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When a nucleus gamma decays, the gamma has its intrinsic spin of ##1\hbar##, but it can also carry away a significant amount of angular momentum in addition to that. Quadrupole radiation is very common, and in exceptional cases you can even get gammas with 5 or ##10\hbar##.
Now suppose I do the following naive estimate of how much angular momentum a 1 MeV gamma *should* be able to carry off (ignoring intrinstic spin). It's radiated from the nucleus, which has a spatial extent of, say, ##r=3\times10^{-15}## m. For a massless particle, ##p=E/c##, so I estimate the maximum angular momentum as ##rE/c\sim10^{-2}\ \hbar##, which is obviously much too small.
Of course this is a naive estimate, and in particular it ignores quantum mechanics except at the very end when I express the result in terms of ##\hbar##. The wavelength of the gamma is about ##10^{-12}## m, which is much bigger than the size of the nucleus, so we shouldn't expect classical physics to be a good approximation. (For an alpha, the corresponding estimate comes out to be more like ##10\hbar##, and we do have ##\lambda\ll r##, so we expect classical physics to work.)
Nevertheless it seems odd that the estimate for a gamma is off by such a vast amount, and I'm unsure as to whether this is a classical issue or a quantum-mechanical issue. Classically, can an antenna of size ##r## emit electromagnetic radiation with energy ##E## and ##L\gg rE/c##? As a heuristic, can one let ##r## equal ##\lambda## rather than the size of the antenna? (Doing so provides just about the right result for the gamma ray.)
Now suppose I do the following naive estimate of how much angular momentum a 1 MeV gamma *should* be able to carry off (ignoring intrinstic spin). It's radiated from the nucleus, which has a spatial extent of, say, ##r=3\times10^{-15}## m. For a massless particle, ##p=E/c##, so I estimate the maximum angular momentum as ##rE/c\sim10^{-2}\ \hbar##, which is obviously much too small.
Of course this is a naive estimate, and in particular it ignores quantum mechanics except at the very end when I express the result in terms of ##\hbar##. The wavelength of the gamma is about ##10^{-12}## m, which is much bigger than the size of the nucleus, so we shouldn't expect classical physics to be a good approximation. (For an alpha, the corresponding estimate comes out to be more like ##10\hbar##, and we do have ##\lambda\ll r##, so we expect classical physics to work.)
Nevertheless it seems odd that the estimate for a gamma is off by such a vast amount, and I'm unsure as to whether this is a classical issue or a quantum-mechanical issue. Classically, can an antenna of size ##r## emit electromagnetic radiation with energy ##E## and ##L\gg rE/c##? As a heuristic, can one let ##r## equal ##\lambda## rather than the size of the antenna? (Doing so provides just about the right result for the gamma ray.)