Gradient Symplectic Algorithms for Solving the Radial Schrodinger Equation

The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators are well known for their excellent conservation properties. The class of {\it gradient} symplectic algorithms is particularly suited for solving harmonic oscillator dynamics. By use of Suzuki's rule for decomposing time-ordered operators, these algorithms can be easily applied to the Schrodinger equation. We demonstrate the power of this class of gradient algorithms by solving the spectrum of highly singular radial potentials using Killingbeck's method of backward Newton-Ralphson iterations.Comment: 19 pages, 10 figure

Pairing correlations beyond the mean field

We discuss dynamical pairing correlations in the context of configuration mixing of projected self-consistent mean-field states, and the origin of a divergence that might appear when such calculations are done using an energy functional in the spirit of a naive generalized density functional theory.Comment: Proceedings of the XIII Nuclear Physics Workshop ``Maria and Pierre Curie'' on ``Pairing and beyond - 50 years of the BCS model'', held at Kazimierz Dolny, Poland, September 27 - October 1, 2006. Int. J. Mod. Phys. E, in prin

A simple parameter-free one-center model potential for an effective one-electron description of molecular hydrogen

For the description of an H2 molecule an effective one-electron model potential is proposed which is fully determined by the exact ionization potential of the H2 molecule. In order to test the model potential and examine its properties it is employed to determine excitation energies, transition moments, and oscillator strengths in a range of the internuclear distances, 0.8 < R < 2.5 a.u. In addition, it is used as a description of an H2 target in calculations of the cross sections for photoionization and for partial excitation in collisions with singly-charged ions. The comparison of the results obtained with the model potential with literature data for H2 molecules yields a good agreement and encourages therefore an extended usage of the potential in various other applications or in order to consider the importance of two-electron and anisotropy effects.Comment: 8 pages, 6 figure

From Microscales to Macroscales in 3D: Selfconsistent Equation of State for Supernova and Neutron Star Models

First results from a fully self-consistent, temperature-dependent equation of state that spans the whole density range of neutron stars and supernova cores are presented. The equation of state (EoS) is calculated using a mean-field Hartree-Fock method in three dimensions (3D). The nuclear interaction is represented by the phenomenological Skyrme model in this work, but the EoS can be obtained in our framework for any suitable form of the nucleon-nucleon effective interaction. The scheme we employ naturally allows effects such as (i) neutron drip, which results in an external neutron gas, (ii) the variety of exotic nuclear shapes expected for extremely neutron heavy nuclei, and (iii) the subsequent dissolution of these nuclei into nuclear matter. In this way, the equation of state is calculated across phase transitions without recourse to interpolation techniques between density regimes described by different physical models. EoS tables are calculated in the wide range of densities, temperature and proton/neutron ratios on the ORNL NCCS XT3, using up to 2000 processors simultaneously.Comment: 6 pages, 11 figures. Published in conference proceedings Journal of Physics: Conference Series 46 (2006) 408. Extended version to be submitted to Phys. Rev.

Density Functional Theory versus the Hartree Fock Method: Comparative Assessment

We compare two different approaches to investigations of many-electron systems. The first is the Hartree-Fock (HF) method and the second is the Density Functional Theory (DFT). Overview of the main features and peculiar properties of the HF method are presented. A way to realize the HF method within the Kohn-Sham (KS) approach of the DFT is discussed. We show that this is impossible without including a specific correlation energy, which is defined by the difference between the sum of the kinetic and exchange energies of a system considered within KS and HF, respectively. It is the nonlocal exchange potential entering the HF equations that generates this correlation energy. We show that the total correlation energy of a finite electron system, which has to include this correlation energy, cannot be obtained from considerations of uniform electron systems. The single-particle excitation spectrum of many-electron systems is related to the eigenvalues of the corresponding KS equations. We demonstrate that this spectrum does not coincide in general with the eigenvalues of KS or HF equations.Comment: 16 pages, Revtex, no figure

Angular versus radial correlation effects on momentum distributions of light two-electron ions

We investigate different correlation mechanisms for two-electron systems and compare their respective effects on various electron distributions. The simplicity of the wave functions used allows for the derivation of closed-form analytical expressions for all electron distributions. Among other features, it is shown that angular and radial correlation mechanisms have opposite effects on Compton profiles at small momenta.Comment: 22 pages, 5 figures, 3 tabl

Quantum calculations of Coulomb reorientation for sub-barrier fusion

Classical mechanics and Time Dependent Hartree-Fock (TDHF) calculations of heavy ions collisions are performed to study the rotation of a deformed nucleus in the Coulomb field of its partner. This reorientation is shown to be independent on charges and relative energy of the partners. It only depends upon the deformations and inertias. TDHF calculations predict an increase by 30% of the induced rotation due to quantum effects while the nuclear contribution seems negligible. This reorientation modifies strongly the fusion cross-section around the barrier for light deformed nuclei on heavy collision partners. For such nuclei a hindrance of the sub-barrier fusion is predicted.Comment: accepted for publication in Physical Review Lette

The evolution operator of the Hartree-type equation with a quadratic potential

Based on the ideology of the Maslov's complex germ theory, a method has been developed for finding an exact solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically concentrated functions. The nonlinear evolution operator has been obtained in explicit form in the class of semiclassically concentrated functions. Parametric families of symmetry operators have been found for the Hartree-type equation. With the help of symmetry operators, families of exact solutions of the equation have been constructed. Exact expressions are obtained for the quasi-energies and their respective states. The Aharonov-Anandan geometric phases are found in explicit form for the quasi-energy states.Comment: 23 pege

Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential

A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where $T\gg1$ is the adiabatic evolution time. A generalization of the Berry phase of the linear Schr\"odinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.Comment: 13 pages, no figure

Optimal use of time dependent probability density data to extract potential energy surfaces

A novel algorithm was recently presented to utilize emerging time dependent probability density data to extract molecular potential energy surfaces. This paper builds on the previous work and seeks to enhance the capabilities of the extraction algorithm: An improved method of removing the generally ill-posed nature of the inverse problem is introduced via an extended Tikhonov regularization and methods for choosing the optimal regularization parameters are discussed. Several ways to incorporate multiple data sets are investigated, including the means to optimally combine data from many experiments exploring different portions of the potential. Results are presented on the stability of the inversion procedure, including the optimal combination scheme, under the influence of data noise. The method is applied to the simulated inversion of a double well system.Comment: 34 pages, 5 figures, LaTeX with REVTeX and Graphicx-Package; submitted to PhysRevA; several descriptions and explanations extended in Sec. I