Feshbach resonance scattering under cylindrical harmonic confinement

A problem of collisions of atoms with two-channel zero-range interaction in an atomic waveguide is solved by using of a renormalization procedure. A matching of the solution to a solution of the related one-dimensional problem leads to relation between the one-dimensional and three-dimensional scattering parameters. The scattering amplitude and bound states for the confined system demonstrate differences from the related free and one-dimensional systems.Comment: Completely rewritten version,8 pages with 5 figures, uses REVTe

Capital Deepening in United States Manufacturing, 1850-1880

Establishment-level data are used to study capital deepening – increases in the capital-output ratio – in U. S. manufacturing from 1850 to 1880. In both nominal and real terms, the aggregate capital-output ratio rose substantially over the period. Capital deepening is shown to be especially important in the larger firms and was associated with the diffusion of inanimate power. Although capital deepening implies a declining average product of capital, rates of return were not necessarily falling if capital’s share was increasing. However, there is strong evidence that returns did, in fact, decline.