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Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
1
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
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
2
Nuclear Binding EnergyMagic
numbers
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
3
Nuclear Binding Energy
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
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
4
Nuclear Binding Energy
~200 MeV
Fission
Fusi
on
Coulomb effectSurface effect
HWc 4HWc 4Think of a computer program to
reproduce this graph.
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
5
Nuclear Binding Energy
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.
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
6
Nuclear Binding Energy
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.
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
7
Nuclear Binding Energy
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
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
8
Nuclear Binding Energy
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.
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
9
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\\
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
10
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.
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
11
Neutron Excess
Remember HWc 1.
Asymmetry
Asymmetry
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
12
Abundance Systematics
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
13
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
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
14
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
15
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.…..
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
16
The Semi-empirical Mass Formula
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
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
17
The Semi-empirical Mass Formula
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
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
18
The Semi-empirical Mass Formula
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
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
19
The Semi-empirical Mass Formula
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
20
The Semi-empirical Mass Formula
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 …..!!!!