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Where does the emission of a radioactive material directed at?

My intuition and background knowledge would firmly say that it is pointing at all directions outward of the atomic nucleus. But let's say we have an atomic nucleus undergoing alpha decay at the origin $(0,0,0)$ in an imaginary cartesian plane, what would be the angle of one specific helium atom at time $t$? Are there any experimental procedures or computations that may resolve this?

I guess encasing the radioactive material inside a sphere that can detect emission would do the trick, but are there any hypothesis or background info to possible relations such that it would "favor" one direction to another?

Furthermore, is it possible to "stop" the emission at a given direction? Not necessarily blocking the material such that the emissions at that plane are absorbed but directing the nucleus to emit in a certain direction.

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  • $\begingroup$ Positron emission ( medical PET scan) produces 2 gamma (?) emission in directly opposite directions . As I understand the only emissions counted are originating point of each of these pairs. $\endgroup$ Aug 3 at 18:46
  • $\begingroup$ One can set up the situation where a nuclei in the lab frame is moving fast enough in a given direction that a decay product cannot propagate back in that direction. But that probably isn't what you were thinking. $\endgroup$
    – Jon Custer
    Aug 3 at 23:38
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Without some external alignment mechanism, such as a strong magnetic field, there is no defined laboratory coordinate system which nuclei (or atoms) match. That means we don't know the atom's/nucleus's coordinate system (for simpicity I'll just use the word nucleus, but it could refer to a more complex system), and consequently the direction of emission of a single particle (massive or photonic) is meaningless to the lab and would look totally random.

To overcome this, we need to measure the relative direction of one emission which is coincident with another from the same nucleus. In other words, an $\alpha$ particle followed by a $\gamma$, or two $\gamma$ rays from one nucleus. In that case, we use the direction of one of the particles to establish the coordinate system of the nucleus relative to the laboratory (usually named the z-axis), then we know the direction of the other particle relative to the nucleus's coordinates.

If we do this enough times, with enough precision, we will get a distinct angular distribution (not random) of the second particle. Theoretically that relates to the quantum angular momentum of the second particle which can be related to several different nuclear model parameters, such as angular momentum change, shape of the nucleus, and nuclear particle interactions.

If we cool the nuclei to very low (millikelvin) temperatures, the nucleus of interest has a non-zero magnetic moment, and we apply a large (> 1 tesla) magnetic field, we can get a large enough population of nuclei which align with field. That way we can learn about the primary particle direction and don't need the coincidence method.

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The question isn't a duplicate, but this description of an underrated classic paper is quite relevant.

That paper and your question discuss "s-wave" decays which have spherical symmetry. Decays which carry nonzero angular momentum can have nontrivial angular distributions from the "p-wave" and higher spherical harmonics. However the spherical symmetry is restored if the ensemble of decaying nuclei is unpolarized. You currently have another answer describing coincidence detection as a tool for identifying angular correlations in cascades of decays from a single nucleus whose initial polarization is unknown.

The weak interaction can also produce parity-violating angular distributions in decays from polarized samples. Parity-violating distributions are typically a small correction to a mostly-spherical distribution of decays, because the weak interaction is ... weak.

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