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The excited states of the Bosonicvan der Waals clusters: A Monte Carlo study

M. Meierovich

Published Jan 1, 1997• 0 citations

Abstract

The computational physics methods of various processes have become very popular during the last several years. Our interest in his field is predominantly motivated by the expectation that it will be possible to perform a detailed comparison between experimental and theoretical results obtained in the study of clusters of a variety of sizes. Algebraic invariants are employed to deal efficiently with the many-body correlations. We study the applicability of the developed trial wave functions over some range of particle masses, from Ar to He and lighter. We compute the ground and excited states energies and various geometric sizes of small clusters as a function of a continuously varied mass parameter. For sufficiently small masses the cluster can no longer support a bound state, and we are interested in particular in the behavior of the clusters in the vicinity of the critical mass, i.e., the point at which the binding energy approaches zero. We show that the use of bosonic polynomials provides enough variational freedom to approximate ground and excited states of clusters of any mass. We discuss how the properties of clusters change with mass.

DOI: 10.23860/diss-4194

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The computational physics methods of various processes have become very popular during the last several years. Our interest in his field is predominantly motivated by the expectation that it will be possible to perform a detailed comparison between experimental and theoretical results obtained in the study of clusters of a variety of sizes. Algebraic invariants are employed to deal efficiently with the many-body correlations. We study the applicability of the developed trial wave functions over some range of particle masses, from Ar to He and lighter. We compute the ground and excited states energies and various geometric sizes of small clusters as a function of a continuously varied mass parameter. For sufficiently small masses the cluster can no longer support a bound state, and we are interested in particular in the behavior of the clusters in the vicinity of the critical mass, i.e., the point at which the binding energy approaches zero. We show that the use of bosonic polynomials provides enough variational freedom to approximate ground and excited states of clusters of any mass. We discuss how the properties of clusters change with mass.

In calculating energy spectra, unlimited accuracy is only obtained if N-body wavefunctions contain N-body correlations except in special cases. These wave-functions are however not practical both for analytic and computational considerations. To this extent, the possiblity of utilizing correlations less than N is investigated. These investigations are based on the hypothesis whereby in D-dimensions, correlations greater than (D + 1)-body correlations are considerably less important. To accomplish these investigations, we compare the quality Q of the wavefunctions, pertaining to two-, three- and four-body correlations, in various dimensions. The trial wavefunctions used in our Monte Carlo method are linear combinations of elementary basis functions that consist of non-linear variational parameters. This method entails a linear optimization nested in a non-linear one. Once these trial wavefunctions are optimized we employ them as basis functions in a correlation function Monte Carlo which reduces systematically the variational bias of the energy estimates. This method is used to calculate ground and excited state energies of small bosonic van der Waal clusters using wavefunctions with two-, three- and four-body correlations. In calculating energy spectra in different dimensions, it was observed that for N atoms there exists an inter-dimensional degeneracy in the energy spectrum for (N − 1)-dimensions and (N + 1)-dimensions. The finite difference method is also used to calculate 'exact' energy spectra of two-body clusters, and these results are used as a benchmark to compare results obtained by our Monte Carlo method. We also describe a method of obtaining better statistics from quantum Monte Carlo estimators based on the assumption that these estimators are afflicted with distributions that resemble the lognormal probability distribution.

Bosonic two-dimensional self-bound clusters consisting of

N

atoms interacting through additive van der Waals potentials become unbound at a critical mass

{m}_{*}^{(N)}

;

{m}_{*}^{(N)}

has been predicted to be independent of the size of the system. Furthermore, it has been predicted that the ground state energy

{E}_{N}

of the

N

-atom system varies exponentially as the atomic mass approaches

{m}_{*}

. This paper reports accurate numerical many-body calculations that allow these predictions to be tested. We confirm the existence of a universal critical mass

{m}_{*}

, and show that the near-threshold behavior can only be described properly if a previously neglected term is included. We comment on the universality of the energy ratio

{E}_{N+1}∕{E}_{N}

near threshold.

Optimized variational calculations have been carried out for clusters of He4 between N=20 and N=1000 atoms. For small cluster sizes with less or equal to 112 particles, where comparisons with existing diffusion Monte Carlo results are possible, we find good agreement for the ground state energies and densities. Using a somewhat simpler approximation, we also calculate the bound state energies of He3 atoms attached to these clusters. We then calculate excitations and the dynamic structure function. The complex and nonlocal self-energy introduced for that purpose gives access to the calculation of both elastic and inelastic scattering processes for He4 and He3 atoms impinging on the clusters.