Number projected statistics and the pairing correlations at high excitation energies

Esebbag, C.; Egido, J.L.

doi:10.1016/0375-9474(93)90464-9

Cited by 55 publications

(44 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The result in (32) can also be derived by writing explicitly the matrix elements of e iϕN in the subspace spanned by the four many-body states [20]. A key difference between our work and the work in Ref.…”

Section: B the Bcs Limitmentioning

confidence: 91%

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

2017

View full text Add to dashboard Cite

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.

show abstract

Section: B the Bcs Limitmentioning

confidence: 91%

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

2017

View full text Add to dashboard Cite

show abstract

“…temperature dependency of gap parameter [17][18][19][20][21][22][23]. We take into account the thermal occupancy of quasi particles.…”

Section: Introductionmentioning

confidence: 99%

Relativistic Mean Field Study of SM Isotopes with FTBCS Approach

Karim¹,

Siddiqui²,

Ahmad³

2015

IJRAP

View full text Add to dashboard Cite

show abstract

“…A way to overcome these problems has been found in Ref. [11] for the particle number projection within the Bardeen-Cooper-Schrieffer (BCS) approximation. General projection formalism in the variation-before-projection (VBP) scheme is developed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Quantum number projection at finite temperature via thermofield dynamics

Tanabe

Nakada

2005

Phys. Rev. C

View full text Add to dashboard Cite

Applying the thermo field dynamics, we reformulate exact quantum number projection in the finite-temperature Hartree-Fock-Bogoliubov theory. Explicit formulae are derived for the simultaneous projection of particle number and angular momentum, in parallel to the zero-temperature case. We also propose a practical method for the variation-after-projection calculation, by approximating entropy without conflict with the Peierls inequality. The quantum number projection in the finite-temperature mean-field theory will be useful to study effects of quantum fluctuations associated with the conservation laws on thermal properties of nuclei.

show abstract

Number projected statistics and the pairing correlations at high excitation energies

Cited by 55 publications

References 22 publications

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

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

Relativistic Mean Field Study of SM Isotopes with FTBCS Approach

Quantum number projection at finite temperature via thermofield dynamics

Contact Info

Product

Resources

About