Convexity and a Stone-type theorem for convex sets in abelian semigroup setting

In this paper, two parallel notions of convexity of sets are introduced in the abelian semigroup setting. The connection of these notions to algebraic and to set-theoretic operations is investigated. A formula for the computation of the convex hull is derived. Finally, a Stone-type separation theorem for disjoint convex sets is established

Heavy Hyperon--Antihyperon Production

Based on the experience from the production of anti-Lambda Lambda and anti-Sigma Sigma pairs at LEAR (experiment PS185) it is suggested to continue the investigations towards the heavier antihyperon--hyperon pairs anti-Xi Xi and anti-Omega Omega in view of: (1) the production dynamics of the heavier antihyperon--hyperon out of the anti-p p annihilation (2) a comparison of the (3s 3anti-s quark system) anti-Omega Omega to the (3 (anti-s s)) 3 phi meson production, where both systems have similar masses (3.345 and 3.057, respectively) and identical valence quark content. A systematic study of the antihyperon--hyperon production with increasing strangeness content is interesting for the following reasons: The anti-Omega Omega production is the creation of two spin 3/2 objects out of the two spin 1/2 anti-p p particles. Results of the PS185 experiments prove a clear dominance of the spin triplet anti-s s dissociation. In the Omega anti-Omega the three s-quarks (three anti-s quarks) are aligned to spin 3/2 each. If the three anti-s s pairs are now all in spin triplet configurations when created out of the gluonic interaction they should have spin parity quantum number as 3^- as long as Omega anti-Omega is created with relative L=0 angular momentum. The comparison of the Omega anti-Omega baryon pair to the phi phi phi three meson production (where the three anti-s s quark pairs might not but can be produced without relative correlation) would provide a unique determination of the intermediate matter state. Measurements of excitation functions and polarization transfers should be used to examine these gluon rich anti-p p --> anti-Omega Omega and anti-p p --> phi phi phi reaction channels. Such experiments should be performed at the PANDA detector at the FAIR facility of the GSI.Comment: 4 pages, 2 figures, Presented at LEAP05: International Conference on Low Energy Antiproton Physics, Bonn - Juelich, Germany, May 16-22, 200

Transport analysis of K+ production in proton-nucleus reactions

The production of $K^+$ mesons in proton-nucleus collisions from 1.0 to 2.3 GeV is analyzed with respect to one-step nucleon-nucleon $(NN\to N Y K^+$) and two-step $\Delta$-nucleon $(\Delta N \to K^+ Y N$) or pion-nucleon $(\pi N \to K^+ Y$) production channels on the basis of a coupled-channel transport approach (CBUU) including the kaon final-state-interactions (FSI). Momentum-dependent potentials for the nucleon, hyperon and kaon in the final state are included as well as $K^+$ elastic rescattering in the target nucleus. The transport calculations are compared to the experimental $K^+$ spectra taken at COSY-J\"ulich. Our systematic analysis of $K^+$ spectra from $^{12}C$, $^{63}Cu$, $^{107}Ag$ and $^{197}Au$ targets as well as their momentum differential ratios gives a repulsive $K^+$ potential of $20\pm 5$ MeV at normal nuclear matter density.Comment: 7 pages, 5 figures, submitted to Eur. Phys. J.

K+^+ production in proton-nucleus reactions and the role of momentum-dependent potentials

The production of $K^+$ mesons in proton-nucleus collisions from 1.0 to 2.5 GeV is analyzed with respect to one-step nucleon-nucleon $(NN\to N Y K^+$) and two-step $\Delta$-nucleon $(\Delta N \to K^+ Y N$) or pion-nucleon $(\pi N \to K^+ Y$) production channels on the basis of a coupled-channel transport approach (CBUU) including the kaon final state interactions. The influence of momentum-dependent potentials for the nucleon, hyperon and kaon in the final state are studied as well as the importance of $K^+$ elastic rescattering in the target nucleus. The transport calculations are compared to the experimental $K^+$ spectra taken at LBL Berkeley, SATURNE, CELSIUS, GSI and COSY-J\"ulich. It is found that the momentum-dependent baryon potentials effect the excitation function of the $K^+$ cross section; at low bombarding energies of $\sim$ 1.0 GeV the attractive baryon potentials in the final state lead to a relative enhancement of the kaon yield whereas the net repulsive potential at bombarding energies $\sim$ 2 GeV causes a decrease of the $K^+$ cross section. Furthermore it is pointed out, that especially the $K^+$ spectra at low momenta (or kinetic energy $T_K$) allow to determine the in-medium $K^+$ potential almost model independently due to a relative shift of the $K^+$ spectra in kinetic energy that arises from the acceleration of the kaons when propagating out of the nuclear medium to free space, i.e. converting potential energy to kinetic energy of the free kaon.Comment: 11 pages, LaTeX, including 10 postscript figures, submitted to Eur. Phys. J.

On the Delta I = 1/2 rule in the Lambda N ----> N N reaction

It is shown that the mass dependence of the $\Lambda$-lifetime in heavy hypernuclei is sensitive to the ratio of neutron-induced to proton-induced non-mesonic decay rates R_n/R_p. A comparison of the experimental mass dependence of the lifetimes with the calculated ones for different values of R_n/R_p leads to the conclusion that this ratio is larger than 2 on the confidence level of 0.75. This suggests that the phenomenological $\Delta$I=1/2 rule might be violated for the nonmesonic decay of the $\Lambda$-hyperon.Comment: 3 pages, 2 figures, to be published in European Physical Journal