NEWS

1
NEWS

• The enrollment cap on P4511 has been raised to
  45. If youre not in, register today!
• Permission numbers will be required for anyone
  registering after today.

2
Fixed Target vs. Colliding Beams

• The CM frame is natural for threshold problems.
  Why not forget the lab and its energy-wasting
  overall motion and collide a speeding particle
  with a speeding particle?

For equal energies E1E2Ebeam, the available
energy for particle creation is 2Ebeam.
? Almost all new major HEP accelerators built
since the 1970s have been colliding beam
machines or have had a colliding beam option.
3
Natural Units
Your unit system is then fully specified with one
more quantity, usually the unit of energy.
Choose for convenience
eV or keV or MeV or GeV or
TeV or mec2 or mpc2 or amu
Thusyour basic units are
4

• Example the energy-momentum invariant

• And a quantity of dimensionality

in natural units becomes
in natural units is equivalent to

• After using NU, convert to real-world units for
  calculation
• Restore missing factors by dimensional analysis
• Use standard conversions

1 fm 10-15 m
5
Example Thomson Scattering ? e- ? ? e- with
E? ltlt mec2
Whats the probability? Whats the cross
section?
in natural units
Compute it
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Mandelstam Variables

• Three independent relativistic invariants that
  together give a complete description of the
  kinematics of this reaction.

(Now in natural units!)
(CM energy)2
(4-momentum transfer)2
(something else)2
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Rutherfords Scattering Experiment
(prototype of nuclear/particle physics
experiments)

• Radioactive source producing beam of ? particles
  (accelerator)
• Gold foil (target)
• ZnS scintillating screen
• Microscope
• Eye
• Brain (online and off-line computers and
  software)

Results

• Most ?s pass through foil undeviated.
• Occasional ? scatters at a large angle even
  backwards.
• Thomsons plum pudding is dead. A nucleus is
  born.

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Rutherford Scattering Classical Treatment
Nonrelativistic v 0.1 c
v?
Point of closest approach
Objective Find the mapping of b into ?.
Projectile charge ze mass m speed v
Scattering angle ?
0
Target charge Ze
Impact parameter b

• Observations
• Trajectory is symmetric about p.o.c.a. (?).
• Central force ? ang. mom. is conserved.

• Warm-up How close does the projectile get?

• For b ? 0, not as close. Ang. mom. w.r.t. 0
  provides centrifugal barrier.

9
Now some Fma
v?
Consider change in the component of linear
momentum along 0D
Mom. change due to component of Coulomb repulsion
force along 0D
10
2T
Next step is to take this b?? relationship for a
Coulomb interaction and turn it into a
description of the scattering process. Need a
quantitative definition of the terminology.