1. 1968-70 Georges Charpak develops the multiwire proportional chamber 1992 Charpak receives the Nobel Prize in Physics for his invention

3. 100 MHz 50 MHz 0. 0.4 0.8 1.2 1.6 2.0 2.4 2.8 800 600 400 200 0 1000 800 600 400 200 0

4. 20  m dia 2 mm spacing argon-isobutane spatial resolutions < 1mm possible

7. DO

10. DØ 5500 tons 120,000 digitized readout channels

11. – 2T super conducting solenoid – disk/barrel silicon detector – 8 layers of scintillating fiber tracker – preshower detectors Shielding New Solenoid & Tracking: Silicon, SciFi, Preshowers + New Electronics, Trigger, DAQ Forward Scintillator Forward Mini- drift chambers

16. The Detector in various stages of assembly 5500 tons 120,000 digitized readout channels

21. Fermilab, Batavia, Illinois CERN, Geneva, Switzerland Protons Anti-protons

22. For “free” particles (unbounded in the “continuum”) the solutions to Schrödinger’s equation with no potential Sorry!…this V is a volume appearing for normalization

23. q q pipi pipi q = k i  k f =(p i -p f )/ħ momentum transfer the momentum given up (lost) by the scattered particle

24. We’ve found (your homework!) the time evolution of a state from some initial (time, t 0 ) unperturbed state can in principal be described using: complete commuting set of observables, e.g. E n, etc… Where the |  t  are eigenstates satisfying Schrödingers equation: Since the set is “complete” we can even express the final state of a system in terms of the complete representation of the initial, unperturbed eigenstates |  t 0 .

25. give the probability amplitudes (which we’ll relate to the rates) of the transitions |  t 0  |  ″ t  during the interval ( t 0, t ). You’ve also shown the “matrix elements” of this operator (the “overlap” of initial and potential “final” states) to use this idea we need an expression representing U !

26. HI(t)HI(t)HI(t)HI(t) Operator on both sides, by the Hamiltonian of the perturbing interaction: Then integrate over (t 0,t) HI(t′)HI(t′) HI(t′)HI(t′)  t0t0 t dt′ t′t′  t0t0 t t′t′  t0t0 t t't'  t 0 t

27. Which notice has lead us to an iterative equation for U I U U I U(t t o ) =U U

28. If at time t 0 =0 the system is in a definite energy eigenstate of H 0 ( intitial state is, for example, a well-defined beam ) H o |E n,t 0 > = E n |E n,t o > then to first order U(t t o )|E n,t 0 > = and the transition probability ( for f  0 ) Note: probability to remain unchanged = 1 – P !!

29. recall: ( homework !) H 0 † = H 0 (Hermitian!) where each operator acts separately on: † So:

30. If we simplify the action (as we do impulse in momentum problems) to an average, effective potential V(t) during its action from (t 0,t) ≈ factor out

31.  E =2 h /  t

32. The probability of a transition to a particular final state |E f t> The total transition probability: If ~ constant over the narrowly allowed  E

33. for scattering, the final state particles are free, & actually in the continuum n=1 n=2 n=3 n=n= 

34. With the change of variables:  

35. Notice the total transition probability  t and the transition rate

36. n=1 n=2 n=3 n=n= E dN/dE Does the density of states vary through the continuum?

37. vxvx vyvy vzvz Classically, for free particles E = ½ mv 2 = ½ m(v x 2 + v y 2 + v z 2 ) Notice for any fixed E, m this defines a sphere of velocity points all which give the same kinetic energy. The number of “states” accessible by that energy are within the infinitesimal volume (a shell a thickness dv on that sphere). dV = 4  v 2 dv