Pair Production Pair Production

Here a photon passes by a nucleus and converts to a particle anti particle pair.

Virtual particlesVirtual particles A system particles that don’t have enough A system particles that don’t have enough

energy to exist are virtual. energy to exist are virtual. How can a particle exist without energy?How can a particle exist without energy? A system can be in a state of higher energy A system can be in a state of higher energy

without violating a law of physicswithout violating a law of physics As long as it “de-excites” to a lower state within As long as it “de-excites” to a lower state within

a very small time interval. a very small time interval. The same relationship is true for momentum and The same relationship is true for momentum and

space. space. These are known as “Heisenberg’s uncertainty These are known as “Heisenberg’s uncertainty

principles. principles.

So what if a particle “decayed into So what if a particle “decayed into two similar mass particles? two similar mass particles?

So what if a particle “decayed into So what if a particle “decayed into two similar mass particles? two similar mass particles?

Momentum must be conserved, Momentum must be conserved, So pSo pii = p = pff

Also EAlso Eii = E = Eff

But if the new particles have mass, there But if the new particles have mass, there could be a problem: could be a problem:

m1

m2

m3

EE22=(pc)=(pc)22 + (mc + (mc22))

If PIf P11 = (p = (p22 + p + p33) = p ) = p

EE11 = (E = (E22 + E + E33) ?) ?

EE1122

= = (pc)(pc)22 + (m + (m11cc22))22

(E(E22 + E + E33))22 = (pc) = (pc)22 + ((m + ((m2 2 +m+m33)c)c22))22

So ESo E11 = (E = (E22 + E + E33) if m) if m1 1 = m= m22 + m + m33

But in pair production m1 = 0 photon, and m2 and m3 have mass! But in pair production m1 = 0 photon, and m2 and m3 have mass!

m1

m2

m3

p1

p2

p3

EE22=(pc)=(pc)22 + (mc + (mc22))22

If PIf P11 = (p = (p22 + p + p33) = p ) = p

Let (ELet (E22 + E + E33)-E)-E11 = = E E

E E t t > > h/2h/2

So So E can be greater than zero as long as E can be greater than zero as long as

The particles exist for less time than The particles exist for less time than t t < < h/(2h/(2E)E)

m1

m2

m3

p1

p2

p3

The virtual particles must The virtual particles must recombine recombine

You would never know it happens

….unless another particle “interferes” by changing the momentum and energy of the system!