In the multipole expansion of the radiation field of a nuclear, it is considered that the odd-ordered poles (like electric octupole) must vanish in order to conserve parity. But there exist many nuclei which have characteristic electric octupole transition rates. I can't get myself to solve this discrepancy.
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The odd-ordered transitions don't vanish — they just have odd parity, and so they are only permitted between states with different parity. For instance a $1^-\to0^+$ transition will be mostly electric dipole (E1) with some smaller contribution from M2 and E3. A $1^+\to0^+$ transition, by contrast, will be a mixture of M1 and E2 (also with smaller contributions from higher-order multipoles).
rob
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