Differences in half lives of odd-A and even-A nuclides

[lavster]

Im bit confused with something I've been reading - was wondering of someone could help me out.
If i can recall correctly, generally, even A nuclei are more stable than neighbouring odd-A nuclei due to a higher binding energy. And to be more specific, due to the nuclear shell model we can deduce that even - even nuclei are the stablest, leading to their greater abundence.

However I have just read the following sentence- "further, as with alpha decay, the half lives [of spontaneous fission] of the odd-A and odd-odd nuclides are considerably longer than interpolation between neighbouring, even species would suggest". This sentence confused me - surely more stable nuclei (ie even A nuclei) would have longer half lives compared to the neighbouring odd -A nuclei? Not the other way round? Is it me misinterpreting this sentence or is my basic knowledge wrong?

Thanks

 

[Bill_K]

I couldn't find much on spontaneous fission, so the following remarks refer to alpha decay.

"The half-life for even-odd emitters is 100 to 1000 times that for an even-even nuclide of the same Z and same energy. The ratio of the actual half-life to that predicted for an even-even nuclide is called the hindrance factor. The pattern for odd-even and odd-odd nuclides is similar."

Why is there a hindrance factor? Variation of the overlap between the nuclear wavefunction of the parent and daughter nuclides is what causes it. The alpha particle is most likely to form from nucleons that are already paired. For an even-even nucleus, an alpha particle can form and slip away without disturbing the other nucleons too much. But if there's an odd nucleon it will typically occupy the highest orbital, and when the alpha particle departs this nucleon must move to a different orbital.

 

[lavster]

thanks for your reply -
are you therefore suggesting that the half life of alpha emission is so low for even-even because it is much easier to form the actual alpha particle and has nothing to do with the binding energy?
Thinking alone the same way, would you say that this can be extended to spontaneous fissiion by again considering the daughter products; from an even nucleus you could get two odd nuclei, which has a lower binding energy and so easier to produce??
Thanks

 

[Bill_K]

There's two effects superposed. The primary relationship between energy vs lifetime for alpha decay is called the Geiger-Nuttall law, usually displayed as a linear plot between ln(t_½) and T_α^-½ where T_α is the kinetic energy of the alpha particle. The fundamental reason behind it is the probability for the alpha particle to penetrate the Coulomb barrier of the nucleus.

Superposed on this is the hindrance factor, which displaces the G-N lines according to whether the nucleus is even-even, even-odd, etc.

 

[lavster]

Cheers :)