# The Semi-empirical Mass Formula

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The Semi-empirical Mass Formula
Variations……. Additional physics…. Fitting……(Global vs. local)….. Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

Quiz Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

Mass Parabolas and Stability
HW 15 Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

Mass Parabolas and Stability
Vertical spacing between both parabolas ? Determine constants from atomic masses. Odd-Odd Even-Even Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

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, (Saed Dababneh).

Nuclear Spin - Z A Spin Natural Abundance Half-life Decay 26 54 0.059
0.059 stable ... 55 3/2 2.7y EC 56 0.9172 57 1/2 0.021 58 0.0028 60 1.5My - Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

Nuclear Spin Z A Spin Natural Abundance Half-life Decay 27 56 4 ...
+ 57 7/2 271d EC 59 1.00 stable 60 5 5.272y - Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

Nuclear Magnetic Moment
Remember, for electrons Revise: Torque on a current loop. Gyromagnetic ratio (g-factor) Z component ?? Experiment, applied magnetic field. Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

Nuclear Magnetic Moment
For Nuclei For free protons and neutrons Proton: g = ±  3.6  Neutron: g = ±  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, (Saed Dababneh).

Nuclear Magnetic Moment
Nuclide Nuclear spin Magnetic moment  (in N) n 1/2 p 2H (D) 1 17O 5/2 57Fe 57Co 7/2 +4.733 93Nb 9/2 Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

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). Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

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