Compton profiles atoms

Experimentally, the EMD function p(q) can be reconstructed from a set of Compton profiles J qz ) s, and B( r) from the EMD. However, A Air) is not a direct experimental product. By combining the experimental B(r) with theoretical B aik (r), we need to derive a semiexperimental AB(r). Since the atomic image is very weak, many problems must be cleared in experimental resolution, in reconstruction (for example, selection of a set of directions and range of qzs), in various deconvolution procedures and so on. First of all, high resolution experiments are desirable. 

It is well known that the energy profiles of Compton scattered X-rays in solids provide a lot of important information about the electronic structures [1], The application of the Compton scattering method to high pressure has attracted a lot of attention since the extremely intense X-rays was obtained from a synchrotron radiation (SR) source. Lithium with three electrons per atom (one conduction electron and two core electrons) is the most elementary metal available for both theoretical and experimental studies. Until now there have been a lot of works not only at ambient pressure but also at high pressure because its electronic state is approximated by free electron model (FEM) [2, 3]. In the present work we report the result of the measurement of the Compton profile of Li at high pressure and pressure dependence of the Fermi momentum by using SR. 

Duncanson and Coulson [242,243] carried out early work on atoms. Since then, the momentum densities of aU the atoms in the periodic table have been studied within the framework of the Hartree-Fock model, and for some smaller atoms with electron-correlated wavefunctions. There have been several tabulations of Jo q), and asymptotic expansion coefficients for atoms [187,244—251] with Hartree-Fock-Roothaan wavefunctions. These tables have been superseded by purely numerical Hartree-Fock calculations that do not depend on basis sets [232,235,252,253]. There have also been several reports of electron-correlated calculations of momentum densities, Compton profiles, and momentum moments for He [236,240,254-257], Li [197,237,240,258], Be [238,240,258, 259], B through F [240,258,260], Ne [239,240,258,261], and Na through Ar [258]. Schmider et al. [262] studied the spin momentum density in the lithium atom. A review of Mendelsohn and Smith [12] remains a good source of information on comparison of the Compton profiles of the rare-gas atoms with experiment, and on relativistic effects. 

The coefficients of the small-p expansion of IIo(p), Eq. (5.40), have been extracted by fitting to experimental Compton profiles for both atoms and molecules [167]. Table V.l gives a flavor of the tense confrontation between... 

Finally, (for atoms), the momentum densities corresponding to hybrid orbitals exhibit a few basic extremal features close to the origin. These depend on the weight that is given to s, p and d contributions, and they determine the basic look of the density. Outwardly, momentum-space hybrids share one feature with a related experimental quantity, the Compton profile they all look alike. On closer inspection, however, there are a variety of complex features, mainly arising from the nodal structure of the orbitals. Apart from the obvious use of hybrids in position space for the description of bond situations, there is another feature that has always captured the interest of scientists and laymen their intricate structure. This feature is less apparent in momentum space, but it is still present. If nothing else, its enjoyment makes a close look at these entities worthwhile. 

P. Kaijser and V.H. Smith Jr. Evaluation of momentum distributions and Compton profiles for atomic and molecular systems. In Advances in Quantum Chemistry, vol. 10. Academic Press, New York, 1977, pp. 37-76. 

In the early 1940s, an investigation of chemical bonding from the momentum-space viewpoint was initiated by Coulson and Duncanson (Coulson, 1941a,b Duncanson, 1941, 1943 Coulson and Duncanson, 1941,1942 Duncanson and Coulson, 1941) based on the Fourier transformation of the position wave function. [They also gave a systematic analysis of the momentum distributions and the Compton profiles of atoms (Duncanson and Coulson, 1944, 1945, 1948).] They first clarified the momentum-space properties of the fundamental two-center MO and VB wave functions, which may be outlined as follows. 

Fig. 20. Differences in the directional Compton profiles for (a) the lscr, state and (b) the 2po-u state of the H2+ system. All values in atomic units. (Reproduced from Koga and Morita, 1981a.)...

In quantum chemistry, the state of a physical system is usually described by a wave function in the position space. However, it is also well known that a wave function in the momentum space can provide complementary information for electronic structure of atoms or molecules [1]. The momentum-space wave function is especially useful to analyse the experimental results of scattering problems, such as Compton profiles [2] and e,2e) measurements [3]. Recently it is also applied to study quantum similarity in atoms and molecules [4]. In the present work, we focus our attention on the inner-shell ionization processes of atoms by charged-particle impact and study how the electron momentum distribution affects on the inner-shell ionization cross sections. 

Application of the electron diffraction method to inorganic compounds is so far apparently limited to TiO and Ti02 . It was claimed that the results implied a change from neutral atoms for TiOo.s2 to ionic charges of 2 in TiOi.26, but the data for Ti02 could not be interpreted on a simple model, and the Compton profiles of TiOo.se and TiOi.25 do not agree significantly... 

Distributions and Compton Profiles for Atomic and Molecular Systems. 

Similar calculations using non-relativistic Hartree-Slater wavefunctions [61] and relativistic Hartree-Slater theory [62] have also provided data for californium. The atomic form factors, the incoherent scattering functions [63], and a total Compton profile have been tabulated for californium [64]. 

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