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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).

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.

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 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).

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