scholarly journals Magic numbers for shape coexistence

2019 ◽  
Vol 26 ◽  
pp. 9
Author(s):  
I. E. Assimakis ◽  
Dennis Bonatsos ◽  
Andriana Martinou ◽  
S. Sarantopoulou ◽  
S. Peroulis ◽  
...  
Keyword(s):  
Harmonic Oscillator ◽  
Three Dimensional ◽  
Wave Functions ◽  
Magic Numbers ◽  
Shape Coexistence ◽  
Quantitative Investigation ◽  
Atomic Nuclei ◽  
Model Wave ◽  
Nilsson Model

The increasing deformation in atomic nuclei leads to the change of the classical magic numbers (2,8,20,28,50,82…) which dictate the arrangement of nucleons in complete shells. The magic numbers of the three-dimensional harmonic oscillator (2,8,20,40,70,…) emerge at deformations around ε=0.6. At lower deformations the two sets of magic numbers antagonize, leading to shape coexistence. A quantitative investigation is performed using the usual Nilsson model wave functions and the recently introduced proxy–SU(3) scheme.

Nuclear Physics

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Nuclear Physics ◽  
Alpha Decay ◽  
Nuclear Fission ◽  
Nuclear Potential ◽  
Magic Numbers ◽  
Ongoing Research ◽  
Strong Force ◽  
Atomic Nuclei ◽  
Nilsson Model ◽  
Semi Empirical

The chapter gives an overview of nuclear physics from the discovery of the neutron to ongoing research topics. General properties of atomic nuclei are considered: the valley of stability, the nuclear potential, the pairing of nucleons and the strong force. The semi-empirical liquid drop model is presented as a description of relatively large atomic nuclei. The nuclear shell model is described, along with its relationship to magic numbers and beta decay, and is then refined to produce the Nilsson model. Gamow tunnelling is used to explain alpha decay and the Geiger–Nuttall law. It is then applied to nuclear fission and used to calculate rates for thermonuclear fusion in stars. ITER and controlled nuclear fusion are also discussed. Production of superheavy nuclei is detailed and the existence of exotic nuclei, such as halo nuclei, is considered. The Yukawa theory of the strong force is discussed, including its relationship to QCD.

scholarly journals A mechanism for shape coexistence

2021 ◽  
Vol 252 ◽  
pp. 02005
Author(s):  
Andriana Martinou
Keyword(s):  
Harmonic Oscillator ◽  
Shell Model ◽  
Magic Numbers ◽  
Shape Coexistence ◽  
Spin Orbit ◽  
Nuclear Shell Model ◽  
Different Types ◽  
Theoretical Predictions ◽  
Different Shapes ◽  
Nuclear Shell

The phenomenon of shape coexistence in a nucleus is about the occurence of two different nuclear states with drastically different shapes, lying close in energy. It is commonly seen in the data, that such coexisting states manifest in specific nuclei, which lie within certain islands on the nuclear chart, the islands of shape coexistence. A recently introduced mechanism predicts that these islands derive from the coexistence of two different types of magic numbers: the harmonic oscillator and the spin-orbit like. The algebraic realization of the nuclear Shell Model, the Elliott SU(3) symmetry, along with its extension, the proxy-SU(3) symmetry , are used for the parameter-free theoretical predictions of the islands of shape coexistence

scholarly journals Nucleon numbers for nuclei with shape coexistence

2019 ◽  
Vol 26 ◽  
pp. 96 ◽  
Author(s):  
Andriana Martinou ◽  
Dennis Bonatsos ◽  
N. Minkov ◽  
T. J. Mertzimekis ◽  
I. E. Assimakis ◽  
...  
Keyword(s):  
Harmonic Oscillator ◽  
Magic Numbers ◽  
Shape Coexistence ◽  
The One

We consider two competing sets of nuclear magic numbers, namely the harmonic oscillator (HO) set (2, 8, 20, 40, 70, 112, 168, 240,...) and the set corresponding to the proxy-SU(3) scheme, possess- ing shells 0-2, 2-4, 6-12, 14-26, 28-48, 50-80, 82-124, 126-182, 184-256... The two sets provide 0+bands with different deformation and bandhead energies. We show that for proton (neutron) numbers starting from the regions where the quadrupole-quadrupole (Q · Q) interaction, as derived by the HO, becomes weaker than the one obtained in the proxy-SU(3) scheme, to the regions of HO shell clo- sure, the shape coexistence phenomenon may emerge. Our analysis suggests that the possibility for appearance of shape coexistence has to be investigated in the following regions of proton (neutron) numbers: 8, 18-20, 34-40, 60-70, 96-112, 146-168, 210-240,...

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

2005 ◽  
Vol 14 (06) ◽  
pp. 931-947 ◽  
Author(s):  
F. PILOTTO ◽  
M. DILLIG
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Relative Energy ◽  
Wave Functions ◽  
Three Dimensions ◽  
State Wave ◽  
Scalar Diquark ◽  
Bound State Wave Function ◽  
Retardation Effects

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

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