abstract

A class of exact interior solutions for a spherically symmetric perfect fluid distributions with nonhomogeneous density and pressure is obtained. It is shown that in some cases the initial outward motion is reversed and finally the system collapses to a singularity of infinite matter density. There are also cases when an initially collapsing system may bounce back so that the ultimate catastrophe can be avoided. The metric obtained is nonsingular and satisfies the conditions that the pressure and matter density within the distribution is nonnegative.

abstract

The mass and rapidity distributions are derived for clusters produced according to a diffractive and a multi-Regge mechanism. The careful treatment of the kinematics is essential. The results are compared with empirical functions. Some constraints on the production mechanisms, which follow from this comparison, are investigated.

abstract

Geometrical scaling connects, at \(t=0\), the phase of the pomeron amplitude \(F(s,t)\) to that of its derivative \(\partial F(s,t)/\partial t\). This intrinsic phase correlation allows one to derive a dispersion sum rule relating the high  and low-energy regions.

abstract

It is shown that the unitarity corrections dramatically change the multiplicity distributions expected from uncorrelated cluster emission models.

abstract

The angular distributions in (d,p) reactions with the target nucleus \(^{12}\)C at energies of the incident deuterons up to 20 MeV are studied. The distributions are compared with predictions of the standard DWBA, the sudden approximation, and model calculations within the latter. The study supports the notion to subject the sudden approximation to some changes in its treatment of the deuteron break-up.

abstract

The eikonal scheme is used to investigate the elastic and inelastic scattering of two charged particles. The \(t\)-matrix is found to be reproduced exactly at all scattering angles and at all energies both in the on-shell situation and for \(n\gg 1\) in the half-off-shell case. The result is a consequence of choosing the direction of the eikonal approximation and the pole of the eikonal free Green function in a particular way so as to depend on the scattering angle. In situations where the Sommerfeld parameter \(\eta = zZe^2(\hslash \nu )^{-1}\) is large, as is a feature of heavy ions, analytic formulae are obtained for the \(t\)-matrix corresponding to scattering by displaced charges. The agreement with the exact result suggests that Coulomb excitation can be treated in this manner. An analytic expression is obtained for the derivative with respect to the nuclear charge of the Coulomb-excitation matrix element and the DWBA formalism is then used. The final result can be put in terms of integrals over the charge of expressions involving the half-off-shell \(t\)-matrix. The calculations refer only to single-step processes.

abstract

It is claimed that the Kerman McManus and Thaler (KMT) optical potential in its commonly used form has to be modified in order to reproduce the correct high energy limit, i.e. the Glauber formula. It is shown that when assuming (apart from the fixed scatterer approximation) the commonly used off-shell prescription for individual projectile-nucleon \(t\)-matrices \(\langle \vec {p}\,'|t|\vec {p}\,\rangle =t(\vec {p}-\vec {p}\,')\), one has to neglect the terms responsible for a multiple scattering of the projectile from the same nucleon in the KMT optical potential. This modification is in fact equivalent to the prescription proposed by us recently for multiple scattering calculations at medium energies. The importance of such a modification is illustrated on the example of proton scattering from He\(^4\).

abstract

It is shown that the minimal extension of the charm scheme leads almost uniquely to definite predictions for the breaking of the new (SU\(_3\))\(_{\rm H}\) symmetry which appears together with 3 new heavy quarks. This symmetry breaking has different patterns than for the old SU\(_3\). There is no preferred (SU\(_2\))\(_{\rm H}\) subgroup, and the neutral heavy vector mesons are bound states of \(\bar {q}q\), practically without mixing. In contrast to the pattern of symmetry breaking, other properties of the new quarks automatically turn out to be the same as in the model of Harari.