Saturnales
Un choix personnel a ete fait d'evenements memorables du programme de physique realise a Saturne-2 pendant les derniers 20 ans.
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arXiv subjects
Colin Wilkin
Publications and source records attributed to Colin Wilkin.
Bound and Unbound Wave Functions at Short Distances
There exists a simple relationship between a quantum-mechanical bound-state wave function and that of nearby scattering states, when the scattering energy is extrapolated to that of the bound state. This relationship is demonstrated numerically for the case of a spherical well potential and analytically for this and other soluble potentials. Provided that the potential is of finite range and that the binding is weak, the theorem gives a useful approximation for the short-distance behaviour of the scattering wave functions. The connection between bound and scattering-state perturbation theory is established in this limit.
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Comparison of the Near-Threshold Production of eta- and K-Mesons in Proton-Proton Collisions
The pp -> pp eta and pp -> pLambda K^+ reactions near threshold are dominated by the first and second S_11 resonance respectively. It is shown that a one-pion-exchange model exciting these isobars reproduces well the ratio of the production cross sections. The consequences for this and other channels are discussed.
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Scattering Wave Functions at Bound State Poles
The normalisation relation between the bound and scattering S-state wave functions, extrapolated to the bound state pole, is derived from the Schroedinger equation. It is shown that, unlike previous work, the result does not depend on the details of the potential through the corresponding Jost function but is given uniquely in terms of the binding energy. The generalisations to higher partial waves and one-dimensional scattering are given.
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Production of $η$ Mesons Near Threshold
It is argued that the strong energy dependence of the $p\, d \rightarrow \,^{3\!}H\!e\, η$ cross section near threshold is due to a final state interaction between the $η$ meson and the $^3$He nucleus. The large scattering length that this implies is in accord with optical potential predictions and is evidence for a nearby virtual `$\!$`bound'$\!$' state in the $η^3$He system. This model suggests that sharp structures should also be seen close to production thresholds on other light nuclei.
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Near-Threshold Production of $η$-Mesons
It is shown that the striking energy variation in the $p\, d \rightarrow \mbox{$^{\, 3}{\rm He}$}\, η$ cross section near threshold is probably due to a final state interaction associated with a large (complex) $η-\mbox{$^{3}{\rm He}$}$ scattering length. The consequences of this hypothesis are studied for the production of the meson in the $η-\mbox{$^{4}{\rm He}$}$ and $η-\mbox{$^{7}{\rm Be}$}$ channels.
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