1. p+p p+p p-n p-n p-p p-p Consider the scattering reactions:
The strong force does not discriminate between nucleon or pion charge.
What can we expect for the cross section of these three reactions?

2. But p+p p+p p-n p-n p- + p  p- + p <p-p|L|p-p> = M + M
If we enforce conservation of isospin
we can only connect initial and final states of the same total I, I3
p+p p+p
p-n p-n
| 3/2, 3/2 >
| 3/2, -3/2 >
| I,I3 >
1 ½ ½
-1 -½ ½
But
p- + p  p- + p
½ ½
means combining:
| > | 1/2, 1/2 > = |3/2, -1/2 > |1/2, -1/2 > )
this interaction involves two matrix elements
<p-p|L|p-p> = M M

3. p+ + p p+ + p a. b. p- + p p- + p c. p- + p p0 + n
1,1
½ ,½
elastic scattering
p- + p p- + p
1,-1
½ ,½
but only one of the above can also participate in a
p- + p p0 + n ?
charge exchange process ?
1,-1
½ ,½
1, 0
½ ,-½
This IS observed!
So all strong interactions
not SIMPLY charge independent.
I3 ISOSPIN independence is more general.

4. p+ + p p+ + p a. b. c. p- + p p- + p p- + p p0 + n p+ p p- p p0 n
1,1
½ ,½
elastic scattering
p- + p p- + p
1,-1
½ ,½
p- + p p0 + n
charge exchange process
1,-1
½ ,½
1, 0
½ ,-½
These three interactions involve the ISOSPIN spaces:
p+ p
p- p 1 3 2 3 -
p0 n 2 3 1 3 + 2 2 M½
Recall:
= Mfi
M3/2
Let’s denote:
same by
I3-indep.

5. a. b. c. p+ + p p+ + p p- + p p- + p p- + p p0 + n p+ p p- p p0 n
elastic scattering
p- + p p- + p
p- + p p0 + n
charge exchange process
p+ p M½
p- p 1 3 2 3 -
M3/2
p0 n 2 3 1 3 + a. b. c.
a  M3/2 2
b | M3/2 + M1/2| 2 1 3 2 3
c | M3/ M1/2| 2 2 3 2 3

6. a : b : c = : : p+ + p p+ + p a. a  M3/2 b. c.
b | M3/2 + M1/2| 2
p- + p p- + p 1 3 2 3
p- + p p0 + n
c | M3/ M1/2| 2 2 3 2 3
a : b : c = : : 2
M3/2 1 9
|M3/2 +2M1/2|2 2 9
|M3/2 - M1/2|2
for the combined cross section of both processes
Now if M3/2=M1/2 then +p = -p
total
but also -p0n=

7.  Measured the depletion of pion beam
2H target S1 S2 S3 S4
Measured the depletion of pion beam
repeated with the tank full, empty
repeated with + and  - beam
for KE  195 MeV
(the resonance of the 3/2-spin )
200
300
Total Cross Section sT
(10-27 cm2)
p- + p
p+ + p
gp po p
p0p
180
250
160
200
140
120
150
100
100 80 50 60 40
Photon Beam Energy (MeV) 20
Lab Energy of Pion Beam (MeV)

8. a : b : c = : : a : b + c = : a : b : c = 9 : 1 : 2 M3/2
|M3/2 +2M1/2|2 2 9
|M3/2 - M1/2|2
a : b + c = : 2
M3/2
a : b : c =
9 : 1 : 2

9.  (U) (U) U† U U†H U= H [H ,U]= 0 [H ,U]= 0 [H ,G]= 0
Symmetry implies any transformation  still satisfies
the same Schrödinger equation, same Hamiltonian: 
(U)
(U)
U† U
U†H U= H
means we must demand:
[H ,U]= 0
Which means that the operator U must be
associated with a CONSERVED quantity!
Though U are UNITARY, not necessarily HERMITIAN, but remember:
where the G is Hermitian!
since
you’ve already shown
[H ,U]= 0
[H ,G]= 0
The GENERATOR of any SYMMETRY OPERATION is an
OPERATOR of a CONSERVED OBSERVABLE (quantum number!)

10. Mesons Baryons isospin mass charge pion 139.569 + +1 134.964 0 0
Particle I MeV/c states Q
pion    +1 -1
eta 
rho    +1 -1
omega 
Baryons
Spin-1/2
nucleon p n
+1/2
-1/2
Spin-3/2
delta    
+3/2
+1/2
-1/2
-3/2

11. “hypercharge” or BARYON NUMBER
Q = I3 + ½Y
“hypercharge” or BARYON NUMBER
because =1 for baryons
0 for mesons

12. cloud chamber cosmic ray event
1947 Rochester and Butler
cloud chamber cosmic ray event
of a neutral object decaying into two pions
K0  + +

13. cloud chamber cosmic ray event
Rochester and Butler
cloud chamber cosmic ray event
of a neutral object decaying into two pions
K0  + +
m = MeV
C. F. Powell
photographic emulsion event
K+  + +
m = MeV

14.   p +  -  - p 1950 Carl Anderson (Cal Tech) m=1115.6 MeV
mp= MeV

15. 1952 Brookhaven Cosmotron 1st modern accelerator
artificially creating these particles for study
GeV p synchrotron Lawrence,Berkeley
GeV p synchrotron CERN, Geneva
33-GeV p synchrotron Brookhaven Lab
GeV e synchrotron Cambridge
GeV p synchrotron Argonne Lab
GeV p synchrotron DESY,Germany
GeV e Linac SLAC (Standford)

16. isospin mass charge Spin-0 Pseudoscalar Mesons
Particle I MeV/c states Q
pion    +1 -1
kaon K K
+1/2
-1/2
kaon K K
+1/2
-1/2
eta 
rho    +1 -1
omega 
Spin-1/2 Baryons
nucleon p n
+1/2
-1/2
lambda 
Sigma    +1 -1
Cascade  
+1/2
-1/2

17. Spin-3/2 Baryons isospin mass charge Delta 1232. ++ +2 + +1 0 0
Particle I MeV/c states Q
Delta    
+3/2
+1/2
-1/2
-3/2
Sigma-star    +1 -1
Cascade-star * *
+1/2
-1/2