Moment of inertia tensors of non-polarized nucleons using a parton model

Neutron star formation is governed by the β-decay nuclear reaction that transforms protons and electrons to neutrons and neutrinos. This study describes a classical model that estimates the Gibbs free energy associated with this phenomenon from the equilibrium constant of the nuclear reaction (K). Previous work based on this idea had assumed a three quark model for the proton and neutron and calculated K by finding the moment of inertia of a rigid asymmetric top for each nucleon.

We build on that method by creating a Jupyter Notebook-based model with the assumption that the proton and neutron’s charges and masses can be modeled as a set number of point-like partons, attributed to Feynman’s Parton Model. Their respective quarks were also considered to be made up of partons. Models were created using known overall mass and charge vs. attributing it to the particular up and down quarks. We used the charge distributions to generate three-dimensional data frames of random points for each nucleon. These were then assigned to a “shell” in the spherical probability distribution we created manually. Finally, we calculated the moment of inertia of each nucleon using the definition for a symmetric spherical body and found K from the ratio of the neutron to the proton. From K, we obtained the Gibbs free energy of the nuclear reaction and compared it to the known estimated energy of a supernova explosion during core collapse. Results were very close to the maximum recorded output in the literature: 10⁴⁶ J.