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+
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+
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
2p1/2
•The effects of spin are much more significant
2p3/2
•But there are still levels!
Fill them from the bottom up
•Example: 16N: Z = 7, A = 16
•7 protons
1d3/2
•9 neutrons
1d5/2
Neutrons can change into protons via - decay
•Most stable nuclei have approximately equal
1p1/2
numbers of protons and neutrons
16N  16O + e- + 
•Z  N, or Z  ½A
1g9/2
1f5/2
1f7/2
2s1/2
1p3/2
1s1/2
Carlson’s rules for stability:
Rule 1: Nuclei prefer to have approximately equal
numbers of protons and neutrons, Z  ½A *
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
* - This rule will later
require modification
1g9/2
2p1/2
2p3/2
1f5/2
1f7/2
1d3/2
1d5/2
2s1/2
1p1/2
1p3/2
1s1/2
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
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
Rule 4: Small A is
approximately 50% (A < 50)
more stable (A  200)
to 40% (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
http://www.nndc.bnl.gov/chart/
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
p+ 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
p+  p+ + 
•The greater the distance, the weaker the force
•But it never really stops!
p+ +   p+
•Electromagnetic forces have infinite range
p+
E
c

t
d
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
E
c
d max

16
8
6.582

10
eV

s
3

10
m/s 


1.5 10
15
m
 130 MeV

•Why is there a minimum energy?
2
2
2
E

pc

mc
 
•The force carrier for strong forces has mass!
•There is a particle called 0 with mass 135 MeV/c2 that is exchanged
p+
p+
p+

p+
0

+ 0
p+ + 0  p+
•Interestingly, there is also a + and a - that can be exchanged
•These particles change the identity of the particles they interact with
+n0  pp+ + n0
p+ + -  n0
p+
n0

2
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
d max 
c
Emin
c 197 MeV  fm


 d max
2
2
mc
mc