No abstract

The dependence of electric quadrupole splitting of nuclear magnetic resonance absorption lines in single crystals on crystal orientation in an external magnetic field is investigated theoretically following earlier work of Pound, of Volkoff, Petch, and Smellie, and of Bersohn. Explicit formulae are given, applicable to non axially symmetric crystalline electric field gradients (η ≠ 0), and valid up to terms of the second order in the quadrupole coupling constant [Formula: see text], for the dependence of the absorption frequencies on the angle of rotation of the crystal about any arbitrary axis perpendicular to the magnetic field. Some formulae including third order effects in Cz are also given. It is shown that an experimental study of the dependence of this splitting on the angles of rotation about any two arbitrary mutually perpendicular axes is sufficient, when second order effects are measurable, to yield the values of | Cz |, η, and the orientation of the principal axes of the electric field gradient tensor at the nuclear sites. In the case that the direction of one of the principal axes is known from crystal symmetry, a single rotation about this axis gives the complete information.A new method of determining nuclear spin I is proposed which depends on comparing first and second order shifts of the resonance frequencies of the strong inner line components. The method will be of interest in those cases where the total number 2I of line components can not be unambiguously ascertained owing to the outer line components being excessively broadened and weakened by crystal imperfections.

Pound's theory of the dependence of electric quadrupole splitting of nuclear magnetic resonance absorption lines in a single crystal on the orientation of the crystal in an external magnetic field is extended to cover the case of a crystal with nonaxially symmetric electric field gradient at the site of the nuclei being investigated. It is shown that an experimental study of the angular dependence of this splitting for three independent rotations of the crystal about any three mutually perpendicular axes will yield complete information about the orientation of the principal axes and the degree of axial asymmetry of the electric field gradient tensor at the site of the nuclei, and also will give the absolute value of the quadrupole coupling constant for those nuclei.The authors' experiments on the splitting of the Li7 absorption lines in a single crystal of LiAl(SiO3)2 (spodumene) are described and are used to illustrate the theory. The absolute value of the quadrupole coupling constant for the Li7 nuclei in spodumene is found to be [Formula: see text]. per sec. The axial asymmetry parameter of the field gradient tensor at the site of the Li nuclei is found to be η≡(ϕxx−ϕvv)ϕzz=0.79 ± 0.01. One of the principal axes of this tensor (the y axis corresponding to the eigenvalue of intermediate magnitude) is experimentally found to coincide with the b crystallographic axis of monoclinic spodumene as required by the known symmetry of the crystal. The other two principal axes are in the ac plane, the z axis (corresponding to the eigenvalue ϕzz of greatest magnitude) lying between the a and c axes at an angle of 48° ± 2° with the c axis.

It is usually stated 1 that general relativity sets an upper limit to the mass and radius of a sphere of constant proper energy density p. This result is obtained by considering only those solutions of Einstein's field equations which give a finite central proper pressure p; the minimum mass and radius for which p first becomes infinite at the center are taken as the limiting values. In his original paper 1 Schwarzschild points out the existence of other solutions with infinite central p, but dismisses them as physically inadmissible because of this singularity without a further discussion of their properties. However, an examination of these solutions, which are described below, shows that they lead to arbitrarily large masses and radii.On the other hand a cold neutron gas model 2 leads to an upper limit on the size of a static sphere. It is of interest to try to account for the difference in behavior of these two models. If for a material consisting of particles in motion (and which may exert forces on each other) the energymomentum tensors for the particles, and for the force fields (apart from gravitation) associated with them, are additive and have non-negative traces, then for such a material T=p -3p==i0 must always hold. The p = const. model for sufficiently high pressures has T<0. This not altogether consistent model corresponds to the case of perfectly incompressible particles packed tightly together and treated essentially nonrelativistically in that the contribution of the forces to p is not taken into account. A negative T near the center of the sphere, such as makes possible an arbitrarily large mass for the p = const, model, may be regarded as analogous to a negative (repulsive) mass which keeps the sphere from collapsing.Both the original Schwarzschild solutions, and the new singular solutions leading to arbitrarily large spheres, may be obtained by a method considerably simpler than the one used by Schwarzschild. Einstein's equations for constant p and for the line-element

The object of this paper is purely pedagogic—to clear up an apparent difficulty in applying Gauss' theorem to the classical electric field associated with a charge moving in an infinite homogeneous nondispersive medium with a constant velocity exceeding the velocity of propagation of light in the medium (conditions under which Cherenkov radiation is emitted). This is done by investigating the behavior of the electric field intensity not only inside the cone defining the region that can be reached by light signals from the charge but also on the cone.