Irreducibility, Brill-Noether loci, and Vojta's inequality

This paper deals with generalizations of Hilbert's irreducibility theorem. The classical Hilbert irreducibility theorem states that for any cover of the projective line defined over a number field , there exist infinitely many -rational points on the projective line such that the fiber of over is irreducible over . In this paper, we consider similar statements about algebraic points of higher degree on curves of any genus. We prove that Hilbert's irreducibility theorem admits a natural generalization to rational points on an elliptic curve and thus, via a theorem of Abramovich and Harris, to points of degree 3 or less on any curve. We also present examples that show that this generalization does not hold for points of degree 4 or more. These examples come from an earlier geometric construction of Debarre and Fahlaoui; some additional necessary facts about this construction can be found in the appendix provided by Debarre. We exhibit a connection between these irreducibility questions and the sharpness of Vojta's inequality for algebraic points on curves. In particular, we show that Vojta's inequality is not sharp for the algebraic points arising in our examples.

     

Pauli exchange effects in the elastic scattering of O + O

The real optical potential for ¹⁶O+¹⁶O system is calculated within a generalized version of the double-folding model with the Pauli knock-on exchange effects between the projectile nucleons and the target nucleons taken into account from first principle. The elastic scattering data at E_lab=350 MeV supplemented by the new measurement at larger angles seem to be the first case in heavy-ion scattering where one can test the reliability of different theoretical heavy-ion optical potentials. Predictions are made for the elastic scattering of ¹⁶O+¹⁶O at laboratory energies of 240–480 MeV to illustrare the energy dependence of the rainbow structure which has been clearly observed in experiment at 350 MeV.     

Random walk near the surface

The random walk of a particle on a three-dimensional semi-infinite lattice is considered. In order to study the effect of the surface on the random walk, it is assumed that the velocity of the particle depends on the distance to the surface. Moreover it is assumed that at any point the particle may be absorbed with a certain probability. The probability of the return of the particle to the starting point and the average time of eventual return are calculated. The dependence of these quantities on the distance to the surface, the probability of absorption and the properties of the surface is discussed. The method of generating functions is used.     

Tunneling dynamics and spatial correlations of long chain growth in solid-state photochlorination of ethylene at low temperatures

A novel method is described for preparing reactive mixed crystals by vapor deposition in argon and subsequent evaporation of the argon. The kinetics of photochlorination chain reactions of ethylene-chlorine mixtures prepared by this method have been studied by dynamic UV and IR spectroscopy. Activationless chain growth occurs with mean length 260±70 in the temperature range 17–45 K. Chain lengths greater than 100 are observed up to 60–70% conversion to products. Comparison of the experimental data with computer simulations shows that the tunneling reaction is due to formation of a close-packed reaction complex with high amplitude zero-point vibrations which lower the vibrationally adiabatic barrier to reaction. The commensurability of reactant and product crystal lattices results in linear propagation of long chains without accumulation of deformation strain. Spatial correlations caused by nonlinear propagation are considered.     

Experimental study of the time-dependent rate of K → πππ

The time-dependence of the decay rate of initially pure K⁰ into the final state (π⁺π⁻π⁰) has been studied in search for the decay k_S⁰→π⁺π⁻π⁰. No evidence is found in a sample of 384 observed events. The ratio of the CP -violating K_S⁰ amplitude and the K_L⁰ amplitude is η₊₋₀ = (0.13_−0.20^+0.17) + i(0.17_−0.26^+0.27); the ratio of the CP-conserving K_S⁰ amplitude and the K_L⁰ amplitude is < 0.4. The energy dependence of the K⁰→π⁺π⁻π⁰ matrix element is found to be a₊₋₀ = −0.31 ± 0.03.     

Numerical comparison of reaction-matrix and Jastrow methods for nuclear matter

The ground-state energy per particle of symmetrical nuclear matter has been calculated as a function of Fermi wave number for two representative central potentials containing hard cores, by means of both reaction-matrix and Jastrow methods. The agreement of results from the two methods is remarkably good in the density region near equilibrium.     

Pb decay and M4 transition probabilities in neutron-deficient lead isotopes

The decay of 6.1 sec ^203mPb has been examined with a high-resolution Ge(Li) spectrometer, and a 5.1 keV M2 transition was found to compete with the 825.2 keV M4 isometric transition. The M4 transition probability, thus corrected, is now found to be consistent with those of the other M4 transitions in the lead region.     

Dynamical consequences of spontaneous breakdown of symmetries

The spontaneous breakdown of a continuous symmetry group generated by conserved currents is considered. In the framework of general quantum field theory the possible dynamical consequences of spontaneous breakdown are analysed: a general relation is derived between n− and (n+1) — point functions involving Goldstone bosons in the limit of zero momentum. The technique is illustrated by a few examples for the SU(2) × SU(2) chiral group and the results generalized relations known from the perturbative treatment of the σ-model.