Why do some isotopes decay and others don’t? Generally, the less energy a nucleus has, the less likely it is to decay Nuclei move in the direction of lower energy The Strong Force What is holding the nucleus together in the first place? Not electromagnetism; the protons repel each other Not gravity, it’s too weak There is a new force holding the nucleus together: The strong force Stronger than electromagnetism (100 times), much stronger than gravity It is attractive between any two nucleons p+p+ p+p+ n0n0 n0n0 p+p+ n0n0 The strong force is short range It is strong within about 1.5 fm At about 8 fm, it is overcome by electric repulsion 1.5 fm p+p+ p+p+ 8 fm

Nuclear Levels and Pauli Exclusion Just like electrons, protons and neutrons have spin ½. They therefore obey the Pauli exclusions principle You can’t put two protons in the same state, nor two neutrons But you can put a proton and a neutron in the same state! Are the levels the same as for hydrogen? The force law is completely different The effects of spin are much more significant But there are still levels! 1s 1/2 1p 3/2 1p 1/2 1d 5/2 2s 1/2 1d 3/2 1f 7/2 2p 3/2 1f 5/2 2p 1/2 1g 9/2 Fill them from the bottom up Example: 16 N: Z = 7, A = 16 7 protons 9 neutrons Neutrons can change into protons via  - decay Most stable nuclei have approximately equal numbers of protons and neutrons Z  N, or Z  ½A 16 N  16 O + e - + 

Carlson’s rules for stability: What if this rule is violated? If you have too many neutrons, you do  – decay If you have too many protons, you do  + decay or electron capture 1s 1/2 1p 3/2 1p 1/2 1d 5/2 2s 1/2 1d 3/2 1f 7/2 2p 3/2 1f 5/2 2p 1/2 1g 9/2 Rule 1: Nuclei prefer to have approximately equal numbers of protons and neutrons, Z  ½A * * - This rule will later require modification Note that every orbital holds two nucleons N = even preferred, Z = even preferred Rule 2: Isotopes with even numbers of protons and/or neutrons are more stable 159 stable nuclei are even-even, 50 are odd-even, 53 are even-odd, and 4 are odd-odd Note there are gaps where the energy jumps Rule 3: Isotopes with N or Z = 2, 8, 20, 28, 50, 82, 126 are especially stable

The problem(s) with rule 1 Rule 1: Nuclei prefer to have approximately equal numbers of protons and neutrons, Z  ½A * We have pretended that protons vs. neutrons is an indifferent choice Protons + electrons are slightly less massive than neutrons Protons preferred for small mass ( 3 He better than 3 H) Protons have electrostatic repulsion – they really dislike each other This effect grows as the number or protons grows At A = 100, about 45% protons At A = 200, about 40% protons Rule 1: Nuclei prefer to have approximately 50% (A 150) protons

Carlson’s Last Rule Recall: The strong force is short range Having nucleons next door makes you happier But, eventually (A > 100), you stop gaining benefits from strong force Rule 4: Small A is more stable (A  200) Recall: Electromagnetism is long range As nuclei get bigger, protons see growing repulsion from other protons After a while (A  140) many nuclei find it better to leave In small chunks -  decay Eventually (A  210) all nuclei find it better to  decay Rule 1: Nuclei prefer to have approximately 50% (A 150) protons Rule 2: Isotopes with even numbers of protons and/or neutrons are more stable Rule 3: Isotopes with N or Z = 2, 8, 20, 28, 50, 82, 126 are especially stable

The Valley of Stability

Forces and Force Carriers p+p+ p+p+ How do we get a short range force for the strong force? How do we get a long range force for electromagnetism? Electromagnetic energy comes in chunks called photons In principle, any charged particle can spit out or absorb a photon Except, this takes energy Uncertainty principle – you can make a photon, for a little while, but you have to get rid of it quick:  t  E < ½   The photon can’t move faster than c, so it can’t go farther than ct The farther the distance, the less energy/momentum it can carry The greater the distance, the weaker the force But it never really stops! Electromagnetic forces have infinite range p +  p + +  p + +   p +

p+p+ Strong Forces and Pions p+p+ p+p+ The strong force has a range of about 1.5 fm or so This implies a “minimum energy” for the force carrier 00 Why is there a minimum energy? The force carrier for strong forces has mass! There is a particle called  0 with mass 135 MeV/c 2 that is exchanged Interestingly, there is also a  + and a  - that can be exchanged These particles change the identity of the particles they interact with n0n0 p+p+ n0n0 -- p +  p + +  0 p + +  0  p + n 0  p + +  - p + +  -  n 0

More about Forces In particle physics, all forces are “mediated” by intermediate particles Because special relativity says no instantaneous action at a distance! These intermediate particles are called force carriers If the force carriers have a mass, they also have a maximum distance