Problem Set 2

Problem 5

Time of Flight

Velocity in terms of momentum:

v =  c*p/Sqrt[p^2 + m^2]

Time (in picoseconds) for 60 cm travel

t  =  60/v /. c ->  .01

Difference in time for two different masses:

deltat = 
      Simplify[(t /. m -> m1) - (t /. m -> m2)]

Solve for difference being 75 psec difference for kaons and pions:

Solve[deltat == 75.  /. {m2 ->  .1396, m1 ->  .4937}, 
      p]

Separation is possible up to 3 GeV.

For kaons and protons:

Solve[deltat == 75.  /. {m2 ->  .4937, m1 ->  .9383}, 
      p]

Spearation is possible up to 5 GeV.

Cerenkov Threshold

Threshold beta:

beta  =  1/1.1

Find momentum corresponding to threshold:

pc  =  
      p /. Solve[beta == p/Sqrt[p^2 + m^2], p][[2]]

Threshold for pions:

pc /. m ->  .1396

Threshold for kaons:

pc /. m ->  .4937

Threshold for protons:

pc /. m ->  .9383