Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
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 A⅓ Why? In a while ……• R = r0 A⅓ with r0 dependent on the method.• Matter distribution charge distribution. [Recently some halonuclei, e.g. 11Li, found]. What is that?
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
2
Nuclear Size
0 = nucleon density near the center.t = “skin” thickness. a = thickness parameter.R = Half-density radius.
HW 4HW 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 3HWc 3Compare for A = 4, 40, 120 and 235.
aRrer
/0
1)(
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
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Nuclear Size
High-energy e scattering
Light nuclei?~
34 3R
A
Constant R A⅓
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
0 decreases with A?YesNo matterech A
Z arg
Why?
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
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Nuclear Size
HW 5HW 5Nucleus 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).
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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.
• 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
NeutronDetector
1 Ci Pu-Be Neutron Source
AbsorberBeam
nto
to
TeIeII
2)(2 RT
From Optical Model
31A
2T
Preferably low
Differenttargets
How can we get r0 from the graph?HW 6HW 6
Dimensions
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
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Nuclear Size
Alpha particle (+2e)
Gold nucleus (+79e)d
Quite old!!!Not exactly for A
u!!!
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
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Nuclear Size
• Closest approach “d”.• E = ECoulomb d = 2kZe2/E
• What about the recoil nucleus?• HW 7HW 7 Show 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 … ?
)(
2 2
mmE
mkZed
N
N
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).
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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 8HW 8if 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:
R
eZZKE
2)1(
5
3