Quantum Physics

990 Chapter 30 Nuclear Energy and Elementary ParticlesCount the baryons on the right:There are three baryons and one antibaryon, so1 1 1 (1) 2.Remarkenergy.Baryon number is conserved in this reaction, so it can occur, provided the incoming proton has sufficientExercise 30.4Can the following reaction occur, based on the law of conservation of baryon number?p n : p p pAnswerNo. (Show this by computing the baryon number on both sides and finding that they’re not equal.)Conservation of lepton number Neutron decay Lepton NumberThere are three conservation laws involving lepton numbers, one for each varietyof lepton. The law of conservation of electron-lepton number states that the sumof the electron-lepton numbers before a reaction or decay must equal the sum ofthe electron-lepton numbers after the reaction or decay. The electron and theelectron neutrino are assigned a positive electron-lepton number L e 1, theantileptons e and e are assigned the electron-lepton number L e 1, and allother particles have L e 0. For example, consider neutron decay:Before the decay, the electron-lepton number is L e 0; after the decay, it is0 1 (1) 0, so the electron-lepton number is conserved. It’s important to recognizethat the baryon number must also be conserved. This can easily be seen by notingthat before the decay B 1, whereas after the decay B 1 0 0 1.Similarly, when a decay involves muons, the muon-lepton number L is conserved.The and the are assigned L 1, the antimuons and are assignedL 1, and all other particles have L 0. Finally, the tau-lepton number L isconserved, and similar assignments can be made for the lepton and its neutrino.n : p e e EXAMPLE 30.5 Checking Lepton NumbersGoal Use conservation of lepton number to determine whether a given process is possible.ProblemStrategyDetermine which of the following decay schemes can occur on the basis of conservation of lepton number.: e : e Count the leptons on either side and see if the numbers are equal. e(1)(2)SolutionBecause decay 1 involves both a muon and an electron, L and L e must both be conserved. Before the decay, L 1and L e 0. After the decay, L 0 0 1 1 and L e 1 1 0 0. Both lepton numbers are conserved,and on this basis, the decay mode is possible.Before decay 2 occurs, L 0 and L e 0. After the decay, L 1 1 0 0, but L e 1. This decay isn’tpossible because the electron-lepton number is not conserved.Exercise 30.5Determine whether the decay : e ecan occur.AnswerNo. (Show this by computing muon-lepton numbers on both sides and showing they’re not equal.)