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I'm going to post this question in a "goal" and "question" format so it is easier to follow along:

The Goal

I'm planning on running a nuclear physics experiment in which I have an arbitrary mass of a stable isotope. Just for example, let's assume we have 10g of 128Te produced from the decay of the short-lived beta emitter 128Sb.

The goal is to irradiate the sample with high energy electrons, such that we can convert protons in the stable isotope nuclei into neutrons, thus transforming 128Te back into 128Sb. (Refer to this previous question for more background on the mechanism)

A detector would be placed near the sample to confirm that protons were successfully transformed into neutrons by checking for beta emission.

The Question(s)

A couple of questions on my setup:

  1. Is it possible to irradiate every single atom in the sample, or get fairly close to achieving that? Keep in mind that the electrons need to have a fairly high energy (a little bit more than 1.29 MeV) in order to induce proton-to-neutron conversion, so the plan was to use a linear accelerator. But how would one go about irradiating an entire sample with a linear accelerator?
  2. Is there any way of ensuring that once a proton-to-neutron conversion has been completed in an atom that further accelerated electrons do not hit that nucleus again?

Thank you all in advance.

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    $\begingroup$ Looks like a tedious combination of energy loss, cross-section, and lifetime calculations. As for part 2, no, you can’t. $\endgroup$
    – Jon Custer
    Commented Apr 29, 2020 at 17:22
  • $\begingroup$ Having looked through ENSDF, I don't see where your 1.29MeV comes from - the Q-valued for the beta decay is 4.363MeV. Further, I'm not sure how you intend to balance energy and momentum in the center of mass frame if you only irradiate with electrons and expect nothing to come out. $\endgroup$
    – Jon Custer
    Commented Apr 29, 2020 at 18:01
  • $\begingroup$ How do you produce/get reasonably pure $^{128}Sb$ in the first place if it's short lived ? $\endgroup$ Commented Apr 29, 2020 at 18:46
  • $\begingroup$ @JonCuster Where I get "1.29MeV" from is for the conversion of a proton into a neutron, it needs at least 1.29MeV of energy. That way, we are taking a proton in the nucleus and converting it into a neutron so that nucleus will undergo decay again. Or is my understanding flawed? $\endgroup$ Commented Apr 29, 2020 at 19:13
  • $\begingroup$ Well, as noted, the Q-value for the beta decay is 4.363MeV - that is the energy released in that reaction. So, yes, your understanding is flawed. $\endgroup$
    – Jon Custer
    Commented Apr 29, 2020 at 19:15

1 Answer 1

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At the level of nuclei and electrons one is in the quantum mechanical framework , which means probabilities, and also the special relativity framework where mass is the four vector length of the energy momentum vector.

Because of this, protons and neutrons bound in a nucleus do not have the mass they have when free.

When nucleons bind together to form a nucleus, they must lose a small amount of mass, i.e., there is a change in mass to stay bound. This mass change must be released as various types of photon or other particle energy as above, according to the relation $E = mc^2$. Thus, after the binding energy has been removed, $binding energy = mass change × c^2$. This energy is a measure of the forces that hold the nucleons together. It represents energy that must be resupplied from the environment for the nucleus to be broken up into individual nucleons.

So the the energy of the beam you design is not enough to change back to a bound proton, as the discussion in the comments.

Let us suppose that you get the correct energy beam and see your questions.

  1. Is it possible to irradiate every single atom in the sample, or get fairly close to achieving that?

No, unless your sample is few atom thick layer. The electrons in the beam will interact in various ways with the electric fields of the lattice and be deflected losing energy so not good for beta+ decay. ( decay because an antineutrino will come out of the process) .

  1. Is there any way of ensuring that once a proton-to-neutron conversion has been completed in an atom that further accelerated electrons do not hit that nucleus again?

It will be hard, and needs experimentation. Take a series of thin film samples. Irradiate them in a time sequence, time sampel1,time sample 2 etc. Record the number of nuclei decaying back (in a fixed larger time). At the time sample where saturation is reached you can assume all of them have been irradiated. Of course if one can calculate the crossections etc one could model this, but I assume this is what you are looking for.

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