Question

Find the threshold energy of gamma quantum required to form
(a) an electron-positron pair in the field of a stationary electron,
(b) a pair of pions of opposite signs in the field of a stationary proton.

Answer 1

The fromula of problem 3.02 gives
`E_(th)=((Sigmam_(i))^(2)-M^(2))/(2M)c^(2)`
when the projectile is a photon
(a) For `gamma+e^(-)rarre^(-)+e^(-)+e^(+)`
`E_(th)=(8m_(e )^(2)-m_(e )^(2))/(2m_(e ))c^(2)= 4m_(e )c^(2)= 2.04MeV`
(b) For `gamma+prarrp+pi^(+)pi^(-)`
`E_(th)=((M_(p)+2m_(pi))^(2)-M_(P)^(2))/(2M_(p))=(4m_(pi)M_(p)+4m_(pi)^(2))/(2M_(P))c^(2)=2(m_(x)+(m_(x)^(2))/(M_(P)))c^(2)= 320.8MeV`