Foundations of a Theory Concerning Hydrogen Centres in Metals

Abstract

The present work is an attempt to treat hydrogen storage in metals with the aid of field theoretical methods. Starting with the many-body Schrödinger equation, an adiabatic decomposition yields an electronic system, a protonic system and a host lattice system. We define a storage energy consisting of a lattice contribution and an electronic part. The latter one will be evaluated by The New Tamm-Dancoff (NTD) procedure. This formalism is a method to compute differences of eigenvalues in quantum mechanical problems. As an example we derive a one-particle equation describing a single hydrogen atom in a metal crystal.

On the Effective Interaction of two Hydrogen Centres in Niobium

“…As with our preceeding papers on the static properties of metal hydrides [9,11] we consider both the protons and the ions of the infinite Nb host lattice as classical pointlike charged particles. This approximation is justified by a twofold adiabatic decoupling: first of the electronic from the protonic and ionic subsystems and secondly the protonic from the ionic subsystem in both the hydrided and the unloaded crystal.…”

“…Such a microscopic theory was introduced by Wahl et al [9] using the New Tamm-Dancoff-method, which was originally applied to the study of elementary particles [10]. The main purpose of this method is to calculate the impurity induced energy changes in the elecronic system of the host crystal.…”

A Higher Order Approximation for the Electronic Structure of Hydrogen in Metals

“…In a preceding paper [1] we discussed a formalism for calculating energy differences o f quantum m e chanical systems. In application to metal hydrides we will now briefly repeat the fundamental ideas, notations, and formulae.…”

“…The present work contains a higher order ap proximation o f a field theoretical m ethod developed in an earlier paper in application on the electronic problem o f hydrogen im purities im plem ented in a metal crystal [1]. The mathematical theory is based on a follow-on procedure o f the so-called N ew Tam m -Dancoff (N T D ) formalism [2], In its original formulation the NTD-procedure consists o f a Field equation for the connection o f r-functions [3].…”

“…Meanwhile, we are successful in establishing a transformation on a self-adjoint theory [1] with orthogonal state vectors as base system in contrast to the nonorthogonal ^-functions. In this formalism the corresponding functional operator is a difference o f two essentially distinct many-particle Hamiltonians.…”