Four-body problem

Jacobi coordinates and the hyperspherical harmonics (h.h) basis are used to solve the four-body problem. The Schroedinger equation is transformed to an infinite set of second order coupled differential equations CDE which are truncated to a finite set. The Numerov method is used to solve CDE. The first term in the expansion of the wave function and the Volkov spin independent potential in terms of h.h are used to solve for the ground state energy and wave function of the α particle. Four energy weighted moments for the electric dipole photoeffect are then calculated. Two, three, or four of these moments are inverted, using S polynomials to determine the photoeffect cross section. Results with different numbers of moments agree with each other to about 15%. The program based on the Numerov algorithm was tested by solving the anisotropic harmonic oscillator in spherical coordinates. The authors found some of the eigenvalues and the ground state eigenfunction. Results agree with the analytic solution to six significant figures