Alpha Decay & Ionization: Modeling an Electron's Tunneling

[terryphi]

Hello,

I'm trying to figure out if an atom undergoing alpha decay can knock out its orbital electrons. I was hoping someone might give me a hand coming up with a model to figure this out.

What I need to figure out is:

How far out does an alpha particle tunnel
can I use a classical approximation of an electron? (IE a particle) if not, how should I handle the quantum mechanics?
At what energy does the alpha particle appear when it first tunnels out?

I don't really have any experience with atomic physics, so any pointers would be appreciated.

 

[SpectraCat]

Hello,

I'm trying to figure out if an atom undergoing alpha decay can knock out its orbital electrons. I was hoping someone might give me a hand coming up with a model to figure this out.

What I need to figure out is:

How far out does an alpha particle tunnel
can I use a classical approximation of an electron? (IE a particle) if not, how should I handle the quantum mechanics?
At what energy does the alpha particle appear when it first tunnels out?

I don't really have any experience with atomic physics, so any pointers would be appreciated.

Well, charge is conserved, so for alpha decay of a neutral atom, *something* has to happen to the "extra" two electrons. My recollection is that they are generally considered to be left behind after the alpha particle splits off, but since dianions are unstable,one of the electrons will auto-detach. The other "extra" electron may also auto-detach if the atom is in an electronically excited state after the decay event. My guess is that these processes do not contribute to a sufficient extent to be noticable (or perhaps even measurable) in bulk samples of alpha-active radio-isotopes .. but I could be wrong about that.

Having said all of that, I really like your idea to simulate the process. I think the right approach would be to do a scattering calculation. As a first approximation you could do a Born-Oppenheimer type treatment where the nuclei are treated classically, and the electrons are treated quantum mechanically. You could potentially then run alpha emission trajectories, running Hartree-Fock or some other electronic structure calculation at each point along the trajectory to see if the electrons are scattered out of the larger decay product by the exiting helium nucleus, or perhaps even captured by the alpha particle (i.e. to form He+). I don't think the latter happens to an appreciable extent, or else alpha particles would not be generally observed/considered to have +2 charge ... again, that last statement is only a supposition on my part.

Sad to say I can't really offer advice on modeling the nuclear decay part of the problem. I doubt that just bunging together the two nuclei and having them spontaneously fly apart is an accurate representation of what really happens.

 

[Drakkith]

Charge conservation has nothing to do with alpha decay. I would venture a guess and say that it is possible for an atom to lose electrons during alpha decay, but I really don't know.

 

[SpectraCat]

Charge conservation has nothing to do with alpha decay.

That strikes me as a weird point of view ... I would say that charge conservation is essential for alpha decay, since charge conservation is what determines which daughter nucleus is left behind.

Furthermore, charge conservation has everything to do with where the electrons end up during alpha decay, which was the OP's question. A uranium atom is neutral, while an alpha particle has a +2 charge .. do you really think the thorium hangs around as a -2 ion?

 

[terryphi]

Well, charge is conserved, so for alpha decay of a neutral atom, *something* has to happen to the "extra" two electrons. My recollection is that they are generally considered to be left behind after the alpha particle splits off, but since dianions are unstable,one of the electrons will auto-detach. The other "extra" electron may also auto-detach if the atom is in an electronically excited state after the decay event. My guess is that these processes do not contribute to a sufficient extent to be noticable (or perhaps even measurable) in bulk samples of alpha-active radio-isotopes .. but I could be wrong about that.

Having said all of that, I really like your idea to simulate the process. I think the right approach would be to do a scattering calculation. As a first approximation you could do a Born-Oppenheimer type treatment where the nuclei are treated classically, and the electrons are treated quantum mechanically. You could potentially then run alpha emission trajectories, running Hartree-Fock or some other electronic structure calculation at each point along the trajectory to see if the electrons are scattered out of the larger decay product by the exiting helium nucleus, or perhaps even captured by the alpha particle (i.e. to form He+). I don't think the latter happens to an appreciable extent, or else alpha particles would not be generally observed/considered to have +2 charge ... again, that last statement is only a supposition on my part.

Sad to say I can't really offer advice on modeling the nuclear decay part of the problem. I doubt that just bunging together the two nuclei and having them spontaneously fly apart is an accurate representation of what really happens.

I actually believe I have experimental evidence that I have collected dianions of polonium on a charged balloon. I haven't had a chance to stick it under a spectrometer, but that should be soon.

My background is engineering. Do you have a primer on scattering calculations?

 

[Drakkith]

That strikes me as a weird point of view ... I would say that charge conservation is essential for alpha decay, since charge conservation is what determines which daughter nucleus is left behind.

Furthermore, charge conservation has everything to do with where the electrons end up during alpha decay, which was the OP's question. A uranium atom is neutral, while an alpha particle has a +2 charge .. do you really think the thorium hangs around as a -2 ion?

Am I misunderstanding something? I thought charge conservation was as below.
From wikipedia:

In physics, charge conservation is the principle that electric charge can neither be created nor destroyed. The quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved.

Also:

This does not mean that individual positive and negative charges cannot be destroyed. Electric charge is carried by subatomic particles such as electrons and protons, which can be created and destroyed. In particle physics, charge conservation means that in elementary particle reactions that create charged particles, equal numbers of positive and negative particles are always created, keeping the net amount of charge unchanged. Similarly, when particles are destroyed, equal numbers of positive and negative charges are destroyed.

I don't see "conservation" as coming into play in your example. The alpha decay from an atom leaves behind an atom that is -2 protons from the original atom. There aren't any particles being created or destroyed, so why would charge conservation decide which nucleus is left behind? Also, I agree that it is likely that the new nucleus will lose two electrons, but I don't know if it is guranteed that it will. I still don't know if the alpha particle will "knock" electrons out of their orbitals though.