Download - The Semi-empirical Mass Formula
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
1
])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, 1st Semester, 2006-2007 (Saed Dababneh).
2
Quiz
?
?
?
),( 2
ZZZAM
?0 min
ZZ
M
A
])2()1([
)(),(
1231
32
AZAaAZZaAaAa
MMZAMZAM
aCSV
Hnn
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
3
Mass Parabolas and Stability
311
31
32
2
4
4)(
),(
AaAa
aAaMM
AaAaAaAM
ZZZAM
Ca
aCHn
aSVn
2
0 min
ZZ
M
A
HW 15HW 15
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
4
Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
5
Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
6
Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
7
Mass Parabolas and Stability
Odd-Odd
Even-Even
Vertical spacing between both parabolas ?
• Determine constants from atomic masses.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
8
Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
9
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) (Isospin).• 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, 1st Semester, 2006-2007 (Saed Dababneh).
10
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, 1st Semester, 2006-2007 (Saed Dababneh).
11
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 -
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
12
Nuclear Magnetic MomentRemember, for electrons Revise: Torque on a current loop.
Z component ?? Experiment, applied magnetic field.
Gyromagnetic ratio (g-factor)
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
13
Nuclear Magnetic MomentFor Nuclei
For free protons and neutronsProton: g = 5.5856912 ± 0.0000022 3.6 Neutron: g = -3.8260837 ± 0.0000018 3.8
The proton g-factor is far from the gS = 2 for the electron, and even the uncharged neutron has a sizable magnetic moment!!!
Internal structure (quarks).
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
14
Nuclear Magnetic Moment
Nuclide Nuclear spinMagnetic moment
(in N)
n 1/2 -1.9130418
p 1/2 +2.7928456
2H (D) 1 +0.8574376
17O 5/2 -1.89279
57Fe 1/2 +0.09062293
57Co 7/2 +4.733
93Nb 9/2 +6.1705
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
15
Nuclear Parity
• (r) (-r) Even.• (r) -(-r) odd.• For a nucleon is either of even ( = +) or odd ( = -) parity.• For the nucleus = 1 2 3 … A.
• Practically not possible.• Overall can be determined experimentally.• Overall for a nucleus (nuclear state).• Transitions and multipolarity of transitions (-emission).
