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Improved algorithms and new parametrisations
of nuclear interactions

Several proposals related to new parametrisations have been formulated. They fall into the category of extensions and improvements of the existing and rather well established microscopic methods. This will allow, first of all, to made a progress in our understanding of the exotic nuclei and various exotic multi-fermion configurations that such nuclei are expected to produce.
In order to solve the first step (new and/or improved parametrisations of the effective nuclear interactions) several standard calculations will needed to be done. This will be a very important but rather tedious and work consuming operation aiming principally at repetitive calculations of the nuclear properties in the ground- and the low-lying excited states by using the following algorithms/techniques:

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Calculations of the potential energy surfaces and equilibrium deformations;
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Calculations of the equilibrium mean square charge radii (MSR);
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Calculations of the equilibrium electric multipole moments.

The calculation will be performed on basis of the microscopic, both non-selfconsistent and self-consistent methods. We feel that an interesting and important progress in the fine tuning of the nuclear hamiltonians can be achieved by addressing in this context the experimental information about relatively less explored nuclear features:

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Proton and neutron (proton vs. neutron) density distributions;
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Neutron halo effect.

The techniques and the computer codes necessary to study these static properties of nuclei at the state-of-the-art level have already been developed and are at the disposal of the future participants. In particular variants of the microscopic-macroscopic method basing on the most realistic macroscopic models have already been advanced. The single particle problem could be solved, depending on the particular context, with various average field hamiltonians by employing either the newest version of the Nilsson, the Woods-Saxon and/or derived from Dirac equation hamiltonians. Of course it is not our intention to repeat the same work with the alternative models. We will rather concentrate the effort on the optimizing one effective, realistic hamiltonian that could serve at the same time to describe the single-nucleonic properties throughout the periodic table including the exotic nuclei.

It is particularly worthwhile at present to revisit the Skyrme-type parametrisation of the effective nuclear forces within the self-consistent Hartree-Fock formalism. The new possibilities are related to the exploration of the time-odd terms in the corresponding effective hamiltonian and the verification of the proposed improvements by using the large high-spin data bank available at present. These interesting new data have been obtained during several years within various international collaboration projects and more recently from the top level projects such as EUROGAM or the US project GAMMASPHERE.

We intend to invest into the improvements of the average field parametrisations of the Woods-Saxon type potentials first. This will be done by taking into account all the available data on the single particle binding energies, the relative order of the (quasi-) particle levels, the root-mean-square radii, the measured equilibrium deformations as well as the information available about fission isomers. This first step will allow us to accumulate and critically approach the existing experimental information. The choice of the Woods-Saxon method has the advantage of being at the same time "realistic" and quick from the numerical point of view.

Main ingredient of the almost all microscopic theories, the usual effective interactions, must be reviewed to be successful also near the neutron drip lines. Some progress have been recently made within the zero-range Skyrme interaction with new set of parameters obtained E. Chabanat and coworkers. It is our intention to extend these efforts in order to obtain the highest standard effective force that can be obtained nowadays by using all empirical information available today (and totally unavailable when some of those concepts have been introduced several years ago).

The Gogny and Skyrme effective interactions will be used to extract the shell effects in proton and neutron density distributions in nuclei and evaluate a new macroscopic formula for the nuclear energy.


next up previous
Next: About this document ... Up: SELECTED MATHEMATICAL METHODS IN Previous: Algebraic Generator Coordinate Method

2000-04-17