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

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

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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 kgelectron ………… …………… ………proton ………… …………… ………neutron ………… …………… ………12C 12 …………… ………

• Avogadro’s number ….. !!• Mass Stability. E = mc2. Tendency towards lower energy Radioactivity. • Neutron heavier than proton “Free” neutron decays (T½ = ???):

_

epn


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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.

http://www.eas.asu.edu/~holbert/eee460/massdefect.html


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The Valley of Stability


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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 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?


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Nuclear Size

aRrer

/0

1)(

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 2HWc 2Compare for A = 4, 40, 120 and 235.


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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


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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~ 3 ×1017 kg/m3.• Neutron stars, 3 solar masses, only 10 km across ….. !!!• Surface effect?


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Nuclear Size

NeutronDetector

1 Ci Pu-Be Neutron Source

AbsorberBeam

nto

to

TeIeII

2)(2 R

From Optical Model

31A

2

Preferably low

Differenttargets


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Nuclear Size

Alpha particle (+2e) Gold nucleus

(+79e)d


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Nuclear Size

• Closest approach “d”.• E = ECoulomb d = 2kZe2/E

• What about the recoil nucleus?• HW 6HW 6 Show 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?

)(

2 2

mmE

mkZed

N

N


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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 7HW 7if 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(

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

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