Projection and ground state correlations made simple

We develop and test efficient approximations to estimate ground state correlations associated with low- and zero-energy modes. The scheme is an extension of the generator-coordinate-method (GCM) within Gaussian overlap approximation (GOA). We show that GOA fails in non-Cartesian topologies and present a topologically correct generalization of GOA (topGOA). An RPA-like correction is derived as the small amplitude limit of topGOA, called topRPA. Using exactly solvable models, the topGOA and topRPA schemes are compared with conventional approaches (GCM-GOA, RPA, Lipkin-Nogami projection) for rotational-vibrational motion and for particle number projection. The results shows that the new schemes perform very well in all regimes of coupling.Comment: RevTex, 12 pages, 7 eps figure

A stabilized pairing functional

We propose a modified pairing functional for nuclear structure calculations which avoids the abrupt phase transition between pairing and non-pairing states. The intended application is the description of nuclear collective motion where the smoothing of the transition is compulsory to remove singularities. The stabilized pairing functional allows a thoroughly variational formulation, unlike the Lipkin-Nogami (LN) scheme which is often used for the purpose of smoothing. First applications to nuclear ground states and collective excitations prove the reliability and efficiency of the proposed stabilized pairing.Comment: 6 pages, 5 figure

Adiabatic time-dependent Hartree-Fock calculation of fusion cross sections: application to 40^{40}Ca-40^{40}Ca

Using the adiabatic time-dependent Hartree-Fock method we calculate the interaction and inertial mass parameter relevant for a heavy-ion collision. In this work, which extends an earlier study for lighter systems, we investigate the case of 40Ca-40Ca for which detailed experimental information is available. As already found for lighter colliding ions, the mass parameter exhibits a large peak for interdistances slightly smaller than the barrier radius. We use our results to evaluate the fusion cross section and we find that the structure in the inertial mass brings the theoretical cross section in close agreement with data. © 1983.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Iterative approaches to the self-consistent nuclear energy density functional problem: Heavy ball dynamics and potential preconditioning

International audienceLarge-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing solvers can become very slow, and their performance dependent on manual fine-tuning of numerical parameters. In addition, convergence can sensitively depend on particularities of the EDF’s parametrisation under consideration. Using the widely-used Skyrme EDF as an example, we investigate the impact of the parametrisation of the EDF, both in terms of the operator structures present and the size of coupling constants, on the convergence of numerical solvers. We focus on two aspects of the self-consistency cycle, which are the diagonalisation of a fixed single-particle Hamiltonian on one hand and the evolution of the mean-field densities and potentials on the other. Throughout the article we use a coordinate-space representation, for which the behaviour of algorithms can be straightforwardly analysed. We propose two algorithmic improvements that are easily implementable in existing solvers, heavy-ball dynamics and potential preconditioning. We demonstrate that these methods can be made virtually parameter-free, requiring no manual fine-tuning to achieve near-optimal performance except for isolated cases. The combination of both methods decreases substantially the CPU time required to obtain converged results. The improvements are illustrated for the MOCCa code that solves the self-consistent HFB problem in a 3d coordinate space representation for parametrisations of the standard Skyrme EDF at next-to-leading order in gradients and its extension to next-to-next-to-leading order