A three-body optical model for two clusters and a meson

Conclusion In a very simplified -²⁰Ne scattering calculation with the fish bone optical model, we have found a big difference between results obtained with two different off-shell versions of the model, when the three-body Pauli potential is neglected. It seems to be safe to say that the three-body force may not be neglected in the M-model. Further calculations will be needed to see whether it may be neglected in the ¯M-model.Presented at the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

Fiber coupling efficiency for random light and its applications to lidar

Employing the van Cittert-Zernike theorem of classical coherence theory, we derive a general expression for the efficiency with which quasi-monochromatic random light can be coupled to an optical fiber by means of a lens. For the important case of a source with Gaussian intensity distribution, we obtain and discuss the dependence of the coupling efficiency to single-mode fibers on the lens-to-fiber coupling geometry as well as on the ratio of lens size to speckle size. A specialization to the emerging fields of both incoherent and coherent fiber-based lidar applications shows that a maximum coupling efficiency of ~42% can be obtained for a monostatic system.     

Quark-quark potentials from the inversion of baryon-spectra and its application to the Roper resonance

We show that it is in principle possible to determine the quark-quark potential, in the nonrelativistic potential model, from the baryon spectrum. The method we propose is based on the fact that the lowest order of the hyperspherical-harmonic expansion method, the hypercentral approximation, is an excellent approximation for confining quark-quark potentials. However, our method applies to all cases where this assumption is valid. Using standard inverse spectrum techniques adapted to our problem we invert the baryon spectrum to obtain the hypercentral potential in the hyperradius of the three-quark system. By means of a new exact relation based on the Abel integral equation, we can invert the hypercentral potential to determine the quark-quark potential.A first application of this new method to the inversion of thes-state baryon spectrum demonstrates in a model-independent way the inability of nonrelativistic two-quark potentials to reproduce the Roper resonance without violating the QCD-motivated concavity requirement.Dedicated to Profs. Erich Schmid and Ivo laus on the occasion of their 60th birthdays     

Rigidity of invariant convex sets in symmetric spaces

The main result implies that a proper convex subset of an irreducible higher rank symmetric space cannot have Zariski dense stabilizer.     

Inversion of neutron reflection data

A method is proposed for determining surface profiles from neutron reflection data by inversion. With the reflectivity and the dwell time regarded as measured input, the complex reflection coefficient is determined in the form of a rational function of the neutron momentum, for which the scattering potential is known in analytic form. A numerical example is given.     

Polygons in Buildings and their Refined Side Lengths

As in a symmetric space of noncompact type, one can associate to an oriented geodesic segment in a Euclidean building a vector valued length in the Euclidean Weyl chamber Δ _euc . In addition to the metric length it contains information on the direction of the segment. In this paper we study restrictions on the Δ _euc -valued side lengths of polygons in Euclidean buildings. The main result is that for thick Euclidean buildings X the set Pn(X){\mathcal{P}n(X)} of possible Δ _euc -valued side lengths of oriented n-gons depends only on the associated spherical Coxeter complex. We show moreover that it coincides with the space of Δ _euc -valued weights of semistable weighted configurations on the Tits boundary ∂ _Tits X. The side lengths of polygons in symmetric spaces of noncompact type are studied in the related paper [KLM1]. Applications of the geometric results in both papers to algebraic group theory are given in [KLM2].     

The Center Conjecture for Spherical Buildings of Types F 4 and E 6

We prove that a convex subcomplex of a spherical building of type F ₄ or E ₆ is a sub-building or the automorphisms of the subcomplex fix a point on it. Our approach is differential-geometric and based on the theory of metric spaces with curvature bounded above. We use these techniques also to give another proof of the same result for the spherical buildings of classical type.