Quantum statistics and isospin invariance

The level density of an ideal Bose or Fermi gas is written in terms of usual phase-space integrals taking isospin conservation into accoutt. This cluster decomposition includes quantum statistics corrections between equal as well as unequal charge states of the considered particles. The isospin weights are given. These results are used to formulate a simple isospin-invariant statistical bootstrap model with Bose statistics. In the framework of this model the production of neutral pions in e⁺e^? and $\text{N}\text{N}$ annihilation is investigated.