Boson distinguished from fermions

Identical bosons (fermions) can collide in even (odd) partial waves. The role of partial waves is discussed in Chapter 1. Here we use f as the corresponding angular momentum quantum number. The first partial-wave contribution for bosons (fermions) is then the -wave with i = 0 (p-wave with = 1) [43]. At ultralow temperatures, only 5-wave collisions are dominant with the consequence that collisions between identical fermions are suppressed. The absence of 5-wave collisions is also the reason why, for instance, direct evaporative cooling cannot be applied to a sample of identical fermions. The situation changes when fermionic atoms are in different internal states, like hyperfine or Zeeman sublevels. The distinguishable particles can then interact in any partial wave. Fermion-composed molecules in 5-wave states are therefore generally associated from ultracold two-component spin mixtures. Interactions in all partial waves are obviously allowed if two different atomic species are involved, regardless of their fermionic or bosonic character. 

In the case of homonuclear diatomic molecules (molecules with two nuclei of the same isotope of the same element), the wave function must not pretend to distinguish between the nuclei, which are indistinguishable from each other. The wave function must be symmetric with respect to interchange of the nuclei if they are bosons and must be antisymmetric with respect to interchange of the nuclei if they are fermions. 

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