O. Aikala’s research while affiliated with University of Turku and other places

Expressions of the Compton profiles for ionic crystals have been presented by employing the density matrix of the crystal derived from the free-ion wavefunctions orthogonalized to each other by Lowdin's symmetrical method. The resulting Compton profiles can then be expressed in an infinite series of the overlap matrix S, the first term being the profile of the free ions. The numerical applications of the present work to LiF and LiCl indicate that the terms of the above series proportional to S and to S2 are important and improve an agreement between theoretical and experimental data.

Directional Compton profiles are calculated for LiH crystal in the main directions (100), (110) and (111) using linear combinations of atomic orbitals based on Lowdin's symmetrical orthogonalization method; these are compared with other theoretical and experimental data.

When orthogonalising the localised basis functions in crystals with Lowdin's symmetrical method (1956), the inverse of the metric matrix plays a crucial role. A practical method of inverting the general metric matrices of crystals is evaluated. The procedure is based on the cluster method, introduced for spherically symmetric states by Lundqvist and Froman (1950), and it exploits completely the rotational symmetry of the crystal. The general equations for solving the elements of the inverse metric matrix are derived, and explicit coefficients are given for s and p states. Calculations have been performed for some alkali halides and magnesium oxide, and numerical results for sodium fluoride are given and considered in some detail. The series expansion approximation for the inverse metric matrix elements is found to be reasonable for alkali halides but not at all suitable for magnesium oxide. However, 'exact' values for inverse metric matrix elements should be used in all accurate theoretical calculations.

The Fourier series method for calculating the inverse of the metric matrix of crystals (needed in the orthogonalisation of one-electron orbitals) is presented for the general case. In this method the matrix is first partially diagonalised by a unitary transformation (the Fourier series). After inverting the small diagonal blocks, the inverse transformation (summation/integration in the Brillouin zone) is performed to obtain the elements of the inverse metric matrix. Crystals with full orthorhombic, hexagonal or cubic site symmetries are considered in detail. Numerical applications to NaF, LiF and MgO crystals with NaCl structure have been performed and the results are compared with those obtained by the cluster method. For ionic crystals the present procedure is better than the cluster one as regards the accuracy and stability of the results even though the computing times become larger in some cases. The computing procedure in this form is found to be unsuitable for metals and several improvements are found necessary.

Compton profiles of NaF and CaO single crystals were measured along the [100] and [110] directions using 60 key gamma rays. A theoretical analysis based on Compton profiles and autocorrelation functions was performed by application of the augmented plane wave (APW) and linear combination of atomic orbitals (LCAO) methods. In the case of NaF both theories agree well with each other but their results differ in a characteristic manner from the experiment. For CaO a good agreement of the APW results and experiment especially for the difference quantities is found whereas the LCAO model yields less satisfying results in this case.

Expressions for energy bands and some related properties for metallic crystals have been derived by using coherent quantum statistical superpositions of single electronic Bloch waves. The theoretical treatment is carried out by constructing first weakly localized wave packets as a statistical superposition of the Bloch waves at temperature T. These wave packets are then used to build LCAO-like crystalline Bloch states for the conduction electrons. As a detailed application, the expressions for energy bands and for momentum density are given to the free-electron-like system. In the continuum limit of a crystal lattice, the discrete sums appearing in the expressions of various quantities are transformed into integrals, and the general results obtained for "free electrons" are reduced to those of the usual free electron model at the absolute zero of temperature.

Compton profile of cobalt has been calculated employing the renormalized-free-atom model for fcc as well as hcp phases choosing several 3d-4s configurations. The results have been compared with recent gamma-ray measurements on polycrystalline Co. Best agreement between theory and experiment is found for 3d 74s 2 configuration. Comparison with free electron model has also been made for this case.

59.54 keV γ-ray Compton profiles of CaF2 along the [100] and [110] directions are reported. Both, the absolute profiles and their anisotropy are derived from the LCAO model and compared with experiments. One-dimensional Fourier transforms are determined from both, experimental and theoretical profiles and compared with each other. Theoretical results are found to be in qualitative agreement with the experiments. It is also shown that momentum distributions are more sensitive to anisotropy in electron distributions than X-ray structure factors. 59,54 keV-γ-Strahlen-Comptonprofile von CaF2 in den [100]- und [110]-Richtungen werden mitgeteilt. Die absoluten Profile und deren Anisotropie werden aus dem, LCAO-Modell abgeleitet und mit Experimenten verglichen. Eindimensionale Fouriertransformationen werden sowohl aus experimentellen als auch aus theoretischen Profilen bestimmt und miteinander verglichen. Es wird gefunden, daß die theoretischen Ergebnisse in qualitativer übereinstimmung mit den Experimenten sind. Es wird ebenfalls gezeigt, daß die Impulsverteilungen empfindlicher gegenüber einer Anisotropie der Elektronenverteilungen sind als die Röntgenstrahlstrukturfaktoren.