Question

Sketch the Feynman diagram if the proposed decay is possible.

$\overline{n}\to p+e^{-}+{\overline{v}}_e$

Short answer

The proposed decay is not possible

Step-by-step solution

Given data

The proposed reaction is $\overline{n}\to p+e^{-}+{\overline{v}}_e$

Concept of Feynman diagram

A Feynman diagram is used to show the interaction of particles in quantum field theory. The particles are represented by the lines in the diagram.

Step 3:Find whether the charge is conserved

Conservation of charge is shown below:

$$\begin{gathered} \overline{n}\to p+e^{-}+{\overline{v}}_e \\ 0\to (+e)+(-e)+\left(0\right) \\ 0\to 0 \end{gathered}$$

Thus, the charge before the decay and after the decay is equal.

Therefore, the charge is conserved.

Find conservation of mass

Conservation of mass or energy is given below:

$$\begin{gathered} \overline{n}\to p+e^{-}+{\overline{v}}_e \\ 940\text{MeV}/{\text{c}}^2\to \left(938\text{MeV}/{\text{c}}^2\right)+\left(0.511\text{MeV}/{\text{c}}^2\right)+\left(0\right) \\ 940\text{MeV}/{\text{c}}^2\to 938.511\text{MeV}/{\text{c}}^2 \end{gathered}$$

The mass after the decay is $938.511\text{MeV}/{\text{c}}^2$ less than that of the initial mass $940\text{MeV}/{\text{c}}^2$.

Find conservation of lepton number

Conservation of lepton number:

$$\begin{gathered} \overline{n}\to p+e^{-}+{\overline{v}}_e \\ \left(0\right)\to \left(0\right)+(+1)+(-1) \\ \left(0\right)\to \left(0\right) \end{gathered}$$

Thus, the lepton numbers before the decay are equal to the lepton numbers after the decay.

Therefore, the lepton numbers are conserved.

Find conservation of baryon number

The conservation of baryon numbers is shown below:

$$\begin{gathered} \overline{n}\to p+e^{-}+{\overline{v}}_e \\ (-1)\to (+1)+\left(0\right)+\left(0\right) \\ (-1)\to (+1) \end{gathered}$$

The baryon number is not conserved.

Hence, the proposed decay is not possible.