n p + e- + e - e- + e + Ne* Ne + N C + e + + e The transition rate, W (the “Golden Rule”) of initialfinal is also invoked to understand ab+c (+ ) decays Some observed decays n p + e- + e - e- + e + Fundamental particle decays Ne* Ne + N C + e + + e Pu U + 20 10 20 10 13 7 13 6 Nuclear decays 236 94 232 92 How do you calculate an “overlap” between ???
J conserved. Any decay that’s possible will happen! It almost seems a self-evident statement: Any decay that’s possible will happen! What makes it possible? What sort of conditions must be satisfied? Total charge q conserved. J conserved.
Nuclear Coulomb potential potential Tunneling finite (but small) probability of being found outside the nucleus at any time always some probability of a piece of the nucleus escaping the nuclear potential Nuclear potential Coulomb potential with a STATIC POTENTIAL this probability is CONSTANT!
must be expressed as a probability per unit time probability of decaying (at any time - now or later) = constant ???? What’s this mean equally likely at any instant ???? must be expressed as a probability per unit time If we observe one, isolated nucleus it is equally likely it decays this moment t as any other moment t (even years from now) It either decays or it doesn’t.
Suppose a given particle has a 0.01 probability of decaying in any given sec. Does this mean if we wait 100 sec it will definitely have decayed? If we observe a large sample N of such particles, within 1 sec how many can we expect to have decayed? Even a tiny speck of material can include well over trillions and trillions of atoms!
# decays N t -constant this is what the means! (counted by a geiger counter) the size of the sample studied t time interval of the measurement each decay represents a loss in the original number of radioactive particles fraction of particles lost Note: for 1 particle this must be interpreted as the probability of decaying. This argues that: -constant this is what the means!