Orbital Electron Capture : Educating Physics

The three types of beta emission are;

Beta-minus ( $\beta^{-}$ ) decay
Beta-plus ( $\beta^{-}$ ) decay – otherwise known as positron emission
Orbital electron capture

$\beta^{-}$ and $\beta^{+}$ emission are discussed here. Orbital electron capture is a process that can occur when the ratio of neutrons to protons is low.

In this process, instead of a proton being converted into a neutron with the emission of a positron (and electron-neutrino), a proton rich nucleus of an electrically neutral atom absorbs an electron from one of the inner electron shells (or energy levels). This process there converts a proton into a neutron;

$^{0}_{-1}e + \ ^{1}_{1}p \ \ \rightarrow \ \ ^{1}_{0}n$

As shown on the page focusing on $\beta^{-}$ and $\beta^{+}$ , nuclear equations need to ensure charge, baryon number and lepton number are conserved, so first lets write a quark equation;

$^{0}_{-1}e + \ ^{1}_{1}p \ \ \rightarrow \ \ ^{1}_{0}n$
$^{0}_{-1}e + uud \ \ \rightarrow \ \ ^udd$
$^{0}_{-1}e + u \ \ \rightarrow \ \ d$

Charge:

$^{0}_{-1}e + u \ \ \rightarrow \ \ d$
$-1 + \frac{2}{3} \ \ \rightarrow \ \ -\frac{1}{3}$
$-\frac{1}{3} \ \ \rightarrow \ \ -\frac{1}{3}$

Charge is conserved. ✓

Baryon number:

$^{0}_{-1}e + u \ \ \rightarrow \ \ d$
$0 + \frac{1}{3} \ \ \rightarrow \ \ \frac{1}{3}$
$\frac{1}{3} \ \ \rightarrow \ \ \frac{1}{3}$

Baryon number is conserved. ✓

Lepton number:

$^{0}_{-1}e + u \ \ \rightarrow \ \ d$
$+1 + 0 \ \ \rightarrow \ \ + 0$
$+1 \ \ \rightarrow \ \ 0$

Lepton number is not conserved. ✓

So an additional particle must be emitted that does not affect the charge or the baryon number but does change the lepton number. What particle has no charge, no baryon number and a lepton number of -1?