The problem of determining the eigenstates of the pairing-force Hamiltonian is reformulated in terms of the eigenstates of a many-boson system with an N-body interaction. The N-body interaction includes the effects of the Pauli principle on the eigenstates of the pairing-force Hamiltonian. Explicit expressions for four types of eigenstates are derived. These four types are the eigenstates of N pairs in one or two multiply degenerate single-particle levels, the one-pair eigenstates and a new restricted class of N-pair eigenstates.

Exact eigenstates of the pairing-force Hamiltonian are used to study paring models of Pb ~°e, Pb 2°* and Pb 2°2. The properties of the eigenstates are discussed as functions of the interaction strength g and numerical results are given for g = 0.146 MeV. This interaction strength is stronger than the value, g = 0.111 MeV, adopted in a previous study of these models which used the approximate methods of the theory of superconductivity. However, using the exact eigen states and the stronger pairing interaction, the experimentally observed spectra of these three nuclei are predicted with an average error of 0.1 MeV. This error is ~ as large as that of the approximate calculation in which the weaker pairing interaction was used.

The Mott series for the Coulomb scattering of electrons by point nuclei have been evaluated numerically with the aid of the UNIVAC computer. Calculations of the series for F(B) and G($)> the scattering cross section, and the polarization asymmetry factor, S(6) =5*, were performed for scattering by nuclei of charge Z equal to 80, 48, and 13 at ratios of electron velocity to light velocity, p~v/c, equal to 0.2, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9. The results are tabulated.

The experiment reported was a measurement of the effect of variations in atmospheric temperatures on the intensity of ju mesons observed underground at a depth of 846 m.w.e. The average energy of these particles is known to be ^2X10 n ev. A total of ^1.2 X10 6 coincidences, between two large trays of Geiger counters located in a salt mine, was collected over a two-year period. The correlation between variations in counting rate and simultaneous variations in effective atmospheric temperature was analyzed. The effective temperature was determined from radiosonde measurements of atmospheric temperatures at pressure levels up to 20 millibars performed by a U. S. Air Force weather observation unit near the salt mine. The resulting temperature coefficient is 0.22±0.06 percent per degree and the correlation coefficient is 0.75. The results are compared with those obtained from similar measurements at 1574 m.w.e. and with the theoretical values of the temperature coefficient derived from various schemes describing the production of n mesons with high energies.

The effect of screening by atomic electrons on the scattering of relativistic electrons by heavy atoms has been computed numerically using different screening models. Exponential and Hartree potentials were used to simulate the screening. The asymmetry factor S(0) and the differential scattering cross section d~(0)/d.Q were computed at 15 degree intervaTs from 15°to 165 °. We report here the results for (a) 121 keV electrons scattered by gold, Z = 79, using two exponential potentials of different range, (b) 79 keV (v/c = 0.5) electrons scattered by mercury, Z = 80, using exponential and Hartree fields, (c) 46 keV (v/c ~ 0.4) electrons scattered by mercury as in (b). The asymmetry factor S(0) and d~/d.Q(0) were computed using a partial wave expansion in which the phase shifts were obtained both by numerical integration of a suitably transformed Dirac radial equation and also computed in WKB approximation. The results are compared with corresponding calculations for the Coulomb field. In general the differences are no more than a few percent, but below 30 ° the screened field cross-sections are as much as 50~o smaller.