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with the annihilation of B\ and after the fermion has emitted B 2i the Fermi particles are annihilated with the emission of B z . A second way in which this process can take place is obtained if the antifermion emits B 2 . The triangles in the two cases differ only in the directions of the Feynman arrows.The only difference in the matrix elements for the two transitions is that the first one contains the trace of the matrix X~X 1 (p l -m)-l X 2 (p2-m)-iXs(p z -m)-\ while the second contains the trace of the matrixwhere pi are appropriate functions of the energy-momentum fourvectors of bosons and Fermi particles combined with -y M according to Feynman. The minus signs of pi in X f occur in the usual way when the behavior of fermions is contrasted with that of antifermions. By Eq.(1) x ,T =(-ycxc-\where r of the matrices Xi satisfy Eq. (1) with the minus sign.Taking the traces of the matrices makes it at once evident that the contributions of the two processes cancel each other if r is odd.Other contributions to the total matrix element are obtained by permuting the processes involving 5», which means orienting the triangle in different ways with respect to the time direction. These contributions can similarly be grouped into pairs.For the sake of simplicity we have considered a triangular loop, but it is obvious that the above argument can be generalized for any closed loop. Hence, we have Furry's theorem for transitions between neutral bosons: processes associated with closed loops which can be traversed in opposite directions are forbidden if an odd number of odd Dirac matrices are associated with that closed loop.Analogous selection rules can be formulated for the case where the bosons in Eq. (2) are neutral and charged mesons. In this case, to every way in which a transition can take place, there corresponds a second way which is obtained by replacing in the Feynman triangle, protons (neutrons) by antineutrons (antiprotons) or vice versa.Let the contribution of the first process depend on the trace of where n (*=1, 2, 3) are the isotopic spin matrices. The contribution from the second process then containswhere the introduction of ri effects the above replacements. SinceT\Ti T -TiTl (*=1, 2),where r denotes the number of odd matrices among Xi (i-1, 2, 3), and ^ the number of neutral mesons. This result can be generalized as follows for transitions between neutral and charged mesons via nucleons: Transitions between charged and neutral mesons associated with reversible closed nucleon loops are forbidden if the sum of the number of odd Dirac interaction matrices and the number of neutral mesons is odd.The first theorem plays a fundamental role in a process like vacuum polarization. The second theorem will apply in cases where, for instance, a heavy charged meson decays into a lighter charged meson and a neutral one. Thus far no such decay process has been observed. i R. P. Feynman, Phys. Rev. 76, 769 (1949). 2\V. H. Furry, Phys. Rev. 51, 125 (1937). 3\V. Pauli, Rev. Mod. Phys. 13, 203 (1941). Our C equals Pauli'...

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New measurements of the differential elastic scattering cross sections of C, Al, Fe, Cu, Sn, Pb, and U for 14.5-Mev neutrons are reported. For Fe, Cu, Sn, and Pb the angular range from 5° to 150° was investigated with ±1° to db3° angular resolution. For the other elements a smaller angular range was investigated. Particular effort was devoted to the problem of discriminating against inelastically scattered neutrons and methods were developed which provided an experimental energy resolution of ^500 kev. Limited differential cross section data for inelastically scattered neutrons of energy greater than 9 Mev are also presented for Fe, Cu, Sn, and Pb.