We investigate a natural extension of the fundamental formula for black hole dynamics found by Christodoulou and Ruffini (1971) for Kerr–Newman black holes, by generalizing it to any value of the mass. New transformations, having irreversible character, are introduced and studied in detail. They are shown to be intimately related to the horizons of the black hole, since during any evolution governed by the improved equations either the area of the event horizon or the area of the antievent horizon are kept constant. We propose a new, more symmetrical form of the fundamental formula and we introduce two new parameters characterizing the black holes which are naturally associated with the set of new transformations. The possible physical implications are also discussed.
The concept of unincreasable angular momentum for a Kerr black hole is introduced and related to the isoareal transformations of the horizons. A thermodynamical interpretation is proposed for the new parameter.
Opposite side rapidity distributions at large p1 are analysed using different hard collision models: qq \(\to \) qq, q\(\overline {\rm q} \to \) M\(\overline {\rm M}\), qM \(\to \) qM. We find the hard scattering cross section \(d\sigma /d\hat {t}\) to be strongly constrained by the data. Some forms for \(d\sigma /d\hat {t}\) proposed previously are found to be inconsistent with the data; but choosing empirical parametrizations all models are able to describe the presently known data. However, at larger trigger transverse momenta we find differences between the models.
Single particle distributions of \(\pi ^+\) and \(\pi ^-\) at large \(p_{\bot }\) are analysed using various hard collision models: qq \(\to \) qq, q\(\overline {\rm q} \to \) M\(\overline {\rm M}\), qM \(\to \) qM. The \(p_{\bot }\) dependence at \(\theta _{\rm cm}=90^{\circ }\) is well described in all models except q\(\overline {\rm q} \to \) M\(\overline {\rm M}\). This model has problems with the ratios (pp \(\to \pi ^++\)X)/(pp \(\to \pi ^-\)+X) at large \(x_{\bot }\) and with (pp \(\to \pi ^0\)+X)/(\(\pi ^{\pm }{\rm p}\to \pi ^0\)+X). Presently available data on rapidity distributions of pions in \(\pi ^-\)p and p\(\overline {\rm p}\) collisions are at rather low \(p_{\bot }\) (however large \(x_{\bot } = 2p_{\bot }\sqrt {s}\)) where it is not obvious that hard collision models should dominate. The data, in particular the \(\pi ^-/\pi ^+\) asymmetry, are well described by all models except qM \(\to \) Mq (CIM). At large values of \(p_{\bot }\) significant differences between the models are predicted.
The relativistic radial equations for two spin—1/2 particles with a static interaction, which were derived previously, turn out to exclude the lowest value \(n_r = 0\) of the radial quantum number. New equations valid for all \(n_r = 0, 1, 2, \dots \) are obtained. They are equivalent to the former for \(n_r \gt 0\) as far as the spectrum of energy levels is concerned, but the former are necessary to supplement new equations in describing the complete set of energy wave functions. Energy levels for Coulomb bound states with \(j = 0\), previously found in an implicit way in the weak-potential approximation, are now calculated numerically for hydrogen and positronium. In Appendix, the relativistic radial equations are derived in the case of a more general interaction including nonstatic Bruit-like terms.
The quark additivity and a class of geometrical hypotheses concerning the spin dependence in two-body processes, are found to be compatible and consistent with experiment only when taken in the same spin frame.
Differential cross sections for elastic scattering of \(\alpha \)-particles from \(^{90}\)Zr, \(^{92}\)Zr, \(^{124}\)Sn and \(^{208}\)Pb were analysed over available energy range in terms of the optical model. New parametrization of the energy dependence of the optical potential parameters was used. Satisfactory agreement of the model predictions and experimental data was obtained.
Properties of fission isomers, like the moment of inertia, pairing energy gap and collective gyromagnetic ratio are investigated or reinvestigated theoretically using the Nilsson potential. In particular, the effect of coupling between the oscillator shells on these properties is researched. The properties are also studied and compared with experiment for the ground state, as a test of the calculations.
As \(\psi \)(3095) and \(\psi '\)(3684) can couple to the photon (as evidenced from the production of the particles concerned in the e\(^+\)e\(^-\)-annihilation experiments), therefore, the decays \(\psi \psi '\to \pi ^+\pi ^-\), K\(^+\)K\(^-\) are theoretically expected to occur but these decays have not been experimentally observed. In this note an explanation for the suppressions of the decays concerned has been given in terms of a dimensionality-based selection rule introduced in a previous paper.
The form of the solution of Einstein’s equations for a spherically symmetric distribution of matter in the co-moving coordinate system has been found. Although the pressure of matter is different from zero, the system is synchronous because of a suitable choice of the equation of state.