Gurney and Condon (1928) and Bethe (1938)

Greetings class,

On Friday we will be discussing the paper “Wave Mechanics and Radioactive Disintegration” by Gurney and Condon from the 28 September 1928 edition of the journal Nature. This very short (1 page) paper discusses how particles can escape from the nucleus.

Some points to ponder…

1) How does this paper reflect particle capture as much as particle decay?

2) What does the curious last paragraph mean?

Please feel free to post your questions below, try not to make them too simplistic!

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10 Responses to “Gurney and Condon (1928) and Bethe (1938)”

  1. Hunter Burgin Says:

    After reading this article several times and consulting many online resources I feel like I have a somewhat stable knowledge of the wave mechanics and radioactive disintegration discussed in Condon/Gurney’s paper. However figure one left me with one question: I understand that the alpha particle present in orbit DF escapes from the nucleus along BM, but is there a chance that the particle in question can become “trapped” within the coulomb’s field of propulsion (D—-B). To ask my question again, can the tunneling alpha particle become trapped within the barrier rather than tunneling all the way through to the other side. I spent quite some time researching this question online and came across a lot of conflicting answers. Please let me know if anyone can shed some light on this question.

    -Hunter Burgin

    • Adam Settimo Says:

      I would think not. To become stationary between DB would suggest that the strong force and the Coulombic forces were completely opposite in both magnitude and vector, while reducing their attractive force for the particle proportionally. Right?

      • profhurst Says:

        Excellent points. The wave can’t be come trapped within the barrier, since technically it doesn’t exist within it. Say with an electron in hydrogen, it can exist in the 1s or 2s orbital, but not in between.

    • Tony J Says:

      For a moment contemplated that myself but I recalled from Theoretical chemistry when we learned about the tunneling electron microscope how tunneling would only occur if the particle (electron in this case) knows it can reach the other side of the barrier and not otherwise.

  2. Porter Marsh Says:

    In Fig 1., because the wave functions overlap “there is small but finite probability that the particle… will escape from the nucleus.” Because of the wave function overlap, the particle was able to move in a way other than the way sum of the forces would predict. Does the overlap of wave functions make it possible for an atom to move contrary to other forces or is it specific to the strong nuclear force? At this level does F not equal MA? Is this a behavior that can observed over time or is it only a single spontaneous occurrence at a time?

  3. Adam Settimo Says:

    I really do hope that I don’t give myself away and sound too simplistic here, but after reading these articles, reviewing to proton-proton chain and the CNO cycle, etc. there are some very simple questions that I always have. My immediate focus always begins with how they initially formed these concepts, then my attention moves to the nuts and bolts of they test these hypotheses. They can gather a lot of information about the sun through the different light emitted, can determine a lot about its size and density from the behaviors of other planetary bodies in relation to it, but to use all that information to formulate these theories is mind blowing to me.
    For the first paper (Condon), I could use anyones input regarding the overlap of wave functions in regions DB and FH and what that is trying to tell me.
    As for Bethe’s, ‘Energy Production in Stars,’ the paper seems to talk almost exclusively about the proton-proton chain with small mention of heavier elements being created in stars larger than ours (CNO cycle). In other web based searches credit for initial mention of the CNO cycle not only goes to Bethe, but also to Carl Friedrich von Weizsäcker who published a year before. I don’t know how much time we’ll be devoting to the subject, but that would maybe be another useful read, along with another I haven’t gotten to: Synthesis of the Elements in Stars, found here.

    https://www.pmf.unizg.hr/_download/repository/burbidge_RMP_29_547_1957.pdf

    • profhurst Says:

      Nice find on that paper, I didn’t see at first that it was 108 pages long!

      • Adam Settimo Says:

        Wow, neither did I. I came across it being referenced in several different online articles, and I planned on coming back to it. It seemed to be an all encompassing paper on the subject.

  4. Kevin Greenwood Says:

    A point that I am still unclear on is the condition of the alpha particle while it is tunnelling. At point D in Condon’s diagram the particle avoids the pull of the strong force and begins to move away from the nucleus beyond the limits set by the strong force exerted by the nucleus. At point B, the particle receives the full force of the electromagnetic repulsion from the other nucleons and is ejected. Between points D and B though, what is the state of the particle? By what mechanism does energy expended while tunnelling translate into distance from the center of the nucleus? What I am getting at is if I was only slightly larger than an alpha particle, could I touch it while it is tunnelling, or does it disappear and reappear like superpositioned electrons?

    Towards the end of the paper, Condon discusses Rutherford & Chadwick’s observations regarding fast alpha particles (higher energies than uranium alpha particles) being fired at a uranium nucleus, and all of them being repelled. However, it is mentioned earlier that the wavefunction for tunnelling moves in both directions, as given by “there will be a wavefunction which will die away exponentially from B to D”. As alpha particles in the nucleus have many, many more opportunities to collide with the energy barrier from within, could particle capture via tunnelling work in the opposite direction, provided the alpha particles from without had the same energy as the particles within the nucleus and one had enough time and uranium laying around?

    • profhurst Says:

      If I understand correctly, than yes. Alpha capture is a well known process, although difficult given the strong Columbic repulsion that exists before the strong force can take over. This is how we get heavier elements such as 16-O and 20-Ne built up in stars.

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