WIGNER-KIRKWOOD METHOD FOR MICROSCOPIC-MACROSCOPIC CALCULATION OF BINDING ENERGIES

2010 ◽  
Vol 19 (04) ◽  
pp. 747-758 ◽  
Author(s):  
A. BHAGWAT ◽  
X. VIÑAS ◽  
R. WYSS ◽  
P. SCHUCK
Keyword(s):  
Fourth Order ◽  
Systematic Study ◽  
Degrees Of Freedom ◽  
Liquid Drop ◽  
Binding Energies ◽  
Deformed Nuclei ◽  
Macroscopic Approach ◽  
Spherical Nuclei

We propose to use the semi-classical Wigner-Kirkwood ħ expansion to calculate shell corrections for spherical and deformed nuclei. The expansion is carried out up to fourth order in ħ. A systematic study of Wigner-Kirkwood averaged energies is presented as a function of the deformation degrees of freedom. The shell corrections, along with the pairing energies obtained by using the Lipkin-Nogami scheme are used in the microscopic-macroscopic approach to calculate binding energies. The macroscopic part is obtained from a liquid drop formula with six adjustable parameters. Considering a set of 367 spherical nuclei, the liquid drop parameters are adjusted to reproduce the experimental binding energies, which yields a rms deviation of 630 keV.

THE EFFECT OF TEMPERATURE IN SPHERICAL AND DEFORMED NUCLEI IN THE DHB APPROXIMATION

2007 ◽  
Vol 16 (09) ◽  
pp. 3032-3036 ◽  
Author(s):  
R. LISBOA ◽  
M. MALHEIRO ◽  
B. V. CARLSON
Keyword(s):  
Mean Value ◽  
Binding Energies ◽  
Effect Of Temperature ◽  
Positive Contribution ◽  
Pairing Interaction ◽  
Deformed Nuclei ◽  
Charge Radii ◽  
Hot Nuclei ◽  
The Mean ◽  
Spherical Nuclei

We present a DHB approximation for excited hot nuclei and calculate the pairing gaps, binding energies, entropy and radii of several spherical and deformed nuclei. We show that the binding energy decreases as the temperature increases, as we would expect from the positive contribution of the thermal energy of the nucleons. The neutron, proton and charge radii of spherical nuclei increase as the temperature increases, while for the deformed 168 Er nucleus these quantities decrease up to T = 2 MeV , the temperature at which the deformation disappears, and increase above this temperature. The pairing interaction is taken into account self-consistently and studied as a function of the temperature: for the even Tin isotopes, the mean value of the neutron pairing gap is almost zero already at T = 1 MeV .

scholarly journals Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method. II. Deformed nuclei

2012 ◽  
Vol 86 (4) ◽  
Author(s):  
A. Bhagwat ◽  
X. Viñas ◽  
M. Centelles ◽  
P. Schuck ◽  
R. Wyss
Keyword(s):  
Binding Energies ◽  
Deformed Nuclei ◽  
Macroscopic Approach

RELATIVISTIC NUCLEAR ENERGY DENSITY FUNCTIONALS

2010 ◽  
Vol 19 (04) ◽  
pp. 548-557 ◽  
Author(s):  
D. VRETENAR ◽  
T. NIKŠIĆ ◽  
P. RING
Keyword(s):  
Energy Density ◽  
Degrees Of Freedom ◽  
Nuclear Energy ◽  
Effective Interaction ◽  
Binding Energies ◽  
Large Set ◽  
Density Functionals ◽  
Heavy Nuclei ◽  
Interaction Terms ◽  
Range Dynamics

A class of relativistic nuclear energy density functionals is explored, in which only nucleon degrees of freedom are explicitly used in the construction of effective interaction terms. Short-distance correlations, as well as intermediate and long-range dynamics, are encoded in the nucleon-density dependence of the strength functionals of an effective interaction Lagrangian. The resulting phenomenological effective interaction, adjusted to experimental binding energies of a large set of axially deformed nuclei, together with a new separable pairing interaction adjusted to reproduce the pairing gap in nuclear matter calculated with the Gogny force, is applied in triaxial relativistic Hartree-Bogoliubov calculations of sequences of heavy nuclei: Th , U , Pu , Cm , Cf , Fm , and No .

AC0-nonconforming quadrilateral finite element for the fourth-order elliptic singular perturbation problem

2018 ◽  
Vol 52 (5) ◽  
pp. 1981-2001 ◽  
Author(s):  
Yuan Bao ◽  
Zhaoliang Meng ◽  
Zhongxuan Luo
Keyword(s):  
Singular Perturbation ◽  
Fourth Order ◽  
Degrees Of Freedom ◽  
Perturbation Parameter ◽  
Singular Perturbation Problem ◽  
Mean Values ◽  
Perturbation Problem ◽  
Convex Quadrilateral ◽  
The Mean ◽  
Quadrilateral Finite Element

In this paper, aC0nonconforming quadrilateral element is proposed to solve the fourth-order elliptic singular perturbation problem. For each convex quadrilateralQ, the shape function space is the union ofS21(Q*) and a bubble space. The degrees of freedom are defined by the values at vertices and midpoints on the edges, and the mean values of integrals of normal derivatives over edges. The local basis functions of our element can be expressed explicitly by a new reference quadrilateral rather than by solving a linear system. It is shown that the method converges uniformly in the perturbation parameter. Lastly, numerical tests verify the convergence analysis.

TWO-OSCILLATOR BASIS EXPANSION FOR THE SOLUTION OF RELATIVISTIC MEAN FIELD EQUATIONS

2000 ◽  
Vol 09 (06) ◽  
pp. 507-520
Author(s):  
S. V. S. SASTRY ◽  
ARUN K. JAIN ◽  
Y. K. GAMBHIR
Keyword(s):  
Ground State ◽  
Mean Field ◽  
Surface Region ◽  
Binding Energies ◽  
Basis Functions ◽  
Field Equations ◽  
Basis Expansion ◽  
Relativistic Mean Field ◽  
Mean Field Equations ◽  
Spherical Nuclei

In the relativistic mean field (RMF) calculations usually the basis expansion method is employed. For this one uses single harmonic oscillator (HO) basis functions. A proper description of the ground state nuclear properties of spherical nuclei requires a large (around 20) number of major oscillator shells in the expansion. In halo nuclei where the nucleons have extended spatial distributions, the use of single HO basis for the expansion is inadequate for the correct description of the nuclear properties, especially that of the surface region. In order to rectify these inadequacies, in the present work an orthonormal basis composed of two HO basis functions having different sizes is proposed. It has been shown that for a typical case of (A=11) the ground state constructed using two-HO wave functions extends much beyond the second state or even third excited state of the single HO wave function. To demonstrate its usefulness explicit numerical RMF calculations have been carried out using this procedure for a set of representative spherical nuclei ranging from 16 O to 208 Pb . The binding energies, charge radii and density distributions have been correctly reproduced in the present scheme using a much smaller number of major shells (around 10) in the expansion.

Towards a Virtual Laboratory for Grain Boundaries and Dislocations

2009 ◽  
Vol 1224 ◽  
Author(s):  
Sebastián Echeverri Restrepo ◽  
Barend J. Thijsse
Keyword(s):  
Molecular Dynamics ◽  
Grain Boundaries ◽  
Systematic Study ◽  
Degrees Of Freedom ◽  
Minimum Energy ◽  
Local Symmetry ◽  
Virtual Laboratory ◽  
Face Centered Cubic ◽  
Face Centered ◽  
Edge Dislocations

AbstractIn order to perform a systematic study of the interaction between grain boundaries (GBs) and dislocations using molecular dynamics (MD), several tools need to be available. A combination of computational geometry and MD was used to build the foundations of what we call a virtual laboratory. First, an algorithm to generate GBs on face-centered cubic bicrystals was developed. Two crystals with different orientations are placed together. Then, by applying “microscopic” rigid body translations along the GB plane to one of the crystals and removing overlapping atoms, a set of initial configurations is sampled and a minimum energy configuration is found. Second, to classify the geometry of the GBs a local symmetry type (LST) describing the angular environment of each atom is calculated. It is found that for a given relaxed GB the number of atoms with different LSTs is not very large and that it is possible to find unique geometrical patterns in each GB. For instance, the LSTs of two GBs having the same “macroscopic” configuration but different “microscopic” degrees of freedom can be dissimilar: the configurations with higher GB energy tend to have a higher number of atoms with different LSTs. Third, edge dislocations are introduced into the bicrystals. We see that full edge dislocations split into Shockley partials. Finally, by loading the bicrystals with tensile stresses the edge dislocations are put into motion. Various examples of dislocation-GB interactions in Cu are presented.

Macroscopic Approach to Pair Transition Density in Well-Deformed Nuclei

1987 ◽  
Vol 3 (3) ◽  
pp. 289-292 ◽  
Author(s):  
P Lotti ◽  
E Maglione ◽  
A Vitturi
Keyword(s):  
Transition Density ◽  
Deformed Nuclei ◽  
Macroscopic Approach
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