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I have read that for a system of 2 particles, the total parity is given by:

$P=P_1 P_2 (-1)^L$ where

  • $ P_1, P_2$= insisec parity of particle 1, 2

  • $L$ = relative angular moment

what's the meaning of "relative angular moment"? Do I have to add the $l$ numbers of the two particles?

And what if I have 3 particles?

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parity (or parity eigenvalues) is either $1$ or $-1$, as such the parity of a compound is (in most cases) the product of parities and $(-1)^f$ which is factor dependent on their interaction. i am not sure what is meant by "relative angular momentum", but in any case, by previous analysis, it depends on the symmetry of rotation wrt to each other which i presume this is what is meant (i.e $L_1 - L_2$) –  Nikos M. Jun 28 at 1:23

1 Answer 1

If you only have two particles, they only have a mutual angular momentum — there's only one $L$.

If you have many particles orbiting a central potential, like electrons in an atom, or if you can get away with pretending like you do, as in the nuclear shell model, then the eigenvalue of the system under parity inversion is the product of the eigenvalues of its components. So a system of positive-parity particles with an odd number of members in odd-$L$ orbitals will have negative parity.

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