Partial virial theorems for atomic-molecular systems |
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Authors: | T K Rebane |
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Institution: | (1) Instituteof Physics, St. Petersburg State University, Peterhof, 198504, Russia |
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Abstract: | New virial relations for three-and four-particle atomic-molecular systems are proposed. Using operators of extension or squeezing of interparticle distances, it is shown that, for all pairs of j and k particles in S states of these systems, the following partial virial relations are valid: 〈2T jk 〉+〈 V jk 〉=0, where 〈V jk 〉 is the average Coulomb interaction energy for a pair of particles and 〈T jk 〉 is a part of the average kinetic energy of the system. There are three and six such relations for three-and four-particle systems, respectively. The conventional virial theorem (〈 2T〉+〈V〉=0) for the average total kinetic and potential energies of the system (〈 T〉 and 〈V〉, respectively) corresponds to the summation of partial virial relations over all pairs of particles. It is shown by an example of variational calculations of the helium atom 4He2+ e ? e ? and the helium muon-electron mesoatom 4He2+μ? e ? that partial virial relations are a highly sensitive indicator of the accuracy of wave functions. |
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