The Extended Nuclear Matter Model with Smooth Transition Surface

TL;DR

This paper investigates how a smooth proton density profile affects the electric field near massive nuclear cores, confirming the existence of a critical electric field and analyzing its characteristics.

Contribution

It extends the nuclear matter model by incorporating a smooth Woods--Saxon density profile, analyzing its impact on electric field behavior near nuclear cores.

Findings

Critical electric field persists with smooth density profiles.

Maximum electric field location and magnitude are altered by the smoother distribution.

Confirmation of electric field near critical value for large nuclear cores.

Abstract

The existence of electric fields close to their critical value $E_c=\frac{m_e^2 c^3}{e \hbar}$ has been proved for massive cores of $10^7$ up to $10^{57}$ nucleons using a proton distribution of constant density and a sharp step function at its boundary. We explore the modifications of this effect by considering a smoother density profile with a proton distribution fulfilling a Woods--Saxon dependence. The occurrence of a critical field has been confirmed. We discuss how the location of the maximum of the electric field as well as its magnitude is modified by the smoother distribution.