Molecular predissociation resonances below an energy level crossing
We study the resonances of $2\times 2$ systems of one dimensional Schrodinger operators which are related to the mathematical theory of molecular predissociation. We determine the precise positions of the resonances with real parts below the energy where bonding and anti-bonding potentials intersect transversally. In particular, we find that imaginary parts (widths) of the resonances are exponentially small and that the indices are determined by Agmon distances for the minimum of two potentials.
Resonance free domain for a system of Schrödinger operators with energy-level crossings
We consider a $2\times 2$ system of 1D semiclassical differential operators with two Schrodinger operators in the diagonal part and small interactions of order $h^\nu$ in the off-diagonal part, where $h$ is a semiclassical parameter and $\nu$ is a constant larger than $1/2$. We study the absence of resonance near a non-trapping energy for both Schrodinger operators in the presence of crossings of their potentials. The width of resonances is estimated from below by $Mh\log(1/h)$ and the coefficient $M$ is given in terms of the directed cycles of the generalized bicharacteristics induced by two Hamiltonians.
Geomagnetic Polarity Epochs: Sierra Nevada Data, 3
Available paleomagnetic and radiometric results for about 60 igneous rocks 3.6 m.y. old or less are consistent with the following geomagnetic polarity epoch time scale: Brunhes normal polarity epoch, 0.0 to 0.85±0.15 million years; Matuyama reversed polarity epoch, 0.85±0.15 to 2.4±0.1 million years; Gauss normal polarity epoch, 2.4±0.1 to 3.35±0.1 million years; Gilbert reversed polarity epoch, 3.35±0.1 million years to (?). A brief interval of normal polarity (the Olduvai event) occurs within the Matuyama reversed epoch at about 1.9 m.y., and a brief interval of reversed polarity (the Mammoth event) occurs within the Gauss normal epoch at about 3.06 m.y. Data for twelve units from eastern California and Nevada, reported here for the first time, are particularly useful in defining the Gauss-Gilbert boundary and for recognizing the Mammoth event.