The little hagedorn that could

Abstract

The Hagedorn exponential mass spectrum with slope 1/TH was erroneously interpreted as fixing an upper limiting temperature TH that the system can achieve. To the contrary, such spectrum indicates a 1st order phase transition at a fixed temperature TH. A much lower energy example is the log linear level nuclear density below the neutron binding energy that prevails throughout the nuclear chart. We show that, for non-magic nuclei, such linearity implies a 1st order phase transition from the pairing superfluid to an ideal gas of quasi particles.