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Register a new userPoisson and Porter-Thomas Fluctuations in off-Yrast Rotational Transitions
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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).
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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.
The phase transition of nuclei to increasing angular momentum (or spin) and excitation energy is one of the most fundamental topics of nuclear structure research. The odd-N nuclei with A equal 160 are widely considered belonging to the well-deformed region, and their excitation spectra are energetically favored to exhibit the rotational characteristics. In the present work, however, there is evidence indicating that the nuclei can evolve from rotation to vibration along the yrast lines while increasing spin. The simple method, named as E-Gamma Over Spin (E-GOS) curves, would be used to discern the evolution from rotational to vibrational structure in nuclei as a function of spin. In addition, in order to get the insight into the rotational-like properties of nuclei, theoretical calculations have been performed for the yrast bands of the odd-A rare-earth nuclei using the total Routhian surfaces (TRS) model. The TRS plots indicate that the 165Yb and 157Dy isotopes have stable prolate shapes at low spin states. At higher rotational frequency (larger than 0.50 MeV), a distinct decrease in the quadrupole deformation is predicted by the calculations, and the isotopes becomes rigid in the gamma deformation.
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.
Taking doubly charged particles, positive-negative charge pair production and the effects of volume fluctuations into account, the Poisson baseline of the fluctuations of net-charge is studied. Within the Poisson baseline, the cumulants of net-charge are derived. Comparing to the Skellam baseline of net-charge, we infer that doubly charged particles broaden the distributions of net-charge, while positive-negative charge pairs narrow the distributions. Using the ratios of doubly charged particles and positive-negative charge pairs from neutral resonance decays to the total positive charges from THERMINATOR 2, the first four orders of moments and the corresponding moment products are calculated in the Poisson baseline for Au + Au collisions at $sqrt{s_{NN}}$ = 200 GeV at RHIC/STAR. We find that the standard deviation is mainly influenced by the resonance decay, while the third and fourth order moments and corresponding moment products are mainly modified and fit the data of RHIC/STAR much better after including the effects of volume fluctuations.
Rotational structures of even-even $^{148-160}$Nd nuclei are studied with the self-consistent deformed Hartree-Fock (HF) and angular momentum (J) projection model. Spectra of ground band, recently observed $K=4^{-}$, $K=5^{-}$ and a few more excited, positive and negative parity bands have been studied upto high spin values. Apart from these detailed electromagnetic properties (like E2, M1 matrix elements) of all the bands have been obtained. There is substantial agreement between our model calculations and available experimental data. Predictions are made about the band structures and electromagnetic properties of these nuclei. Some 4-qasiparticle K-isomeric bands and their electromagnetic properties are predicted.
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