Variational Monte Carlo for Microscopic Cluster Models

Abstract

We examine the application of the Variational Monte Carlo (VMC) method to a cluster model for halo nuclei. Particular attention is paid to the error estimate in the presence of correlations in the underlying random walk. We analyse the required steps for a reliable application of the VMC in the case of a complicated many-body problem such as the direct solution of the nuclear hamiltonian with realistic interactions. We also examine the possibility of variance reduction through the 'zero variance principle', paying particular attention to the complexity of the many-body problem.

State-dependent correlated wavefunctions forsd-shell nuclei

“…In table 1 we show the ground-state energy for the spin/isospin saturated nuclei from 20 Ne to 40 Ca obtained from the different wavefunctions considered here. Some of the results correspond to values previously obtained in [21], where different trial wavefunctions not including operatorial correlations were obtained for the 4n 24 Mg to 40 C nuclei. The J-SU(3) results shown in table 1 coincide, within the statistical error, with the Jastrow energies of [21] because they are calculated with the same variational anstatz.…”

“…Here we have optimized the state independent wavefunction based on the multi-cluster model, i.e., we have optimized the Jastrow parameters, the oscillator parameters of the different clusters and the inter-cluster distances. The results obtained from SU(3) model wavefunctions are labeled as J-SU(3) while those calculated from the multi-cluster one as J-MB-nc, where 'n' stands for the number of clusters in the configuration (2 or 5 for 20 Ne, 3 for 24 Mg and 4 for 28 Si). The set of optimum parameters obtained in an state independent calculation is used in the spin and isospin dependent trial wavefunction.…”

“…The clusters considered in the present work can be both α-particles and 16 O. This clustering scheme has been previously used; see, e.g., [12] and references therein, where the 12 C, 24 Mg and 48 Cr nuclei were studied by using a different nuclear potential.…”

“…The point symmetry group of this geometry is C 3v . For 24 Mg we have worked with an isosceles triangle, with an 16 O cluster in one vertex and two 4 He clusters in the others. For this geometry we have two characteristic distances and the point symmetry group is C 2v .…”

“…This ansatz has been successfully applied to p-shell nuclei with semirealistic interactions [19] and with deformation and angular momentum projection [20]. This scheme has been extended in two directions: (i) the study of sd-shell nuclei with a simplified wavefunction not including state-dependent correlations [21] and (ii) the use of a model wavefunction that accounts for clustering effects [22][23][24][25].…”