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Unit-4
Gell-Mann–Nishijima Scheme
Gell-Mann–Nishijima Scheme
Charge relation and classification of hadrons
Introduction
The Gell-Mann–Nishijima scheme relates the electric charge of a hadron
to its internal quantum numbers like isospin and hypercharge.
It was very important before the quark model.
Q = I3 + Y/2
Where:
- Q = Electric charge
- I3 = Third component of isospin
- Y = Hypercharge
Y = B + S
- B = Baryon number
- S = Strangeness
Application to Baryons
| Particle |
B |
S |
Y |
I3 |
Q |
| Proton (p) |
1 |
0 |
1 |
+1/2 |
+1 |
| Neutron (n) |
1 |
0 |
1 |
−1/2 |
0 |
| Λ0 |
1 |
−1 |
0 |
0 |
0 |
Worked Examples
Proton
Q = 1/2 + 1/2 = 1
Neutron
Q = −1/2 + 1/2 = 0
Lambda
Q = 0 + 0 = 0
Application to Mesons
For mesons, B = 0
Y = S
| Meson |
S |
Y |
I3 |
Q |
| π+ |
0 |
0 |
+1 |
+1 |
| π0 |
0 |
0 |
0 |
0 |
| K+ |
+1 |
+1 |
+1/2 |
+1 |
Summary
✔ Q = I3 + Y/2
✔ Y = B + S
✔ Classifies hadrons
✔ Foundation of SU(3)