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**Unformatted text preview: **or a LH parBcle state to a LH anBparBcle state etc. 9 Isospin in Strong InteracBons (Review) We learned earlier that the strong interacBons of nucleons (protons and neutrons) do not depend on the nucleon species (so pp, np, and nn experience the same strong interacBons). ⎛ p⎞
We wrote a two component object, the nucleon as N = ⎟ . ⎜
⎝n⎠ More formally, we can represent the isospin wavefuncBon of a nucleon as a linear combinaBon of the two states: ⎛1⎞
χ1 = ⎜ ⎟ = p
⎝0⎠
⎛ 0⎞
χ2 = ⎜ ⎟ = n
⎝ 1⎠ isospin “up” isospin “down” And we can introduce the isospin operator τ which has components 1 ⎛0 1⎞
τ1 = ⎜
⎟
2 ⎝1 0⎠ 1 ⎛ 0 −i⎞
τ2 = ⎜
⎟
2⎝i 0 ⎠ 1 ⎛1 0 ⎞
τ3 = ⎜
⎟
2 ⎝ 0 −1⎠ Except for factors of ½ these are the Pauli spin matrices describing spin ½ parBcles. 10 In fact, the Pauli spin matrices describe any system that has two possible states. Note that 1 ⎛ 1 0 ⎞⎛ 1⎞ 1 ⎛ 1⎞ 1
τ3 p = ⎜
⎟⎜ ⎟ = ⎜ ⎟ = p
2 ⎝ 0 −1⎠⎝ 0⎠ 2 ⎝ 0⎠ 2 1 ⎛1 0 ⎞⎛0⎞
1 ⎛0⎞
1
τ3 n = ⎜
=− ⎜ ⎟=− n
⎟⎜ ⎟
2 ⎝0 −1⎠⎝1⎠
2 ⎝1⎠
2 τ...

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