Alpha decay and magnetic fields

[andresB]

How is the alpha decay of a given nucleus affected by the presence of an external electromagnetic field?

It's probably an easier question that I think but I've been unable to find a treatment of the tunneling of the alpha particle using WKB method in the presence of a magnetic field.

 

[ChrisVer]

How is the alpha decay of a given nucleus affected by the presence of an external electromagnetic field?

I don't think it is?

 

[mfb]

I don't see any setup where a magnetic field would be strong enough to have any notable effect. The energies involved in the magnetic field are 600 neV/Tesla, the strongest permanent magnetic fields we can generate are about 100 T, and typical alpha decay energies are in the MeV range. You can get higher fields in crystal lattices, but not that much higher.

 

[andresB]

I don't know if a magnetic field would have, by itself**, an effect at all the WKB tunnelling time but I've also not seen a proof or an argument that say it doesn't.

(**I say by itself because a magnetic field can affect the electronic configuration around the atom and in that way affect the potential the alpha particle have to tunnel, but I'm not interested in that effect at the moment).

But Well, in stars there are quite high magnetic field even bigger that the so called critical field of QED yet I can't find any reference to a change in the alpha decay for thiese high fields (my search prowess is not that good, though)

 

[mfb]

But Well, in stars there are quite high magnetic field even bigger that the so called critical field of QED yet I can't find any reference to a change in the alpha decay for thiese high fields (my search prowess is not that good, though)

Not in normal stars, not even in neutron stars. In doubt, supernovae have stronger everything than everything else, but I still don't see where fields that strong would come from. But even with 4.3 GT you still get just a few keV. Spin orientations of everything would depend on the magnetic field of course.

 

[ChrisVer]

Not in normal stars, not even in neutron stars. In doubt, supernovae have stronger everything than everything else, but I still don't see where fields that strong would come from. But even with 4.3 GT you still get just a few keV. Spin orientations of everything would depend on the magnetic field of course.

So isn't alpha emission a random process [on which I based my initial answer with questionmark] but it depends on the environmental conditions?

 

[mfb]

That does not exclude each other.

Alpha particles as even-even nuclei don't care about spin anyway.

 

[andresB]

So, mfb, you are saying that if I have a nucleus and switch on a magnetic field (even a strong field) the effect of these field will be very small because the energy related to it is very small?. why the small value of the energy of the magnetic field matters that much?

 

[andresB]

In the end I thing the real question I'm interested is why a magnetic field would not change the wkb calculation for the tunnelling time.

 

[mfb]

why the small value of the energy of the magnetic field matters that much?

What else would influence anything? The tunneling is given by the potential, and this potential gets some tiny deviation from the magnetic field. It gets velocity-dependent, but I plugged in the speed of light so this is a very conservative overestimate already.

 

[Vanadium 50]

but I've also not seen a proof

The effect is non-zero. The effect is also far, far too small to see. So you won't find a proof that it's identically zero, because it's not. But it is so small we don't worry about it, just like we don't worry about the gravity of Pluto when calculating the trajectory of a baseball.

Alpha particles as even-even nuclei don't care about spin anyway.

True, but the parent nuclei do. U-235 has a magnetic moment of about 0.3 nuclear magnetons, and Th-231 must have a magnetic moment of similar magnitude (although I can't seem to find it). Put them in a magnetic field and the Q value will be shifted by the Zeeman splitting (about 10^-8 eV/T) and thus the alpha energy and in turn the tunneling rate. But since alphas are 5 MeV, you need to be in the 100 gigatesla range to see a substantial effect. You can get fields close to this in magnetars. Unfortunately, you don't have nuclei any more in magnetars.

 

[mfb]

The surface could have a thin layer of nuclei. The rapid rotation should mean they see a mixture of electric and magnetic fields.

 

[snorkack]

But since alphas are 5 MeV, you need to be in the 100 gigatesla range to see a substantial effect. You can get fields close to this in magnetars. Unfortunately, you don't have nuclei any more in magnetars.

Um? Pressure and density drop to zero on surface of neutron star. Magnetic field does not.