Why do some isotopes decay and others don’t?

1. Nuclear Structure and Stability • 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 • What is holding the nucleus together in the first place? • Not electromagnetism; the protons repel each other • Not gravity, it’s too weak The Strong Force • 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 n0 n0 n0 p+ p+ p+ 1.5 fm • The strong force is short range • It is strong within about 1.5 fm • At about 8 fm, it is overcome by electric repulsion p+ p+ 8 fm

2. Nuclear Levels and Pauli Exclusion 1g9/2 2p1/2 1f5/2 2p3/2 1f7/2 1d3/2 2s1/2 1d5/2 1p1/2 1p3/2 1s1/2 • 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! • Fill them from the bottom up • Example: 16N: 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 16N  16O + e- + 

3. Carlson’s rules for stability: 1g9/2 2p1/2 1f5/2 2p3/2 1f7/2 1d3/2 2s1/2 1d5/2 1p1/2 1p3/2 1s1/2 Rule 1: Nuclei prefer to have approximately equal numbers of protons and neutrons, Z  ½A * * - This rule will later require modification • 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 • 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

4. 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 (3He better than 3H) • 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 < 50) to 40% (A > 150) protons

5. 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 • 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 < 50) to 40% (A > 150) protons Rule 4: Small A is more stable (A 200) 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

6. The Valley of Stability http://www.nndc.bnl.gov/chart/

7. Forces and Force Carriers • 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+

8. Strong Forces and Pions • The strong force has a range of about 1.5 fm or so • This implies a “minimum energy” for the force carrier • Why is there a minimum energy? • The force carrier for strong forces has mass! • There is a particle called 0 with mass 135 MeV/c2 that is exchanged 0 p+ p+ + 0 p+ p++ 0 p+ p+ • Interestingly, there is also a + and a - that can be exchanged • These particles change the identity of the particles they interact with p+ - n0 p+ + - n0 p+ + - n0 p+ n0

9. 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