Nuclear sizes derived from high-energy reaction cross sections

An analysis has been made of reaction cross sections for negative pions on a range of nuclei in the momentum region from 20 to 60 GeV/c. Data for C, Al, Sn and Pb are analysed in terms of nuclear sizes. Assuming the neutron and proton distributions in C are identical it is found that for Pb the best agreement with experiment is obtained using neutron density distributions which have similar geometrical parameters to that of the proton distribution. The accuracy with which the neutron distribution can be determined by these experiments is considered. The analysis is also extended to similar measurements for K⁻ mesons and antiprotons.     

Forward pion-nucleus elastic scattering amplitudes

Values for the real part of the forward scattering amplitude have been obtained using dispersion relations from an analysis of pion-nucleus total cross sections for ⁴He, ⁶Li and ¹²C. The results are compared with measured values and those predicted by simple optical models. The dependence of the derived values for the forward scattering amplitudes on uncertainties in the measured cross sections is also discussed.     

Bounded Laplace transforms,primitives and semigroup orbits

Let $f : \mathbb{R}_{+} \rightarrow \mathbb{C}$ be an exponentially bounded, measurable function whose Laplace transform has a bounded holomorphic extension to the open right half-plane. It is known that there is a constant C such that $\mid \int\limits^t_0 f(s) ds \mid\, \leq C (1 + t)$ for all $t \geq 0$. We show that this estimate is sharp. Furthermore, the corresponding estimates for orbits of $C_0$-semigroups are also sharp. Received:17 January 2001; revised manuscropt accepted: 8 February 2001     

Dissipative mappings with approximately invariant subspaces

Dissipative linear mappings Z defined on the dense union of an increasing sequence of closed subspaces E_n of a Banach space E are studied. It is shown that Z is the pregenerator of a contraction semigroup on E provided that is the quotient map of $\text{E}\text{onto}\text{E}\text{E}{}_{\mathrm{n}}$. This generalises results of Kishimoto and Jørgensen.     

On the spectral and growth bound of semigroups associated with hyperbolic equations

Some new and quite general conditions are presented to ensure equality of the spectral bound and the growth bound for those strongly continuous semigroups governing second-order (in time) equations in a Banach (or Hilbert) space. A counterexample arising from higher-order PDEs is given to show that the growth bound could be arbitrarily large while the spectral bound remains zero.     

On topological reflexivity of the groups of*-automorphisms and surjective isometrics of ∇ (H)

This research was partially carried out while the first author was a visitor to Abteilung Viathematik V, UniversitÄt Ulm, Germany. The second author's research was partially supported by the Hungarian National Research Foundation (OTKA), Grant No. F-019322     

Measurement of strong interaction effects in kaonic atoms

X-rays produced by kaons stopping in targets of O, Mg, Al, Si, S, Co, Ni, Cu, Ag, Cd, In and Sn have been observed. The shifts, widths and yields of the last observed mesic X-ray due to the effects of the strong interaction have been measured. The results are compared with optical-model predictions.     

Pionic x-rays and the neutron radius of 44Ca

Differences between strong interaction level shifts and widths for 2p states in pionic atoms of ^44,40Ca have been measured. Analysis in terms of an effective pion-nucleus potential leads to a difference in neutron rms radii of r_n(44)?r_n(40) = 0.05 ± 0.05 fm.