The growth of a radiation pulse traversing a medium with an inverted population is described by nonlinear, time-dependent photon transport equations, which account for the effect of the radiation on the medium as well as vice versa. The equations are solved in closed form for an arbitrary input pulse and an arbitrary initial distribution of inverted population. The solutions are discussed in detail for the particular cases of a square pulse and a Lorentzian pulse, both with a uniform initial population inversion.
It is shown that a straightforward version of a classical Kaluza-Klein theory predicts the existence of classical vacuum polarization and that if the ^55 field carries a mass than the theory admits centrally symmetric solutions for which the Schwarzschild singularity becomes a naked point singularity with no event horizon and for which the electric field is everywhere finite.PACS numbers: 04.50.4-h Five-dimensional generalizations of Einstein's general theory incorporating the electromagnetic and gravitational fields were first considered by Kaluza and Klein.^'"^ In this paper we consider a straightforward version of a classical theory of this type wherein the metric component ^55 depends on the four-dimensional position but is independent of the fifth coordinate. It is shown that the theory predicts the existence of classical vacuum polarization and admits solutions for which there is no Schwarzschild singularity (no event horizon) and for which the electric field due to a 8-function charge distribution is everywhere finite.Charge-space-time will be described in terms of a five-dimensional Une element dP = g^^dx^ dx^, where the five-dimensional metric g^,^, does not depend explicitly on x^. The electromagnetic field enters in through the four-potential A^hy means of the relations i^v = Si^v + (4G/c'^)a^^ ^^A ^, g^s = issA ^.The component ^55 will be written in terms of a dimensionless four-scalar a as ^55= (4G/c'^)a^, where G is the Newtonian gravitational constant; we require o: = 1 in the limiting case of flat space-time and zero charge. The five-dimensional line element then takes on the form
Differential cross sections and polarizations for the elastic scattering of protons by carbon at energies between 7 and 20 Mev have been analyzed according to the diffuse-surface optical model of the nucleus. The model parameters were varied systematically, the best fits to the experimental data being determined by a method of least squares. Various forms of the absorptive part of the potential were investigated, although the main part of the analysis was carried out with a surface-plus-volume absorption potential. It was found that the model could not account satisfactorily for the data below about 12 Mev, and the presentation of results is limited to the region 11.85 Mev^Eiab^ 19.4 Mev. Excellent fits can be obtained over the latter region with generally reasonable values of the model parameters, although some features of their behavior as a function of energy remain to be explained. The most striking feature of the results is the thin absorptive shell and small volume absorption which characterizes the potential. Although the predicted reaction cross sections appear generally too low, the experimental data are not sufficiently precise to warrant drawing a definite conclusion.
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