Nuclear Mass

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# Nuclear Mass - PowerPoint PPT Presentation

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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Presentation Transcript
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 …………… ………
• 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 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

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

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 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.

HWc 2

Compare for A = 4, 40, 120 and 235.

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

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 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).

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 Size

Alpha particle (+2e)

Gold nucleus (+79e)

d

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

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
• 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).