Sternheimer equation

This is similar to the usual perturbation theory in quantum mechanics, in particular when solving the Sternheimer equation for as a sum over states. Note however that it is, in the case of DFPT, a self consistency equation, as depends on n )(r). As with standard DFT, two methods can be used for determining either by direct minimization of F > [196] or by successive... 

To be specific, consider the neutron-to-proton mass difference. To zeroth order, n and p are degenerate, with a symmetric spatial wave function. If now the mass difference 8m and electromagnetic interaction are switched on, small mixed-symmetry components are allowed, that can be treated perturbatively, exactly as the nonpotential harmonics of section 5.4 (the usual source of inaccuracy in this type of calculations consists of selecting a priori a few neighbouring states of the unperturbed Hamiltonian that are believed to mix with the main component the Sternheimer equations of section 5.4 are by far more powerful [50]). One can even optimize the starting point by adopting an inverse... 

J. P. Vigier, M. Flato, D. and J. Sternheimer, and G. Wathaghin, On the masses on non-strange pseudo-scalar mesons and the generalized Klein-Gordon equation (1966). 

In practice, one can first compute the bound state in the approximation of potential harmonics, with a fairly large Then the effect of nonpotential harmonics of low L, say can be estimated by solving Sternheimer-type equations. If... 

Some nuclear properties of these elements are outlined in Table 1. The relaxation time is determined by three principal factors in a given chemical environment (Chapter 5, Section 4.5), the spin quantum number, /, the quadrupole moment, Q, and the Sternheimer quadrupolar antishielding factor, y, which terms appear in the various equations for quadrupole relaxation in the form... 

---