Hybrid Schrödinger-Ginzburg-Landau approach is based on the fact of the mathematical similarity of Ginzburg-Landau (GL) and Schrödinger formalisms. Starting from Schrödinger approach by replacing the ...term V (x)−E with the term α(x)+β(x)|ψ(x)|
2
we get the Ginzburg-Landau equation. In the proposed relaxation algorithm, we use one- and two-dimensional ground energy solutions of the Schrödinger equation and apply them as a starting trial solution for the GL relaxation method. The obtained numerical results and used methodology form the basis of the simulation platform for studying superconducting integrated structures and modeling various superconducting devices, including their time-dependent geometry.
The nuclear Hamiltonian with a Yukawa-folded mean-field potential is diagonalized within the basis of a deformed harmonic-oscillator in Cartesian coordinates. The nuclear shape is characterized by ...the equivalent sharp surface described either by the well known Funny–Hills or the Trentalange–Koonin–Sierk parametrizations. They are both able to describe a very vast variety of nuclear deformations, including necked-in shapes, left–right asymmetry and non-axiality. The only imposed limitation on the nuclear shape is the z-signature symmetry, which corresponds to a symmetry of the shape with respect to a rotation by an angle π around the z-axis. On output, the computer code produces for a given nucleus with mass number A and charge number Z the energy eigenvalues and eigenfunctions of the mean-field Hamiltonian at chosen deformation.
Program title: yukawa
Catalogue identifier: AEYI_v1_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYI_v1_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 78599
No. of bytes in distributed program, including test data, etc.: 1551468
Distribution format: tar.gz
Programming language: Fortran 77.
Computer: Any PC machine.
Operating system: Windows or a system based on Linux.
RAM: bytes: 0.5 GB or more
Classification: 17.19.
Nature of problem: The full single-particle nuclear Hamiltonian composed of the Yukawa-folded central, spin–orbit and Coulomb potentials is generated and diagonalized. The only symmetry of the problem is the so called z-signature symmetry which limits the nuclear shapes to those, being invariant with respect to a rotation by an angle π around the z-axis.
Solution method: The mean-field Hamiltonian is expressed in matrix form in the basis of an anisotropic harmonic-oscillator potential written in Cartesian coordinates, where the basis parameters are adjusted to the actual deformed nuclear shape. The eigensolutions of the Hamiltonian are determined by diagonalization of the corresponding matrix.
Running time: For a nucleus of spherical shape, with the inclusion of NMAX=14 major oscillator shells and including the option of printing out all the eigenfunctions, one program run takes around 7 s on an average dual-core 2 GHz notebook of 1 GB RAM memory. The same type of calculation for a complicated non-axial left–right asymmetric shape requires around 11 s.
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Proton emission is described using a model which has previously given good results in the description of
α
and cluster radioactivity. The simple phenomenological formalism, based on the Gamow ...theory for alpha decay, is now extended by including the centrifugal term. The model contains only one parameter: the effective nuclear radius constant. Its value was once found for alpha and cluster emitters. A good agreement with the experimental half-lives for proton radioactivity is achieved without any additional fitting procedures to the data for proton emission.
.
The fission fragments mass-yield of
236
U is obtained by an approximate solution of the eigenvalue problem of the collective Hamiltonian that describes the dynamics of the fission process whose ...degrees of freedom are: the fission (elongation), the neck and mass-asymmetry modes. The macroscopic-microscopic method is used to evaluate the potential energy surface. The macroscopic energy part is calculated using the liquid drop model and the microscopic corrections are obtained using a Woods-Saxon single-particle levels. The four-dimensional modified Cassini ovals shape parametrization is used to describe the shape of the fissioning nucleus. The mass tensor is taken within a cranking-type approximation. The final fragment mass distribution is obtained by weighting the adiabatic density distribution in the collective space with the neck-dependent fission probability. The neck degree of freedom is found to play a significant role in determining the final fragment mass distribution.
Shape isomers in Pt, Hg and Pb isotopes with N≤126 Pomorski, K.; Nerlo-Pomorska, B.; Dobrowolski, A. ...
The European physical journal. A, Hadrons and nuclei,
2020/4, Volume:
56, Issue:
4
Journal Article
Peer reviewed
Open access
Deformation-energy surfaces of 54 even-even isotopes of Pt, Hg and Pb nuclei with neutron numbers up to 126 are investigated within a macroscopic-microscopic model based on the Lublin-Strasbourg-Drop ...macroscopic energy and shell plus pairing-energy corrections obtained from a Yukawa-folded mean-field potential at the desired deformation. A new, rapidly converging Fourier shape parametrization is used to describe nuclear shapes. The stability of shape isomeric states with respect to non-axial and higher-order deformations is investigated.
The fission-fragment mass and total kinetic energy (TKE) distributions are evaluated in a quantum mechanical framework using elongation, mass asymmetry, neck degree of freedom as the relevant ...collective parameters in the Fourier shape parametrization recently developed by us. The potential energy surfaces (PES) are calculated within the macroscopic-microscopic model based on the Lublin-Strasbourg Drop (LSD), the Yukawa-folded (YF) single-particle potential and a monopole pairing force. The PES are presented and analysed in detail for even-even Plutonium isotopes with
A
= 236–246. They reveal deep asymmetric valleys. The fission-fragment mass and TKE distributions are obtained from the ground state of a collective Hamiltonian computed within the Born-Oppenheimer approximation, in the WKB approach by introducing a neck-dependent fission probability. The calculated mass and total kinetic energy distributions are found in good agreement with the data.
.
A certain number of yet unknown super- and hyper-deformed shape isomeric states are predicted in even-even nuclei of the region between Pt and Ra, using the macroscopic-microscopic model based on ...the Lublin Strasbourg Drop for the macroscopic energy and shell plus pairing corrections evaluated through the Yukawa-folded mean-field potential for the microscopic part. A new, rapidly converging shape parametrization is used to describe the vast range of nuclear deformations between the ground and the fission isomeric states up to near the scission configuration. Quadrupole moments are evaluated in the local minima and turn out to be in good agreement with the experimental data wherever available.
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