Positron states evolution

The two quantities which can be observed when an individual positron annihilates in condensed matter are the positron age r, which is the time interval between implantation and annihilation of the positron, and the momentum p of the annihilating positron-electron pair. Time-resolved information on the evolution of positron states is obtained by correlated measurements of the individual positron lifetime (= positron age) and the momentum of the annihilating positron-electron pair (Age-Momentum Correlation, AMOC). AMOC measurements are an extremely powerful tool for the study of reactions involving positrons. It not only provides the information obtainable from the two constituent measurements but allows us to follow directly, in the time domain, changes in the e+e momentum distribution of a positron state (cf. Sect. 1). 

The evolution operator 5(oo, —00) is called the 5-matrix. Let be the state vectors for the system of noninteracting electrons (positrons) and photons. These vectors are the eigenfunctions of the Hamiltonian Ho- We assume that ... 

The free-volume concept dates back to the Clausius [1880] equation of state. The need for postulating the presence of occupied and free space in a material has been imposed by the fluid behavior. Only recently has positron annihilation lifetime spectroscopy (PALS see Chapters 10 to 12) provided direct evidence of free-volume presence. Chapter 6 traces the evolution of equations of state up to derivation of the configurational hole-cell theory [Simha and Somcynsky, 1969 Somcynsky and Simha, 1971], in which the lattice hole fraction, h, a measure of the free-volume content, is given explicitly. Extracted from the pressure-volume-temperature PVT) data, the dependence, h = h T, P), has been used successfully for the interpretation of a plethora of physical phenomena under thermodynamic equilibria as well as in nonequilibrium dynamic systems. 

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