22.02

INT R ODUCTION T O

A P P L I E D N U C L E A R PH Y SICS

Spring 2012 Prof. Paola Cappellaro

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G O ALS OF 22.02

I ntro duction to A pplied N ucl ear P hysics

Learn the basic principles of nuclear and radiation science

After taking this class, you will able to study (and understand) any application of nuclear and radiation science

Keyword: WHY ?

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YO U R G O A L S ?

What are your goals and INTERESTS?

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NUCLEAR PH Y SICS

Describes nuclear properties and radiation: structure and characteristics of nuclei radiation sources and interaction with matter

T o understand nuclear structure and radiation we study: nuclei, nucleons and electrons

microscopic processes

T o understand we need modern physics Quantum mechanics

(Special Relativity)

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W H A T A R E T H E M AG I C N U M B E R S ?

Image by MIT OpenCourseWare.

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W H A T A R E T H E M AG I C N U M B E R S ?

A computer

pr ogram variable ? Rock band?

Iphone App?

Games to win to clinch the season?

Number of jobs?

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W H A T A R E T H E M AG I C N U M B E R S ?

© Wikimedia Foundation. License CC BY-SA. This content is excluded from our Creative Commons license. For more inf o 7 rmation, see http://ocw.mit.edu/fairuse .

W H A T A R E T H E M AG I C N U M B E R S ?

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App screenshot © Design7; "The Magic Numbers" cover art © EMI; news article excerpt © The New York Times Company . All rights reserved. This content is exclude d from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse .

W H A T A R E T H E M AG I C N U M B E R S ?

In nuclear physics?

2 8 20 28 50 82 126

And why are they magic?

You’ll find out at the end of this lecture

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BINDING ENERGY

Mass-energy equivalence

E = mc 2

Nuclei are composed of protons and neutrons,

held together by some energy

Z m proton + N m neutron / = M Nucleus

Dif ference in mass ➜ dif ference in energy

This explains why we get energy from nuclear fission, from fusion, from radioactive decay products...

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NUCLEAR NOMENCL A TURE

Atoms/nuclei are specified by # of neutrons: N

protons: Z

[Z electron in neutral atoms]

Atoms of same element have same atomic number Z

Isotopes of the same element have same atomic number Z but dif ferent number of neutrons N

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A X

Z

NUCLEAR NOMENCL A TURE

Isotopes are denoted by

X is the chemical symbol

A = Z + N is the mass number

E.g. : 235 U, 238 U [Z is redundant here]

92

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NUCLEAR NOMENCL A TURE

N uclide

atom/nucleus with a specific N and Z

I sobar

nuclides with same mass # A ( ≠ Z,N)

I sotone

nuclides with same N, ≠ Z

I somer

same nuclide (but dif ferent energy state)

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BINDING ENERGY

Mass-energy equivalence

E = mc 2

Nuclei are held together by the binding energy

Z m proton + N m neutron / = M Nucleus

Dif ference in mass ➜ dif ference in energy

Why is there a mass dif ference?

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BINDING ENERGY

Binding Energy = [Mass of its constituents-Nucleus Mass] x c 2

B = ⇥ Z m p + N m n — ( A X ) ⇤ c 2

In terms of measurable quantities:

B = Z m p + N m n — [ m A ( A X ) — Z m e ] c 2

B is always n p e o g s a i t t i i v v e e for stable nuclei

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SEMI-EMPIRIC AL MASS FORMULA

M ( Z, A ) = Z m ( 1 H ) + N m n — B ( Z, A ) /c 2

From a simple model of the nucleus, described as a liquid drop

➜ formula for B(Z,A)

5 terms, plot B(Z,A) vs. A

Photo courtesy of cdw9 on Flickr. License CC BY-NC.

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SEMI-EMPIRIC AL MASS FORMULA

M ( Z, A ) = Z m ( 1 H ) + N m n — B ( Z, A ) /c 2

With binding energy given by:

Surface Coulomb

B ( A, Z ) = a v A — a s A 2 / 3 — a c Z ( Z — 1) A — 1 / 3

Volume ( A — 2 Z ) 2

A

+ δ a p A

— 3 / 4

symmetry pairing

Photo courtesy of cdw9 on Flickr. License CC BY-NC.

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SEMF: Binding Energ y per Nucleon

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5

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A (Mass number)

0 50 100 150 200 250

B(Z,A)/A ~ cst.(8 MeV) - corrections

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B/A: JUMPS

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8

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6

5

4

3

A (Mass number)

0 50 100 150 200 250

“Jumps” in Binding energy from experimental data

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AT O M S P E R I O D I C P R O P E R T I E S

‡ Ê Ionization Energy (similar to B per nucleon)

‡ Ê

2000

‡ Ê

‡ Ê 20

‡ Ê 40 60 80 100

‡ Ê ‡ Ê

Z

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AT O M I C P E R I O D I C TA B L E

Periodic properties → atomic structure Ionization Energy (similar to B per nucleon)

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CHA R T OF NUCL ID ES

http://ww w .nndc.bnl.gov/chart/

“Periodic” , more complex properties → nuclear structure

© Brookhaven National Laboratory. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse.

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W H A T A R E T H E M AG I C N U M B E R S ?

2 8 20 28 50 82 126

And why are they magic?

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W H A T A R E T H E M AG I C N U M B E R S ?

2 8 20 28 50 82 126

And why are they called magic?

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W H A T A R E T H E M AG I C N U M B E R S ?

2 8 20 28 50 82 126

And why are they called magic?

Maria Goeppert Mayer “discovered” them in ~1945 Observation of periodicity in binding energy

➜ shell model for nuclei

Eugene Wigner believed in liquid-drop model, did not trust new theory

➜ called these numbers “magic”

Quantum mechanics only can explain them As well as many other “misteries”,

e.g. randomness of radioactive decay

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22.02 SPRING 2012

Class Logistics

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RECI T A TIONS

There will be weekly recitations

Recitations will review some topics from lecture and mathematical background

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TEXTBOOKS

Lecture notes

Usually posted before the lecture

Kenneth S. Krane,

Introductory Nuclear Physics, Wiley

David J. Griffiths

Introduction to Quantum Mechanics, 2nd edition Pearson Prentice Hall, 2005

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P-S ETS

The problem sets are an essential part of the course T ry solving the Pset on your own

Discuss with other students Attend recitations

Ask T A and Professor

P- sets will be posted

9 P-sets, tentative schedule in Syllabus hand-out P-set solutions will be posted

No p-sets will be accepted after the deadline

W orst P-set grade will be dropped

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GRADING

Homework 25%

W orst P-set grade will be dropped

Mid- T erm 30%

W eek before Spring Break: Conflicts?

Final exam 40%

“Mostly” on second part of class Class Participation 5%

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CLASS P A R TICI P A TION

xkcd.com

Courtesy of xkcd.com . License CC BY-NC.

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QU E S T I O N S ?

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MIT OpenCourseWare http://ocw.mit.edu

22.02 Introduction to Applied Nuclear Physics

Spring 2012

For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .