The delimiting/frontier lines of the constituents of matter

TL;DR

This paper investigates the delimiting lines of nuclides in the chart of nuclides, using a semi-empirical mass formula and quantum uncertainty principles, revealing an agreement with observed stability boundaries and discussing astrophysical nucleogenesis.

Contribution

It introduces a simple calculation method combining the semi-empirical mass formula and quantum mechanics to approximate the frontier lines of nuclides, linking nuclear stability with fundamental physics.

Findings

The calculated frontier lines align well with the observed limits of nuclide stability.

The approach provides a theoretical basis for understanding the boundaries of matter in the universe.

Discussion of nucleogenesis processes connects nuclear physics with astrophysical phenomena.

Abstract

Looking at the \emph{chart of nuclides} displayed at the URL of the International Atomic Energy Agency (IAEA) \cite{IAEA} -- that contains all the known nuclides, the natural and those produced artificially in labs -- one verifies the existence of two, not quite regular, \emph{delimiting lines} between which dwell all the nuclides constituting matter. These lines are established by the highly unstable radionuclides located the most far away from those in the central locus, the\emph{valley of stability}. Here, making use of the "old" semi-empirical mass formula for stable nuclides together with the energy-time uncertainty relation of quantum mechanics, by a simple calculation we show that the obtained \emph{frontier lines}, for proton and neutron excesses, present an appreciable agreement with the delimiting lines. For the sake of presenting a somewhat comprehensive panorama of the matter in our Universe and their relation with the frontier lines, we narrate, in brief, what is currently known about the astrophysical nucleogenesis processes.