A. Martin

Pade approximants and the anharmonic oscillator

The diagonal Pade approximants of the perturbation series for the eigenvalues of the anharmonic oscillator (a βκ^1 perturbation of p^2 + κ^2) converge to the eigenvalues.

A simultaneous fit of bb, cc,ss (bcs Pairs) and cs spectra

Abstract A previous fit of the J/ψ and γ levels and leptonic widths by a power-like phenomenological potential is modified to include systems containing strange quarks. In spite of the smallness of the strange quark mass, the fit is astonishingly good.

Inequalities on heavy quark-antiquark systems

Abstract We obtain inequalities and estimates on the radii and kinetic energies of heavy quark-antiquark systems in the framework of non-relativistic quantum mechanics. We also establish theorems on the mass dependence of the kinetic energy. These are used to derive bounds on the mass difference between the c quark and the b quark from experimental data on the J/ ψ and Y systems. We also obtain tight upper and lower bounds on the masses of mixed flavour systems, on the mass of the toponium as a function of the t mass, and on the energy gap between a hidden flavour mass and the threshold for flavour pair production.

Order of levels in potential models

Abstract Various extensions of a previously derived theorem on the order of levels of quantum mechanical systems are discussed. Local conditions on the potential are given, such that the n th level of angular momentum l lies above (or below) the (n − 1)th level with angular momentum l + α. Some improved versions are formulated as conjectures and are shown to be true in certain limiting situations. As possible applications we discuss besides heavy-quark systems the level order in atomic physics.

Analysis of π−p → π−π+n data at 17.2 GeV/c

Abstract We propose an amplitude analysis for π − p → π − π + n data which allows for the possibility of A 2 exchange as well as absorbed pion exchange in a model independent way. This leads to an improved extrapolation method for extracting ππ phase shifts. Using the recent CERN-Munich data at 17.2 GeV/ c we isolate the π and A 2 exchange contributions and determine the form of the absorptive corrections. No evidence for an exchange contribution with the quantum numbers of the A 1 is found.

Bound states in one and two spatial dimensions

In this article we study the number of bound states for potentials in one and two spatial dimensions. We first show that in addition to the well-known fact that an arbitrarily weak attractive potential has a bound state, it is easy to construct examples where weak potentials have an infinite number of bound states. These examples have potentials which decrease at infinity faster than expected. Using somewhat stronger conditions, we derive explicit bounds on the number of bound states in one dimension, using known results for the three-dimensional zero angular momentum. A change of variables which allows us to go from the one-dimensional case to that of two dimensions results in a bound for the zero angular momentum case. Finally, we obtain a bound on the total number of bound states in two dimensions, first for the radial case and then, under stronger conditions, for the noncentral case.

Polarization relations in charge and hypercharge exchange reactions

Abstract Relations between polarizations in charge and hyperchange exchange reactions are derived. The idea is that K∗(890) and K∗∗(1400) exchange, including unspecified absorptive corrections, are related to ϱ and A2 exchanges by SU(3) octet symmetry, with a scale factor to represent symmetry breaking between the ϱ−A2 and the K∗−K∗∗ trajectories. This hypothesis is consistent with the present data on K N → πΣ(πΛ) and πN → KΣ(KΛ). It leads to simple relations between the polarized cross sections P dσ/dt, relating the above reactions to K − p → K o n , K+n → Kop, π−p → πon, π−p → νon. Predictions are made, on this basis, for polarization in K−p → Kon, K+n → Kop and π−p → νon at 4 GeV/c and for K − p → K o n at 7 GeV/c. Finally, some supplementary conjectures lead to predictions about polarization in baryon-baryon and baryon-anti-baryon reactions, np → pn, p p → n n , p p → Λ Λ , etc., and also in KLop → KSop regeneration.

A theorem on the order of levels in confining potentials

Abstract We prove that in a two-body, non-relativistic system interacting via a potential V = − g 2 / r + V c ( r ), where V c is a confining potential non-singular at the origin, the 2S level is above the 2P level if V c satisfies the following sufficient condition: This covers the well-known cases of linear potentials or harmonic oscillator potentials, which were considered in charmonium models, but also more generally, for instance, V c ( r ) = r α , α >0.

The "Herbst Hamiltonian" and the mass of boson stars

Abstract We present new accurate lower bounds on the ground state of the Hamiltonian p 2 +m 2 − α r . From these, we obtain a lower bound on the maximum mass of a boson star in the semirelativistic framework, and we compare it to a variational upper bound. We get 0.846 ( Gm ) −1 M max Gm ) −1 , where G is Newtons constant and m the boson mass.

η and η′ production at high energies

Abstract We discuss η and η ′ production by pseudoscalar mesons. Small η − η ′ mixing is found. Production mechanisms are considered, and an explanation is given for the striking dipwhich is observed in the K − p → ηλ cross-section at − t ∼ 0.4 GeV 2 .