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Themes and challenges of Modern Science. Complexity out of simplicity – Microscopic How the world, with all its apparent complexity and diversity can be constructed out of a few elementary building blocks and their interactions Simplicity out of complexity – Macroscopic - PowerPoint PPT Presentation
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Themes and challenges of Modern Science
Complexity out of simplicity – Microscopic
How the world, with all its apparent complexity and diversity can be constructed out of a few elementary building blocks and their interactions
Simplicity out of complexity – Macroscopic
How the world of complex systems can display such remarkable regularity and simplicity
vibration rotation fission
individual excitations of nucleons
The three faces of the shell model
Experimental single-particle energies
208Pb → 209Bi Elab = 5 MeV/u
1 h9/2
2 f7/2
1 i13/2 1609 keV
896 keV
0 keV
γ-spectrumsingle-particle energies
12620983Bi
Experimental single-particle energies
208Pb → 207Pb Elab = 5 MeV/u
γ-spectrum
single-hole energies
3 p1/2
2 f5/2
3 p3/2 898 keV
570 keV
0 keV
12520782Pb
Experimental single-particle energies
209Pb209Bi
207Pb207Tl
)2()()( 2/9208209 gEPbBEPbBE
)3()()( 2/1208207 pEPbBEPbBE
energy of shell closure:
432.3
)(2)()()3(2 2082072092/12/9
PbBEPbBEPbBEpEgE
)1()()( 2/9208209 hEPbBEBiBE
)3()()( 2/1208207 sEPbBETlBE
MeV
PbBETlBEBiBEsEhE
211.4
)(2)()()3(1 2082072092/12/9
1 h9/2
2 f7/2
1 i13/21609 keV
896 keV
0 keV
12620882Pb
particle states
hole states
protons neutrons
Level scheme of 210Pb
0.0 keV
779 keV
1423 keV
1558 keV
2202 keV
2846 keV
-1304 keV (pairing energy)
M. Rejmund Z.Phys. A359 (1997), 243
12720982Pb
Evolution of nuclear structure
as a funtion of nucleon number
Experimental observables in even-even nuclei
1 12 4 2( ; )B E
1000 4+
2+
0
400
0+
E ( keV) Jπ
1 12 2 0( ; )B E
)2(
)4(
1
12/4
E
ER
22
12
1;2 if
ifi EM
JJJEB
Neutron number 68 70 72 74 76 78 80 82
Val. Neutr. number 14 12 10 8 6 4 2 0
(Z = 52)Systematics of the Te isotopes (Z=52)
(Z = 52)Systematics of the Te isotopes (Z=52)
0+
2+4+
2+
0+
120Te 130Te 134Te
0+ 0+
2+
2+
2+ 4+4+ 6+
Case of few valence nucleons: lowering of energies, development of multiplets. R4/2 → ~2-2.4
0.56
1.10
1.161.20
0.84
1.591.63 1.69
1.58
1.28
(Z = 52)Electric fields of multipoles
r
r
d
In general the electric potential due toan arbitrary charge distribution is
'
'
'
d
rr
rrU p
expansion
',',12
4'
'
1 *
01
m
mm YY
r
r
rr
special case: electric quadrupole matrixelement
'',''', ** dYrrmM mp
2
20*
4
3,2
ReZ
mM
multipole moments
B(E2)-value: 2* ,2);2(
mMiiiffffi
f
KMImMKMIIIEB
mMYr
rU m
m
m
,2,1
5
4 *,23
2
2
special case: electric quadrupole potential
