Nuclear distortion

This new, approximate macromolecular density matrix (q K ), K [A]) for the new, slightly distorted nuclear geometry K1 is also idempotent with respect to multiplication involving the actual new overlap matrix S(K... 

If the original macromolecular density matrix is already available, then such approximate macromolecular electron densities for slightly distorted nuclear geometries are simpler to calculate than the full recalculation of an ADMA macromolecular density matrix that involves a new fragmentation procedure. 

In the calculations done by us and presented here we account for the static Coulomb term, vf, and the electromagnetic spin-orbit part of t, cn,m> where, cn,m is the free nucleon-nucleon Coulomb distorted nuclear t-matrix. Estimates of the (G2. - g) term, representing medium corrections, are also given. Electromagnetic effects are usually ignored in the second-order optical potential. 

Recently Elster, Liu and Thaler (ELT) [El 91] proposed a novel method for dealing with the momentum space Coulomb problem, which is, in principle, exact and may be less prone to numerical difficulties than the VP method. Their approach is based on the separation of the optical potential in eq. (3.63) and employs the two-potential formula [Ro 67] to express the full scattering amplitude as a sum of the point Coulomb amplitude and the point Coulomb distorted nuclear amplitude. The latter is obtained by numerically solving an integral equation represented in terms of Coulomb wave function basis states rather than the usual plane wave states. 

In eqs. (3.101)-(3.103) (vf) is the local, static Coulomb term and should include the relativistic correction factor, rj (see section 3.4). In eq. (3.101) ( ,cn,m) interpreted as the empirical, on-shell Coulomb distorted nuclear t-matrix obtained from phase shift analyses. The (, cn.m) contain... 

Schematic drawing illustrating these aspects in case of NbsGe is presented in Fig. 27.6. The Fu phonon mode covers out-of phase stretching vibration of two perpendicular Nb chains in two planes - see Fig. 27. Id. For simplicity, drawing of only a single chain of Nb atoms in a plane (e.g. b-c plane) is sketched in Fig. 27.6. For equilibrium high-symmetry structure (Req) on the crude-adiabatic level, the highest electron density is localized at equilibrium position of Nb atoms in a chain - Fig. 27.6a. For distorted nuclear geometry (Rd,cr) in the Fn mode, electron density is polarized and the highest value is shifted into the inter-site positions-bipolarons are formed. The Fig. 27.6b corresponds to compression period in stretching vibration of Nbl-Nb2 which induces increase of Nbl-Nb2 inter-site electron density and decreases of Nb2-Nb3 electron density. For an expansion period. Fig. 27.6c, situation is opposite. Inter-site electron density is decreased for Nbl-Nb2 and increased for Nb2-Nb3. On the lattice scale, increase and decrease of electron density is periodic. On the adiabatic level, alternation of electron density is bound to vibrations at equilibrium nuclear positions (Fig. 27.6a-c).

Based on the ab initio theory of complex electronic ground state of superconductors, it can be concluded that e-p coupling in superconductors induces the temperature-dependent electronic structure instability related to fluctuation of analytic critical point (ACP - maximum, minimum or saddle point of dispersion) of some band across FL, which results in breakdown of the adiabatic BOA. When ACP approaches FL, chemical potential Pad is substantially reduced to IJ-antiadilJ-ad > Pantiad < b(o). Under these circumstances the system is stabilized, due to the effect of nuclear dynamics, in the antiadiabatic state at broken symmetry with a gap in one-particle spectrum. Distorted nuclear structure, which is related to couple of nuclei in the phonon mode r that induces transition into antiadiabatic state, has fluxional character. It has been shown that until system remains in antiadiabatic state, nonadiabatic polaron - renormalized phonon interactions are... 

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