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We show that the degeneracy parameter of a trapped Bose gas can be changedadiabatically in a reversible way, both in the Boltzmann regime and in thedegenerate Bose regime. We have performed measurements on spin-polarized atomichydrogen in the Boltzmann regime demonstrating reversible changes of thedegeneracy parameter (phase-space density) by more than a factor of two. Thisresult is in perfect agreement with theory. By extending our theoreticalanalysis to the quantum degenerate regime we predict that, starting closeenough to the Bose-Einstein phase transition, one can cross the transition byan adiabatic change of the trap shape.Comment: 4 pages, 3 figures, Latex, submitted to PR

Adiabatically Changing the Phase-Space Density of a Trapped Bose Gas