Neutron width statistics in a realistic resonance-reaction model

Fanto, P.; Bertsch, G. F.; Alhassid, Y.

doi:10.1103/physrevc.98.014604

Cited by 12 publications

(14 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the case of statistical density operators, this sign ambiguity can be resolved by relating the trace over the Fock space to a pfaffian [27]. In a forthcoming publication, we will show how to extend this pfaffian approach to the traces involved in the particle-number projection at finite temperature [28].…”

Section: Discussionmentioning

confidence: 99%

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

2017

Self Cite

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: Discussionmentioning

confidence: 99%

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

2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…[13], depends upon σ. That changes the form of the probability distribution (10) for σ in a non-universal way. The maximum is obtained by putting the derivative with respect to 2σ 2 equal to zero.…”

Section: B Distribution With Cutoffmentioning

confidence: 99%

“…The results of Refs. [1,2] have, therefore, caused quite a stir in the theoretical nuclear-physics community [5][6][7][8][9][10][11]. The Porter-Thomas distribution follows from orthogonal invariance, one of the pillars of random-matrix theory for time-reversal invariant systems.…”

Section: Introductionmentioning

confidence: 99%

“…The terms that couple an orthogonally invariant Hamiltonian to the neutron channel and the numerous gamma channels break orthogonal invariance and may cause deviations of the distribution of reduced partial neutron widths from the Porter-Thomas distribution. That possibility has been investigated in a number of papers [6][7][8][9][10][11]. It is now firmly established, however, that breaking of orthogonal invariance due to coupling to the channels is by far too weak to account for the discrepancy found in Refs.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Tests of the Porter-Thomas Distribution for Reduced Partial Neutron Widths

Harney,

Weidenmüller

2021

Preprint

View full text Add to dashboard Cite

Given N data points drawn from a χ 2 -distribution, we use Bayesian inference to determine most likely values and N -dependent confidence intervals for the width σ and the number k of degrees of freedom of that distribution. Using reduced partial neutron widths measured in a number of nuclei, a guessed value of σ, and a maximum-likelihood approach (different from Bayesian inference), Koehler et al.[1] and Koehler [2] have determined the most likely k-values of χ 2 -distributions that fit the data. In all cases they find values for k that differ substantially from k = 1 (the value characterizing the Porter-Thomas distribution (PTD) predicted by random-matrix theory). The authors conclude that the validity of the PTD must be rejected with considerable statistical significance. We show that the value of σ guessed in Refs. [1,2] lies far outside the Bayesian confidence interval for σ, casting serious doubt on the results of and the conclusions drawn in Refs. [1,2]. We also show that σ and k must both be determined from the data. Comparison of the results with the Bayesian confidence intervals would then decide on acceptance or rejection of the PTD.

show abstract

“…In light nuclei the shift due to the principal-value integral is known as the Thomas-Ehrman shift. Several authors [5][6][7] have addressed the question whether that enhancement may be responsible for deviations of the distribution of partial neutron resonance widths from the PTD. In all these works, the gamma channels were neglected (except for a constant imaginary shift in the GOE energies).…”

Section: Statistical Modelmentioning

confidence: 99%

The Statistical Model of Nuclear Reactions: Open Problems

Fanto,

Alhassid,

Weidenmüller

2018

Preprint

Self Cite

View full text Add to dashboard Cite

Several experiments [1][2][3] show significant deviations from predictions of the statistical model of nuclear reactions. We summarize unsuccessful recent theoretical efforts to account for such disagreement in terms of a violation of orthogonal invariance caused by the Thomas-Ehrman shift. We report on numerical simulations involving a large number of gamma decay channels that also give rise to violation of orthogonal invariance but likewise do not account for the discrepancies. We discuss the statistical model in the light of these results.

show abstract

Neutron width statistics in a realistic resonance-reaction model

Cited by 12 publications

References 21 publications

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

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

Tests of the Porter-Thomas Distribution for Reduced Partial Neutron Widths

The Statistical Model of Nuclear Reactions: Open Problems

Contact Info

Product

Resources

About