Pion LINAC as an Energy-Tagged Neutrino Source

The energy spectrum and flux of neutrinos from a linear pion accelerator are calculated analytically under the assumption of a uniform accelerating gradient. The energy of a neutrino from this source reacting in a detector can be determined from timing and event position information.Comment: 16 pages, 4 figures. Replacement of Section II.D and minor corrections elsewhere. The basic point and conclusions of the paper are unchanged. Phys. Rev. ST Accel. Beams 11,124701 (2008); Erratum submitte

Charmed Mesons Have No Discernable Color-Coulomb Attraction

Starting with a confining linear Lorentz scalar potential V_s and a Lorentz vector potential V_v which is also linear but has in addition a color-Coulomb attraction piece, -alpha_s/r, we solve the Dirac equation for the ground-state c- and u-quark wave functions. Then, convolving V_v with the u-quark density, we find that the Coulomb attraction mostly disappears, making an essentially linear barV_v for the c-quark. A similar convolution using the c-quark density also leads to an essentially linear tildeV_v for the u-quark. For bound cbar-c charmonia, where one must solve using a reduced mass for the c-quarks, we also find an essentially linear widehatV_v. Thus, the relativistic quark model describes how the charmed-meson mass spectrum avoids the need for a color-Coulomb attraction.Comment: 9 pages, 5 PDF figure

Scattering amplitudes to all orders in meson exchange

As the number of colors in QCD, N{sub C}, becomes large, it is possible to sum up all meson-exchange contributions, however arbitrarily complicated, to meson-baryon and baryon-baryon scattering. A semi-classical structure for the two-flavor theory emerges, in close correspondence to vector-meson-augmented Skyrme models. In this limit, baryons act as extended static sources for the classical meson fields. This leads to non-linear differential equations for the classical meson fields which can be solved numerically for static radial (hedgehog-like) solutions. The non-linear terms in the equations of motion for the quantized meson fields can then be simplified, to leading order in 1/N{sub C}, by replacing all factors of the meson field but one by the previously-found classical field. This results in linear, Schroedinger-like equations, which are easily solved. For the meson-baryon case the solution can be subsequently analyzed to obtain the phase shifts for the scattering and, from these, the baryon resonance spectrum of the model. As the warm-up, we have carried out this calculation for the simple case of {sigma} mesons only, finding sensible results. 8 refs., 3 figs

Analysis of Dislocation Mechanism for Melting of Elements: Pressure Dependence

In the framework of melting as a dislocation-mediated phase transition we derive an equation for the pressure dependence of the melting temperatures of the elements valid up to pressures of order their ambient bulk moduli. Melting curves are calculated for Al, Mg, Ni, Pb, the iron group (Fe, Ru, Os), the chromium group (Cr, Mo, W), the copper group (Cu, Ag, Au), noble gases (Ne, Ar, Kr, Xe, Rn), and six actinides (Am, Cm, Np, Pa, Th, U). These calculated melting curves are in good agreement with existing data. We also discuss the apparent equivalence of our melting relation and the Lindemann criterion, and the lack of the rigorous proof of their equivalence. We show that the would-be mathematical equivalence of both formulas must manifest itself in a new relation between the Gr\"{u}neisen constant, bulk and shear moduli, and the pressure derivative of the shear modulus.Comment: 19 pages, LaTeX, 9 eps figure

Solving the radial Dirac equations: a numerical odyssey

We discuss, in a pedagogical way, how to solve for relativistic wave functions from the radial Dirac equations. After an brief introduction, in Section II we solve the equations for a linear Lorentz scalar potential, V_s(r), that provides for confinement of a quark. The case of massless u and d quarks is treated first, as these are necessarily quite relativistic. We use an iterative procedure to find the eigenenergies and the upper and lower component wave functions for the ground state and then, later, some excited states. Solutions for the massive quarks (s, c, and b) are also presented. In Section III we solve for the case of a Coulomb potential, which is a time-like component of a Lorentz vector potential, V_v(r). We re-derive, numerically, the (analytically well-known) relativistic hydrogen atom eigenenergies and wave functions, and later extend that to the cases of heavier one-electron atoms and muonic atoms. Finally, Section IV finds solutions for a combination of the V_s and V_v potentials. We treat two cases. The first is one in which V_s is the linear potential used in Sec. II and V_v is Coulombic, as in Sec. III. The other is when both V_s and V_v are linearly confining, and we establish when these potentials give a vanishing spin-orbit interaction (as has been shown to be the case in quark models of the hadronic spectrum).Comment: 39 pages (total), 23 figures, 2 table

Effect of Hadron Dynamics on the Proton Lifetime

A detailed, quantitative re-examination of the effect of hadron dynamics on baryon decay, modeled in terms of Skyrme-field tunneling, indicates that any hadronic suppression should be quite mild. This appears to be another illustration of the `Cheshire-cat' phenomenon, that variation of the apportionment between description of the nucleon as a bag of quarks and description as a Skyrme field configuration has little influence on many nucleon properties. Perhaps the largest remaining uncertainty in evaluating the decay rate has to do with the overlap between a specified quark-antiquark configuration and a final meson state.Comment: minor corrections, 19 pages, 9 figure

Pion-Nucleon Scattering in a Large-N Sigma Model

We review the large-N_c approach to meson-baryon scattering, including recent interesting developments. We then study pion-nucleon scattering in a particular variant of the linear sigma-model, in which the couplings of the sigma and pi mesons to the nucleon are echoed by couplings to the entire tower of I=J baryons (including the Delta) as dictated by large-N_c group theory. We sum the complete set of multi-loop meson-exchange \pi N --> \pi N and \pi N --> \sigma N Feynman diagrams, to leading order in 1/N_c. The key idea, reviewed in detail, is that large-N_c allows the approximation of LOOP graphs by TREE graphs, so long as the loops contain at least one baryon leg; trees, in turn, can be summed by solving classical equations of motion. We exhibit the resulting partial-wave S-matrix and the rich nucleon and Delta resonance spectrum of this simple model, comparing not only to experiment but also to pion-nucleon scattering in the Skyrme model. The moral is that much of the detailed structure of the meson-baryon S-matrix which hitherto has been uncovered only with skyrmion methods, can also be described by models with explicit baryon fields, thanks to the 1/N_c expansion.Comment: This LaTeX file inputs the ReVTeX macropackage; figures accompany i

Melting as a String-Mediated Phase Transition

We present a theory of the melting of elemental solids as a dislocation-mediated phase transition. We model dislocations near melt as non-interacting closed strings on a lattice. In this framework we derive simple expressions for the melting temperature and latent heat of fusion that depend on the dislocation density at melt. We use experimental data for more than half the elements in the Periodic Table to determine the dislocation density from both relations. Melting temperatures yield a dislocation density of (0.61\pm 0.20) b^{-2}, in good agreement with the density obtained from latent heats, (0.66\pm 0.11) b^{-2}, where b is the length of the smallest perfect-dislocation Burgers vector. Melting corresponds to the situation where, on average, half of the atoms are within a dislocation core.Comment: 18 pages, LaTeX, 3 eps figures, to appear in Phys. Rev.