Phase transitions three-electron atoms

The above approach, the analogy between symmetry breaking and phase transitions, was generalized to treat the large-dimensional model of the N-electron atoms [30], simple diatomic molecules [31,42], both linear and planar one-electron systems [32], and three-body Coulomb systems of the general form ABA [43]. 

The stability of three-body Coulomb systems is an old problem which has been treated in many particular cases [143-145] and several authors reviewed this problem [146,147]. For example, the He atom (ae e ) and H2 (ppa ) are stable systems, H (pe e ) has only one bound state [108], and the positronium negative ion Ps (e+e e ) has a bound state [148], while the positron-hydrogen system (e pe+) is unbound and the proton-electron-negative-muon pe i ) is an unstable system [149]. In this section, we show that all three-body ABA Coulomb systems undergo a first-order quantum phase transition from the stable phase of ABA to the unstable breakup phase of AB + A as their masses and charges varies. Using the FSS method, we calculate the transition line that... 

The internal spin interaction Hamiltonian Hmt can be decomposed into spatial Tm[ ua(l) ] and spin Sm degrees of freedom Hin (t) = 2mTm[ ua(t) ]Sm. The spatial contribution, hereafter an NMR interaction rank-2 tensor T, is a stochastic function of time Tm[ ua(t) because it depends on generalized coordinates < ( ) of the system (atomic and molecular positions, electronic or ionic charge density, etc.) that are themselves stochastic variables. To clarify the role of these coordinates in the NMR features, a simple model is developed below.19,20 At least one physical quantity should distinguish the parent and the descendant phase after a phase transition. For simplicity, we suppose that the components of the interaction tensor only depend on one scalar variable u(t) whose averaged value is modified from m to m + ( at a phase transition. To take into account the time fluctuations, this variable is written as the sum of three terms, i.e. u(t) — m I I 8us(t). The last term is a stationary stochastic process such that — 0, where <.) denotes a... 

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