Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh). 1 501503742 Nuclear...

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

1

501503742 Nuclear and Radiation Physics

Before we start, let us tackle the following:

• Why nuclear physics?• Why radiation physics?• Why in Jordan?• Interdisciplinary.• Applied.

Nuclear Physics at BAU http://nuclear.bau.edu.jo/

This coursehttp://nuclear.bau.edu.jo/nuclear-radiation/

http://nuclear.bau.edu.jo/nuclear-radiation/

http://nuclear.bau.edu.jo/nuclear-radiation/


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General subjects to be covered

This phenomenological course provides the launch point for other nuclear physics courses that will follow.

This is an introductory course that will cover the following general subjects

• Nuclear properties.• Binding energy and nuclear stability.

• Nuclear models.• Spin and moments.

• Nuclear forces.• The structure of the nucleus.

• Nuclear reactions: energetics and general cross-section behavior.• Neutron moderation, fission, controlled fission and fusion.

• Radioactive decays.• Interactions of nuclear radiations (charged particles, gammas, and neutrons) with

matter.


3

Level Test

•This is not intended to be a marked exam. •The purpose is to collect information about your background.•You are NOT required to write your name, but you can do so if you wish.


4

Grading

Mid-term Exam 25%Project, quizzes and HWs 25%Final Exam 50%

• Homeworks are due after one week unless otherwise announced.• Remarks or questions marked in red without being announced as homeworks should be also seriously considered!• Some tasks can (or should) be sent by email:

[email protected]

mailto:[email protected]


5

Proposed Projects• Experiments to determine nuclear properties.• Nuclear power generation.• Nuclear safety.• Environmental radioactivity.• Medical applications.• Health physics and radiation protection.• Nucleosynthesis.• Technological applications (e.g. Material Science).• Radioactive ion beams.• Neutrino physics.• Accelerator driven systems.• ….. or (your own selected subject).

Decide on the title of your project within two weeks. Due date (for written version): May 11th. Presentation: Will be scheduled later.


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Scale and ObjectivesDimensional scale: Order of magnitude of 1 x 10-15 m 1 femtometer 1 fm 1

fermi.Too small for direct investigation.What about time and energy scales?

We need to answer …..1. What are the building blocks

of a nucleus?2. How do they move relative to

each other?3. What laws governing them?We need to understand:• Nuclear forces (Q2, Q3).• Nuclear structure (Q2, Q3).

We also need High Energy Physics (to answer Q1).


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http://physics.nist.gov/cuu/Constants/index.html

Constants

http://physics.nist.gov/cuu/Constants/index.html


8

Nomenclature

NAZ X

Element vs. Nuclide.>90 natural chemical elements, total > 100.Element Atomic number (Z) chemically identical.~3000 nuclides……? How many are stable?Same Z but different neutron number (N) Isotopes.Total number of nucleons = Z+N = A mass number.

XA 112211Na Na23 Na24

Radioactive Stable Radioactive

Same mass number Isobars chemically dissimilar, parallel nuclear features (Radius …). decay.Same neutron number Isotones ?????.Same Z and same A Isomers metastable.Stable isotope (Isotopic) Abundance.Radioactive isotope Half-life.

XAm

Chart of N

uclides

Chart of N

uclides

redundant

C:\Program Files\NuChart\NUCHRT.exe


9

Stable Nuclides

HWc 1HWc 1

Odd A Even A

Nuclide N Z N Z

Then plot Z vs. N.Odd A Even A


10

Properties Structure

The energy of the nucleon in the nucleus is in the order of 10 MeV.

HW 1HW 1 Calculate the velocity of a 10 MeV proton and show that it is almost 15% of the speed of light. (Perform both classical and relativistic calculations). Relativistic effects are not important in considering the motion of nucleons in the nucleus.

HW 2HW 2 Calculate the wavelength of a 10 MeV proton and compare it with the nuclear scale. (Perform both classical and relativistic calculations). Is the nucleus thus a classical or a quantum system?

HW 0HW 0 Krane, Ch. 2. HW 3HW 3 Calculate the wavelength for an electron of the same energy to show that it is much too large to be within the nucleus. (Perform both classical and relativistic calculations). Discuss the proton-electron nuclear hypothesis!

Basic Nuclear Properties

Chadwick, neutron.


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Basic Nuclear PropertiesStatic nuclear properties (Time-independent):Electric charge, radius, mass, binding energy, angular momentum, parity, magnetic dipole moment, electric quadrupole moment, energies of excited states.Dynamic properties (Time-dependent):• Self-induced (Radioactive decay).• Forced (Nuclear reactions) cross sections.

The key: Interaction between individual nucleons.

Excited states: atomic intervals ~ eV.nuclear intervals ~ 104 – 106 eV.

Decays and reactions: Conservation laws and selection rules.

HWc 2HWc 2 Where to find nuclear data???


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Nuclear Mass (Introduction)

• Unified atomic mass unit u based on 12C.• Replaced both physical and chemical amu based on 16O and natural oxygen, respectively (Find conversion factors).• 1 u = M(12C)/12 = ……… kg = …………… MeV/c2.• Rest masses

u MeV/c2 kgelectron ………… …………… ………proton ………… …………… ………neutron ………… …………… ………12C 12 …………… ………

• Avogadro’s number .. !! What is the number of atoms in 1 kg of pure 238U?• Mass Stability. E = mc2. Tendency towards lower energy Radioactivity. • Neutron heavier than proton “Free” neutron decays (T½ = ???):

_

epn


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Nuclear Mass (Introduction)

• Nuclear masses measured to high accuracy:• mass spectrograph.• energy measurement in nuclear reactions.

• Mass decrement = difference between actual mass and mass number:Δ = m – A

• Δ of parent(s) > Δ of product(s) radioactivity.• Binding Energy?• Stability?• Fission?• Fusion?

• More later ……..

Usually atomic masses are tabulated. Mass of the atom < ZmH + Nmn.


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The Valley of Stability


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Nuclear Size• Different experiments give different results Radius not well defined.• Depends on probe and relevant physics.• Probes should be close to the order of the size of the nucleus ~ 10-14 m.

• Visible light? much larger.

• 1 MeV ? = ?? x 10-12 m. Interacts with orbital electrons.• Suitable probes: p, n, , e .... Charge distribution. Mass distribution.• All experiments agree qualitatively and somehow quantitatively.• Project ….

• R A⅓

• R = r0 A⅓ with r0 dependent on the method.• Matter distribution charge distribution. [Recently some halonuclei, e.g. 11Li, found]. What is that?

constant~

34 3R

A


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Nuclear Size

0 = nucleon density near the center.t = “skin” thickness. a = thickness parameter.R = Half-density radius.

HW 4HW 4 • Experiments show that t = (2.4 ± 0.3) fm for all nuclei

t/R A-1/3 • Is surface effect the same for all nuclei?

HWc 3HWc 3Compare for A = 4, 40, 120 and 235.

aRrer

/0

1)(


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Nuclear Size

High-energy e scattering

Light nuclei?

R A⅓

From some experiments….!Charge distribution: r0 = 1.07 fm. a = 0.55 fm.Matter distribution: r0 = 1.25 fm. a = 0.65 fm.

0 decreases with A?YesNo matterech A

Z arg

Why?


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Nuclear Size

HW 5HW 5Nucleus Z/A Charge density

40Ca ….. ….. 59Co ….. …..115In ….. ….. 197Au ….. …..

• Charge radius ~ nuclear radius, even though heavy nuclei have more neutrons than protons. Explain…• Density of ordinary atomic matter ~ 103 kg/m3. Density of nuclear matter~ 1017 kg/m3.• Neutron stars, 3 solar masses, only 10 km across ….. !!!• Surface effect?


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Nuclear Size

Three conclusions can be drawn:

• Inside the nucleus the density is fairly uniform.• The transitional surface layer is thin.• The central density has a similar value for different nuclei.

• Saturation?• Get an estimate for nuclear density and thus inter-nucleon distance.


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Nuclear Size

NeutronDetector

1 Ci Pu-Be Neutron Source

AbsorberBeam

nto

to

TeIeII

2)(2 RT

From Optical Model

31A

2T

Preferably low

Differenttargets

How can we get r0 from the graph?HW 6HW 6

Dimensions


21

Nuclear Size

Alpha particle (+2e)

Gold nucleus (+79e)d

Quite old!!!Not exactly for A

u!!!


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Nuclear Size

• Closest approach “d”.• E = ECoulomb d = 2kZe2/E

• What about the recoil nucleus?• HW 7HW 7 Show that

where mN : mass of the nucleus m : mass of alpha

What are the values of d for 10, 20, 30 and 40 MeV on Au?How does this explain … ?

)(

2 2

mmE

mkZed

N

N


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Nuclear Shape

• Crude Nucleons in the nucleus are confined to an approximately spherically symmetric structure Nuclear radius.• Deformations…! Consequences….!!• Is there a sharp spherical wall…???!!!

• HW 8HW 8if it is assumed that the charge is uniformly spherically distributed in a nucleus, show that the electric potential energy of a proton is given by:

R

eZZKE

2)1(

5

3


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Nuclear Binding Energy

Btot(A,Z) = [ ZmH + Nmn - m(A,Z) ] c2 Bm

Bave(A,Z) = Btot(A,Z) / A HW 9HW 9 Krane 3.9Atomic masses from: HW 10HW 10 Krane 3.12http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&all=all&ascii=ascii&isotype=all

Separation Energy Neutron separation energy: (BE of last neutron)Sn = [ m(A-1,Z) + mn – m(A,Z) ] c2

= Btot(A,Z) - Btot(A-1,Z) HW 11HW 11 Show that

HW 12HW 12 Similarly, find Sp and S.

HW 13HW 13 Krane 3.13 HW 14HW 14 Krane 3.14

Magicnumbers

http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&all=all&ascii=ascii&isotype=all


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Nuclear Binding EnergyMagic

numbers


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In generalX Y + aSa(X) = (ma + mY –mX) c2

= BX –BY –Ba The energy needed to remove a nucleon from a nucleus ~ 8 MeV average binding energy per nucleon (Exceptions???).

Mass spectroscopy B.Nuclear reactions S.Nuclear reactions Q-value


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~200 MeV

Fission

Fusi

on

Coulomb effectSurface effect

HWc 4HWc 4Think of a computer program to

reproduce this graph.


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HW 15HW 15A typical research reactor has power on the

order of 10 MW.

a) Estimate the number of 235U fission events that occur in the reactor per second.

b) Estimate the fuel-burning rate in g/s.


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Is the nucleon bounded equally to everyother nucleon?C ≡ this presumed binding energy.Btot = C(A-1) A ½Bave = ½ C(A-1) Linear ??!!! Directly proportional ??!!! Clearly wrong … ! wrong assumption finite range of strong force, and force saturation.


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Lead isotopes Z = 82

For constant ZSn (even N) > Sn (odd N)For constant NSp (even Z) > Sp (odd Z)

Remember HW 14 (Krane 3.14).

208Pb (doubly magic) can then easily remove the “extra” neutron in 209Pb.

Neutron Number N

Ne

utr

on

Se

pa

ratio

n E

nerg

y S

n (

Me

V)

208 P

b


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Extra Binding between pairs of “identical” nucleons in the same state (Pauli … !) Stability (e.g. -particle, N=2, Z=2).

Sn (A, Z, even N) – Sn (A-1, Z, N-1)This is the neutron pairing energy.

even-even more stable than even-odd or odd-even and these are more tightly bound than odd-odd nuclei.


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Abundance SystematicsOdd N Even N Total

Odd Z

Even Z

Total

Compare:• even Z to odd Z.• even N to odd N.• even A to odd A.• even-even to even-odd to odd-even to odd-odd.

HWc 1HWc 1\\


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Neutron ExcessZ Vs N (For Stable Isotopes)

0

10

20

30

40

50

60

70

80

90

0 20 40 60 80 100 120 140N

Z

Odd A

Even A

Z = NAsymmetry

AsymmetryRemember HWc 1.


34

Neutron Excess

Remember HWc 1.

Asymmetry

Asymmetry


35

Abundance Systematics


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Abundance Systematics

NEUTRON NUMBER

MASS NUMBER

AB

UN

DA

NC

EN

EU

TR

ON

CA

PT

UR

E

CR

OS

S S

EC

TIO

N

r s r s

Formation process

Abundance


37


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The Semi-empirical Mass Formula

• von Weizsäcker in 1935.• Liquid drop. Shell structure.• Main assumptions:

1. Incompressible matter of the nucleus R A⅓.

2.Nuclear force saturates.• Binding energy is the sum of terms:1. Volume term. 4. Asymmetry term.2. Surface term. 5. Pairing term.3. Coulomb term. 6. Closed shell term.…..


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Volume Term Bv = + av ABv volume R3 A Bv / A is a constant i.e. number of neighbors of each nucleon is independent of the overall size of the nucleus.

The other terms are “corrections” to this term.

A

BV constant


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Surface Term Bs = - as A⅔

• Binding energy of inner nucleons is higher than that at the surface.

• Light nuclei contain larger number (per total) at the surface.• At the surface there are:

32

2

322

0 44

Ar

Ar

o

Nucleons.

31

1

AA

Bs

Remember t/R A-1/3


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Coulomb Term BC = - aC Z(Z-1) / A⅓

• Charge density Z / R3.• W 2 R5. Why ???• W Z2 / R. • Actually: W Z(Z-1) / R. • BC / A = - aC Z(Z-1) / A4/3

Remember HW 8 … ?!

3

3

4r

drr24


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43


Quiz 1Quiz 1

...)1()(),( 31

32

AZZaAaAaMMZAMZAM CSVHnn

From our information so farso far we can write:

For A = 125, what value of Z makes M(A,Z) a minimum?

Is this reasonable…???

So …..!!!!

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