Semi-classical calculation of the shell energies of even-even nuclei with the help of Casimir forces
Abstract
In the present paper we calculate in semi-classical approximation the shell energies of even-even nuclei with the help of Casimir forces. We first demonstrate that for the total binding energy of the helium nucleus, essentially tangential and radial Casimir forces, introduced by us, are responsible. In a second step, we carry out the same calculation for the beryllium nucleus and in this case we also find out that for the total binding energy of the beryllium nucleus, essentially tangential and radial Casimir forces, introduced by us, are responsible. Finally, we calculate some characteristic shell quantities of selected even-even nuclei – 8Be, 16O, 24Mg, 32S, 40Ca, 48Cr, 56Ni, 64Ge, 96Cd – and we show that with increasing shell radius a strongly declining shell energy spectrum follows. We give the shell energy spectrum of the exemplary selected nucleus 96Cd and we show how the shell energies are composed of tangential and radial acting Casimir energies. Altogether, we obtain a fascinatingly simple and intuitive model of even-even nuclei; its correctness however can only be verified by solving the fundamental equations of quantum hydrodynamics in the interior of the nucleons.
Key words: shell energies and the total binding energy of even-even nuclei, tangential and radial acting Casimir forces, shell energy spectrum of even-even nuclei, fundamental equations of quantum hydrodynamics.