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We have this well known case of ~4.2 MeV α-particle being emitted from the U-238 nucleus but the α-particle emitted from the Po-212 which has the energy of ~9MeV cannot penetrate it. This phenomenon is explained by the tunneling effect from quantum mechanics.

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Now, of the tunneling can happen from the inside to the outside, then why can't it happen from the outside to the inside?

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    $\begingroup$ It can happen the other way, but it's not what you consider when you want to describe a nucleus leaking an alpha-particle. $\endgroup$ – Raskolnikov Jan 28 at 13:50
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    $\begingroup$ Yes, it can go inside. $\endgroup$ – Raskolnikov Jan 28 at 14:01
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    $\begingroup$ @Korra: it would if it was directed properly! $\endgroup$ – Gert Jan 28 at 14:23
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    $\begingroup$ Directed toward the $Po-212$ nucleus. $\endgroup$ – Gert Jan 28 at 14:37
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    $\begingroup$ No, any old $\alpha$ will do. Directed properly, of course. $\endgroup$ – Gert Jan 28 at 14:47
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Now, if the tunneling can happen from the inside to the outside, then why can't it happen from the outside to the inside?

Given the correct initial state ─ an $\alpha$ particle directed at the nucleus at the right energy, going radially inwards, and for a sufficient length of time ─ the reverse tunnelling process can indeed happen. (Indeed it must happen, because unitary evolution in QM is invariant under time reversal.)

However, that reversed initial state is far les common than the $\alpha$-particle-inside-the-nucleus state, so you don't see it in practice.

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  • $\begingroup$ What is unitary evolution...? And why do we have to consider time reversal? Also, what do you mean by"sufficient length of time"? The velocity of the incoming alpha particle?? $\endgroup$ – Korra Jan 28 at 14:46
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    $\begingroup$ @Korra unitary evolution = time passes while you aren't looking at stuff. $\endgroup$ – John Dvorak Jan 28 at 14:52
  • $\begingroup$ Thanks @John Dvorak for the support ready explanation though I looked it up on PSE. But what does time reversal has to do in this? $\endgroup$ – Korra Jan 28 at 14:57
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    $\begingroup$ @Korra the process of an alpha particle embedding itself into a nucleus is the same as a spontaneous emission of an alpha particle by the new nucleus happening backwards. Time reversal invariance means the same things happen in reverse if you reverse time. In rigid body physics, time reversal means stopping everything at the same time and sending it in the opposite direction and with the same speed, for example. $\endgroup$ – John Dvorak Jan 28 at 15:22
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    $\begingroup$ @Korra Inverse alpha decay, often called alpha capture, has indeed been observed experimentally (though I'm unsure whether it's been observed for the particular nuclei you mention). $\endgroup$ – Emilio Pisanty Jan 28 at 16:51

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