Fourier transformed Compton profiles of semiconductors

The Fourier transformed Compton profiles of several semiconductors are calculated by using a set of realistic Wannier functions. The results obtained in silicon, where experimental information exists, are used to test the one-electron approximation. The study of a series of semiconductors shows the effect of their electronic structure on the Compton scattering.     

Compton scattering study of orthorhombic sulphur

The Compton profiles of orthorhombic sulphur crystals have been measured the scattering vector perpendicular to the crystal planes (110) and (001) using 60 keV radiation from a ²⁴¹Am source. Significant anisotropy was observed in the electron momentum distribution. Fourier transformed Compton profiles were compared with theoretical autocorrelation functions for a S₈ ring molecule. It is shown that the observed anisotropy can be only partially interpreted in terms of intermolecular interactions. The strong correlation, observed in the direction perpendicular to the plane of the S₈ ring indicates a meaningful ring — ring interaction in the orthorhombic sulphur crystal.     

键长-键角和Radau坐标下哈密顿算符在傅里叶基组表象下的厄米性

在量子动力学计算中,有时候为了规避奇点问题或者节省计算量,我们经常需要对哈密顿量进行变换. 然而,在使用傅里叶基矢计算时,哈密顿量的变换形式容易导致哈密顿矩阵失去厄米性,进而有些情况下使数值计算变得不稳定. 本文主要讨论构建具有厄米性的哈密顿算符的方法. 以三原子分子为例,构建了键长—键角和Radau坐标下描述分子运动的各种形式的哈密顿量. 基于这些哈密顿量,采用含时波包方法计算了OClO分子的吸收光谱,讨论了非厄米性矩阵对计算结果的影响. 本文所得到的结论对基于基函数展开的量子动力学计算都是适用的.     

Electron momentum distribution in multiply-ionized neon atoms

We present momentum-space properties of multiply ionized neon atoms as a function of the degree of ionization of the atom. In particular, we have calculated the Compton profiles of all possible ionized states of neon atoms with electronic configurations 1s^m2sⁿ2p^q, m=1-2, n=0-2, q=0-6. The radial single-electron radial wave functions, obtained from the Hartree-Fock atomic model, were converted into momentum space wave functions by applying appropriate Fourier transformation. The values of the Compton profiles from the present calculation can be used to interpret experimental cross sections of variously ionized neon atoms colliding with other atoms. Compton profiles of neutral neon atoms, available in the literature, are in excellent agreement with the present calculation.     

Fermi surface parameters from the Fourier analysis of Compton profiles

A new approach to the analysis and interpretation of Compton profiles, based on the properties of the Fourier transform of the profiles, is presented. The method is applied to the determination of Fermi momenta for some simple metals. The remarkable precision of the results obtained in this way illustrates both the power of the technique and also the manner in which this approach enables one to circumvent some major problems inherent in the usual analysis of Compton data.     

Hartree-Fock investigation of the electron momentum distribution in metallic beryllium

The wave function resulting from an accurate Hartree-Fock computation has been used to describe the electron momentum distribution in beryllium metal. Appreciable discrepancies are found with respect to a simple model that amounts to filling with plane waves the first plus second Brillouin zone. In comparing the calculated with the experimental directional Compton profiles, very close agreement is found in particular with a recent set of accurate -ray profiles. The differential Compton profiles are also semiquantitatively reproduced, better on average than with all previous calculations. Concerning the Fourier transforms of the Compton profiles, all the features of the experimental curves are accurately reproduced, in particular the position of the zero passages, which is a powerful test of the adequacy of a theoretical model to account for the metallic nature of the solid. The possible influence of the correlation correction is discussed, and it is shown that such a correction would substantially improve the overall agreement with the experiment.     

Determination of Fermi momentum using Fourier transformed Compton profile

We examine the effect of electron correlations on the Fourier transformed Compton profile (FTCP) and on the use of FTCP for determining the Fermi momentum.     

Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators

We construct a time-dependent double well potential as an exact spectral equivalent to the explicitly time-dependent negative quartic oscillator with a time-dependent mass term. Defining the unstable anharmonic oscillator Hamiltonian on a contour in the lower-half complex plane, the resulting time-dependent non-Hermitian Hamiltonian is first mapped by an exact solution of the time-dependent Dyson equation to a time-dependent Hermitian Hamiltonian defined on the real axis. When unitary transformed, scaled and Fourier transformed we obtain a time-dependent double well potential bounded from below. All transformations are carried out non-perturbatively so that all Hamiltonians in this process are spectrally exactly equivalent in the sense that they have identical instantaneous energy eigenvalue spectra.     

Investigation of the Compton profiles for C,Si, and Ge

The Compton profiles of C, Si, and Ge are calculated for free atoms, and also taking into account their valence states in crystals. In order to obtain the distribution functions of the electrons with respect to momentum, a study is made of generalized hydrogen-like analytic orbitals. It is shown that the excitation of the electrons into the valence state leads to decrease of the Compton profiles and to the best agreement with their measured values.     

Derivation of the radial distribution function from experimental Compton profiles

The analysis of experimental Compton profiles in position rather than momentum space provides a useful method of interpreting Compton data. A density matrix approach is employed to establish the relationship between the Compton profile J(p), and the Fourier transform of the momentum density B(r), and, for a homogeneous system, the radial distribution function g(r). An earlier Compton profile measurement on sodium provides the data for a demonstration of the long range charge correlations in a metal, in analogy with the Friedel oscillations in a screening charge.     

Exactly Solved Fermion-Boson Model for Heavy-Fermion Alloys

The exact eigenstates of the Hamiltonian of the fermion-boson model for heavy-fermion alloys are constructed by using the Bethe ansatz. The Bethe ansatz equations are obtained from the periodic boundary conditions.     

Directional compton profile studies of GaP

59.54 keV gamma ray Compton profiles (CP) of GaP along (100) and (1 1 1) directions are reported. The measured anisotropy has qualitatively similar features as given by the recent pseudopotential calculations for other III–V compound semiconductors. The average valence profile is found to be more peaked compared to that of the pure covalent semiconductors Si and Ge. This suggests that inonicity has the effect of making the valence-electron wave functions of compound semiconductors more diffused. Theoretical calculations on the directional Compton profiles of GaP will be of great use for an exact comparision with the present data, which will help in detailed understanding of the electronic structure of GaP.     

SOLVABLE BOSON-FERMION MODEL FOR MIXED-VALENCE SYSTEMS

Using the Bethe ansatz technique, the exact eigenstates of the Hamiltonian of the boson-fermion model for mixed-valence systems are constructed. The Bethe ansatz equations are obtained from the periodic boundary conditions.     

Molecular Compton profiles from SCF-MO wavefunctions

This paper considers the dependence of Compton profiles calculated from molecular wavefunctions on the atomic basis set used. For fluoromethane there is no significant difference between profiles calculated with a Slater minimal basis set and with STO-3G, STO-4G and STO-5G sets. A Slater double-zeta set and Dunning's gaussian basis give essentially the same profile and the addition of polarization functions to the Dunning basis has little effect. For methanol, methylamine and ethane there is a significant difference between the STO-3G profiles and those calculated from extended basis sets but again the addition of polarization functions has little effect. The use of Dunning's basis would seem to be adequate for Compton profile calculations for molecules of medium size. As one goes along the series from ethane to fluoromethane the Compton profile becomes broader.     

Calculation of valence electron momentum densities using the projector augmented-wave method

We present valence electron Compton profiles calculated within the density-functional theory using the all-electron full-potential projector augmented-wave method (PAW). Our results for covalent (Si), metallic (Li, Al) and hydrogen-bonded ((H₂O)₂) systems agree well with experiments and computational results obtained with other band-structure and basis-set schemes. The PAW basis set describes the high-momentum Fourier components of the valence wave functions accurately when compared with other basis set schemes and previous all-electron calculations.     

Analysis of the 3-dimensional electron distribution in silicon using directional Compton profile measurements

A method of reconstructing the electron momentum density (p), and its Fourier transform,B(t), from a series of directional Compton profiles is described. It is based on a double Fourier inversion technique and an expansion in lattice harmonic functions. The effect of random errors has been analysed, and the implications for the data collection discussed. We have used the reconstruction technique to obtain (p) andB(t) for silicon from six directional Compton profiles measured with 412 KeV gamma-radiation. The experimental result is in good agreement with earlier measurements and with available solid state theories. A recent Wannier function calculation for silicon using orthogonalised bond orbitals provides a useful tool for identifying the physical origins of the observed anisotropies. A comparison between the information presented in position and momentum space shows that the ease of interpretation depends upon the degree to which the various interactions give rise to localised features in each representation.     

APW-Xα Compton profiles in crystalline rare gases

Augmented Plane Wave, local exchange (APW-Xα) one-electron wave functions have been used to calculate Compton profiles for crystalline Ne at three different lattice constants for two values of the local exchange parameter. Some results for Ar, Kr, and Xe are also presented. The impulse approximation is used. The crystalline calculations are little different from the isolated atom results. A variety of difficulties, primarily due to the energy-dependent nature of the APW basis, are explored. A translational symmetry restriction that is particularly severe for APW calculations of Compton profiles is studied. In all, it is concluded that the APW scheme is ill-suited to the computation of the sort of non-energy quantity represented by a Compton profile.     

Anisotropy in the compton profile of copper

Directional Compton profiles of high statistical accuracy are measured by means of a 412 keV gamma-ray Compton spectrometer. The experimental anisotropies are in very satisfactory agreement with earlier measurements and there is good qualitative agreement between the experimental data and a recent band structure calculation. Quantitatively, however, the experimental anisotropy is significantly smaller than predicted by theory.A simple model calculation based on the Seitz approximation, in which higher order Fermi surface volumes all of spherical shape are taken into account in obtaining the momentum density, demonstrates that the major contribution to the Compton profile anisotropy in copper is due to the hybridization which has mixedd-electrons and nearly-free electrons in the top band. Any fine structure in the theoretical anisotropy due to the detailed shape of the Fermi surface cannot be resolved in the present experiment.The potential of analysing the electronic structure of transition metals in terms ofB(r), the Fourier transform of the momentum density, is discussed in detail. The major contribution to the anisotropy arises from localised peaks inB(r) centered on the sites of the translational lattice. Within the Seitz approximation it could be shown that these secondary maxima are caused by the presence of localisedd-electrons in the highest partly occupied band. In conclusion we anticipate that a proper treatment of electron correlation would produce a marked quantitative improvement in the agreement between the present experimental data and the Compton profiles obtained from current band structure calculations.