# Electron capture and heavy nuclei

Hi, is it true that the heavy atoms decaying only by electron capture should have globally a half-life shorter than ligher nuclei (decaying also only by electron capture)? This assumption comes from the fact heavy atoms have inner electron "closer" to their nucleus than the lighter ones and so a probability of finding electron inside the nucleus higher than for the ligher atoms (because their inner electrons are "further" from the nucleus).

If this is true, why is it not what we observe:

On this picture, I plotted the half-life of all the nuclei decaying only by electron capture as a function of their atomic number Z. Data come from NNDC. I just plotted naively th whole data so maybe there is a smarter way to do but basically I expected to see a general decrease of the half-life with respect to the Z. However, it looks rather flat.
Do you have any explanation?

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For such a global trend, all other things would have to be equal. They are not.

You introduce a bias by the requirement of only electron capture, for example. For small atoms, this means beta+ decays are missing between ~0 and ~1 MeV to be available. For heavier atoms this value is lower - electron capture happens mainly from the innermost shells where the electrons have a lower energy. You might see some trend if you make categories for the neutrino energy.

Also, how exactly do you get the data points? The whole 83+ group can decay via alpha decay, for example. Did you use the partial widths for the points?

Oh yeah, you are right. So if I understood correctly, if nuclei would decay only by electron capture, lifetime of heavy nuclei should be smaller than the one of the lighter nuclei? Right? And still if I understood correctly, it is possible to observe a trend if we plot data as a function of Z because other decay process play a role.

I will try to plot the same figure including all the nuclei decaying by electron capture (even if they decay also by other processes), just to see what happen.

About the data, I do not remember how did I download them but basically I got a text file where I extract lifetime of nuclei decaying by electron capture. For nuclei with Z>=83, as I said I extracted only nuclei decaying only by electron capture. Most of the Z>=83 nuclei decay by alpha emission but few of them, such as 232Np are know, for now, to decay only by electron capture. However, I did not consider only nuclei decaying only by electron capture (probably because my database was not up-to-date) because for example I included 251Fm that decays by alpha emission with a probability of 1.80% (the rest by electron capture)

DIT:I found back where I got the data. They come from this Web page. Select the decay mode, a range in Z, and check "Formatted File".

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