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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 1 Neutron Excess Remember HWc 1. Asymmetry

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 2 Abundance Systematics

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 3 Abundance Systematics NEUTRON NUMBER MASS NUMBER ABUNDANCE NEUTRON CAPTURE CROSS SECTION r s Formation process Abundance

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 4

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5 The Semi-empirical Mass Formula von Weizsäcker in Liquid drop. Shell structure. Main assumptions: 1.Incompressible matter of the nucleus R A. 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. …..

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 6 The Semi-empirical Mass Formula Volume Term B v = + a v A B v volume R 3 A B v / 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. constant

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 7 The Semi-empirical Mass Formula Surface Term B s = - a s A 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

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 8 The Semi-empirical Mass Formula Coulomb Term B C = - a C Z(Z-1) / A Charge density Z / R 3. W 2 R 5. Why ??? W Z 2 / R. Actually: W Z(Z-1) / R. B C / A = - a C Z(Z-1) / A 4/3 Remember HW 8 … ?!

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 9 The Semi-empirical Mass Formula

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 10 The Semi-empirical Mass Formula Quiz 1 so far 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 …..!!!!

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Nuclear and Radiation Physics, BAU, Second Semester, (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. B a / A = - a a (N-Z) 2 / A 2. Back to this when we talk about the shell model. Asymmetry Term B a = - a a (A-2Z) 2 / A

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 12 The Semi-empirical Mass Formula Pairing Term B p = 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. HWc 1 \ Remember HWc 1 \ ….?! B p 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.

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 13 The Semi-empirical Mass Formula Closed Shell Term B shell = Extra binding energy for magic numbers of N and Z. Shell model. 1 – 2 MeV more binding.

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 14 The Semi-empirical Mass Formula Fitting to experimental data. More than one set of constants a v, a s ….. In what constants does r 0 appear? Accuracy to ~ 1% of experimental values (BE). Atomic masses 1 part in Uncertainties at magic numbers. Additional term for deformation.

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 15 The Semi-empirical Mass FormulaVariations……. Additional physics…. Fitting……(Global vs. local)…..

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 16 Work it out …

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 17 Mass Parabolas and Stability HW 16

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 18 Mass Parabolas and Stability

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 19 Mass Parabolas and Stability Double decay! Both Sides!

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 20 Mass Parabolas and Stability

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 21 Mass Parabolas and Stability Odd-Odd Even-Even Vertical spacing between both parabolas ? Determine constants from atomic masses.

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 22 Mass Parabolas and Stability

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 23 Nuclear Spin Neutrons and protons have s = ½ (m s = ± ½) so they are fermions and obey the Pauli-Exclusion Principle. IsospinThe 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.

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 24 Nuclear Spin ZASpin Natural Abundance Half-lifeDecay stable / yEC stable /20.021stable stable My -

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Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh). 25 Nuclear Spin ZASpin Natural Abundance Half-lifeDecay d / dEC 27597/21.00stable y -

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