Introductory Nuclear Physics

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PHY431 Lecture 7 15 3/24/2000 8.10.1. The Experiment by C.S. Wu et al. An elegant experiment was devised by C.S. Wu and collaborators from the National Bureau of Stan- dards, following the suggestion in Lee and Yang’s article to use polarized 60 Co: “A relatively simple possibility is to measure the angular distribution of the electrons coming from β decays of oriented nuclei. If θ is the angle between the orientation of the parent nucleus and the momentum of the electron, an asymmetry of distribution between and 180 °− constitutes an unequivocal proof that parity in not conserved in decay.” This can be easily visualized as follows. Denoting the 60Co spin vector as J , and the electron momen- tum as p e , parity transformation on J p e (proportional to cos ) would give J p e cos = cos( π−θ ). Parity invariance, therefore, requires the angular distribution to be symmetric around =90 ° ! Looking at a more visual representation: 11 60 60 22 Co( 6 ) Ni( 5 ) ( ) ( ) e JJ e s s ν ⇑⇑ =→ = += The radioactive element 60 Co was polarized in a very strong magnetic field and “frozen” in by cooling down to 0.02 K. Cobalt is a strongly paramagnetic ele- ment, and therefore even a relatively weak external magnetic field aligns the atomic magnetic fields (from the d -shell electrons) efficiently, leading to a much stronger internal mag- netic field at the site of the cobalt nucleus. Because the nuclear magne- ton is much smaller than the Bohr magneton, even for a large magnetic field (> 50 T) the temperature needs to be very low in order to populate the lowest nuclear energy level (which has its spin aligned with the field) preferentially over the other two (higher lying) magnetic sublevels: the level separa- tion is µ N B =10 -8 eV/T, which has to be made large compared to the Bolzmann energy kT =3.18 × 10 -6 eV/K! 60 Co ( J =5) beta-decays to an excited J =4 state 60 Ni* with emission of an electron and an anti-neutrino. Because one unit of angular momentum is car- J 60 Co P p e p J 60 Co p e p A B J 60 Co p e p C mirror M R z ( π )
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PHY431 Lecture 7 16 3/24/2000 ried off by the spin-½ leptons, the daughter nucleus and both leptons must all have a spin in the same direction as the parent 60 Co. Under the Parity operation, the spins do not flip sign, while the momenta do; see the Figure above. Also shown (top to bottom) is the Mirror Reflection transformation, which equals the parity transfor- mation modulo a simple rotation. Parity invariance requires all situations to be equally likely to occur, e.g. right-handed electrons and left-handed electrons should be equally likely, and so should right- handed anti-neutrinos and left-handed anti-neutrinos. Experimental evidence is quite different: situa- tion A is found very much less frequent than situation B! All is consistent with the statement that “Par- ity is maximally broken” in weak interactions, i.e. situation A is completely suppressed in the limit θ 0. Another way of viewing this is the statement that weak interactions involve only left-handed
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Lecture 07 - PHY431 Lecture 7 15 3/24/2000 8.10.1. The...

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