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**Nuclear Size Quite old!!! Not exactly for Au!!!**

Alpha particle (+2e) Gold nucleus (+79e) d Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**Nuclear Size Closest approach “d”. E = ECoulomb d = 2kZe2/E**

What about the recoil nucleus? HW 7 Show that where mN : mass of the nucleus m : mass of alpha What are the values of d for 10, 20, 30 and 40 MeV on Au? How does this explain … ? Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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Nuclear Shape Crude Nucleons in the nucleus are confined to an approximately spherically symmetric structure Nuclear radius. Deformations…! Consequences….!! Is there a sharp spherical wall…???!!! HW 8 if it is assumed that the charge is uniformly spherically distributed in a nucleus, show that the electric potential energy of a proton is given by: Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**Nuclear Binding Energy**

Btot(A,Z) = [ ZmH + Nmn - m(A,Z) ] c Bm Bave(A,Z) = Btot(A,Z) / A HW 9 Krane 3.9 Atomic masses from: HW 10 Krane 3.12 Separation Energy Neutron separation energy: (BE of last neutron) Sn = [ m(A-1,Z) + mn – m(A,Z) ] c2 = Btot(A,Z) - Btot(A-1,Z) HW 11 Prove that HW 12 Similarly, find Sp and S. HW 13 Krane 3.13 HW 14 Krane 3.14 Magic numbers Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**Nuclear Binding Energy**

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

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**Nuclear Binding Energy**

In general X Y + a Sa(X) = (ma + mY –mX) c2 = BX –BY –Ba 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 Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**Nuclear Binding Energy**

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

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**Nuclear Binding Energy**

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

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**Nuclear Binding Energy**

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

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**Nuclear Binding Energy**

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

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**Nuclear Binding Energy**

Extra Binding between pairs of “identical” nucleons in the same state (Pauli … !) Stability (e.g. -particle, N=2, Z=2). Sn (A, Z, even N) – Sn (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. Symmetry? Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**Abundance Systematics**

Odd N Even N Total Odd Z Even Z HWc 1\ 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. Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

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**Neutron Excess Asymmetry Remember HWc 1. Odd A Even A Z = N**

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

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**Neutron Excess Asymmetry Remember HWc 1.**

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

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Chapter 4 The Masses of Nuclei

Chapter 4 The Masses of Nuclei

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