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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 1 Nuclear Binding Energy B tot (A,Z) = [ Zm H + Nm n - m(A,Z) ] c 2 B m HW 9 B ave (A,Z) = B tot (A,Z) / A HW 9 Krane 3.9 HW 10 Atomic masses from: HW 10 Krane Separation Energy Neutron separation energy: (BE of last neutron) S n = [ m(A-1,Z) + m n – m(A,Z) ] c 2 HW 11 = B tot (A,Z) - B tot (A-1,Z) HW 11 Show that HW 12 HW 12 Similarly, find S p and S. HW 13HW 14 HW 13 Krane 3.13HW 14 Krane 3.14 Magic numbers

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 2 Nuclear Binding Energy Magic numbers

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 3 Nuclear Binding Energy In general X Y + a S a (X) = (m a + m Y –m X ) c 2 = B X –B Y –B a The energy needed to remove a nucleon from a nucleus ~ 8 MeV average binding energy per nucleon (Exceptions???). Mass spectroscopy B. Nuclear reactions S. Nuclear reactions Q-value

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 4 Nuclear Binding Energy ~200 MeV Fission Fusion Coulomb effectSurface effect HWc 4 Think of a computer program to reproduce this graph.

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 5 Nuclear Binding Energy HW 15 A typical research reactor has power on the order of 10 MW. a) Estimate the number of 235 U fission events that occur in the reactor per second. b) Estimate the fuel-burning rate in g/s.

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 6 Nuclear Binding Energy Is the nucleon bounded equally to every other nucleon? C this presumed binding energy. B tot = C(A-1) A ½ B ave = ½ C(A-1) Linear ??!!! Directly proportional ??!!! Clearly wrong … ! wrong assumption finite range of strong force, and force saturation.

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 7 Nuclear Binding Energy Lead isotopes Z = 82 For constant Z S n (even N) > S n (odd N) For constant N S p (even Z) > S p (odd Z) Remember HW 14 (Krane 3.14). 208 Pb (doubly magic) can then easily remove the extra neutron in 209 Pb. Neutron Number N Neutron Separation Energy S n (MeV) 208 Pb

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 8 Nuclear Binding Energy Extra Binding between pairs of identical nucleons in the same state (Pauli … !) Stability (e.g. -particle, N=2, Z=2). S n (A, Z, even N) – S n (A-1, Z, N-1) This is the neutron pairing energy. even-even more stable than even-odd or odd-even and these are more tightly bound than odd-odd nuclei.

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 9 Abundance Systematics Odd NEven NTotal Odd Z Even Z Total Compare: even Z to odd Z. even N to odd N. even A to odd A. even-even to even-odd to odd-even to odd-odd. HWc 1 \

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 10 Neutron Excess Odd A Even A Z = N Asymmetry Remember HWc 1.

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 11 Neutron Excess Remember HWc 1. Asymmetry

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 12 Abundance Systematics

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 13 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, First Semester, (Saed Dababneh). 14

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 15 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, First Semester, (Saed Dababneh). 16 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, First Semester, (Saed Dababneh). 17 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, First Semester, (Saed Dababneh). 18 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, First Semester, (Saed Dababneh). 19 The Semi-empirical Mass Formula

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Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh). 20 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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