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Nuclear Mass

Nuclear Mass. Unified atomic mass unit u based on 12 C. Replaced both physical and chemical amu based on 16 O and natural oxygen, respectively ( Find conversion factors ). 1 u = M( 12 C)/12 = ……… kg = …………… MeV/c 2 . Rest masses u MeV/c 2 kg

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Nuclear Mass

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  1. Nuclear Mass • Unified atomic mass unit u based on 12C. • Replaced both physical and chemical amu based on 16O and natural oxygen, respectively (Find conversion factors). • 1 u = M(12C)/12 = ……… kg = …………… MeV/c2. • Rest masses • u MeV/c2 kg • electron ………… …………… ……… • proton ………… …………… ……… • neutron ………… …………… ……… • 12C 12 …………… ……… • Avogadro’s number ….. !! • Mass  Stability. E = mc2.Tendency towards lower energy  Radioactivity. • Neutron heavier than proton  “Free” neutron decays (T½ = ???): Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  2. Nuclear Mass • Nuclear masses measured to high accuracy: • mass spectrograph. • energy measurement in nuclear reactions. • Mass decrement = difference between actual mass and mass number: • Δ = m – A • http://www.eas.asu.edu/~holbert/eee460/massdefect.html • Negative Δ mass into energy. • Binding Energy? • Stability? • Fission? • Fusion? • More later …….. • Usually atomic masses are tabulated. • Mass of the atom < ZmH + Nmn. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  3. The Valley of Stability Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  4. Nuclear Size • Different experiments give different results  Radius not well defined. • Depends on probe and relevant physics. • Probes should be of the same order of the size of the nucleus ~ 10-14 m. • Visible light?  much larger. • 1 MeV ?  = 1.2 x 10-12 m. But interacts with orbital electrons. • Suitable probes: p, n, , e, X. Charge distribution. Mass distribution. • All experiments agree qualitatively and somehow quantitatively. • Project …. • R  A⅓Why? In a while …… • R = r0 A⅓with r0 dependent on the method. • Matter distribution  charge distribution. [Recently some halo • nuclei, e.g. 11Li, found]. What is that? Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  5. Nuclear Size HW 4 • Experiments show that t = (2.4 ± 0.3) fm for all nuclei  t/R A-1/3 • Is surface effect the same for all nuclei? 0 = nucleon density near the center. t = “skin” thickness. a = thickness parameter. R = Half-density radius. HWc 2 Compare for A = 4, 40, 120 and 235. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  6. Nuclear Size 0 decreases with A? No Yes High-energy e scattering Constant R  A⅓ Light nuclei? From some experiments….! Charge distribution: r0 = 1.07 fm. a = 0.55 fm. Matter distribution: r0 = 1.25 fm. a = 0.65 fm. R = r0 A⅓ Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  7. Nuclear Size HW 5 Nucleus Z/A Charge density 40Ca …..….. 59Co …..….. 115In …..….. 197Au …..….. • Charge radius  nuclear radius, even though heavy nuclei have more neutrons than protons. Explain… • Density of ordinary atomic matter ~ 103 kg/m3. Density of nuclear matter • ~ 3 ×1017 kg/m3. • Neutron stars, 3 solar masses, only 10 km across ….. !!! • Surface effect? Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  8. Nuclear Size 1 Ci Pu-Be Neutron Source Neutron Detector Absorber Beam From Optical Model Different targets Preferably low  Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  9. Nuclear Size Alpha particle (+2e) Gold nucleus (+79e) d Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  10. Nuclear Size • Closest approach “d”. • E = ECoulomb d = 2kZe2/E • What about the recoil nucleus? • HW 6Show that • where mN : mass of the nucleus • m : mass of alpha • What are the values of d for 10, 20, and 30 MeV  on Au? Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  11. 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 7 • 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, 1st Semester, 2006-2007 (Saed Dababneh).

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