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**Neutron Excess Asymmetry Remember HWc 1.**

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

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**Abundance Systematics**

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

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**Abundance Systematics**

NEUTRON CAPTURE CROSS SECTION Formation process Abundance NEUTRON NUMBER ABUNDANCE r s r s MASS NUMBER Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).**

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**The Semi-empirical Mass Formula**

von Weizsäcker in 1935. Liquid drop. Shell structure. Main assumptions: Incompressible matter of the nucleus R A⅓. Nuclear force saturates. Binding energy is the sum of terms: Volume term. 4. Asymmetry term. Surface term. 5. Pairing term. Coulomb term. 6. Closed shell term. ….. Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**The Semi-empirical Mass Formula**

Volume Term Bv = + av A Bv 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. constant The other terms are “corrections” to this term. Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**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: Nucleons. Remember t/R A-1/3 Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**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 … ?! Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**The Semi-empirical Mass Formula**

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

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**The Semi-empirical Mass Formula**

Quiz 1 From our information so 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, (Saed Dababneh).

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**The Semi-empirical Mass Formula**

Asymmetry Term Ba = - aa (A-2Z)2 / A 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. Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**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 1\ ….?! Bp expected to decrease with A; effect of unpaired nucleon decrease with total number of nucleons. But empirical evidence show that: A-¾ . Effect on: Fission. Magnetic moment. Effect of high angular momentum. Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**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, (Saed Dababneh).

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**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, (Saed Dababneh).

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**The Semi-empirical Mass Formula**

Variations……. Additional physics…. Fitting……(Global vs. local)….. Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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Work it out … Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**Mass Parabolas and Stability**

HW 16 Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**Mass Parabolas and Stability**

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

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**Mass Parabolas and Stability**

Double decay! Both Sides! Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**Mass Parabolas and Stability**

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

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**Mass Parabolas and Stability**

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

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**Mass Parabolas and Stability**

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

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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, Second Semester, (Saed Dababneh).

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**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, Second Semester, (Saed Dababneh).

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**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, Second Semester, (Saed Dababneh).

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DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.

DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.

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