Asymptotic channels and gauge transformations of the time-dependent Dirac equation for extremely relativistic heavy-ion collisions

We discuss the two-center, time-dependent Dirac equation describing the dynamics of an electron during a peripheral, relativistic heavy-ion collision at extreme energies. We derive a factored form, which is exact in the high-energy limit, for the asymptotic channel solutions of the Dirac equation, and elucidate their close connection with gauge transformations which transform the dynamics into a representation in which the interaction between the electron and a distant ion is of short range. We describe the implications of this relationship for solving the time-dependent Dirac equation for extremely relativistic collisions.Comment: 12 pages, RevTeX, 2 figures, submitted to PR

A light-fronts approach to electron-positron pair production in ultrarelativistic heavy-ion collisions

We perform a gauge-transformation on the time-dependent Dirac equation describing the evolution of an electron in a heavy-ion collision to remove the explicit dependence on the long-range part of the interaction. We solve, in an ultra-relativistic limit, the gauged-transformed Dirac equation using light-front variables and a light-fronts representation, obtaining non-perturbative results for the free pair-creation amplitudes in the collider frame. Our result reproduces the result of second-order perturbation theory in the small charge limit while non-perturbative effects arise for realistic charges of the ions.Comment: 39 pages, Revtex, 7 figures, submitted to PR

Kinetics, specificity: alkyl/arylamines, alkylamines with OH, O, SH, NH₂, ROCO, RSCO and H₂PO_-4-groups, methylaminostyryl, rhodamine, acridine, phenanthrene and cyanine compounds

The efflux of [3H] choline+ from the proximal tubular lumen was measured by using the stop-flow microperfusion method. The 2-s efflux of [3H] choline+ follows kinetics with a Michaelis constant, Km = 0.18 mmol x l-1, maximal flux, Jmax = 0.43 pmol x cm-1 x s-1 and a permeability term = 38.0 micron2 (small middle dot)-1. Replacement of Na+by N-methyl-D-glucamine+ or Li+, or a change of luminal pH do not alter choline+ efflux. Replacement of Na+ by Cs+ inhibits 2-s choline+ (0. 01 mmol x l-1) efflux by 22% and replacement by K+ inhibits by 49%, indicating that the electrical potential difference across the brush border membrane acts as driving force for choline+ transport. Comparing the apparent luminal inhibitory constant values for choline (app. Ki,l,choline+) with the chemical structure of inhibiting substrates, it was found that the inhibitory potency of amines with high pKa values, i.e. high basicity, and of quaternary ammonium compounds (tetraethyl to tetrahexylammonium) increases with their hydrophobicity in a similar manner as was observed previously against the contraluminal N1-methylnicotinamide (NMeN+) transporter and the luminal H+ /organic cation (N-methyl-4-phenylpyridinium) (MPP+) exchanger. Independently of their hydrophobicity, an increase in the inhibitory potency of the homologous series of aminoquinolines against the choline+ transporter was observed with increasing pKa values, i.e. increasing basicity, as was found previously against the two other organic cation transporters. A third parameter influencing the interaction with the choline+ transporter is the presence of two amino groups with high pKa values or one amino group and a permanent positive charge, as is documented with the two-ring aminostyryl and rhodamine compounds, as well as three-ring aminoacridine, aminophenanthrene and cyanine compounds. Thus with the aminostyryl, pyridinium+, rhodamine, phenanthridium+ and cyanine+ dyes app.Ki,l,choline+ values of between 0.01 and 0.07 mmol x l-1 have been found. A fourth parameter influencing the choline+ transporter is the presence of an OH group on the C atom next to that bearing the N atom (as in choline+) or an ester-OCOR group (acetylcholine+, butyrylcholine+) or a thioester-SCOR-group (acetylthiocholine+, butyrylthiocholine+); or an -OP(OH)2(OR) group (glycerylphosphoryl-choline+), resulting in app.Ki,l,choline+ values of 0.3-1.0 mmol x l-1. Thus the substrates for the luminal choline+ transporter have general features in common with the luminal H+/organic cation exchanger and the contraluminal organic cation transporter, i.e. hydrophobicity and basicity. Additional parameters for interaction are an OH (or similar) group positioned a favourable distance from the N atom or a second amino/ammonium group in multi-ring compounds