculated heat capacity varies smoothly with the temperature, indicating a gradual transition from the superfluid to the normal phase.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of pairing transition in hot nuclei

2015

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The pairing correlations in hot nuclei $^{162}$Dy are investigated in terms of the thermodynamical properties by covariant density functional theory. The heat capacities $C_V$ are evaluated in the canonical ensemble theory and the paring correlations are treated by a shell-model-like approach, in which the particle number is conserved exactly. A S-shaped heat capacity curve, which agrees qualitatively with the experimental data, has been obtained and analyzed in details. It is found that the one-pair-broken states play crucial roles in the appearance of the S shape of the heat capacity curve. Moreover, due to the effect of the particle-number conservation, the pairing gap varies smoothly with the temperature, which indicates a gradual transition from the superfluid to the normal state.Comment: 13 pages, 4 figure

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“…(15) and (16) of Ref. [6], one can reduce the grand-canonical partition function to an approximate canonical partition function by a 2D saddlepoint approximation and then compute the state density by the saddle-point approximation given in Eq.…”

Section: Hf B N P(n)mentioning

confidence: 99%

“…[14]. Particle-number PAV has also been applied at finite temperature in the context of the BCS approximation [15]. However, in the HFB case, the general formalism includes a sign ambiguity.…”

Section: Introductionmentioning

confidence: 99%

Particle-number projection in the finite-temperature mean-field approximation

2017

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Calculation of statistical properties of nuclei in a finite-temperature mean-field theory requires projection onto good particle number, since the theory is formulated in the grand canonical ensemble. This projection is usually carried out in a saddle-point approximation. Here we derive formulas for an exact particle-number projection of the finite-temperature mean-field solution. We consider both deformed nuclei, in which the pairing condensate is weak and the Hartree-Fock (HF) approximation is the appropriate mean-field theory, and nuclei with strong pairing condensates, in which the appropriate theory is the Hartree-Fock-Bogoliubov (HFB) approximation, a method that explicitly violates particle-number conservation. For the HFB approximation, we present a general projection formula for a condensate that is time-reversal invariant and a simpler formula for the BardeenCooper-Schrieffer (BCS) limit, which is realized in nuclei with spherical condensates. We apply the method to three heavy nuclei: a typical deformed nucleus 162 Dy, a typical spherical nucleus 148 Sm, and a transitional nucleus 150 Sm in which the pairing condensate is deformed. We compare the results of this projection with results from the saddle-point approximation and exact shell model Monte Carlo calculations. We find that the approximate canonical HF entropy in the particlenumber projection decreases monotonically to zero in the limit when the temperature goes to zero. However, in a nucleus with a strong pairing condensate, the approximate canonical HFB entropy in the particle-number projection decreases monotonically to a negative value, reflecting the violation of particle-number conservation. Computationally, the exact particle-number projection is more efficient than calculating the derivatives required in the saddle-point approximation.

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Effects of particle-number conservation on heat capacity of nuclei

Cited by 25 publications

References 16 publications

Level densities and thermodynamical quantities of heatedMo93−98isotopes

Level densities and thermodynamical quantities of heatedMo93−98isotopes

Thermodynamics of pairing transition in hot nuclei

Particle-number projection in the finite-temperature mean-field approximation

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