Nuclear Structure and Stability
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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?

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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


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- + 


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


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 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


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 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

  • 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


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


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