abstract

We consider a simple model of transition between a radiation dominated isotropic Universe and the de Sitter Universe. We show that the expansion rate within a few \(e\)-folding times approaches a constant value. The temperature of radiation decreases more slowly and it approaches the Hawking temperature after about 10 \(e\)-folding times. Hawking radiation does not influence the dynamics of the inflation.

abstract

The effect of the Coulomb potential on the chiral symmetry breaking in a model of QCD is analyzed. The renormalized gap equation for massless quarks interacting through the Lorentz vector potential \(V(\overline {r})\sim \sigma r - \frac {\alpha _{\rm s}}{r}\) is solved numerically. The chiral parameters are calculated for several values of \(\alpha _{\rm s}\).

abstract

A black hole can be seen as a particle-like solution of the equations of General Relativity. In this set of lectures it is explained why one expects that these objects must emit radiation by applying quantum field theory in the space-time environment of a black hole, as was discovered by S. Hawking. But the result seems to contradict the notion that black holes are just another kind of (more or less elementary) particles. The author then shows that the derivation is incomplete because gravitational self-interactions between in- and outgoing particles are ignored. It may well be that a more precise treatment does produce “decent” quantum mechanical behaviour of black holes but it seems that a new formulation of quantum mechanics in the presence of space-time horizons will be needed. A possible alley towards such a theory is outlined.

abstract

A class of Dirac field models with non-linear terms in the form of fractional powers of the scalar field invariants is discussed. The resulting equations contain a simple mechanism which implies that the solutions have compact supports and form what may be called soft or hard bags. The usual MIT bag is obtained as a limiting case (hardest bag). In the case of interacting coloured and flavoured quark fields introduction of some terms weakly breaking the SU\(_{\rm c}\)(3) symmetry provides a simple and rigorous mechanism of quark confinement. In several physically interesting cases this symmetry breaking may even not show up, so this mechanism may be called “hidden symmetry breaking”.

abstract

Second Born approximation corrections to electron scattering by nuclei with arbitrary spin are considered. Explicit integral expressions for the charge, magnetic dipole and interference differential cross sections are obtained. Magnetic and interference relative corrections are then investigated in the case of backward electron scattering using shell model form factors for nuclear targets \(^9\)Be, \(^{10}\)B, and \(^{14}\)N. To understand exponential growth of these corrections with square of the electron energy \(K^2_0\), the case of electron scattering by \(^6\)Li is considered using monopole model charge form factor with power-law asymptotics.

abstract

The excitation functions for various exit channels of \(^{12}\)C + \(^{16}\)O reactions, leading to different final states of \(^{24}\)Mg, \(^{26}\)Al and \(^{27}\)Al, were measured in 53.6 keV steps over the incoming energy interval of 160 ions from 12.4 to 13.9 MeV in the c.m. system. All measurements were performed at fixed lab. angle of 30\(^{\circ }\). Subsequent fluctuation analysis concerned excitation functions for several states of each final nucleus with excitations ranging up to 10 MeV and 4 MeV in \(^{24}\)Mg and \(^{26}\)Al, respectively, and from 6.4 to 11.4 MeV in \(^{27}\)Al. Statistical tests applied to these excitation functions have revealed pronounced non statistical structures at the incident energies of 12.57, 12.73, 13.11 and 13.41 MeV in c.m. system.