Clustering Effects in the Equation of State on Nuclear Matter

Document Type


Degree Name

Master of Science (MS)


Physics and Astronomy

Date of Award

Spring 2015


In Nuclear AstroPhysics, clustering refers to the process by which atomic elements, known as nuclei, are formed from pre-existing nucleons such as protons and neutrons. This process called nucleosynthesis, is thought to occur under the following scenarios: Big Bang nucleosynthesis, Stellar nucleosynthesis, explosive nucleosynthesis and nucleosynthesis derived from fragmentation processes in nuclear reactions. In the case of all except the latter, which deals with radioactive decay and fission (the dissociation of larger nuclei into smaller ones), nucleosynthesis is predominantly the result of fusion, which is the creation of larger nuclei from smaller ones.To date, our current understanding of nuclei formation has crucial limitations, which is due to the complexity of stellar-nucleosynthesis and related processes. To overcome this gap in our understanding, of particular note and interest is explosive nucleosynthesis which involves the r-process, rp-process, s-process and p-process which are theorized to be the means by which elements more massive than iron are formed.Furthermore, the processes governing the different types of nucleosynthesis are additionally delineated by the relative rate at which nuclei formation occurs - which ranges from very rapidly in the order of seconds, to extremely long in the order of centuries, depending on the element and process in question. In attempting to reach an understanding of these processes, an additional caveat appears in that most of these processes are theorized to occur near the end of life of star - i.e. in a supernova event which is thought to supply both the high energy, temperatures and pressure with which to form these heavy nuclei. Consequently, neutron stars, which are highly dense stellar remnants of core-collapse supernova events, are potential candidates whose environments and existence are theorized to provide the ideal physical characteristics for the aforementioned processes hence explaining the formation of nuclei heavier than iron in neutron star mergers events. Although similar has work done on clustering in determining the physics, structure and evolution of neutron stars and their associated equations of state, it is not well known how such considerations derived from statistical physics affects heavy nuclei formation. Subsequently, one means of understanding these processes is to approach everything from a rigorous thermodynamical treatment. However, as nuclear species can vary up in relative occupied volumes, we must account for the thermodynamic potential variance due to the occupied nuclear volume for interacting species in our treatment. And, as that variance could be potentially large, this fact violates the core tenet of the ideal gas law as we can no longer treat the particles as point particles but rather as particles with definite and non-infinitesimal volumes - which means that we can assert that the particles affect the occupied volume of the space in which they interact and occupy. Consequently, any treatment and inclusion of the ideal gas law and any derived thermodynamical potentials cannot be used or applied as the physics of those treatments are inapplicable in this situation. What this means is that for us to perform any useful calculation, we must account for the occupied particle species volumes in any thermodynamical potential - something that has to be derived and verified from scratch with many possible alternative methods.This idea of volume isolation or more accurately, exclusion, is called excluded-volume mechanism (excluded-volume can be thought to be the occupied volume minus the total volume occupied by all the particles), an approach that is fairly common in BioPhysics, but one that is not so common in nuclear astrophysics, with particular attention to how such an approach affects the formation of nuclei and the associated equations of state.To determine the effects, if any, that excluded volume may have on the equation of state, we begin by applying excluded-volume mechanism on classical thermodynamics and associated thermodynamical potentials by modifying the standard methodology of considering the non-relativistic energetics of non-interacting particles from a purely statistical mechanical approach, known as a Maxwell-Boltzmann statistics. Having considered excluded-volume statistically, we can derive thermodynamical potentials of interest such the reduced Gibb's Free Energy, which can be used to formulate a rudimentary equation of state.But, as this approach doesn't consider readily apparent physics that dominate neutron stars such as quantum mechanics, we have to extend this treatment even further by such an inclusion (via energy degeneracy and the inclusion of bound and occupied states of the particles), in addition to angular momentum and relativistic effects to create a more realistic physical model which can be applied and used in determining the associated equations of state and how nuclei formation is affected as a result.Summarily, as the thermodynamics determines the inter-particle distance due to arguments based on particle energy, degeneracy, chemical potential, etc., it is our hope that such a treatment will not only prove to be definitive, but useful in constraining our understanding of these processes having utilized the relatively unexplored mechanism of excluded-volume, in its determination of the equation of state and how that affects nuclei formation in neutron stars.This work has been done in collaboration with the nuclear astrophysics group of Catania, Sicily, under the leadership of Prof. Spitaleri and with Dr. Stefan Typel from GSI, Darmstadt, Germany.


William G Newton

Subject Categories

Physical Sciences and Mathematics | Physics