For high perfection of structure in Nd-YAG laser crystals grown by the Czo-chralski method, the dislocation density of the crystals must be decreased. Research study seems to indicate that the direction of dislocation propagation is perpendicular to the solid-liquid interface. In crystals grown with a Convex solid-liquid interface, the low dislocation density is due to spreading out of the dislocations in the central part towards the surrounding areas and the edges. Hence, by applying suitable technology i. e. intentionally changing the shape of the solid-liquid interface, we can obtain crystals in which not only the dislocations are decreased, but also the facets are eliminated.

In this paper we use the microscopic 'double well-cluster shell model' to discuss the existence of spurious states of motion of the center of mass during nuclear fission and heavy ion reactions. We outline the derivation of the general formulae with which the ,wave functions of the motion of the center of mass can be separated. Taking Be8 as an example, the existence of the spurious states is illustrated, and the components of these states and their corrections to the energy matrix elements are quantitatively evaluated.Through the analysis of the results of Be8 mentioned above, we conclude: although the propartion of the spurious states is only several per cent, their corrections to the fission barrier are significant, even larger then the corrections due to coulomb energy, and it is necessary to take them into account in accurate quantitative calculations. For a heavier nucleus, or higher excited states, the spurious states of the motion of the center of mass should be considered in more detail.

Dyson representation is applied to find out whether the scaling property can be derived without reliance on the knocked-out mechanism. It is shown that, provided the spectral function in the Dyson represention of the matrix element of the current operators commutator has the proper behavior for large m2, the scaling property then follows for large v. No restriction whatever is required for q2, which may be very small even approaching zero. This characteristic seems to be consistent with the experiments. Furthermore, for a given v, the structure tensor Wμv is only determined by the spectral function inside the region m2≤Mpv, with no dependence on the true asymptotic behavior at m2→∞. Therefore the present observed scaling may only be a phenomena within a certain range. As v becomes still larger, the situation will probably change qualitatively.

The present paper starts from the Bethe-Salpeter equation for the bound states of a fermion and anti-fermion pair. Assuming that the interaction between the straton and anti-straton can be represented approximately by an instantaneous interaction in the center of mass system, we obtain the following main conclusions: (1) the solution of the Bethe-Salpeter equation may be carried out in ordinary three dimensional space and the numbers of components of the wave functions for the pseudo-scalar and vector mesons reduce respectively from 4 and 8 to 2 and 4; (2) If the interaction is spherically symmetrical in space and its spinor structure is of the diagonal coupling type, then it is seen from the equation for the pseudo-scalar mesons that the meson mass appears as a quadratic eigen value in the equation, without leading to the negative energy excitation usually encountered in the fourdimensional equation; (3) The structure wave function obtained in the instantaneous interaction may be used to study both the mass spectra of the bound states, and the processes involving only the center of mass system.