THE NEW COORDINATE SYSTEMS IN PHYSICS AND MAGIC NUMBERS

This paper presents two new coordinate systems (s, t, u, v) and (s*, t*, u*, v*). There is a transformation of relations between (s, t, u, v) and (x, y, z) - cartesian between (s*, t*, u*, v*) and (x, y, z), between (s, t, u, v) and (s*, t*, u*, v*). The theory is an attempt to account for the existence of magic numbers in terms of interactions between an individual nucleon and a force field produced by all the other nucleons. Combination of the cartesian coordinate system with our news coordinates arise as very firmly fastening structure for description of nuclear spheres (shells).

INTRODUCTION

Nuclei with equal numbers of protons and neutrons are especially stable, as are nuclei with even numbers of protons and neutrons. Thus such nuclei as ₂He⁴, ₆C¹², and ₈O¹⁶ appear as peaks on the on the empirical binding energy per nucleon curve. Nuclei with 2, 8, 20, 28, 50, 82, 126, and 152 neutrons or protons are more abundant than other nuclei of similar mass numbers, suggesting that their structures are more stable.

Other evidence also points out to significance of numbers 2, 8, 20, 28, 50, 82, 126, and 152 which have become known as magic numbers, in nuclear structure. An example is the observed pattern of nuclear electric quadrupole moments, which are measures of the departures of nuclear charge distribution from sphericity. A spherical nucleus has no quadrupole moment. Nuclei of magic N and Z are found to have zero quadrupole moments, hence, are spherical. Theory "THE NEW COORDINATE SYSTEMS IN PHYSICS" is an attempt to account for the existence of magic numbers in terms of interactions between an individual nucleon and a force field produced by all the other nucleons.