# Beta decay equations in shorthand

I'm not sure what the correct notation for $$\beta^{+}$$ decay is when using the shorthand notation.

For the reaction $$a+X\rightarrow b+Y$$ it would be $$X(a,b)Y$$. However, for $$\beta^{+}$$ decay, $$X\rightarrow Y+e^{+}+\nu_{e}$$ there is no reacting "$$a$$" particle and two "$$b$$" daughter particles.

Would the shorthand notation be $$X(a+b)Y?$$ If so, is it taken for granted from common knowledge that this is $$\beta^{+}$$ decay, and so these must be the products (as there is no comma to place them either as reacting or product particles)? Or is there no shorthand notation for such a reaction?

The notation (incoming, outgoing) is for scattering processes, not for spontaneous decays.

The scattering notation includes hooks for the detected final state, e.g., deep inelastic electron scattering off a target proton is:

$$e(p,e')X$$

indicating and electron ($$e$$) scatters off a proton ($$p$$) and is detected ($$e'$$) with kinematics such that proton breaks up ($$X$$).

Likewise, photo disintegration of the deuteron (were the final state proton has more energy than the beam, ensuring there is only an undetected neutron) is written:

$$d(\gamma,p)n$$

If this notation were applied to beta decay (it's not), it would be:

$$(n,e^-)pX$$

where modern understanding allows us to fill in $$X$$:

$$(n,e^-)p\bar{\nu}_e$$

The $$n$$ is inside the parenthesis because the notation is generally used in fixed target experiments:

$${beam}({target}, { detected}) { undetected}$$

• Typo: it's usually "target(beam, detected)undetected". I have never see any variation of this notation used to describe a spontaneous decay, even for a beam experiment; do you have a reference to a publication that does so?
– rob
Commented Oct 22, 2021 at 18:05