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##.(adsbygoogle = window.adsbygoogle || []).push({});

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.)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Order-of magnitude estimate fails for angular momentum in decay

Tags:

Loading...

Similar Threads for Order magnitude estimate |
---|

A NLO and NNLO order calculation for HardQCD in PYthia8.2 |

I Why do particle physicists use Gaussian error estimates? |

I What order should we take when calculating QFT amplitudes? |

A Highest loop order of experimental relevance? |

**Physics Forums | Science Articles, Homework Help, Discussion**