Simple method for estimating the energies of Coulomb mesic molecules

By considering Coulomb systems with continuously changing charges of the particles involved, it is shown, with the aid of the Hellmann-Feynman theorem and the virial theorem, that the energy of a neutral four-particle Coulomb system is approximately equal to half the sum of the energies of all its three-particle subsystems. This rule is verified for all 35 symmetric four-particle mesic molecules X±X±Y±Y±, whose energies are presently known, and its accuracy is found as a function of the particle masses. With allowance for correction factors depending on the particle masses, the nonrelativistic energies of asymmetric four-particle Coulomb mesic molecules d+t+p-p-, p+K+π-π-, d+K+π-π-, t+K+π-π-, p+K+μ-μ-, d+K+μ-μ-, t+K+μ-μ-, π+μ+μ-μ-, π+μ+π-π-, and π+μ+π-μ- are predicted on the basis of this rule. It is shown that the energy of a neutral N-particle Coulomb system is approximately equal to the ratio of the sum of the energies of all its (N-1)-particle subsystems (there are N such subsystems) to (N-2). This rule is verified for the boson analog of the six-particle positronium molecule e+e-e+e-e+e-