A Proposed Z 1/3 – Dependence Formula for Nuclear Potential Radii with Constant Parameter for both Heavy and Light Nuclei

Abstract

The size of the nucleus is the fundamental static properties of nucleus
which has been studied to acquire some information on the complexity
of nuclear many-body problems. This study built a picture of atomic
nucleus as a finite-sized central object with positive charge +Ze,
equals in magnitude with negative charge (-e) of orbiting leptons.
From this picture a simple relation, that could be applied to calculate
the size of the fields originated from the positively charged protons, is
deduced. This simple relation, RZ = rZZ
1/3
, which is a function of
proton charge Z, successfully provides a constant radius parameter
for both light and heavy nuclei. The relation could also be applied to
search information on the size of the unknown atomic nuclei. For this
reason, the A – dependence formula, R = r0A
1/3
, for measuring the size
of atomic nuclei could be replaced by the Z – dependence formula.
This support the idea that the charge radii for the atomic nuclei are
more directly related to its charge number, RZ, rather than its mass
number, R. Therefore, this work offers an easy way to measure or
predict the nuclear charge radius for both light and heavy nuclei from
the assumption of nuclear finite sized model. This development in
nuclear size measurement could improve simplifying the complexity in
nuclear structure and dynamic.