Chapter 32, Problem 6Q

To determine

Why is it that a neutron decays via the weak interaction even though the neutron and one of its decay products (proton)are strongly interacting?

Answer to Problem 6Q

Solution:

The reason is because neutron decay occurs in the weak force range. That is, 10^-18 m. Strong force interacts in a range of 10^-15 m

Explanation of Solution

Introduction:

The neutron decay scheme can be shown below:

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

Or, in terms of Feynman’s diagram we have:

According to the Feynman diagram given above, neutron decay occurs through the $W^{-}$ boson. This boson interacts with a range of 0.1% of the diameter of the proton, that is; in the range of 10^-18m, in this range the interactions are dominated by the weak force changing the identity of a quark down by a quark up. Although, the intensity of the strong force is greater than the weak force, but; its range is on the order of 10^-15 m, which is to say approximately the average diameter of a nucleus.