Related papers: Magic numbers for shape coexistence
Three-dimensional central symmetric bodies different from spheres that can float in all orientations are considered. For relative density rho=1/2 there are solutions, if holes in the body are allowed. For rho different from 1/2 the body is…
Three stable isobars, $^{96}_{40}$Zr$_{56}$, $^{96}_{42}$Mo$_{54}$ and $^{96}_{44}$Ru$_{52}$, which are in the vicinity of the harmonic oscillator proton shell closure Z=40 and the spin-orbit neutron shell closure N=50, are investigated for…
The nuclear shell structure, which originates in the nearly independent motion of nucleons in an average potential, provides an important guide for our understanding of nuclear structure and the underlying nuclear forces. Its most…
We consider quantum models corresponding to superymmetrizations of the two-dimensional harmonic oscillator based on worldline $d=1$ realizations of the supergroup SU$(\,{\cal N}/2\,|1)$, where the number of supersymmetries ${\cal N}$ is…
The atomic nucleus is a quantum many-body system whose constituent nucleons (protons and neutrons) are subject to complex nucleon-nucleon interactions that include spin- and isospin-dependent components. For stable nuclei, already several…
The ground state properties of even mass Cr and Fe isotopes are studied using the generalized hybrid derivative coupling model. The energy surface of each isotope is plotted as a function of the mass quadrupole moment. The neutron numbers…
We consider the problem of distinguishing convex subsets of $n$-cyclotomic model sets $\varLambda$ by (discrete parallel) X-rays in prescribed $\varLambda$-directions. In this context, a `magic number' $m_{\varLambda}$ has the property that…
Nuclides sharing the same mass number (isobars) are observed ubiquitously along the stability line. While having nearly identical radii, stable isobars can differ in shape, and present in particular different quadrupole deformations. We…
We introduce Magic Gems, a geometric representation of magic squares as three-dimensional polyhedra. By mapping an n times n magic square onto a centered coordinate grid with cell values as vertical displacements, we construct a point cloud…
In addition to shape oscillations, low-energy excitation spectra of deformed nuclei are also influenced by pairing vibrations. The simultaneous description of these collective modes and their coupling has been a long-standing problem in…
The neutron numbers N = 32 and 34 are new magic numbers suggested in neutron-rich $pf$-shell nuclei. In this article, we discuss the experimental observables and state-of-the-art theoretical calculations that characterize and explain the…
We note an intriguing coincidence in nuclear levels, that the subshells responsible for doubly magic numbers happen to bracket nuclei at the energies of the Standard Model bosons. This could show that these bosons actually contribute to the…
By using Supersymmetric Quantum Mechanics and Semiclassical Quantization, one may argue that the low-lying excited states of any quantum system can be modeled by a set of harmonic oscillators. In the present paper, we fit the experimental…
Masses, deformations, radii, and single-particle properties of the very neutron-rich Sulfur isotopes are investigated in the framework of the selfconsistent mean-field theory. The stability of the N=28 magic gap around $^{44}$S is…
Atomic nuclei have a shell structure where nuclei with 'magic numbers' of neutrons and protons are analogous to the noble gases in atomic physics. Only ten nuclei with the standard magic numbers of both neutrons and protons have so far been…
Beyond uranium heavy elements rapidly become increasingly unstable with respect to spontaneous fission as the proton number Z increases, because of the disruptive effect of the long-range Coulomb force. However, in the region just beyond Z…
We investigate the shell structure of bubble nuclei in simple phenomenological shell models and study their binding energy as a function of the radii and of the number of neutron and protons using Strutinsky's method. Shell effects come…
We show that the Liquid Drop Model is best suited to describe the masses of prolate deformed nuclei than of spherical nuclei. To this end three Liquid Drop Mass formulas are employed to describe nuclear masses of eight sets of nuclei with…
We suggest that the emergence of a large deformation in the magnesium, Mg, nuclides, especially at the Z = 12, N = 12, should be associated with an octahedral deformed shape. Within the framework of molecular geometrical symmetry, we find a…
Shell structure in the single particle spectrum of deformed harmonic oscillator potentials when a term proportional to $(\vec L)^2$ is added is analyzed for a large particle number. A scaling law which gives a dividing line between regular…