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Around $$\theta_{\pi}=$$90$$^\circ$$, the coupling to the $$\rho^\circ N$$ channel leads to a good accounting of the charged pion exclusive photoproduction cross section in the energy range 3 < E_γ < 10 GeV, where experimental data exist. Starting from a Regge Pole approach that successfully describes vector meson production, the singular part of the corresponding box diagrams (where the intermediate vector meson-baryon pair propagates on-shell) is evaluated without any further assumptions (unitarity). Such a treatment provides an explanation of the $$s^{-7}$$ scaling of the cross section. Furthermore, elastic rescattering of the charged pion improves the basic Regge pole model at forwardmore » and backward angles.« less

In the Russell–Saunders limit, when the electrostatic interactions between the electrons of an atom are large compared to spin-orbit interactions, the atomic levels fall into distinct multiplets. Within each multiplet, the levels are ordered with respect to J, the quantum number of the total angular momentum, and the Landé interval rule is obeyed. Let us imagine a gradual increase of the strength of the spin-orbit interaction, H_so. At first, the multiplets expand in a way that preserves the interval rule; but as matrix elements of H_so between adjacent multiplets become more and more important, levels with similar J repel onemore » another and distortions occur. It would be expected that multiplet structures characteristic of Russell–Saunders coupling would disappear as soon as adjacent multiplets begin to overlap. Naively, we would expect a complex scrambling of the atomic levels as the transition to jj coupling takes place. However, it has become clear over the last decade that extremely regular multiplets can be often picked out from a morass of levels. A good example is given in Fig. 1, in which five low-lying multiplets of the configuration 4f25d of Pr iii are plotted out. The data are those of Sugar. Each multiplet comprises an orderly progression of levels, in spite of the fact that severe overlapping takes place. This phenomenon forms the subject of this letter.« less

It is shown that in a class of models of the quantum field theory the perturbation expansion of the resolvent operator, (H - z)^-1, converges for all complex z. The class of models consists of all theories with Yukawa coupling in which the vacuum polarization was neglected. Finally, the method used was that of comparison with the exactly solvable neutral scalar model.

A study has been made of the bound states of the Bethe-Salpeter equation for the nucleon-antinucleon system, including the ladder and pair-annihilation diagrams. For simplicity, nucleons and mesons were taken to be scalar, the latter having zero rest mass. Pair effects enter only in S-states with the bound states corresponding to the poles of the meson propagator D_F'. The Bethe-Salpeter equation is closely related to the integral equation for the generalized vertex operator Γ; this has been solved by using an integral-transform method similar to that of Wick and Cutkosky, under the assumption that the nucleon mass is large comparedmore » to the binding energy. Further, after performing a self-energy subtraction, the energy eigenvalues are found as a function of the coupling constant. These have the form given by the usual Bohr formula plus corrections. Finally, some comments are made with respect to the extension of the formalism to mesons with nonzero mass and spinor nucleons.« less

The dispersion relations are used to predict the values at zero kinetic energy, of the derivatives, $$\frac{\partial D_{±⁡} (0)}{\partial k^2}$$, of the real parts, D₊⁡(0) and D_–⁡(0), of the forward elastic scattering amplitudes for π⁺ and π^– mesons scattered by protons. The experimental value of $$\frac{\partial D_{+⁡} (0)}{\partial k^2}$$ is fairly well known, and, when compared with the predicted value, yields a determination of the coupling constant, f² = 0.104 ± 0.014. The predicted value for $$\frac{\partial D_{-⁡} (0)}{\partial k^2}$$ disagrees badly with experiment, especially with an f² as large as 0.10. The dispersion relations are modified by introducing anmore » extra energy denominator in such a way as to contain, as the additional constants, the derivatives $$\frac{\partial D_{±⁡} (0)}{\partial k^2}$$. This enables us to check the values of $$\frac{\partial D_{±⁡} (0)}{\partial k^2}$$ obtained from the usual dispersion relations as well as the assumption that ω^–2⁢T_±⁡(ω) vanishes at infinity. Here it is found that as long as the agreement with experiment obtained for the π⁺ relation is retained, no appreciable change in the values of $$\frac{\partial D_{±⁡} (0)}{\partial k^2}$$ is possible and that the high-energy behavior of T_±⁡(ω), usually assumed, is correct. The predicted value for $$\frac{\partial D_{-⁡} (0)}{\partial k^2}$$ strongly suggests a nonzero effective range for α₁ and a relatively large α₁₁.« less

In a paper with the above title, Brueckner and Watson' have given a method for constructing scattering kernels in quantum field theories by means of an inductive technique starting from the Lippmann-Schwinger integral equation. Here we wish to show that the same results can be achieved quite simply by a specified method of successive elimination of the components of the state vector from the usual Schrodinger equation.

A conjecture made in a previous paper concerning the non-convergence of the series of adiabatic nuclear potentials for meson pair theory obtained by means of perturbation methods is shown to be incorrect. The correct series is derived and summed and is in agreement with a result given previously by Wentzel. The same methods suffice for the derivation and summation of two additional series of potentials of the pseudoscalar theory with pscudoscalar coupling. One of these has as its leading term the one-pair potential of fourth order, and the other begins with the leading term of sixth order. Each series hasmore » the same radius of convergence which is determined by the condition xe^x>2α, where x is the separation of the nucleons in units of the meson Compton wavelength and α = (g²/4π) (μ/2M). With (g²/4π) =15, perturbation theory converges for x>0.85; with (g²/4π) = 10, for x>0.57. The convergence for x≲1 is in any case very slow for these values of the coupling constant. Further, the possibility remains that for substantially smaller values of the coupling constant, as are suggested by the inclusion of radiative corrections, perturbation calculations of adiabatic potentials may yield a meaningful first approximation when used in conjunction with a suitable cut-off.« less