Re: Pair production derivation

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Mon, 29 Apr 2002, Ivan Rouse wrote:

> ... derive an equation for the minimum photon energy, in the
> presence of a heavy particle, to create an electron positron
> pair.  The derivation should include consideration of both
> conservation of momentum and energy and the result should
> include the mass of the heavy nucleus.

Let the incident photon have energy E_min.  At the threshhold for
pair production, the products (m + 2m_e) are at rest in the CM
frame and, therefore, move together with momentum p in the lab
frame.

So, in units where c = 1, we have:

Conservaton of momentum =>   E_min = p

Conservation of energy  =>   E_min + m = sqrt[p^2 + (m+2m_e)^2]

Eliminate p and solve for E_min:

     E_min = 2m_e(1 + m_e/m)

This all makes sense.  For infinite m, we get the standard result,
as m decreases, the threshhold energy has to increase.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm