1968-70 Georges Charpak develops the multiwire proportional chamber 1992 Charpak receives the Nobel...
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![Page 1: 1968-70 Georges Charpak develops the multiwire proportional chamber 1992 Charpak receives the Nobel Prize in Physics for his invention.](https://reader034.fdocuments.us/reader034/viewer/2022051517/5697bfc31a28abf838ca53e7/html5/thumbnails/1.jpg)
1968-70 Georges Charpak develops the multiwire proportional chamber
1992 Charpak receives the Nobel Prize in Physics for his invention
![Page 2: 1968-70 Georges Charpak develops the multiwire proportional chamber 1992 Charpak receives the Nobel Prize in Physics for his invention.](https://reader034.fdocuments.us/reader034/viewer/2022051517/5697bfc31a28abf838ca53e7/html5/thumbnails/2.jpg)
![Page 3: 1968-70 Georges Charpak develops the multiwire proportional chamber 1992 Charpak receives the Nobel Prize in Physics for his invention.](https://reader034.fdocuments.us/reader034/viewer/2022051517/5697bfc31a28abf838ca53e7/html5/thumbnails/3.jpg)
100 MHz
50 MHz 0. 0.4 0.8 1.2 1.6 2.0 2.4 2.8
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
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20 m dia 2 mm spacing
argon-isobutane
spatial resolutions < 1mm possible
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![Page 6: 1968-70 Georges Charpak develops the multiwire proportional chamber 1992 Charpak receives the Nobel Prize in Physics for his invention.](https://reader034.fdocuments.us/reader034/viewer/2022051517/5697bfc31a28abf838ca53e7/html5/thumbnails/6.jpg)
![Page 7: 1968-70 Georges Charpak develops the multiwire proportional chamber 1992 Charpak receives the Nobel Prize in Physics for his invention.](https://reader034.fdocuments.us/reader034/viewer/2022051517/5697bfc31a28abf838ca53e7/html5/thumbnails/7.jpg)
DO
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![Page 9: 1968-70 Georges Charpak develops the multiwire proportional chamber 1992 Charpak receives the Nobel Prize in Physics for his invention.](https://reader034.fdocuments.us/reader034/viewer/2022051517/5697bfc31a28abf838ca53e7/html5/thumbnails/9.jpg)
DO
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DØ 5500 tons120,000 digitized readout channels
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– 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 ScintillatorForward Mini-drift chambers
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![Page 13: 1968-70 Georges Charpak develops the multiwire proportional chamber 1992 Charpak receives the Nobel Prize in Physics for his invention.](https://reader034.fdocuments.us/reader034/viewer/2022051517/5697bfc31a28abf838ca53e7/html5/thumbnails/13.jpg)
![Page 14: 1968-70 Georges Charpak develops the multiwire proportional chamber 1992 Charpak receives the Nobel Prize in Physics for his invention.](https://reader034.fdocuments.us/reader034/viewer/2022051517/5697bfc31a28abf838ca53e7/html5/thumbnails/14.jpg)
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The Detector in various stages of assembly
5500 tons
120,000 digitized readout channels
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Fermilab, Batavia, Illinois
CERN, Geneva, Switzerland
Protons
Anti-protons
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/1 rpii
ieV
)r(
For “free” particles (unbounded in the “continuum”)
/1 rpif e
V)r(
f
the solutions to Schrödinger’s equation
with no potential
Sorry!…this V is a volume appearingfor normalization
rkiie
rkie
f
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3* )(),( drrVkkF
V
iffi
iffi
M
3/)( )( drrVe irppi
fi
3)( )( drrVe irkki
fi
3)()( drrVeqF irqi
q q
pi
pi q = ki kf =(pi-pf )/ħ
momentum transferthe momentumgiven up (lost)
by the scatteredparticle
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00 ),( tdtttU
tttdt
di I )(H
We’ve found (your homework!) the time evolution ofa state from some initial (time, t0) unperturbed state
can in principal be described using:
complete commuting set of observables, e.g. En, 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 | t0.
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tttttUt ),( 0000
give the probability amplitudes (which we’ll relate to the rates)
of the transitions | t0 |″ t during the interval ( t0, 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 !
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00 ),( tdtttU HI(t) HI(t)Operator on both sides, by the Hamiltonian of the perturbing interaction:
Then integrate over (t0,t)
00 ),( tdtttU HI(t′) HI(t′)t0
t
dt′t′ t0
tdt′t′
tdtdttd
di
0
t0
tdt′
0
0
tdtdi t
t
dttti 00
0
td
td
tdtdi
dt′dt′
t'
t0
t
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dtttitdttUtt
t 000I ) ()(H0
dttidtti 000
I 0 idtti
Which notice has lead us to an iterative equation for U
IU) (U)(H 0I0
iitdtttt
t
I
U U I
U(t to) = tdttti t
t ) (U)(H1 0I
0U
U
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If at time t0=0 the system is in a definite energy eigenstate of H0
(intitial state is, for example, a well-defined beam)
Ho|En,t0> = En |En,to >then to first order
U(t to)|En,t0> = 0)(10
tEtdti
n
t
t HI
and the transition probability2
000 00
2
0 )( tdtEtHtEi
EUEt
Ifff
2
000 02)(
1tdtEtHtE
t
If ( for f 0 )
Note: probability to remain unchanged = 1 – P !!
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recall: 00 )()( )(0
tHitHi etVeUtVUtH (homework!)
H0†=H0 (Hermitian!)
where each operator acts separately on:
00
0
0
0
tEe
etE
itH
tHif
2))(/(
000 02
2
00)(
1tdetEtVtEEUE tEEit
fff
†
So:
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If we simplify the action (as we do impulse in momentum problems)to an average, effective potential V(t) during its action from (t0,t)
≈factor out
2
0
/
E
i
tt
t
tEie
2/
2
2
1 E
Etie
tEE
EE
tEVtEEUE f
f
efff
f 0
20
2
0002
0 cos-1 )(
2
0
))(/(2
0002
2
00
1tdetEVtEEUE
t tEEieffff
f
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tEE
EE
tEVtEEUE f
f
efff
f 0
20
2
0002
0 cos-1 )(
2
sin 4 02 tEE f
E=2h/t
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The probability of a transition to a particular final state |Ef t>
2
sin
||4 2
2
2tEE
EE
EVEP if
if
if
The total transition probability:
2
sin
||4 2
2
2tEE
EE
EVEP iN
iN
iN
Ntotal
If < EN|V|Ei > ~ constant over the narrowly allowed E
N iN
iN
iNtotalEE
tEE
EVEP 2
2
2 2sin
||4
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for scattering, the final state particles are free, & actually
in the continuum
n=1
n=2
n=3
n=
N
2
iN
iN2
2
iNtotal EE2
tEEsin
E|V|E4P
2
i
i2
2
itotal E)N(E2
tE)N(Esin
dN E|V|)N(E4P
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With the change of variables:
2
22
/2
sin2||4
tx
xdx
tdE
dNEVEP iNtotal
2/ )( tENEx i dNdN
dEtdx
2
dx
x
xt
dE
dNEVEP iNtotal 2
22 sin
2||4
2
i
i2
2
itotal E)N(E2
tE)N(Esin
dN E|V|)N(E4P
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Notice the total transition probability t
dE
dNEVE
tP iNtotal
2||
2
and the transition rate
dE
dNEVEtPW iNtotal
2||2
/
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n=1
n=2
n=3
n=
E
dN/dE
Does the densityof states varythrough thecontinuum?
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vx
vy
vzClassically, for free particlesE = ½ mv2 = ½ m(vx
2 + vy2 + vz
2 )
Notice for any fixed E, m this definesa 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 = 4v2dv