Parity

The term is used in two ways, first, as the operation P of spatial inversion, and the second as a numerical quantity associated with the system. Parity in the second sense is a multiplicative quantum number (► Quantum numbers) which could be + 1 or −1. In quantum mechanics the operation of spatial inversion is described by equation ${\bf{P}} \Psi (\vec{r}) = {\rm{P}} \Psi(- \vec{r})$), where the unitary parity operator P acting on a ► wave function Ψ has only two eigenvalues P=+1 or P=−1 which correspond to even and odd parity, respectively.

By convention, protons and neutrons have been assigned the same positive intrinsic parity. The intrinsic parity of the pion has been established experimentally to be negative. The total parity of the system of particles is the product of their intrinsic parities and the spatial parity given by (−1)^l, where l denotes the angular momentum of the wave function of the system. Thus the parity of a particle of spin l decaying into two pions is just (−1)^l and that of a particle of spin l decaying into three pions equals (−1)^l+1.