ELSEVIER Computer Physics Communications 97 (1996) 175-184 Computer Physics Communications Monte Carlo calculation of muonic molecules S.A. Nemnyugin *, A.M. Petrov Department of Computational Physics, Sankt-Petersburg State University, ul. Ulyanovskaya 1, Petrodoorets, Sankt Petersburg, 198904, Russian Federation Abstract In this paper we report the results of the Green Function Monte Carlo calculation of ground state parameters for a wide set of muonic molecules. Properties of muonic molecules attract a lot of attention due to several reasons. The main one is related to the hope on efficiency of muon catalyzed thermonuclear fusion. The ground state energy, sticking probability for dt/x, pd/x and dd/z molecules have been estimated. Also more exotic complexes including light nuclei 3He and 4He were considered. It was supposed that only Coulomb interactions act between particles. In all cases geometric parameters of the molecule were calculated. Graphs of ground state wave functions obtained by the GFMC make it possible to compare the structure of the bound state in different cases. Despite the yet unsolved problem of the influence of nuclear forces on the fusion characteristics, this kind of calculations help to evaluate the contribution of Coulombic interactions into the physical picture of muon catalysed fusion. 1. Introduction A lot of problems in quantum chemistry, atomic and molecular physics cannot be solved exactly on the basis of modem mathematics. In this case approximate methods of numerical analyses along with effective algorithms and powerful computers are required. Effective numerical algorithms have to match a computer's architecture, which often is a multiprocessor in large-scale calculations today. Special attention in this case leads to algorithms which make it possible to get accurate numerical solutions of complicated computational tasks and may be parallelized in a natural way. Statistical simulation methods lead to a wide class of such algorithms. Their cost weakly depends on the dimensionality of a problem and its complexity. Statistical simulation methods have other attracting peculiarities [1,2]. Quantum few-body physics is an important area of application of the Monte Carlo technique. Among the other computational methods such as variational [3], adiabatic [4], and numerical solution of the Faddeev equations [5], the Monte Carlo method already yielded a lot of numerical results for ground-state properties of the electron gas [6], LiH, Cull [7,8], light nuclei [9], etc. The present paper deals with the application of the Green Function Monte Carlo (GFMC) method to the evaluation of some ground-state characteristics of muonic molecules. Muonic molecules are positive ions (AH/z) ÷, where A is a light nucleus (hydrogen or helium isotopes), H is the hydrogen isotope and /x is the mu-meson. A great interest to the quantum systems of this kind is connected with the idea of muon catalysed thermonuclear fusion (/xCF) which was first suggested by Frank [10] and Sakharov [11] in 1947-48. An * Corresponding author. Tel. + 7(812)4284343; fax: + 7(812)4287240; e-mail: nemnugin@ snoopy.niif.spb.su. 0010-4655/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PH S0010-465 5(96)00030-6