SIMPLE METHOD FOR ESTIMATING THE ENERGIES OF COULOMB MESIC MOLECULES

By considering Coulomb systems with continuously changing charges of t he particles involved, it is shown, with the aid of the Hellmann-Feynm an theorem and the virial theorem, that the energy of a neutral four-p article Coulomb system is approximately equal to half the sum of the e nergies of all its three-particle subsystems. This rule is verified fo r all 35 symmetric four-particle mesic molecules X+/-X+/-Y-/+Y-/+, who se energies are presently known, and its accuracy is found as a functi on of the particle masses. With allowance for correction factors depen ding on the particle masses, the nonrelativistic energies of asymmetri c four-particle Coulomb mesic molecules d(+)t(+)p(-)p(-), p(+)K(+)pi(- )pi(-),d(+)K(+)pi(-)pi(-), d(+)K(+)mu(-)mu(-), t(+)K(+)mu(-)mu(-), pi( +)mu(+)mu(-)mu(-),pi(+)mu(+)pi(-)pi(-), and pi(+)mu(+)pi(-)mu(-) are p redicted on the basis of this rule. It is shown that the energy of a n eutral N-particle Coulomb system is approximately equal to the ratio o f the sum of the energies of all its (N - 1)-particle subsystems (ther e are N such subsystems) to (N - 2). This rule is verified for the bos on analog of the six-particle positronium molecule e(+)e(-)e(+)e(-)e()e(-).