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While the nuclide $^{148}\mathrm{Gd}$ is only known to undergo $\alpha$ decay, with a half-life of $86.9$ years, I noticed that it has higher energy than its isobar $^{148}\mathrm{Eu}$: $m_{^{148}\mathrm{Gd}}=147.9181214(16)\,\mathrm{amu}$, $m_{^{148}\mathrm{Eu}}=147.918086(11)\,\mathrm{amu}$, which means that $$ ^{148}\mathrm{Gd}+e^-\to\,^{148}\mathrm{Eu}+\nu_e $$ is energetically possible, with $Q_{\mathrm{EC}}$ lying between $21.2\,\mathrm{keV}$ and $44.7\,\mathrm{keV}$. Such an energetically allowed but unobserved $\beta$ decay mode occurs also for $^{222}\mathrm{Rn}$, but the latter only has an $\alpha$ half-life of $3.8$ days, so seeing $^{148}\mathrm{Gd}$ undergoing electron capture should have been easier.

So I was wondering: Have experiments been carried out to try to observe this decay mode? Is there any experimentally known lower limit on the EC half-life?

If not, could there be any prediction based on the value of $Q_{\mathrm{EC}}$ on the half-life of electron capture of $^{148}\mathrm{Gd}$ that would help me to get a picture of the order to magnitude of the EC half-life? In other words, would you expect the half-life to be too long to make the decay mode observable, compared with its short $\alpha$ half-life?

Thank you in advance for any information/references/suggestions.

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The ground state of $^{148}\mathrm{Gd}$ is a $0^{+}$ state while the ground state of $^{148}\mathrm{Eu}$ is a $5^{-}$ state.

The transition from $^{148}\mathrm{Gd}$ to $^{148}\mathrm{Eu}$ involves both a change in parity $\Delta\pi = 1$ and a change in angular momentum of $\Delta J = 5$. Therefore, this decay is a fifth-order forbidden decay with a parity change. The matrix elements for such transitions are significantly suppressed, making the probability of observing this decay practically zero.

Even when considering decays to higher excited states of $^{148}\mathrm{Eu}$, such as the second excited state at $6^{-}$, the third at $7^{-}$, and so on, does not alleviate the situation due to the increasing order of forbiddenness and the associated suppression of the decay probability.

A list of levels for $^{148}\mathrm{Gd}$ can be found here and a list of levels for $^{148}\mathrm{Eu}$ can be found here.

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    $\begingroup$ Thanks for the explanation! $\endgroup$ Commented Mar 3 at 19:25

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