Van Vleck theory

First, we note that the determination of the exact many-particle operator U is equivalent to solving for the full interacting wavefunction ik. Consequently, some approximation must be made. The ansatz of Eq. (2) recalls perturbation theory, since (as contrasted with the most general variational approach) the target state is parameterized in terms of a reference iko- A perturbative construction of U is used in the effective valence shell Hamiltonian theory of Freed and the generalized Van Vleck theory of Kirtman. However, a more general way forward, which is not restricted to low order, is to determine U (and the associated amplitudes in A) directly. In our CT theory, we adopt the projection technique as used in coupled-cluster theory [17]. By projecting onto excited determinants, we obtain a set of nonlinear amplitude equations, namely,... 

J. H. Van Vleck, Theory of Electric and Magnetic Susceptibilities, Oxford University Press, London, 1932. 

J. van Vleck, Theory of the variations in paramagnetic anisotropy among different salts of the iron group, Phys. Rev. 41 (1932) 208. 

In the case of certain of the R metals, the presence of localized moments due to partially filled f-levels on each atom results in another contribution, Xm, to Ya-Where this contribution is present, it is also dominant. To the extent that these 4f states are localized and highly-correlated, the metallic ions approximate free ionic configurations well, and the Van Vleck theory of paramagnetism (Van Vleck 1932) can be applied to such states of well-defined angular momentum. For a system of interacting moments, a Curie-Weiss-law temperature dependence is to be expected ... 

Our search of all the magnetization measurements which are presently available, leads us to regret that they are often incomplete. Susceptibility measurements at elevated temperature are rare, yet they would reveal readily whether Jq-J mixing occurs, i.e. whether at high temperature the Van Vleck theory has to be applied. Very often susceptibility values below the Neel temperature are not given or plotted. Yet, they would allow us to draw important conclusions. For isotropic exchange in cubic samples the susceptibility must become temperature independent below TJm. Any upturn of the inverse susceptibility below in cubic samples means necessarily that... 

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