Hi everybody, I was studyng a photon disintegrating in one electron and one positron in the presence of a heavy atomic core; I want to find the final momentum of the atomic core
Conservation of energy: Eγ=2me+Sqrt(Mn2+Pn2)
Conservation of momentum Pγ=Pn
Relation between the energy and momentum of a maseless particle Pγ=Eγ
The Attempt at a Solution
From the conservation of energy: (Eγ-2me)2=Mn2+Pn2; and since Pn=Eγ, operating after developing (Eγ-2me)2, I obtain Pn=4me-(Mn2/me). If I introduce the values in units of atomic mass, I obtain a negative value of Pn, the momentum of the atomic core.
Can anyone please tell me what am I doing wrong?