THE CMP-INVARIANCE FOR SYMMETRICAL COULOMB 4-BODY SYSTEMS WITH UNIT CHARGES

The bound state spectra in the symmetrical Coulomb four-body systems w ith unit charges X(+)X(+)Y(-)Y(-) are considered. The total energy and other properties for such systems depend only on the mass ratio s = m (Y)/m(X). It is shown that there is an additional charge-mass-permutat ion invariance in these systems. By applying this invariance we can de termine the total energies for the systems with s greater than or equa l to 1 if the energy dependence is known for s less than or equal to 1 , and vice versa. To produce quite accurate interpolation formulas for the total energies we have made calculations for a number of exotic s ystems, including Ps(2), p(+)p(+)mu(-)mu(-), d(+)d(+)pi(-)pi(-) and ei ght others. For all these systems the variational results are the best values to date; This is the first study based on numerical results of bound state spectra for Coulomb four-body systems with unit charges.