Positron wave function

Earlier studies of positron-molecule elastic scattering did not involve such detailed descriptions of the scattering process as do the variational and R-matrix formulations. Instead, the interaction between the positron and the molecule was represented by a relatively simple model potential, and the positron wave function F(r 1) was assumed to satisfy the equivalent single-particle Schrodinger equation... 

Equation (3.125) is the required transformed Hamiltonian, and we see that in the representation in which (3 is diagonal, the Dirac equation decomposes into uncoupled equations for the upper and lower components of the wave function, i.e. for electron and positron wave functions. Setting (3 equal to +1 gives the positive energy (electron) states, whilst (3 equals -1 gives the negative energy (positron) states. 

Physical chemistry of the positron and Ps is unique in itself, since the positron possesses its own quantum mechanics, thermodynamics and kinetics. The positron can be treated by the quantum theory of the electron with two important modifications the sign of the Coulomb force and absence of the Pauli exclusion principle with electrons in many electron systems. The positron can form a bound state or scatter when it interacts with electrons or with molecules. The positron wave function can be calculated more accurately than the electron wave function by taking advantage of simplified, no-exchange interaction with electrons. However, positron wave functions in molecular and atomic systems have not been documented in the literature as electrons have. Most researchers perform calculations at certain levels of approximation for specific purposes. Once the positron wave function is calculated, experimental annihilation parameters can be obtained by incorporating the known electron wave functions. This will be discussed in Chapter 2. 

APW wave function inside muffin-tin sphere APW wave function between muffin-tin spheres positron wave function component of electron wave function with angular momentum I and energy E angular frequency atomic volume gradient operator... 

This basic quantity may be related to the true electron momentum distribution when the positron wave function is known through calculations. The many-body factor y f) is known to play some role but it has been established that the correlations have no effect on the position of the Fermi surface breaks (Majumdar 1965). Equation (1) shows that positron annihilation is well suited for Fermi surface studies as only ni(k) has breaks. This can be further seen if one expresses the positron and electron wave functions as Bloch wave functions. One obtains... 

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