A Levinson theorem for scattering from a Bose-Einstein condensate

A relation between the number of bound collective excitations of an atomic Bose-Einstein condensate and the phase shift of elastically scattered atoms is derived. Within the Bogoliubov model of a weakly interacting Bose gas this relation is exact and generalises Levinson's theorem. Specific features of the Bogoliubov model such as complex-energy and continuum bound states are discussed and a numerical example is given.Comment: 4 pages, 3 figure

Molecular gas and stars in the translucent cloud MBM 18 (LDN 1569)

Seven of ten candidate H-alpha emission-line stars found in an objective grism survey of a 1 square degree region in MBM 18, were observed spectroscopically. Four of these have weak H-alpha emission, and 6 out of 7 have spectral types M1-M4V. One star is of type F7-G1V, and has H-alpha in absorption. The spectra of three of the M-stars may show an absorption line of LiI, although none of these is an unambiguous detection. For the six M-stars a good fit is obtained with pre-main-sequence isochrones indicating ages between 7.5 and 15Myr. The molecular cloud mass, derived from the integrated 12CO(1-0) emission, is 160Mo (for a distance of 120pc), much smaller than the virial mass (10^3Mo), and the cloud is not gravitationally bound. Nor are the individual clumps we identified through a clump-finding routine. Considering the relative weakness or absence of the H-alpha emission, the absence of other emission lines, and the lack of clear LiI absorption, the targets are not T Tauri stars. With ages between 7.5 and 15Myr they are old enough to explain the lack of lithium in their spectra. Based on the derived distances (60-250pc), some of the stars may lie inside the molecular cloud (120-150pc). From the fact that the cloud as a whole, as well as the individual clumps, are not gravitationally bound, in combination with the ages of the stars we conclude that it is not likely that (these) stars were formed in MBM 18.Comment: Accepted for publication in Astronomy & Astrophysics (20 pages