spectroscopy w. udo schröder, ncss 2012 nuclear spectroscopy 1
TRANSCRIPT
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Spectroscopy
W. Udo Schröder, NCSS 2012
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NUCLEARSPECTROSCOPY
SURVEY
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Chemical Evolution of our Universe
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S. Mason. Chemical Evolution (Clarendon Press, 1992), pp. 40-45.
Chemical Evolution of our Universe
Nuc
lear
Spe
ctro
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y4
W. Udo Schröder, NCSS 2012
Probes for Nuclear Structure
To “see” an object, the wavelength l of the light used must be shorter than the dimensions d of the object (l ≤ d). (DeBroglie: p=ħk=ħ2p/l)Rutherford’s scattering experiments dNucleus~ few 10-15 m
Need light of wave length l < 1 fm, equivalent energy E
2
2 2 2 22
2 2
4 2 2
2
200: 2 6 1.2
1
( ) , . ., ( 1), 0.9 :
200 2
2 2 2 1.8
80 10 1 800
( 100) : 1
p p
p
c MeV fmPhotons E pc kc GeV
fm
Massive m Am particle e g proton A m c GeV
k ck MeV fmpE
m m Am c AGeV
MeV fmMeV
AGeV fm A
Heavy ions A fm cla
ssical particles
Not easily available as light
Can be made with charged particle acceleratorsScan energy states of nuclei. Bound systems have discrete energy
states unbound E continuum
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What Structure? - Spectroscopic Goals
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Bound systems have discrete energy states unbound E continuum Scan energy states of nuclei.
Desired information on nuclear states (“good quantum numbers”):
• Energy relative to ground state (g.s.) (Ei, i=0,1,…; E*)
• Stability, life time against various decay modes ( , , a b g,…)
• Electrostatic moments Qj see below• Magnetostatic moments Mi see below
• Angular momentum (nuclear spin)• Parity (=spatial symmetry of quantum y)
• Nucleonic (neutron & proton) configuration (e.g., “isospin” quantum #)
Nuclear Level
Scheme
+
0
-
E*
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Particle and g Spectroscopy
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Individual ormulti detector setups, spectrometersOff-line activation measurements
Identify scattered/transmuted projectile & target nuclei, measure m, E, A, Z, I,.. of all ejectiles (particles and g-rays).
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How to Excite Nuclei: Inelastic Nuclear Reactions
Coulomb excitation of rotational motion for deformed targets or vibrations.
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p, n,..transfer rxns,e.g., (d, n), (3He,d).Final state is excited
Target
Projectile
Fusion/compound nucleus reactions, Final state is highly excited, thermally metastable
Scan the bound nuclear energy level scheme
Defl. angles , L
q
Defl. angles , L
Coulomb Excitation (Semi-Classical)
238
Deformed Charge
Distribution U
r RI
spherical
deformed
0I I L
Ruthi fi f
d dP
d d
Excitation probability in perturbation theory:
* *2
( )i
E E tfii fi fi f
f
Coul
iP b b dt e f H t i
Transition amplitude Fourier transform of transition ME
elm projectile - target interaction H V j A
For small energy losses (weak excitations: * *
i fE E
tt(R0)
Vcoul(t)
0
1R
tcoll
0:
1 1 sin 2 2 arctana
R L
18
00-q
Torque exerted on deformed target excitation of collective nuclear rotations Transfer of angular momentum from relative motion:
Angular dependence of excitation probability:
21 2e Z Z
Sommerfeld Parameter :
Adiabaticity Condition:Fast “kick” will excite nucleus
Otherwise adiabatic reorientation of deformed nucleus to minimize energy
11 * *0
* *
.
2 1
1: 1
4
coll fiifrel
fi coll ifrel
Collision time rot period
RE E
E
Adiabaticity param
E
eter
!
* *i finitial E final E
W. Udo Schröder, 2012
Mean
Fie
ld 9
Observation of Collective Nuclear Rotations
20 0
4( , ) 1 ( , )
3 5R
R R YR
z
b ab := quadrupole deformation parameter
Quadrupole moment (Deviation from spherical nucleus )
Wood et al.,Heyde
2
15 182
Typical values
keV
;2
a bR R a b
20
20
2
:
21 0.31
12
5:
98
rig
I
irr
even I
only
Rigid body moment
ofi nertia
MR
Hydro dynamical
MR
E I I
3 2 2 2
0 03
( ) 3cos 1 1 0.165
eZQ eZ d r r r R
Deexcitation-Gamma Spectra
Measured energies (keV)
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Method: Particle Spectroscopy
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0
(A+a) Excited states
Energy Spectrum of Products b
Particle Energy Eb
Counts
Excited States g.s.
Particle a Beam
QuadrupoleMagnet
Faraday Cup Populate (excite) the spectrum of
nuclear states. Measure probabilities for excitation and de-excitation
Reconstruct energy states Ei,Ii,pi from energy, linear and angular momentum balance.Obtain structure information from probabilities.
Bound systems have discrete energy states unbound E continuum
Reaction A(a,b)B*E
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Method: Simultaneous Absorption & Emission Spectroscopy
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Reaction 64Ni(p,p’)64Ni* :inelastic proton scattering, absorb E from beam
64Nigs+g1+g2+g3+…
g
pE
pD
pC
pB
pA
Scattered Proton Spectrum p-energy loss
Deexcitation g Spectrum
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Example: Inelastic Particle Scattering
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238U+d 238U*+d’
Scattered deuteron kinetic energy spectrum
E’d = E’d (qd , Ed)
Beam
HPGe
HPGe
HPGe
Deexcitation-g Spectrum
Coincident g cascades
Coincident g cascades indicate nuclear band structure (rotational, vibrational,...)
Measuring Energy Transfer: The Q Value Equation
Cross Section, Kinematics & Q Values
W. U
do S
chrö
der,
20
08
1
3
i i i
3 3 4 4
3 3 4 4 1
3 4 1
Lab System (target initially at rest , p 0) :
p 2m E
p sin p sin
p cos p
linear momentum
Process Energy Release
e.g. : mass loss (
y compone
Q 0),
inter
nt
x compone
nal excitat
cos p
Q E E
ion(
nt
Q
E
0)
3 4
3p
4p
1Projectile p
3 3 31 3 13 1
14
34
34
2 m m Em mQ 1 E 1 coE , s
m m mE E
Measure kinetic energy E3 vs. angle q3 to determine reaction Q value.Predict energies of particles at different angles as functions of Q.
4, 4Eliminate E
How to interpret energies of scattered particles:
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Transmutation in Compound Nucleus Reactions
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Q
Decay of CN populates states of the “evaporation residue” nucleus
Use mass tables to calculate Q
g.s.
EER*
Excited levels of ER
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Technology: Typical Setups Particle Experiments
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Modified, after K.S. Krane, Introduction to Nuclear Physics, Wiley&Sons, 1988
Simultaneous measurement of time of flight, specific energy loss and residual energy of particles E, Z, A
Simultaneous measurement of specific energy loss DE and residual energy E of particles E, Z, (A)
Particle
Particle
DE-E/TOF Setup
DE-E Setup
= Total Energy
Residual Energy
E
= ToF
Time of Flight
Tota
l En
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Particle ID (Z , A, E) Specific energy loss, spatial ionization density, TOF
Particle ID with Detector Telescopes
Si Telescope Massive Reaction Products SiSiCsI Telescope (Light Particles)
HeLiBe
NaNe
F
O
N
C
B
20Ne + 12C @ 20.5 MeV/u - qlab = 12°
DE
E-DE
E-E Telescope
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W. Udo Schröder, NCSS 2012
THE CHIMERA DETECTOR
THE CHIMERA DETECTOR
Chimera mechanical structure 1m
1°
30°
REVERSE EXPERIMENTAL APPARATUS
TARGETBEAM
Experimental Method
E-E ChargeE-E E-TOF Velocity, MassPulse shape Method LCP
Basic element Si (300m) + CsI(Tl) telescope
Primary experimental observables
TOF t 1 nsKinetic energy, velocityE/E Light charged particles 2%Heavy ions 1%
Total solid angle /4
94%
Granularity 1192 modules
Angular range 1°< < 176°
Detection threshold
<0.5 MeV/A for H.I. 1 MeV/A for LCP
CHIMERA characteristic features
688 telescopes
Laboratori del Sud, Catania/Italy
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GRETA Detector ConfigurationTwo types of irregular hexagons, 60 each,3 crystals/cryostat= 40 modulesDetector – target distance = 15 cm$750k GRETINA
Technology in g spectroscopy Greta HPGe Array
Realistic coverage: Ω/4p=0.8Spatial resolution: ∆x=2 mm
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I.-Y. Lee, LBNL, 2011
Use Compton scattering laws to identify & track interactions of all g’s. Conventional method requires many detectors to retain high resolution and avoid summing.
g-Ray Tracking with HPGe Detector Array
2
1
1 1 cose
E EE m c
g gg
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Characteristic Examples of Level Schemes
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Single-particle spectra: Irregular sequence, half-integer spins, various parities.
Collective vibrations:
O+ g.s., even spins & parity, regular sequence with bunching of (0+,2+,4+) triplet
Collective rotations: Regular quadratic sequence 0+,2+,4+,….
Only even or only odd spins, I=2, uniform parity.
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Characteristic Level Schemes-Light Nuclei
Different densities of states.
Similarities in energies, spin, parity sequence for mirror nuclei:(N, Z)=(a, b)=(b,a)mirror
W. Udo Schröder, 2011
Gam
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2
Gamma Decay of Isobaric Analog States
For same T, wfs for protons and neutrons are similar
“Mirror Nuclei” 19Ne and 19F
W.u.
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Examples of Level Schemes: SM vs. Collective
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Example ofg –particle
Spectroscopy
W. Udo Schröder, 2012
Pri
nci
ple
s M
eas
2
5
Example
159
1037660
33
0
241Am
237Np
5.378 MeV
5.433 M
eV
5.47
6 M
eV
5.50
3 M
eV
5.54
6 M
eV
380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550
30
40
50
60
70
80
90
100
110
120
a Energy (keV) - 5 MeV
g E
nerg
y
(keV
)
a-Decay of 241Am, subsequent g emission from daughter
Find coincidences
(Ea, Eg)
9 g-rays, 5 a
W. Udo Schröder, 2012
Pri
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s M
eas
2
6
Example
159
1037660
33
0
241Am
237Np
5.378 MeV
5.433 M
eV
5.47
6 M
eV
5.50
3 M
eV
5.54
6 M
eV
380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550
30
40
50
60
70
80
90
100
110
120
a Energy (keV) - 5 MeV
g E
nerg
y
(keV
)
a-Decay of 241Am, subsequent g emission from daughter
Find coincidences
(Ea, Eg)
9 g-rays, 5 a
W. Udo Schröder, 2012
Pri
nci
ple
s M
eas
2
7
Example
159
1037660
33
0
241Am
237Np
5.378 MeV
5.433 M
eV
5.47
6 M
eV
5.50
3 M
eV
5.54
6 M
eV
380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550
30
40
50
60
70
80
90
100
110
120
a Energy (keV) - 5 MeV
g E
nerg
y
(keV
)
W. Udo Schröder, 2012
Pri
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s M
eas
2
8
Example
159
1037660
33
0
241Am
237Np
5.378 MeV
5.433 M
eV
5.47
6 M
eV
5.50
3 M
eV
5.54
6 M
eV
380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550
30
40
50
60
70
80
90
100
110
120
a Energy (keV) - 5 MeV
g E
nerg
y
(keV
)
W. Udo Schröder, 2012
Pri
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s M
eas
2
9
Example
159
1037660
33
0
241Am
237Np
5.378 MeV
5.433 M
eV
5.47
6 M
eV
5.50
3 M
eV
5.54
6 M
eV
380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550
30
40
50
60
70
80
90
100
110
120
a Energy (keV) - 5 MeV
g E
nerg
y
(keV
)
W. Udo Schröder, 2012
Pri
nci
ple
s M
eas
3
0
Example
159
1037660
33
0
241Am
237Np
5.378 MeV
5.433 M
eV
5.47
6 M
eV
5.50
3 M
eV
5.54
6 M
eV
380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550
30
40
50
60
70
80
90
100
110
120
a Energy (keV) - 5 MeV
g E
nerg
y
(keV
)
W. Udo Schröder, 2012
Pri
nci
ple
s M
eas
3
1
Example
159
1037660
33
0
241Am
237Np
5.378 MeV
5.433 M
eV
5.47
6 M
eV
5.50
3 M
eV
5.54
6 M
eV
380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550
30
40
50
60
70
80
90
100
110
120
a Energy (keV) - 5 MeV
g E
nerg
y
(keV
)
No -a g coincidences ! must be g.s. transition
W. Udo Schröder, 2012
Pri
nci
ple
s M
eas
3
2
Example
159
1037660
33
0
241Am
237Np
5.378 MeV
5.433 M
eV
5.47
6 M
eV
5.50
3 M
eV
5.54
6 M
eV
380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550
30
40
50
60
70
80
90
100
110
120
a Energy (keV) - 5 MeV
g E
nerg
y
(keV
)
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Exercises
Exercises: Nuclear Electrostatic Moments
Consider a nucleus with a homogeneous, axially symmetric charge distribution 1. Show that its electric dipole moment Q0 is zero.
2. Assume for the charge distribution a homogenously charged rotational ellipsoid with semi axes a and b, given by .
Show that
3. From the measured 242Pu and 244Pu g spectra determine the deformation parameters b of these two isotopes.
W. Udo Schröder, 2007
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Defo
rmati
on
s 3
4
r
2 2 20
2 4 4
5 5 51
; ;2
Q eZ b a eZR R eZR
R a b R b a R R
2 2 2 2 2 1x y a z b
Alpha-Gamma Spectroscopy
• 251Fm247Cf
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Defo
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s 3
5
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g SpectroscopyTheoretical Tools
Spectroscopic vs. Intrinsic Quadrupole Moment
W. Udo Schröder, 2010
Gam
ma D
eca
y 3
7
mI=I
z
q 1I I
I 2
01ˆ 3cos 12z
I I
I IQ Q Q
m I m I
I≠0: Transformation body-fixed to lab system
1 cos cos1
II
m I I II I
0 (2 1
20 ,1 2)
10z for I
IQ Q
I
23 ( 1)
( )2 1
Iz I z I
m I IQ m Q m I
I I
Any orientation
quadratic dependence of Qz on mI
“The” quadrupole moment
Electromagnetic Radiation
Gam
ma-G
am
ma C
orr
ela
tion
s 3
8
Protons in nuclei = moving charges emits electromagnetic radiation, except if nucleus is in its ground state!
Heinrich Hertz
E. Segré: Nuclei and Particles, Benjamin&Cummins, 2nd ed. 1977 Point
ChargesNuclearCharge
Distribution
Monopole ℓ = 0
Dipole ℓ = 1
Quadrupole ℓ =2
Propagating Electric Dipole Field
Gam
ma-G
am
ma C
orr
ela
tion
s 3
9
Nuclear Electromagnetic Transitions
Conserved: Total energy (E), total angular momentum (I) and total parity (p):
222
.
( ) ( , )mi
Initial Nucl State
j r Y
Ip
2+
1-
0+
Ei
g g g
i fi fi fE E E I I I
111
.
( ) ( , )mf
Final Nucl State
j r Y g ( ) ( , )I
mE
Photon WF
r Y
Consider often only electric multipole transitions.Neglect weaker magnetic transitions due to changes in current distributions.
Ip
2+
1-
0+
Ef
g
Initial Ni spatial symmetry retained in overall combination Nf +g
Illustration conserved spatial symmetry
Gam
ma-G
am
ma C
orr
ela
tion
s 4
0
Selection Rules for Electromagnetic Transitions
Conserved: Total energy (E), total angular momentum (I, Iz), total parity (p):
g g g
i fi fi fE E E I I I
iiI
f
fI
iI
z
mi
mf
fI
mg
i f
i f
i fi f
fi i fi i
i f
Electric dipole radiation
Angular momenta I I
direction undetermi
I I I
ned
Projections conserved
m m m m m
Other types magnetic and multipolarities
have other se
m m
I I I
m
Ig
g
g
[ 1( )]
,
.
, ,
( )
:
, 1 , 1
lection rules.
g
Coupling of Angular Momenta
Quantization axis : z direction. Physical alignment of I possible (B field, angular correlation)
g
W. Udo Schröder, 2011
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Transition Probabilities: Weisskopf’s s.p. Estimates
Consider single nucleon in circular orbit (extreme SM)
2 12 2 21
2
4.4( 1) 3 10( )
3 197(2 1)!!
RP E
MeV fm s
2 12 2 2 21
2
1.9( 1) 3 10( )
2 197(2 1)!!
RP M
MeV fm s
WeisskopfEstimates
Nucleus NucleusLow energy long wave length limit k R R fm
MeV fmE c k MeV fm k MeV
fm
krj kr for kr j kr j kr k k
g
g g g
g
1 1
/ : 1, 10
200200 20
10
( ) 1 ( ) ( ) :2 1 !!
W. Udo Schröder, 2011
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Weisskopf’s Eℓ Estimates
T1/2 for solid lines have been corrected for internal conversion.
2 1 2 3
:
( )
single particle
P E E Ag
Experimental E1: Factor 103-107 slower than s.p. WE Configurations more complicated than s.p. model, time required for rearrangement
Experimental E2: Factor 102 faster than s.p. WE Collective states, more than 1 nucleon.
Experimental Eℓ (ℓ>2): App. correctly predicted.
W. Udo Schröder, 2011
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Weisskopf’s Mℓ Estimates
T1/2 for solid lines have been corrected for internal conversion.
2 1 ( 1)2 3
:
( )
single particle
P M E Ag
Experimental Mℓ: Several orders of magnitude weaker than Eℓ transitions.
W. Udo Schröder, 2011
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Isospin Selection Rules
Reason: n/p rearrangements multipole charge distributions
photon interacts only with 1 nucleon (t = 1/2) DT = 0, 1
Example E1 transitions:
zE p cm i cmp i i
O e r R e r R iso vector op 11ˆ ( )2
Enhanced (collective) E2, E3 transitions DT = 0
Collective (rot or vib) WF does not change in transition.
n
M i p i n ii i i
n p i n p i ii i
iso scalar iso vector
zi
z z
n
zi i i
zi
pProjection operator
n
O g s g s
I g g s g g s l
g
P
1
0
11ˆ : (1 2 )2 0
1 1 1ˆ ˆ ˆ ˆ(1 2 ) (1 2 ) (1 2 )2 2 2
1 1 ˆˆ ˆ ˆ( 1) ( )2 2
3
pg .8 5.6
W. Udo Schröder, 2011
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Gamma Decay of Isobaric Analog States
For same T, wfs for protons and neutrons are similar
“Mirror Nuclei” 19Ne and 19F
W.u.
3
32 2
2 23 3
3
2
2
23
(
1
cos
3co
)
s
. ..
1
.. .
Z
Zd r r
Zd r r
er r
e rV r e d r
r r
e e Z
e e Z
e e ZZd r
e r dr r
Qr
r err
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Defo
rmati
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s 4
6
Electrostatic Multipole (Coulomb) Interaction
Monopoleℓ = 0
Dipole ℓ = 1 Quadrupole ℓ =2
Point Charges
Nuclear charge distribution
|e|Z
e
q
z
r
r
r r r
symmetry axis
Quadrupole Q ≠0,indicates deviation from spherical shape
Different multipole shapes/ distributions have different spatial symmetries
3 2
3
(cos )
,
1
d r r dr d d
azimuth polar angles
d r r
2 1.44e MeV fm
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Sp
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Magnetization: Magnetic Dipole Moments
Moving charge e current density j vector potential , influences particles at via magnetic field
r
p
e,m
r
r
3 3 30 03
( ) 1 1( ) ( ) ( ) ..
4 4j r
A r d r d r j r d r r r j rr r r r
3 30 03 3
1 1( ) ( ) .. ..
4 4( )A r d r r r j r d j r rr r
r r
03 3
3
1
1: [ ( )]
2
( )4
Magnetic dipole moment
rA r higher multipole momen Bts
r
r r j r
r
d
3
( ) ( ) . .
( ) ( ) ( ) ;
( ) ( )2 2 2r r R qu mech
er j r r r p r r p L
m
e e ed r r L r L g
m m m
0B H A
70 104
VsAm
mLoop = I x A= current x Area(inside)current loop:
=0
2
current
I e r
current density
j e
A r
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End Spectroscopy
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Lecture Plan Intro to Nuclear Structure
W. Udo Schröder, NCSS 2012
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Day Time Topic
Monday 6/25
09:00-10:0010:30-11:30
How do we know about NS? Nuclear Spectroscopy.Nucleon-Nucleon forces and 2-body Systems
Tuesday 6/26
09:00-10:0010:30-11:30
Mean Field and its Symmetries, Spin and IsospinFermi Gas Model
Wednesday 6/27
09:00-10:0010:30-11:30
Spherical Shell ModelSimple Predictions and Comparisons
Thursday 6/28
09:00-10:0010:30-11:30
Residual Interactions/ PairingDeformed Nuclei and their Spectroscopy
Friday 6/29
09:00-11:30 Final Exam