NDLI: Partial virial theorems for atomic-molecular systems

Content Provider	Springer Nature Link
Author	Rebane, T. K.
Copyright Year	2004
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 $^{4}$He$^{2+}$ e $^{−}$ e $^{−}$ and the helium muon-electron mesoatom $^{4}$He$^{2+}$μ$^{−}$ e $^{−}$ that partial virial relations are a highly sensitive indicator of the accuracy of wave functions.
Starting Page	829
Ending Page	833
Page Count	5
File Format	PDF
ISSN	0030400X
Journal	Optics and Spectroscopy
Volume Number	97
Issue Number	6
e-ISSN	15626911
Language	English
Publisher	Nauka/Interperiodica
Publisher Date	2004-01-01
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Optical Spectroscopy, Ultrafast Optics
Content Type	Text
Resource Type	Article
Subject	Atomic and Molecular Physics, and Optics Electronic, Optical and Magnetic Materials

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