nuclear and radiation physics, bau, second semester, 2009-2010 (saed dababneh). 1 nuclear magnetic...
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Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
1
Nuclear Magnetic MomentRemember, for electrons Revise: Torque on a current loop.
Z component ?? Experiment, applied magnetic field.
Gyromagnetic ratio (g-factor)
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Nuclear Magnetic MomentFor Nuclei
For free protons and neutronsProton: g = 5.5856912 ± 0.0000022 3.6 Neutron: g = -3.8260837 ± 0.0000018 3.8
The proton g-factor is far from the gS = 2 for the electron, and even the uncharged neutron has a sizable magnetic moment!!!
Internal structure (quarks).
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Nuclear Magnetic Moment
Nuclide Nuclear spinMagnetic moment
(in N)
n 1/2 -1.9130418
p 1/2 +2.7928456
2H (D) 1 +0.8574376
17O 5/2 -1.89279
57Fe 1/2 +0.09062293
57Co 7/2 +4.733
93Nb 9/2 +6.1705
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Nuclear Parity
• (r) (-r) Even.• (r) -(-r) odd.• For a nucleon is either of even ( = +) or odd ( = -) parity.• For the nucleus = 1 2 3 … A.
• Practically not possible.• Overall can be determined experimentally.• Overall for a nucleus (nuclear state).• Transitions and multipolarity of transitions (-emission).
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Electromagnetic moments
• Electromagnetic interaction information about nuclear structure.• Charge electric; current magnetic.• Electromagnetic multipole moments.Field1/r2 (zeroth, L=0) electric monopole moment. 1/r3 (first, L=1) electric dipole moment.
1/r4 (second, L=2) quadrupole moment. ……… 1/r2 magnetic monopole (questionable….!). Magnetic Dipole (familiar).
Higher order magnetic moments.
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Electromagnetic moments
• Expectation value of the moment.
• Each multipole moment has a parity, determined by the behavior of the multipole operator when r -r.• Parity of does not change the integrand.• Electric moments: parity (-1)L.• Magnetic moments: parity (-1)L+1.• Odd parity vanish.
electric dipole.magnetic quadrupole.electric octupole.…………
dv *
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Electromagnetic moments
e
TA ;
e
2 r v r2 ;
evr
2
emvr2m
; epr2m
; e
2mL
• Electric monopole: net charge Ze.• Magnetic dipole: (already discussed).
• g-factors.
iA
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Electromagnetic moments• The nucleus has charge (monopole moment).• No dipole moment since it is all positive.• But if the nucleus is not spherically symmetric, it will have a quadrupole moment.
Classical moments
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Electric Quadrupole Moment• For a point charge e: eQ = e(3z2 - r2).• Spherical symmetry x2 = y2 = z2 = r2/3 Q = 0.• For a proton:
• In the xy-plane: Q - r2.• r2 is the mean square radius of the orbit.• Along z: Q +2 r2.• Expected maximum er0
2A2/3.• 6x10-30 to 50x10-30 em2.• 0.06 to 0.5 eb.
dvrzeeQ )3( 22*
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Electric Quadrupole Moment
Nuclide Q (b)2H (D) +0.00288
17O -0.0257859Co +0.4063Cu -0.209133Cs -0.003161Dy +2.4176Lu +8.0209Bi -0.37
• Closed shell Spherically symmetric core. • Test for shell model• Strongly deformed nuclei…..!
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Nuclear Force (Origin of Binding)
RecallRecall Atomic Binding Energies for hydrogen like atoms:
Dimensionless fine structure constant.137
1
4,
)()(
0
2
c
e
r
ZcrV
Ne
Nen mm
mm
n
ZcE
,
2
12
222
with Bohr radii:2n
crn
• Coupling constant Strength.• Charge. • Mediators (Bosons).
=1
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Nuclear Force
The deuteron: proton-neutron bound state.
1.04
,)(
)(0
2
c
q
r
crV S
SS
np
npSn mm
mm
ncE
,
1
2
12
22
2nc
rS
n
Hydrogen: E1 = … eV r1 = …x10-10 mPositronium: E1 = … eVDeuteron: E1 = … MeV r1 = …x10-15 m
HW 17HW 17
!!!!!!!!!
!!!!!!!!!
QCDQCD
Color charge!
Color charge!
QFTQFT
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Nuclear Force
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
14
Nuclear ForceAttractive but repulsive corerepulsive core. At what separation?
• Saturation?• Get an estimate for nuclear density and thus inter-nucleon distance. Have you done that?
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Is the nucleon bounded equally to everyother nucleon?C ≡ this presumed binding energy.Btot = C(A-1) A ½Bave = ½ C(A-1) Linear ??!!! Directly proportional ??!!! Clearly wrong … ! wrong assumption finite range finite range of strong force, and force saturation.
Nuclear Force
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Nuclear Force
• Rate of decay or interaction R (E).• Coupling constant . Vertices in the diagrams.• For decays R 1/T. (T Lifetime).• The density of states is a measure of the number of quantum mechanical states per unit energy range that are available for the final products. The more states that are available, the higher the transition rate.• The coupling constant can be interpreted as an intrinsic rate.