New Statistical Methods for Systematizing the Nuclei Fission Fragments: Post-Scission Approach

Abstract

A new statistical method for systematizing the nuclei fission fragments, investigation of their mass and charge spectra and neutron fission parameters has been suggested. In proposed method, the mass and charge yields of nucleons are determined from the equilibrium conditions of the nuclear fragments post-fission ensemble. Here we consider protons and neutrons of different fragments as statistically non-equivalent. The abilities of the proposed statistical method for explanation of the U, Pa, Th, Ac and Ra post-fission fragments ordering and neutron emission function calculation have been demonstrated.

Calculation of the fission-fragment yields of the pre-actinide nuclei by the example of the Pbnat isotopes

“…Theoretical studies of the peculiarities of energetic structure and medium heavy nuclei fission are significantly limited and concerns to the calculation of transient configurations and statistical characteristics of pre-actinide nuclei in the fission reactions, see [6,7]. This work continued previous investigations [8] and is devoted to systematization of medium heavy nuclei fragments on example of Pb isotopes fission (mass and charge yields) in the frame of previously proposed statistical method [9]. Particularly, the possible asymmetry of fission fragment yields, the role of shell effects and the interpretation of experimental data where these yields have a symmetrical (one-humped) form is discussed.…”

“…In this article the calculation of the mass/charge yields of output nucleus fission fragments with atomic mass А 0 and charge Z 0 is carried out in the frame of proposed statistical method based on the following assumptions [9]:…”

“…In this article the calculation of the mass/charge yields of output nucleus fission fragments with atomic mass А 0 and charge Z 0 is carried out in the frame of proposed statistical method based on the following assumptions [9]:  The character of the mass/charge yields is determined by condition of thermodynamic ensemble's adjustment that contains clusters of fission fragments;  The nuclei fragments fission ensemble is a constant pressure ensemble, and its thermodynamic parameters: P (pressure) and T (temperature) is determined by state of initial nucleus;  In computing of configurational entropy the statistical non-equivalence of nucleons with different binding fraction of each fission fragments should be considered;  The nuclear particles emission (fission neutrons, gamma radiation) maintains the constancy of the thermodynamic parameters of the nuclear fragments ensemble, namely, system's thermostat;  During the fission neutrons' emission the internal energy of fragment nuclei changes are in process, owing to execution of work while reducing the volume of the initial nucleus at constant pressure;  Inasmuch as atomic nuclei are small systems, it should be appreciated the fluctuations of thermodynamic parameters in the calculation of the equilibrium configurations of the nuclear fragments ensemble.…”

Super-heavy nuclei with Z = 118 and their mass and charge spectrum of fission fragments

“…Recent works [13,14] propose a new theoretical method which is able to calculate the charge/mass spectra of the fission of nuclei with mass A and charge Z based on the conditions of ordering an ensemble of all possible clusters of nuclear fission fragments.…”

“…where S is a configuration entropy, U the internal energy, T the temperature, P the pressure and V the volume. We chose the isobaric term in (1) as a linear one with respect to the number of fission neutrons, n. In carrying out calculations the value of the isobaric term can be chosen [14] in a form of P V = P (V 0 −ν 0 n), where V 0 is the initial volume of the primary nucleus, P is the nucleon "gas" pressure in the primary nucleus, ν 0 is the average volume related to a single fission neutron. The isobaric constant P V 0 value can be evaluated as 3-4 MeV from the condition that the average fission neutron number n at T =1 MeV does not exceed 2-3 neutron/fission.…”