Orbital interaction angular dependence

On the basis of polarization experiments ( Fig. 2.1), one can conclude that the nucleon-nucleon force depends on the relative alignment of the spins with respect to the relative orbital angular momenta. The spin-orbit interaction term depends, indirectly, on the relative velocity. 

Important aspects of the interaction of strong laser fields with molecules can be missed in standard TOF experiments, most notably the population of electronically excited states. However, by studying vibrational excitation, the frequency and dephasing of the vibrational motion can be used to identify the electronic state undergoing the vibrational motion. In some cases, this turns out to be a ground state, and in others, an excited state. Once we have identified an excited state, we are left with the question of how and why the state was populated by the strong field. In one example above (the Ij A state discussed in Sect. 1.3.3), the excited state is formed by the removal of an inner orbital electron, in this case a iru electron. This correlates with the measured angular dependence for the ionization to this state. 

A reduced variational space method, related to the KM procedure, has been developed in which the orbitals of one fragment are optimized in the field of the frozen orbitals of its partner. Truncation of the variational space by deletion of unoccupied orbitals of one partner or the other is the pathway to evaluation of polarization, charge-transfer, and BSSE terms. When applied to the water dimer -", the Coulomb and exchange sum dominates the interaction but charge transfer and polarization terms are needed for proper angular dependence. 

Section 3 is a theoretical discussion that covers the free-ion Hamiltonian, crystal-field theory, and intensities. We discuss the effect of interelectronic Coulomb interactions and the spin-orbit interaction in determining the structure of the free-ion levels. Several additional interactions that are weaker than the above shift the free-ion levels by a few hundred wavenumbers and are necessary to give good agreement between calculated free-ion levels and experiment. These include spin-independent configuration interaction by the Coulomb interaction, spin-dependent configuration interaction by the spin-orbit interaction, and relativistic interactions that couple orbital and spin angular momenta of different electrons. 

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