Study of the Born-Oppenheimer Approximation for Mass-Scaling of Cold Collision Properties

Asymptotic levels of the A $^1\Sigma_u^+$ state of the two isotopomers $^{39}{\rm K}_2$ and $^{39}{\rm K}^{41}{\rm K}$ up to the dissociation limit are investigated with a Doppler-free high resolution laser-spectroscopic experiment in a molecular beam. The observed level structure can be reproduced correctly only if a mass dependent correction term is introduced for the interaction potential. The applied relative correction in the depth of the potential is $10^{-6}$, which is in the order of magnitude expected for corrections of the Born-Oppenheimer approximation. A similar change in ground state potentials might lead to significant changes of mass-scaled properties describing cold collisions like the s-wave scattering length.Comment: 8 pages, 6 figure

High precision spectroscopy on beams of atoms and dimers

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Termination of Integer Term Rewriting

Recently, techniques and tools from term rewriting have been successfully applied to prove termination automatically for different programming languages. The advantage of rewrite techniques is that they are very powerful for algorithms on user-defined data structures. But in contrast to techniques for termination analysis of imperative programs, the drawback of rewrite techniques is that they do not support data structures like integer numbers which are pre-defined in almost all programming languages. To solve this problem, we extend term rewriting by built-in integers and adapt the dependency pair framework to prove termination of integer term rewriting automatically. Our experiments show that this indeed combines the power of rewrite techniques on user-defined data types with a powerful treatment of pre-defined integers