Transcript Document

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
⅓
• R = r0 A
•
Why? In a while ……
with 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).
1
Nuclear Size
HW 4
• Experiments show that
t = (2.4 ± 0.3) fm for all nuclei 
t/
-1/3

A
R
• Is surface effect the same for all
nuclei?
 (r) 
0
1 e
r  R  / a
0 = nucleon density near the center.
t = “skin” thickness.
Compare for A = 4, 40, 120 and 235.
a = thickness parameter.
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008
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R
=
Half-density
radius.
(Saed Dababneh).
HWc 3
Nuclear Size
0 decreases with A?
No
 ch arg e 
Yes
Z
 matter
A
High-energy e scattering
A
4 3
R
3
~ Constant  R
R = r0 A⅓
 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.
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008
(Saed Dababneh).
Why?
3
Nuclear Size
HW 5
Nucleus
Z/A
40Ca
…..
…..
…..
…..
59Co
115In
197Au
Charge density
…..
…..
…..
…..
• 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).
4
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 internucleon distance.
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008
(Saed Dababneh).
5
Nuclear Size
1 Ci Pu-Be Neutron Source
I  I o e t  I o e T nt
From Optical Model
Dimensions
 T  2 ( R   )
T
2
Preferably low 
Absorber
Neutron
Detector
Beam
2
Different
targets
A
1
3
HW 6
How can we get r0 from the graph?
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008
(Saed Dababneh).
6
Nuclear Size
Alpha particle
(+2e)
d
Gold nucleus
(+79e)
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008
(Saed Dababneh).
7
Nuclear Size
• Closest approach “d”.
• E = ECoulomb  d = 2kZe2/E
• What about the recoil nucleus?
• HW
7
Show that
2kZe2 mN
d
E
(
m

m
)

N

: mass of the nucleus
where mN
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).
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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 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:
3 Z ( Z  1)e
E K
5
R
Nuclear and Radiation Physics, BAU, First Semester, 2007-2008
(Saed Dababneh).
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