nuclear and radiation physics, bau, second semester, 2009-2010 (saed dababneh). 1 neutron excess...
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Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
1
Neutron Excess
Remember HWc 1.
Asymmetry
Asymmetry
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
2
Abundance Systematics
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
3
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, Second Semester, 2009-2010 (Saed Dababneh).
4
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
5
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, Second Semester, 2009-2010 (Saed Dababneh).
6
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, Second Semester, 2009-2010 (Saed Dababneh).
7
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, Second Semester, 2009-2010 (Saed Dababneh).
8
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, Second Semester, 2009-2010 (Saed Dababneh).
9
The Semi-empirical Mass Formula
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
10
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 …..!!!!
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
11
The Semi-empirical Mass Formula
• Light nuclei: N = Z = A/2 (preferable).• Deviation from this “symmetry” less BE and stability.• Neutron excess (N-Z) is necessary for heavier nuclei.• Ba / A = - aa (N-Z)2 / A2.• Back to this when we talk about the shell model.
Asymmetry Term Ba = - aa (A-2Z)2 / A
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
12
The Semi-empirical Mass Formula
Pairing Term Bp = Extra Binding between pairs of identical nucleons in the same state (Pauli !) Stability (e.g. -particle, N=2, Z=2).even-even more stable than even-odd or odd-even and these are more tightly bound than odd-odd nuclei.Remember HWc 1HWc 1\\ ….?!Bp expected to decrease with A; effect of unpaired nucleon decrease with total number of nucleons. But empirical evidence show that:
A-¾ .
oddZoddNAa
oddA
evenZevenNAa
p
p
43
43
0
Effect on:• Fission.• Magnetic moment.Effect of high angular momentum.
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
13
The Semi-empirical Mass Formula
Closed Shell Term Bshell =
• Extra binding energy for magic numbers of N and Z.• Shell model.• 1 – 2 MeV more binding.
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
14
The Semi-empirical Mass Formula
• Fitting to experimental data. • More than one set of constants av, as …..
• In what constants does r0 appear?• Accuracy to ~ 1% of experimental values (BE).• Atomic masses 1 part in 104.• Uncertainties at magic numbers.• Additional term for deformation.
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
15
])2()1([
)(),(
1231
32
AZAaAZZaAaAa
MMZAMZAM
aCSV
Hnn
The Semi-empirical Mass Formula
Variations…….Variations…….Additional physics….Additional physics….Fitting……(Global vs. local)…..Fitting……(Global vs. local)…..
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
16
Work it out …
?
?
?
),( 2
ZZZAM
?0 min
ZZ
M
A
])2()1([
)(),(
1231
32
AZAaAZZaAaAa
MMZAMZAM
aCSV
Hnn
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
17
Mass Parabolas and Stability
311
31
32
2
4
4)(
),(
AaAa
aAaMM
AaAaAaAM
ZZZAM
Ca
aCHn
aSVn
2
0 min
ZZ
M
A
HW 16HW 16
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
18
Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
19
Mass Parabolas and Stability
Double decay! Both Sides!
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
20
Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
21
Mass Parabolas and Stability
Odd-Odd
Even-Even
Vertical spacing between both parabolas ?
• Determine constants from atomic masses.
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
22
Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
23
Nuclear Spin• Neutrons and protons have s = ½ (ms = ± ½) so they are fermions and obey the Pauli-Exclusion Principle.•The Pauli-Exclusion Principle applies to neutrons and protons separately (distinguishable from each other) (IsospinIsospin).• Nucleus seen as single entity with intrinsic angular momentum .• Associated with each nuclear spin is a nuclear magnetic moment which produces magnetic interactions with its environment. •The suggestion that the angular momenta of nucleons tend to form pairs is supported by the fact that all nuclei with even Z and even N have nuclear spin =0. • Iron isotopes (even-Z), for even-N (even-A) nuclei =0. • Odd-A contribution of odd neutron half-integer spin.• Cobalt (odd-Z), for even-N contribution of odd proton half-integer spin.• Odd-N two unpaired nucleons large integer spin.
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Nuclear Spin
Z A SpinNatural
AbundanceHalf-life Decay
26 54 0 0.059 stable ...
26 55 3/2 ... 2.7y EC
26 56 0 0.9172 stable ...
26 57 1/2 0.021 stable ...
26 58 0 0.0028 stable ...
26 60 0 ... 1.5My -
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
25
Nuclear Spin
Z A SpinNatural
AbundanceHalf-life Decay
27 56 4 ... 77.7d +
27 57 7/2 ... 271d EC
27 59 7/2 1.00 stable ...
27 60 5 ... 5.272y -
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