SADDLE-POINT SHAPES OF HEAVY AND SUPERHEAVY NUCLEI

2008 ◽  
Vol 17 (01) ◽  
pp. 168-176 ◽  
Author(s):  
A. SOBICZEWSKI ◽  
M. KOWAL ◽  
L. SHVEDOV
Keyword(s):  
Potential Energy ◽  
Saddle Point ◽  
Large Deformation ◽  
Ground State ◽  
Neutron Number ◽  
Superheavy Nuclei ◽  
Deformation Space ◽  
Microscopic Approach ◽  
Main Attention ◽  
Heavy And Superheavy Nuclei

The potential energy of the heaviest nuclei is analyzed in a large deformation space. The main attention is given to shapes of these nuclei at their saddle point and to the comparison of these shapes with those at the ground state. The shapes are analyzed in a 10-dimensional deformation space. The analysis is performed within a macroscopic-microscopic approach. Even-even nuclei with proton number 98 ≤ Z ≤ 126 and neutron number 138 ≤ N ≤ 194 are considered.

PROPERTIES OF HEAVIEST NUCLEI AT THE SADDLE-POINT CONFIGURATION

2010 ◽  
Vol 19 (05n06) ◽  
pp. 1055-1063 ◽  
Author(s):  
A. SOBICZEWSKI ◽  
P. JACHIMOWICZ ◽  
M. KOWAL
Keyword(s):  
Saddle Point ◽  
Neutron Number ◽  
Shell Correction ◽  
Superheavy Nuclei ◽  
Deformation Space ◽  
Microscopic Approach ◽  
Main Attention ◽  
Point Configuration ◽  
Heavy And Superheavy Nuclei ◽  
Large Shell

Properties of heaviest nuclei at their saddle point are studied in a multidimensional deformation space. The main attention is given to deformation and the shell correction to energy of the nuclei at this point. The analysis is performed within a macroscopic-microscopic approach. A 10-dimensional deformation space is used. A large number of about 300 even-even heavy and superheavy nuclei with proton number 98 ≤ Z ≤ 126 and neutron number 134 ≤ N ≤ 192 are considered. Detailed results are illustrated for nuclei of the element 120. A large shell correction (up to about 7 MeV) is found for these nuclei. For most of them, the correction is larger than the height of the barrier, itself, as the macroscopic contribution to this height is negative.

EFFECT OF NON-AXIAL DEFORMATIONS ON THE FISSION BARRIER OF HEAVY AND SUPERHEAVY NUCLEI

2009 ◽  
Vol 18 (04) ◽  
pp. 914-918 ◽  
Author(s):  
M. KOWAL ◽  
A. SOBICZEWSKI
Keyword(s):  
Large Deformation ◽  
Neutron Number ◽  
Quadrupole Deformation ◽  
Fission Barrier ◽  
Superheavy Nuclei ◽  
Deformation Space ◽  
Microscopic Approach ◽  
Proton Number ◽  
Heavy And Superheavy Nuclei

The effect of the non-axial quadrupole deformation γ2 on the height of the static fission barrier B f of heaviest nuclei is studied. Even-even nuclei with the proton number 92 ≤ Z ≤ 122 and the neutron number 136 ≤ N ≤ 188 are considered. The analysis is done within a macroscopic-microscopic approach with the use of a large deformation space. It is found that the effect reduces B f by up to about 2 MeV.

EFFECT OF NON-AXIAL DEFORMATIONS OF HIGHER MULTIPOLARITY ON THE FISSION-BARRIER HEIGHT OF HEAVIEST NUCLEI

2010 ◽  
Vol 19 (04) ◽  
pp. 493-499 ◽  
Author(s):  
A. SOBICZEWSKI ◽  
P. JACHIMOWICZ ◽  
M. KOWAL
Keyword(s):  
Barrier Height ◽  
Neutron Number ◽  
Fission Barrier ◽  
Superheavy Nuclei ◽  
Deformation Space ◽  
Microscopic Approach ◽  
Main Attention ◽  
Proton Number ◽  
Heavy And Superheavy Nuclei

The static fission-barrier height [Formula: see text] of heaviest nuclei is studied in a multidimensional deformation space. The main attention is given to the effect of the hexadecapole non-axial shapes on [Formula: see text]. The analysis is performed within a macroscopic-microscopic approach. A 10-dimensional deformation space is used. A large number of about 300 even-even heavy and superheavy nuclei with proton number 98 ≤ Z ≤ 126 and neutron number 134 ≤ N ≤ 192 are considered. It is found that the inclusion of the non-axial hexadecapole shapes lowers the barrier by up to about 1.5 MeV.

DEFORMATIONS OF MULTIPOLARITY SIX AT THE SADDLE POINT OF HEAVIEST NUCLEI

2008 ◽  
Vol 17 (01) ◽  
pp. 265-271 ◽  
Author(s):  
L. SHVEDOV ◽  
S. G. ROHOZIŃSKI ◽  
M. KOWAL ◽  
S. BELCHIKOV ◽  
A. SOBICZEWSKI
Keyword(s):  
Potential Energy ◽  
Saddle Point ◽  
General Type ◽  
Superheavy Nucleus ◽  
Deformation Space ◽  
Microscopic Approach ◽  
Main Attention ◽  
Point Configuration ◽  
Independent Parameters

Saddle-point configuration of heaviest nuclei is studied in a multidimensional deformation space. Main attention is given to the role of the deformation of multipolarity six of a general type, described by four independent parameters. The dependence of the potential energy of a superheavy nucleus on these parameters at the saddle-point configuration is illustrated. The analysis is performed within a macroscopic-microscopic approach.

ROLE OF THE NON-AXIAL OCTUPOLE DEFORMATION IN THE POTENTIAL ENERGY OF HEAVY NUCLEI

2010 ◽  
Vol 19 (04) ◽  
pp. 768-773 ◽  
Author(s):  
P. JACHIMOWICZ ◽  
M. KOWAL ◽  
P. ROZMEJ ◽  
J. SKALSKI ◽  
A. SOBICZEWSKI
Keyword(s):  
Potential Energy ◽  
Large Deformation ◽  
Neutron Number ◽  
Deformation Space ◽  
Heavy Nuclei ◽  
Microscopic Approach ◽  
Large Space ◽  
Global Energy ◽  
Octupole Deformation

Role of the non-axial octupole deformation a32(Y32 + Y3-2) on the potential energy of heavy nuclei is studied in a large deformation space. The study is performed within a macroscopic-microscopic approach. A large region of nuclei with proton number 88 ≤ Z ≤ 112 and neutron number 128 ≤ N ≤ 156 is considered. It is found that while the a32 deformation alone lowers the energy of the nuclei by up to about 3 MeV (for nuclei around 238 Fm ), it has practically no effect on the global energy minima of considered nuclei, when the analysis is done in a large space.

SADDLE-POINT SHELL EFFECTS OF HEAVIEST NUCLEI

2008 ◽  
Vol 17 (01) ◽  
pp. 259-264 ◽  
Author(s):  
M. KOWAL ◽  
L. SHVEDOV ◽  
A. SOBICZEWSKI
Keyword(s):  
Potential Energy ◽  
Saddle Point ◽  
Equilibrium Point ◽  
Ground State ◽  
Shell Correction ◽  
Deformation Space ◽  
Microscopic Approach ◽  
Shell Effects ◽  
State Point

The shell correction to the potential energy of heaviest nuclei is studied in a multidimensional deformation space. The correction is calculated at the saddle point of the nuclei and compared with that obtained at the equilibrium (ground state) point. Although generally much smaller than at the equilibrium point, the correction at the saddle point is still found to be large and significant. The analysis is performed within a macroscopic-microscopic approach.

TEST OF TETRAHEDRAL SYMMETRY FOR HEAVY AND SUPERHEAVY NUCLEI

2011 ◽  
Vol 20 (02) ◽  
pp. 514-519 ◽  
Author(s):  
P. JACHIMOWICZ ◽  
P. ROZMEJ ◽  
M. KOWAL ◽  
J. SKALSKI ◽  
A. SOBICZEWSKI
Keyword(s):  
Potential Energy ◽  
Ground State ◽  
Potential Energy Surfaces ◽  
Superheavy Nuclei ◽  
Dimensional Manifold ◽  
Microscopic Method ◽  
Tetrahedral Symmetry ◽  
Heavy And Superheavy Nuclei ◽  
Quantum Objects ◽  
Energy Surfaces

In the recent years an interesting suggestion has been made that nucleus, like many other quantum objects, can have tetrahedral shape at the ground state. We test this hypothesis within the macroscopic-microscopic method, by using a 12 dimensional manifold of shapes, including: axial, nonaxial and reflection-asymmetric ones. We systematically calculate potential energy surfaces for even-even heavy and superheavy nuclei in the range of proton numbers 82 ≤ Z ≤ 128 and neutron numbers 98 ≤ N ≤ 194. We find that in the whole region of the investigated superheavy nuclei, tetrahedral symmetry does not play a significant role at the ground state.

ROLE OF HIGHER-MULTIPOLARITY DEFORMATIONS IN THE POTENTIAL ENERGY OF HEAVIEST NUCLEI

2007 ◽  
Vol 16 (02) ◽  
pp. 425-430 ◽  
Author(s):  
M. KOWAL ◽  
A. SOBICZEWSKI
Keyword(s):  
Potential Energy ◽  
General Feature ◽  
Degrees Of Freedom ◽  
Deformation Parameter ◽  
Superheavy Nucleus ◽  
Deformation Space ◽  
Microscopic Approach ◽  
Deformation Parameters ◽  
6 Degrees Of Freedom

Potential energy of the superheavy nucleus 284114 is analyzed in a 6-dimensional deformation space. This space includes two quadrupole, three hexadecapole and one multipolarity-6 deformation parameter. The energy is minimized simultaneously in all 6 degrees of freedom. The analysis is done within a macroscopic-microscopic approach. As in the studies of other superheavy nuclei, the result is found to be very individual for a given nucleus. A more general feature is a small effect of one (γ4) of the hexadecapole deformation parameters on the energy of the nucleus.

Structural properties of heavy and superheavy nuclei in a semi-microscopic approach

2016 ◽  
Vol 25 (01) ◽  
pp. 1650004 ◽  
Author(s):  
M. Ismail ◽  
A. Y. Ellithi ◽  
A. Adel ◽  
Hisham Anwer
Keyword(s):  
Total Energy ◽  
Structural Properties ◽  
Theoretical Models ◽  
Nucleon Nucleon ◽  
Deformation Energy ◽  
Superheavy Nuclei ◽  
Microscopic Approach ◽  
Heavy And Superheavy Nuclei ◽  
Energy Part ◽  
Nucleon Nucleon Interaction

The structure of some heavy and superheavy nuclei with [Formula: see text] and [Formula: see text] is studied using a semi-microscopic model. In this approach, the macroscopic energy part of the total energy of a nucleus is obtained from the Skyrme nucleon–nucleon interaction in the semi-classical extended Thomas–Fermi approach. The microscopic shell-plus pairing correction energies are calculated in Strutinsky’s approach. Within this semi-microscopic approach, the total energy surfaces are investigated in multidimensional deformation space. For each nucleus, the model predictions for the binding energy, deformation energy, the deformation parameters and comparison with other theoretical models are presented. The proposed model shows a significant consistency with other models, and it is found to be successful in reproducing the structural properties of nuclei in heavy and superheavy region.

SHELL CORRECTIONS FOR HEAVY AND SUPERHEAVY NUCLEI

2012 ◽  
Vol 21 (06) ◽  
pp. 1250062 ◽  
Author(s):  
M. ISMAIL ◽  
A. ADEL
Keyword(s):  
Degrees Of Freedom ◽  
Energy Levels ◽  
Superheavy Nuclei ◽  
Magic Numbers ◽  
Deformation Space ◽  
Harmonic Oscillator Basis ◽  
Pairing Interaction ◽  
Heavy And Superheavy Nuclei ◽  
Shell Closures ◽  
Oscillator Basis

The shell and pairing correction energies are calculated for heavy and superheavy nuclei (SHN) by means of the Strutinsky's method. The single-particle (s.p.) energy levels are obtained from the diagonalization of the Woods–Saxon s.p. Hamiltonian in the deformed harmonic oscillator basis for both neutrons and protons. The residual pairing interaction is calculated by means of the usual Bardeen–Cooper–Schrieffer (BCS) approximation. A two-dimensional deformation space describing axially and reflection-symmetric shapes of nuclei has been used. Based on the shell and pairing correction energies, the signatures of the magic numbers appear at the spherical shell closures Z = 82, 114, 164 and N = 126, 184, 228 and 308. There are also signatures for some other shell closures at, e.g., Z = 108 and N = 162 which appear only when the deformation degrees of freedom is taken into account.

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