Fast convergent hyperspherical harmonic expansion for three-body systems

A method of acceleration of the convergence of the hyperspherical harmonic expansion, which allows very accurate direct solution of nonrelativistic three body equations, is presented. The detailed description of the method, which combines the use of the Jastrow correlation factors and of the hyperspherical formalism, is given. The calculation of the ground-state wavefunctions of the helium atom and of expectation values of different operators is carried out for cases of finite and infinite nuclear masses and shows that the accuracy of the method is comparable to the most sophisticated variational calculations. The influence of different choices of correlation functions is discussed. The convergence patterns are analyzed and compared with the results of the computation.