【正文】 chard Kass Parity Example: determination of the parity of the p using pd?nn. For this reaction we know many things: a) sp=0, sn=1/2, sd=1, orbital angular momentum Ld=0, Jd=1 b) We know (from experiment) that the p is captured by the d in an swave state. Thus the total angular momentum of the initial state is just that of the d (J=1). c) The isospin of the nn system is 1 since d is an isosinglet and the p has I=|1,1 note: a |1,1 is symmetric under the interchange of particles. (see below) d) The final state contains two identical fermions and therefore by the Pauli Principle the wavefunction must be antisymmetric under the exchange of the two neutrons. Let’s use these facts to pin down the intrinsic parity of the p. i) Assume the total spin of the nn system =0. Then the spin part of the wavefunction is antisymmetric: |0,0 = (2)1/2[|1/2,1/2|1/21/2|1/2,1/2|1/2,1/2] To get a totally antisymmetric wavefunction L must be even (0,2,4…) Cannot conserve momentum (J=1) with these conditions! ii) Assume the total spin of the nn system =1. Then the spin part of the wavefunction is symmetric: |1,1 = |1/2,1/2|1/2,1/2 |1,0 = (2)1/2[|1/2,1/2|1/21/2+|1/2,1/2|1/2,1/2] |1,1 = |1/2,1/2|1/2,1/2 To get a totally antisymmetric wavefunction L must be odd (1, 3, 5…) L=1 consistent with angular momentum conservation: nn has s=1, L=1, J=1? 3P1 The parity of the final state is: nnnn(1)L= (+)(+)(1)1= The parity of the initial state is: npnd(1)L= np(+)(1)0 = np Parity conservation gives: nnnn(1)L = npnd(1)L ? np = Spring 2022 L6 Richard Kass Parity There is other experimental evidence that the parity of the p is : the reaction pd?nn p0 is not observed the polarization of g’s from p0?gg Some use “spinparity” buzz words: buzzword spin parity particle pseudoscalar 0 p, k scalar 0 + higgs (none observed) vector 1 g, r, w, f, y, U pseudovector 1 + A1 (axial vector) How well is parity conserved? Very well in strong and electromagic interactions (1013) not at all in the weak interaction! The qt puzzle and the downfall of parity in the weak interaction In the mid1950’s it was noticed that there were 2 charged particles that had (experimentally) consistent masses, lifetimes and spin = 0, but very different weak decay modes: q+? p+ p0 t+? p+ p p+ The parity of q+ = + while the parity of t+ = Some physicists said the q+ and t+ were different particles, and parity was conserved. Lee and Yang said they were the same particle but parity was not conserved in weak interaction! Lee and Yang win Nobel Prize when parity violation was discovered. Note: q+/t+ is now known as the K+. Mamp。 Spring 2022 L6 Richard Kass Parity Let us examine the parity operator (P) and its eigenvalues. The parity opera