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K. Varga

Publications and source records attributed to K. Varga.

44 records · Page 3Linked to original sources
arXiv1995

Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis

Precise variational solutions are given for problems involving diverse fermionic and bosonic $N=2-7$-body systems. The trial wave functions are chosen to be combinations of correlated Gaussians, which are constructed from products of the single-particle Gaussian wave packets through an integral transformation, thereby facilitating fully analytical calculations of the matrix elements. The nonlinear parameters of the trial function are chosen by a stochastic technique. The method has proved very efficient, virtually exact, and it seems feasible for any few-body bound-state problems emerging in nuclear or atomic physics.

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arXiv1995

Precise solution of few-body problems with the stochastic variational method

A precise variational solution to $N$=2--6-body problems is reported. The trial wave functions are chosen to be combinations of correlated Gaussians, which facilitate a fully analytical calculation of the matrix elements. The nonlinear parameters of the trial function are selected by a stochastic method. Fermionic and bosonic few-body systems are investigated for interactions of different type. A comparison of the results with those available in the literature shows that the method is both accurate and efficient.

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arXiv1994

Shell model on a random gaussian basis

Pauli-projected random gaussians are used as a representation to solve the shell model equations. The elements of the representation are chosen by a variational procedure. This scheme is particularly suited to describe cluster formation and cluster decay in nuclei. It overcomes the basis-size problem of the ordinary shell model and the technical difficulties of the cluster-configuration shell model. The model reproduces the $α$-decay width of $^{212}$Po satisfactorily.

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arXiv1994

Microscopic multicluster description of the neutron-rich helium isotopes

The neutron halo structure of $^{6}$He and of $^{8}$He is studied in a microscopic three-body and five-body model, respectively. Various cluster arrangements are included to embody a variety of correlations between the clusters. The intercluster wave function is determined with the stochastic variational method. The $^{6}$He and $^{8}$He energies are reproduced with the same effective force very well. The radii and densities are compared with the results of empirical analyses. The calculated difference of the neutron and proton radii exceeds 0.8 fm, confirming the thick neutron skin. The two-neutron removal spectroscopic amplitudes are calculated and used for evaluating the momentum distribution and the $β$ decay spectrum, which are sensitive to the halo structure. A fair agreement with experiment is obtained.

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arXiv1993

Two-body matrix elements of Pauli-projected excentric single-particle orbits

We present explicit analytical formulae for two-body matrix elements between Pauli-projected single-particle orbits generated by gaussians shifted from the centre of a nuclear core, which is populated by nucleons occupying harmonic-oscillator orbits. Such shifted gaussian orbits appear in the generator-coordinate model of two-cluster systems and, as ingredients of generating functions, in the resonating group model as well. A Pauli projection is to be understood as a projection onto the subspace not occupied by the core nucleons. This is an exact procedure to take into account the Pauli principle in the limit in which the core is infinitely heavy, thus the procedure to be presented is very useful in the microscopic description of large-core plus small-cluster systems, such as involved in $α$-decay problems.

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arXiv1993

A combined mathematica--fortran program package for analytical calculation of the matrix elements of the microscopic cluster model

We present a computer code that analytically evaluates the matrix elements of the microscopic nuclear Hamiltonian and unity operator between Slater determinants of displaced gaussian single particle orbits. Such matrix elements appear in the generator coordinate model and the resonating group model versions of the microscopic multicluster calculations.

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arXiv1993

Microscopic multicluster description of neutron-halo nuclei with a stochastic variational method

To test a multicluster approach for halo nuclei, we give a unified description for the ground states of $^6$He and $^8$He in a model comprising an $α$ cluster and single-neutron clusters. The intercluster wave function is taken a superposition of terms belonging to different arrangements, each defined by a set of Jacobi coordinates. Each term is then a superposition of products of gaussian functions of the individual Jacobi coordinates with different widths, projected to angular momenta $l=0$ or 1. To avoid excessively large dimensions and ``overcompleteness", stochastic methods were tested for selecting the gaussians spanning the basis. For $^6$He, we were able to calculate ground-state energies that are virtully exact within the subspace defined by the arrangements and $l$ values, and we found that preselected random sets of bases (with or without simulated annealing) yield excellent numerical convergence to this ``exact" value with thoroughly truncated bases. For $^8$He good energy convergence was achieved in a state space comprising three arrangements with all $l=0$, and there are indications showing that the contributions of other subspaces are likely to be small. The $^6$He and $^8$He energies are reproduced by the same effective force very well, and the matter radii obtained are similar to those of other sophisticated calculations.

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