Narrow Results

The influence of pure statistical fluctuations on K/π ratio is investigated in an event-by-event way. Poisson and the modified negative binomial distributions are used as the multiplicity distributions since they both have statistical background. It is shown that the distributions of the ratio in these cases are Gaussian, and the mean and relative variance are given analytically.

According to the third law of Thermodynamics, it takes an infinite number of steps for any object, including black holes, to reach zero temperature. For any physical system, the process of cooling to absolute zero corresponds to erasing information or generating pure states. In contrast with the ordinary matter, the black hole temperature can be lowered only by adding matter–energy into it. However, it is impossible to remove the statistical fluctuations of the infalling matter–energy. The fluctuations lead to the fact that the black holes have a finite lower temperature and, hence, an upper bound on the horizon radius. We make an estimate of the upper bound for the horizon radius which is curiously comparable to Hubble horizon. We compare this bound with known results and discuss its implications.

The pairing phase transition is investigated in hot even–even and even–odd Pd isotopes such as 106 ≤ A ≤ 108 in a framework of a microscopic approach that takes into account the statistical fluctuations. In this aim, one considers the Modified BCS method (MBCS). The latter is extended to the odd system case, where the blocking effect is included. The model was applied to the evaluation of the thermal properties such as the excitation energy, entropy and heat capacity. The obtained results are compared on one hand to the usual finite temperature BCS (FTBCS) method and on the other hand to the experimental data. The obtained results allow to show that the thermal fluctuations smooth out the superfluid-normal (SN) phase transition observed in the usual FTBCS results. Moreover, in the region where the pairing phase transition occurs, the experimental data of thermal properties are better reproduced when statistical fluctuations are considered in MBCS method instead of the FTBCS approach.

We propose to study the thermal two-neutron separation energy in the case of Erbium isotopes: 80 ≤ N ≤ 108. In this aim, one used the finite temperature Bardeen Cooper Schrieffer (FTBCS) method where the statistical fluctuations are treated as a part of Landau prescription. The behavior of this quantity according to the neutron number and temperature provides indication about the nuclear shape transition, and disappearance of shell effects. The obtained results allow to show that the inclusion of statistical fluctuations in the calculation have a nonnegligible effect. Indeed, the fact that this kind of fluctuations effect is important at high temperatures induces a smooth decrease of pairing gap parameter. As a consequence, the persistence of pairing effect at high temperature leads a change on the shell effect. Indeed, when statistical fluctuations are considered, the shell effect persists at high temperature which is not the case of the usual FTBCS approach.

We propose to study the thermal properties of the odd isotopes of Tin: ${}^{117,119,121}$Sn. To this end, one used two methods to evaluate the properties of these elements. The first theoretical consideration uses a simple prescription to perform the calculation of these properties based on those of even–even neighboring isotopes, assuming the quasi-particle entropy extensivity. The even–even elements are treated as part of the Modified Lipkin–Nogami (MLN) method that allows to take into account the quantal and statistical fluctuations. The second theoretical approach consists of the generalization of the MLN formalism in the case of odd systems, by using the blocking technique. Then, this approach is applied to evaluate the thermal properties of the considered elements. The obtained results by both theoretical approaches are compared to the experimental data. The latter are deduced from the experimental level density within the canonical ensemble. It appears that the assumption of quasi-particle entropy extensivity at low excitation energy allows a simple and an effective treatment of thermal properties of odd nuclei. Indeed, this approach allows to give a good reproduction of experimental data in the particular in the region where the pairing transition occurs.