Solving exactly solvable pairing models

The algebraically solvable pairing models, pioneered by Racah, Richardson and Gaudin, have only recently gained wider popularity. Recent advances in numerical methods now allow to actually solve the algebraic equations, for boson and fermion pairs. I have applied this method to the pairing model in atomic nuclei. The pairing Hamiltonian for several tens of particles distributed over several mayor shells can now be solved exactly in a matter of seconds. This makes these models truly 'exactly-solvable'. The models are relevant in other fields of physics too. For example, they can be used to quantify the influence of the Pauli principle on the Bose-Einstein condensation of bosons that are made up of fermionic atoms or particles. It turns out that these condensates have a maximal condensed fraction, solely determined by Pauli-exclusion effects and the structure of the order parameter.