Compton scattering beyond the impulse approximation

We treat the non-relativistic Compton scattering process in which an incoming photon scatters from an N-electron many-body state to yield an outgoing photon and a recoil electron, without invoking the commonly used frameworks of either the impulse approximation (IA) or the independent particle model (IPM). An expression for the associated triple differential scattering cross section is obtained in terms of Dyson orbitals, which give the overlap amplitudes between the N-electron initial state and the (N-1) electron singly ionized quantum states of the target. We show how in the high energy transfer regime, one can recover from our general formalism the standard IA based formula for the cross section which involves the ground state electron momentum density (EMD) of the initial state. Our formalism will permit the analysis and interpretation of electronic transitions in correlated electron systems via inelastic x-ray scattering (IXS) spectroscopy beyond the constraints of the IA and the IPM.Comment: 7 pages, 1 figur

DFT study on size-dependent geometries, stabilities, and electronic properties of AunM2 (M = Si, P; n = 1–8) clusters

The ab initio method based on density functional theory at the PW91PW91 level has been employed to systematically study the structures, stabilities, electronic, and magnetic properties of gold clusters with or without silicon/phosphorus doping. The optimized geometries show that the most stable isomers for AunSi2 and AunP2 (n = 1–8) clusters prefer a three-dimensional structure when n = 2 and n = 3 upwards, respectively, and they can be viewed as grown from the already observed Aun−1M2 (M = Si, P). The relative stabilities of calculated AunM2 (M = Si, P) clusters have been analyzed through the atomic average binding energy, fragmentation energy, second-order difference of energy, and HOMO-LUMO gap. A pronounced odd-even alternative phenomenon indicates that the clusters with even-numbered valence electrons possess a higher stability than their neighboring ones. For both systems, natural population analysis reveals that electronic properties of dopant atoms in the corresponding configuration are mainly related to s and p states. We also investigated magnetic effects of clusters as a function of cluster size, however, their oscillatory magnetic moments were found to vary inversely to the fragmentation energy, second-order difference of energy, and HOMO-LUMO gap