Nuclear mass
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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 uMeV/c 2 kg

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Nuclear Mass

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Nuclear mass

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

  • uMeV/c2 kg

  • electron ………… …………… ………

  • proton ………… …………… ………

  • neutron ………… …………… ………

  • 12C12 …………… ………

  • 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).


Nuclear mass1

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).


    The valley of stability

    The Valley of Stability

    Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).


    Nuclear size

    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).


    Nuclear size1

    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).


    Nuclear size2

    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).


    Nuclear size3

    Nuclear Size

    HW 5

    Nucleus Z/ACharge 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).


    Nuclear size4

    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).


    Nuclear size5

    Nuclear Size

    Alpha particle (+2e)

    Gold nucleus (+79e)

    d

    Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).


    Nuclear size6

    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).


    Nuclear shape

    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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