Nuclear fragmentation and its parallels

Abstract

A model for the fragmentation of a nucleus is developed. Parallels of the description of this process with other areas are shown which include Feynman's theory of the λ transition in liquid Helium, Bose condensation, and Markov process models used in stochastic networks and polymer physics. These parallels are used to generalize and further develop a previous exactly solvable model of nuclear fragmentation. An analysis of some experimental data is given.

The thermodynamic model for nuclear multifragmentation

“…That is, for any given permutation, the total A is equal to the sum of the cycle length times the number of cycles of that length in that specific permutation. The canonical partition function for non-interacting particles such as Fermi-Dirac or Bose-Einstein particles in a box or in a one body potential well such as a harmonic oscillator well has a form given by eq.2 in section 2 [85,86,87]. For identical particles in a box of volume V and a system at temperature T , the ω weight factor for a cycle of length k is that of eq.6 with the q k = 1 in that equation for Bose-Einstein particles and q k = (−1) (k+1) for Fermi-Dirac particles.…”

Equipartitions and a distribution for numbers: A statistical model for Benford's law

“…We note that unrestricted partition problems have been used previously to analyze fragmentation of nuclei [11,[15][16][17][18]. By contrast, here we consider the re-stricted partition number P H (X), that is, the number of ways to partition an integer X into the set of integers H = {x 1 = 1, x 2 , .…”

Heated Nuclear Matter, Condensation Phenomena, and the Hadronic Equation of State

“…Most treatments of the equation of state have treated heated nuclear matter as a homogeneous system. Statistical [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and percolation [24][25][26] models have been used by many groups to study nuclear multifragmentation and the role of clusters on nuclear properties. This paper explores various thermodynamic properties using an exactly solvable canonical ensemble model that allows for clusterization and leads to simple analytic expressions for thermodynamic quantities such as the equation of state.…”

“…In earlier papers [20][21][22][23] the question of the thermodynamics of a fragmenting system was raised. There, it was assumed that the thermodynamic variables were contained in a single parameter x such that the weight of a particular cluster partition was proportional to x m , where m is the total number of clusters in that partition.…”

“…Applying the usual relations between the thermodynamic functions and the partition function, the result for the specific heat and pressure is A , namely [23],…”