On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

Study of the 26Al(n,p)26Mg and 26Al(n,α)23Na reactions using the 27Al(p,p')27Al inelastic scattering reaction

26Al was the first cosmic radioactivity ever detected in the galaxy as well as one of the first extinct radioactivity observed in refractory phases of meteorites. Its nucleosynthesis in massive stars is still uncertain mainly due to the lack of nuclear information concerning the 26Al(n,p)26Mg and 26 Al(n,α)23Na reactions. We report on a single and coincidence measurement of the 27Al(p,p')27Al(p)26Mg and 27Al(p,p')27Al(α)23Na reactions performed at the Orsay TANDEM facility aiming at the spectroscopy study of 27Al above the neutron threshold. Fourteen states are observed for the first time within 350 keV above the 26Al+n threshold