Study Of Matrix Elements Research Articles

Understanding atomic processes in terms of Coulomb singularities

Many aspects of high-energy atomic processes can be described in terms of singularities of a many-body Hamiltonian using the generalized asymptotic Fourier transform (AFT) theory. The study of matrix elements in different kinematic regimes is related to the study of singularities (points of nondifferentiability) of the wave functions and the e-γ interaction. These singularities reflect the singularities of the many-body Hamiltonian. We illustrate the principles of the AFT approach in the simple example of photoabsorption by the electron bound in a potential with a Coulomb singularity. We exhibit two general results that are important for any many-body system: (1) the quality of approximate results in different forms (“gages”) depends on the quality of the description of the wave functions in the vicinity of singularities, and (2) due to the character of the Coulomb singularity, photoabsorption cross sections converge slowly to their asymptotic form as the energy increases. However, the slowly converging behavior of these cross sections is due to one common factor (the Stobbe factor), which can be obtained analytically in terms of the characterization of the vicinity of the singularity. The common Stobbe factor explains why ratios of cross sections converge more rapidly than the cross sections themselves.

β-decay matrix elements from the study of asymmetric emission from polarised nuclei: γ-tagging – a new method for complex β-decay

A new method is introduced designed to facilitate study of matrix elements in complex β-decay through the measurement of asymmetric β-emission from a low-temperature polarised source. The method involves coincident detection of the β-emission with subsequent γ-transitions to tag the β-spectrum component. The method is demonstrated by application to the decay of 140La.