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).

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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).

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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