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Register a new userTests of the Porter-Thomas Distribution for Reduced Partial Neutron Widths
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Given N data points drawn from a chi-square distribution, we use Bayesian inference to determine most likely values and N-dependent confidence intervals for the width sigma 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 sigma, and a maximum-likelihood approach (different from Bayesian inference), Koehler et al. and Koehler have determined the most likely k-values of chi-square 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 sigma guessed in these papers lies far outside the Bayesian confidence interval for sigma, casting serious doubt on the results of and the conclusions drawn there. We also show that sigma 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.
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The Porter-Thomas (PT) distribution of resonance widths is one of the oldest and simplest applications of statistical ideas in nuclear physics. Previous experimental data confirmed it quite well but recent and more careful investigations show clear deviations from this distribution. To explain these discrepancies the authors of [PRL textbf{115}, 052501 (2015)] argued that to get a realistic model of nuclear resonances is not enough to consider one of the standard random matrix ensembles which leads immediately to the PT distribution but it is necessary to add a rank-one interaction which couples resonances to decay channels. The purpose of the paper is to solve this model analytically and to find explicitly the modifications of the PT distribution due to such interaction. Resulting formulae are simple, in a good agreement with numerics, and could explain experimental results.
Fluctuations associated with stretched E2 transitions from high spin levels in nuclei around $^{168}$Yb are investigated by a cranked shell model extended to include residual two-body interactions. It is found that the gamma-ray energies behave like random variables and the energy spectra show the Poisson fluctuation, in the cranked mean field model without the residual interaction. With two-body residual interaction included, discrete transition pattern with unmixed rotational bands is still valid up to around 600 keV above yrast, in good agreement with experiments. At higher excitation energy, a gradual onset of rotational damping emerges. At 1.8 MeV above yrast, complete damping is observed with GOE type fluctuations for both energy levels and transition strengths(Porter-Thomas fluctuations).
The partial decay widths of lowest lying negative parity baryons belonging to the 70-plet of SU(6) are analyzed in the framework of the 1/Nc expansion The channels considered are those with single pseudo-scalar meson emission. The analysis is carried out to sub-leading order in 1/Nc and to first order in SU(3) symmetry breaking. Conclusions about the magnitude of SU(3) breaking effects along with predictions for some unknown or poorly determined partial decay widths of known resonances are obtained.
The 16.1MeV 2+ resonance in 12C situated slightly above the proton threshold can decay by proton-, $alpha$-, and $gamma$ emission. The partial width for proton emission cannot be directly measured due to the low proton energy and the small branching ratio. Instead it must be indirectly derived from other observables. However, due to several inconsistent data the derived partial width varies by almost a factor 2 dependent on the data used. Here we trace the majority of this inconsistency to different measurements of the $(p,alpha)$ cross sections. We have remeasured this cross section using modern large area silicon strip detectors allowing to measure all final state particles, which circumvents a normalization issue affecting some of the previous measurements. Based on this we determine $Gamma_{p}$ = 21.0(13)eV. We discuss the implications for other observables related to the 16.1 MeV $2^{+}$ resonance and for isospin symmetry in the $A=12$ system. In addition, we conclude that the dataset currently used for the NACRE and NACRE II evaluation of the $^{11}mathrm{B}(p,3alpha)$ reaction should be scaled by a factor of 2/3. This impacts the reaction rate accordingly.
The equation of state (EOS) for neutron star (NS) crusts is studied in the Thomas-Fermi (TF) approximation using the EOS for uniform nuclear matter obtained by the variational method with the realistic nuclear Hamiltonian. The parameters associated with the nuclear three-body force, which are introduced to describe the saturation properties, are finely adjusted so that the TF calculations for isolated atomic nuclei reproduce the experimental data on masses and charge distributions satisfactorily. The resulting root-mean-square deviation of the masses from the experimental data for mass-measured nuclei is about 3 MeV. With use of the nuclear EOS thus determined, the nuclei in the crust of NS at zero temperature are calculated. The predicted proton numbers of the nuclei in the crust of NS are close to the gross behavior of the results by Negele and Vautherin, while they are larger than those for the EOS by Shen et al. due to the difference in the symmetry energy. The density profile of NS is calculated with the constructed EOS.
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