Richard S. Christian

An analysis of the high energy (40 and 90 Mev) experimental neutron-proton scattering results is presented. It is shown that there is good agreement with the theoretical predictions based on a potential model having a $\frac{1}{2}(1+{P}_{x})$ exchange dependence and a "long-tailed" radial dependence. There is evidence, furthermore, from the scattering for the inclusion of a tensor force. A comparison of the predictions of square well, exponential, and Yukawa radial dependences is included to illustrate the effect of different shape characteristics.

Measurements and theoretical calculations of timpani modal frequencies and decay times are made for the cases of no kettle enclosure and kettle enclosures of varying volume. For the calculations, the timpani membrane is assumed to be ideal and the kettle is assumed to be a rigid cylinder which is volume equivalent to the actual kettle. A Green function method is used for calculating the effects of air loading. The calculated modal frequencies and decay times are generally in good agreement with the experimental measurements. In particular, for typical kettle enclosures, the frequency ratios f11 : f21 : f31 ; f41 are found to be close to the harmonic ratios 2 : 3 : 4 : 5 over the normal playing range 100 Hz≲f11≲175 Hz.

The expansion in energy of the cross section for central force scattering proposed by Chew and Goldberger is extended to tensor force scattering. The change due to the addition of tensor forces, in both the effective range and in the shape dependent coefficient, is shown to be small. Hence, as has been previously shown by Blatt and Jackson for central forces, scattering below 10 Mev is practically independent of the potential shape assumed and is completely characterized by the scattering length and effective range.