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501503747 Nuclear Reactors. Nuclear Physics at BAU http://nuclear.bau.edu.jo/ This course http://nuclear.bau.edu.jo/Reactors Prerequisites Nuclear and Radiation Physics 742 http://nuclear.bau.edu.jo/nuclear-radiation Advanced Statistical Mechanics 761. General subjects to be covered.

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501503747

Nuclear Reactors

  • Nuclear Physics at BAU

  • http://nuclear.bau.edu.jo/

  • This course

  • http://nuclear.bau.edu.jo/Reactors

  • Prerequisites

  • Nuclear and Radiation Physics 742

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

  • Advanced Statistical Mechanics 761

Nuclear Reactors, BAU, First Semester, 2007-2008

(Saed Dababneh).


General subjects to be covered

  • Review of relevant studied material in nuclear physics.

  •        Concepts in neutron physics.

  •       The relevant physics related to nuclear technology:

    • Fission chain reaction.

    •   Neutron diffusion and moderation.

    • Heat removal from nuclear reactors.

    • Isotope separation.

    •   …

  •      Components of nuclear reactors.

  •       Nuclear reactor fuels and fuel cycles.

  • •       Nuclear reactor theory.

  • •       Basic concepts of radiation protection and nuclear safety, shielding and waste disposal.

  • •       Issues and prospects of nuclear power today and in the future.

  • Nuclear Reactors, BAU, 1st Semester, 2007-2008

    (Saed Dababneh).


    Grading

    Review Test 05%

    Mid-term Exam 20%

    Projects, 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]

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Review Test

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Projects

    • Consider nuclear fuel cycles with emphasis on front ends.

      • Work as a team. Divide and organize the job among you.

      • Try to explore local applicability.

      • Due date (for written version): December 5th.

      • Presentation: Will be scheduled later.

  • Other small projects will be announced in class.

  • Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Nuclear Reaction Energetics (revisited)

    • Conservation Laws

    • Charge, Baryon number, total energy, linear momentum, angular momentum, parity, (isospin??)…….

    b

    pb

    gs

    a

    pa

    X

    +ve Q-value  exoergic reaction.

    -ve Q-value  endoergic reaction.

    pY

    Y

    Stationary X ??

    +ve Q-value  reaction possible if Ta 0.

    -ve Q-value  reaction not possible if Ta 0. (Is Ta > |Q| sufficient?).

    Conservation of momentum ……

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Nuclear Reaction Energetics (revisited)

    HW 1

    • Conservation of momentum.

    • We usually do not detect Y.

    • Show that:

    • The threshold energy (for Ta): (the condition occurs for  = 0º).

    • +ve Q-value  reaction possible if Ta 0.

    • Coulomb barriers…….!!!

    • -ve Q-value  reaction possible if Ta> TTh.

    double valued !?

    solve for Q

    Q < 0

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Nuclear Reaction Energetics (revisited)

    HW 1(continued)

    • The double valued situation occurs between TTh and the upper limit Ta\.

    • Double-valued in a forward cone.

    Q < 0

    Discuss the elasticand inelastic scatteringof neutronsusing these relations.

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Nuclear Reaction Energetics (revisited)

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Nuclear Reaction Energetics (revisited)

    What about neutron induced reactions?

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Nuclear Reaction Energetics (revisited)

    What about neutron induced reactions?

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Nuclear Reaction Energetics (revisited)

    What about neutron induced reactions?

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Nuclear Reaction Energetics (revisited)

    • If the reaction reaches excited states of Y

    58Ni(,p)61Cu

    even less ….

    less proton energy

    Highest proton energy

    See Figures 11.4 in Krane

    What about neutron induced reactions?

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Neutron Interactions (revisited)

    • Chadwick’s discovery.

    • Neutrons interact with nuclei, not with atoms. (Exceptions).

    • Recall from Nuclear Physics 742:

      • Inelastic scattering (n,n\). Q = -E* Inelastic gammas. Threshold?

      • Elastic scattering (n,n). Q = ?? (Potential and CN). Neutron moderation?

      • Radiative capture (n,). Q = ?? Capture gammas.

      • (n,), (n,p). Q = ?? Absorption Reactions.

      • (n,2n), (n,3n) Q = ?? Energetic neutrons on heavy water can easily eject the loosely bound neutron.

      • Fission. (n,f).

    • HW 2 Examples of such exo- and endo-thermic reactions with Q calculations.

    Non-elastic

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Neutron Scattering (revisited)

    • Elastic or inelastic.

    • Analogous to diffraction.

    • Alternating maxima and minima.

    • First maximum at

    • Minimum not at zero (sharp edge of the nucleus??)

    • Clear for neutrons.

    • Protons? High energy, large angles. Why?

    • Inelastic  Excited states, energy, X-section and spin-parity.

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Reaction Cross Section (revisited)

    • Probability.

    • Projectile a will more probably hit target X if area is larger.

    • Classically:  = (Ra + RX)2.

    • Classical  = ??? (in b)n+ 1H, n + 238U, 238U + 238U

    • Quantum mechanically:  =  2.

    • Coulomb and centrifugal barriers  energy dependence of .

    • What about neutrons?

    • Nature of force:

    • Strong: 15N(p,)12C  ~ 0.5 b at Ep = 2 MeV.

    • Electromagnetic: 3He(,)7Be  ~ 10-6 b at E = 2 MeV.

    • Weak: p(p,e+)D  ~ 10-20 b at Ep = 2 MeV.

    • Experimental challenges to measure low X-sections..

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Reaction Cross Section (Simple terms)

    A (Area of the beam!!)

    |v|

    X

    Position of a neutron 1 s before arriving at target

    Target with N atoms.cm-3 or NAX atoms.

    Monoenergetic neutrons of speed v (cm.s-1) and density n (cm-3)

    Volume = vA

    containing nvA neutrons that hit the “whole” target in 1 s.

    Beam Intensity InvA/A = nv (cm-2s-1)

    Number of neutrons interacting with target per second

     I, A, X and N

    = t I N A X

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Reaction Cross Section (Simple terms)

    • Number of neutrons interacting with target per second

    • = t I N A X

    • Number of interactions with a single nucleus per second

    • = t I Interpretation and units of .

    • nvA= IA neutrons strike the target per second, of these

    • tI neutrons interact with any single nucleus. Thus,

    • measures the probability for a neutron to hit a nucleus.

    Study examples in Lamarsh

    Total cross section

    Total number of nuclei in the target

    Effective cross-sectional area of the nucleus.

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Reaction Cross Section (Simple terms)

    Number of neutrons interacting with target per second

    = t I N A X

    Number of interactions per cm3 per second (Collision Density)

    Ft= t I N = I t

    t= N t

    Study examples in Lamarsh

    Total cross section

    Volume of the target

    Macroscopic total cross section.

    Probability per unit path length.

    Attenuation not moderation !

    Mean free path

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Reaction Cross Section (Simple terms)

    Homogeneous Mixture

    Molecule xmyn Nx=mN, Ny=nN

    given that events at x and y are independent.

    Study examples in Lamarsh

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Reaction Cross Section (revisited)

    Look for b

    Detector for particle “b”

    d

    Ia

    “b” particles / s

    ,

    cm2

    “X“ target Nuclei / cm2

    “a” particles / s

    Typical nucleus (R=6 fm): geometrical R2  1 b.

    Typical : <b to >106 b.

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Reaction Cross Section (revisited)

    Many different quantities are called

    “cross section”.

    Krane Table 11.1

    Angular distribution

    Units … !

    “Differential” cross section

    (,) or ( )

    or “cross section” …!!

    Doubly differential

    t for all “b” particles.

    Energy state in “Y”

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    n-TOF

    CERN

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Different Features (revisited)

    1/v

    Fast neutrons should be moderated.

    235U thermal cross sections

    fission  584 b.

    scattering  9 b.

    radiative capture  97 b.

    Fission Barriers

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Neutron Induced Reactions (revisited)

    X(n,b)Y

    b(Q+En)

    n(En)

    Probability to penetrate the potential barrier

    Po(Ethermal) = 1

    P>o(Ethermal) = 0

    For thermal neutrons

    Q >> En

    b(Q)  constant

    Non-resonant

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Neutron Induced Reactions (revisited)

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Statistical Factor (revisited)

    HW 3

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Resonance Reactions (revisited)

    J

    Ex

    a + X  Y + b Q > 0

    b + Y  X + a Q < 0

    Excited

    State

    Entrance Channel

    a + X

    Exit

    Channel

    b + Y

    Inverse Reaction

    Compound Nucleus C*

    Identical

    particles

    • Nature of force(s).

    • Time-reversal invariance.

    Statistical

    Factor ()

    QM

    HW 4

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Resonance Reactions (revisited)

    Projectile

    Projectile

    Target

    Target

    Q-value

    Q-value

    Q + ER = Er

    E = E + Q - Eex

    Direct Capture

    (all energies)

    Resonant Capture

    (selected energies with large X-section)

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Resonance Reactions (revisited)

    Damped Oscillator

    Oscillator strength

    Damping

    factor

    eigenfrequency

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Resonance Reactions (revisited)

    Breit-Wigner formula

    • All quantities in CM system

    • Only for isolated resonances.

    Reaction

    Elastic scattering

    Usually a>> b.

    HW 5When does R take its maximum value?

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Resonance Reactions (revisited)

    Exit

    Channel

    b + Y

    Ja + JX + l = J

    (-1)l(Ja) (JX) = (J)

    (-1)l = (J) Natural parity.

    J

    Ex

    Excited

    State

    Entrance Channel

    a + X

    Compound Nucleus C*

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Resonance Reactions (revisited)

    What is the “Resonance Strength” …?

    What is its significance?

    In what units is it measured?

    Charged particle

    radiative capture (a,)

    (What about neutrons?)

    Cross section

    EC

    a

    

    Energy

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Neutron Resonance Reactions (revisited)

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


    Neutron Activation Analysis (revisited)

    (Z,A) + n (Z, A+1)

    -

     (-delayed -ray)

    (Z+1, A+1)

    http://ie.lbl.gov/naa !

    Project 1

    Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).


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