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Understanding Nuclear Size and Density: Insights from Empirical Experiments

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  1. Nuclear Size • Different experiments give different results  Radius not well defined. • Depends on probe and relevant physics. • Probes should be close to the order of the size of the nucleus ~ 10-14 m. • Visible light?  much larger. • 1 MeV ?  = ?? 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, First Semester, 2007-2008 (Saed Dababneh).

  2. 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? HWc 3 Compare for A = 4, 40, 120 and 235. 0 = nucleon density near the center. t = “skin” thickness. a = thickness parameter. R = Half-density radius. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  3. 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 Why? Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  4. 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 • ~ 1017 kg/m3. • Neutron stars, 3 solar masses, only 10 km across ….. !!! • Surface effect? Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  5. Nuclear Size • Three conclusions can be drawn: • Inside the nucleus the density is fairly uniform. • The transitional surface layer is thin. • The central density has a similar value for different nuclei. Liquid Drop Short range of nuclear force • Saturation? • Get an estimate for nuclear density and thus inter-nucleon distance. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  6. Nuclear Size 1 Ci Pu-Be Neutron Source Neutron Detector Absorber Beam From Optical Model Dimensions Different targets HW 6 How can we get r0 from the graph? Preferably low  Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  7. Nuclear Size Alpha particle (+2e) Gold nucleus (+79e) d Not exactly for Au!!! Quite old!!! Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  8. Nuclear Size • Closest approach “d”. • E = ECoulomb d = 2kZe2/E • What about the recoil nucleus? • HW 7Show 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, First Semester, 2007-2008 (Saed Dababneh).

  9. 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, First Semester, 2007-2008 (Saed Dababneh).

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