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  1. Normal-Product Quantization of Currents in Lagrangian Field Theory

    Lowenstein, J. H. - Physical Review. D, Particles Fields
    Techniques for quantizing currents in Lagrangian field theory are developed with the aid of Zimmermann's normal products. These methods greatly simplify the derivation of single-current generalized Ward identities and may be used to justify the heuristic use of formal arguments in discussing broken symmetries. Finally, applications to the energy-momentum tensor in the A4 model and to the current of broken orthogonal symmetry in a two-component scalar model are presented.

  2. A necessary and sufficient condition for the softness of the trace of the energy-momentum tensor

    Schroer, B. - Lettere al Nuovo Cimento
    Here we show in a direct fashion that the asymptotic softness for the trace of the correct renormalized energy momentum tensor is equivalent with the coupling constant being equal to a Gell-Mann Low eigenvalue. From the softness of the trace one obtains the asymptotic conformal invariance at the Gell-Mann Low eigenvalue. For coupling constants different from this special value we only obtain the softness of the integral over the trace which leads just to asymptotic dilatation invariance.

  3. Locally Generated Dilatation Charge in the Thirring Model

    Lowenstein, J. H. ; Schroer, B. - Physical Review. D, Particles Fields
    By applying a "normal-product quantization" the energy-momentum tensor of the Thirring model is constructed as a local function of the Thirring fields. It is shown that the commutation relation of the dilatation current with the field is anomalous, and that the space integrals converge on a dense set of states to the group generators. Additionally, the appearance of anomalous dimensions for local products of Thirring fields is discussed in the special case of a bilinear mass interaction.

  4. Spectra of High-Energy Electron Beams in Water

    Kessaris, Nikitas D. - Radiation Research
    The spectra of electrons in the energy range 10-20 MeV incident on water are obtained theoretically by solving the appropriate transport equation by the moment method. The spectra of the primary (incident) electrons as a function of depth are obtained first, and they subsequently serve as the source of secondaries for which an analogous equation is solved.

  5. Ground-State Energy Eigenvalues and Eigenfunctions for an Electron in an Electric-Dipole Field

    Turner, J. E. ; Anderson, V. E. ; Fox, Kenneth - Physical Review
    Ground-state energy eigenvalues and eigenfunctions are obtained by a variational method for an electron in the field of a finite, stationary, permanent electric dipole. The dipole moments studied cover the range from the minimum value required for binding (Dmin =0.6393 ea0) to D =400 ea0, where the system is equivalent to the hydrogen atom perturbed slightly by a distant stationary negative charge. The eigenvalues obtained agree with those reported by Wallis, Herman, and Milnes, who determined them by another method in the range D =0.84ea0 to 30⁢ea0. The normalized eigenfunctions display the manner in which the electronic charge density changesmore » from that of the hydrogen atom at very large D to a flat distribution approaching that which is characteristic of a zero-energy continuum state as the minimum moment is approached from above. Optimized variational wave functions for different values of D are presented for use in other calculations. Contour maps and profiles of electronic charge density are shown for a number of values of D. Mean values of the powers -1, 1, and 2 of the distances of the electron from the dipole charges are also calculated.« less

  6. Limited Applicability of the Theory of Nucleon Tunneling

    Breit, G. - Physical Review
    The assumptions made in the theory of the tunneling process of single-nucleon transfer are reviewed and their shortcomings discussed. A schematic form of a black-box treatment is systematized and assumptions made are pointed out. The reason for the agreement between results obtainable from this form and the earlier way of ascertaining quantum-mechanical corrections is discussed. Among the assumptions made is the legitimacy of neglecting terms that vanish when the ratio of the nucleon mass to the reduced mass is set equal to zero. The character of effects arising from these terms is illustrated by means of a one-dimensional model, andmore » the associated inadequacy of dealing only with the relative motion of the heavy aggregates without including effects of motion with respect to the inertial system is pointed out. Further discussion concerns itself with the effects of the angular momentum of the transferred nucleon in the emitting nucleus and in the receiving one on the space dependence of the transfer function; the symmetrized forms of the transfer cross section; the effect of the relative velocity of the emitter and receiver nuclei on the matching of the angular momentum of the nucleon; the transition from the isotropic-transfer quantum treatment to the corresponding semiclassical one, including the double-limit situation involved in making the scattering angle and the space-decay parameter approach zero; the questions involved in the consideration of the exterior region, including the possible effect of deuteron, triton, alpha particle and other types of tentacles in configuration space; and the distinction between the nucleon configuration and wave-function assignments of shell-structure theory and the nucleon configurations and wave functions that matter more directly for the treatment of the exterior region and of single-nucleon transfer. The bearing of virtual Coulomb-excitation processes on applications of usual potential-barrier penetrability estimates for reaction-yield estimates made in astrophysics is mentioned, and it is pointed out that as the kinetic energy is decreased, the nuclear radii in ordinary estimates must be increased.« less

  7. Dynamical Approach to the Unitary-Symmetry Mass Formula Based on ω − ϕ Mixing

    Sakurai, J. J. - Physical Review
    Possible dynamical mechanisms that give rise to the

  8. Polarization in 217-Mev p – n and p – p Scattering

    Tinlot, John H. ; Warner, Robert E. - Physical Review
    The polarization in 217-Mev quasi-elastic p-n scattering from deuterium is nmeasured by CD2- C subtraction. These data cover the angular range 40° to 120° (c.m. system) and are in agreement with the predictions of phase- shift analyses. The polarization in elastic p-p scattering is measured in the angular range 30° to 90° (c.m. system) at an energy of 210 Mev using a liquid hydrogen target, and from 60° to 120° (c.m. system) at 217 Mev using CH2-C subtraction. These two measurements are in agreement over their common angular range. The data are somewhat better fitted by the predictions of amore » boundary- condition model than by phaseshift analyses. The polarization in 217-Mev quasi- elastic p-p scattering from deuterium is measured over the angular range 60° to 110° (c.m. system) by CD2-C subtraction; these data agree with the elastic p-p polarization results within the statistical precision of the measurements (about 1.5%).« less

  9. Pion Production and the Second Pion-Nucleon Resonance

    Goebel, Charles J. ; Schnitzer, Howard J. - Physical Review
    A model for the reaction π + N → 2π + N at low energies, which includes pion-pion interaction and final state interactions in the (3,3) state, is discussed. The theory involves two parameters which are related to the S-wave and P-wave π - π scattering lengths. These parameters are chosen from a fit to the total cross section for π-+ p → π- + π+ + n. Meson production is predicted to be primarily in the T = $$\frac{1}{2}$$ state. Predictions are made for the total cross sections of the various channels (e,g. π++ p → π+ + π+more » + n, etc.) in the energy range from threshold to approximately 500 Mev, in good agreement with experiments. Angular distributions are predicted which are in qualitative agreement with the π+ angular distribution for π-+ p → π- + π+ + n. From these data it is suggested that S wave π-π scattering length has opposite sign to P wave scattering length. A conjecture concerning rapidly rising inelastic cross sections in a single partial wave is made to connect the large T = $$\frac{1}{2}$$, D$$\frac{3}{2}$$ production cross sections with the T = $$\frac{1}{2}$$, D$$\frac{3}{2}$$ pion-nucleon resonance. The π-π scattering length found are a0 = -0.290μ-1, a1 = 0.122μ-1 and $$\frac{a_2}{a_0}$$ = $$\frac{2}{5}$$ by hypothesis.« less

  10. The influence of isotopic composition on the maximum in the cosmic ray energy spectra

    Rao, M. Appa ; Kaplon, M. F. - Nuovo Cimento
    The maximum often observed at low energies in primary cosmic ray spectra is examined with respect to the possible effect of isotopic composition. Here, it is shown that a maximum can arise if He3 and He4 are not distinguished and spectra are plotted on the basis of energy per nucleon instead of rigidity. The discussion is extended to the case of protons, deuterons, and tritons.
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