Estimates of the number of quantal bound states in one and three dimensions

Using the relation between the number of bound states and the number of zeros of the radial eigen-functionψ(r), or equivalently, that ofφ(r)=rψ(r) in the range 0⩽r⩽∞, the upper bounds on the number of bound states generated by potentialV(r) in different angular momentum channels are obtained in three dimension. Using a similar procedure, the upper bound on the number of bound states in one dimension is also deduced. The analysis is restricted to a class of potentials for whichE=0 is the threshold. By taking a number of specific examples, it is demonstrated that both in one and three dimensions, the estimate of the upper bound obtained by this procedure is very close to or equal to the exact number of bound states. The correlation of the present method with the Levison’s theorem and WKB approximation is discussed.     

Electroweak form factors of non-strange baryons

We compute electroweak form factors of the nucleon and photon transition form factors of non-strange baryon resonances up to the third resonance region in a model with instanton-induced interaction. The calculation is based on the Bethe-Salpeter equation for three light constituent quarks and is fully relativistic (U. L?ring et al., Eur. Phys. J. A 10, 309 (2001)). Static nucleon properties and photon resonance couplings are in good agreement with experiment and the Q² behaviour of the experimentally known form factors up to large momentum transfer is accounted for. Received: 4 April 2002 / Accepted: 2 May 2002     

A mathematical programming system for preference and compatibility maximized menu planning and scheduling

In this paper, the analytical representation of food preference is used in a separable non-linear program to yield the serving frequencies of menu items for a finite time horizon. The frequencies obtained in this way insure cost and nutritional control. Subsequently, the scheduling problem dealing with item assignments to meals and days is formulated as an integer program consisting of several transportation problems linked by weekly nutritional constraints. This problem is solved using a branch and bound algorithm which employs Lagrangian relaxation to obtain bounds and to decide on branching strategy.     

Integer programming duality: Price functions and sensitivity analysis

Recently a duality theory for integer programming has been developed. Here we examine some of the economic implications of this theory, in particular the necessity of using price functions in place of prices, and the possibility of carrying out sensitivity analysis of optimal solutions. In addition we consider the form of price functions that are generated by known algorithms for integer programming.This research was supported in part by a Senior Visiting Research Fellowship from the Science Research Council at the London School of Economics while the author was on leave from CORE, Université Catholique de Louvain, at Louvain-la-Neuve.     

The concentration profiles of the recoil implanted oxygen in Si after ion implantations into SiO2-Si substrates

Abstract

The annealing of bare thermal oxide on silicon at 400–500°C in a hydrogen bearing gas results in a reduced density of states N_ss at the substrate silicon/oxide interface. Treatments of this type have played a role in MOS processing schedules for several years. However, a similar approach applied to large areas (cm²) of poly-silicon coated oxide appears to be less effective in reducing N_ss. This may be due to the polysilicon acting as a partially impermeable barrier which tends to starve the substrate/oxide interface of hydrogen.

In the present work hydrogenation of 2-inch diameter, polysilicon coated wafers has been accomplished by hydrogen ion implantation. H2⁺ ions of 135 kV energy were implanted (to a dose of 10¹⁵ cm^?2) through a 7000 Å polysilicon coating into an underlying 1400 Å SiO₂ layer. The polysilicon was removed after 30-min anneals carried out in pure N₂ at 300, 400 or 500°C. Aluminium dots, 1 mm in diameter were then deposited on to the oxide and high frequency (1 MHz) and quasistatic C-V curves recorded for determinations of Nss. Control anneals on unimplanted material were carried out in pure N₂ and N₂-H₂ ambients. Control samples annealed in pure N₂ with their polysilicon coating intact had mid-gap N_ss values of not less than 4 × 10¹⁰ cm^?2 eV^?1. The corresponding value after N₂-H₂ anneals on polysilicon-free wafers was 3 × 10¹⁰. H₂ ⁺ implanted samples annealed in pure N₂ with their polysilicon intact had mid-gap N_ss values of 1 × 10¹⁰ cm^?2 eV^?1.

The effectiveness of ion beam hydrogenation may depend upon confinement of the associated displacement damage to the polysilicon. This allows the implanted hydrogen to be activated within the SiO₂ at temperatures similar to those employed for normal hydrogeneous gas annealing of the substrate silicon/oxide interface.     

Instability of bound states for abstract nonlinear Schrödinger equations

We study the instability of bound states for abstract nonlinear Schrödinger equations. We prove a new instability result for a borderline case between stability and instability. We also reprove some known results in a unified way.     

Analytical treatment of the oscillating Yukawa potential

Using a suitable Laguerre basis set that ensures a tridiagonal matrix representation of the reference Hamiltonian, we were able to evaluate in closed form the matrix elements of the generalized Yukawa potential with a complex screening parameter. This enabled us to treat analytically both the cosine and sine-like Yukawa potentials on equal footing and compute their bound states spectrum as the eigenvalues of the associated analytical matrix representing their Hamiltonians. Finally we used a carefully designed complex scaling method to evaluate the resonance energies and compared our results satisfactorily with those obtained in the literature for the cosine-like Yukawa potential.     

Spin-rotation coupling in compound spin objects

We generalize spin-rotation coupling to compound spin systems. In the case of muons bound to nuclei in a storage ring the decay process acquires a modulation. Typical frequencies for Z/A∼1/2$Z/A\sim 1/2$ are ∼3×10⁶ Hz$\sim 3\times {10}^6\text{Hz}$, a factor 10 higher than the modulation observed in g−2$g-2$ experiments.     

Effective field theory for bound state reflection

Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory for elastic reflection of shallow dimers from hard-wall surfaces using effective field theory. We show that there is a small expansion parameter for analytic calculations of the reflection scattering length. We present a calculation up to second order in the effective Hamiltonian in one, two, and three dimensions. We also provide numerical lattice results for all three cases as a comparison with our effective field theory results. Finally, we provide an analysis of the compressibility of the alpha particle confined to a cubic lattice with vanishing Dirichlet boundaries.