Transcript Folie 1
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
individual excitations
of nucleons
Simplicity out of complexity – Macroscopic
How the world of complex systems can display such remarkable regularity and
simplicity
vibration
rotation
fission
The three faces of the shell model
Experimental single-particle energies
γ-spectrum
single-particle energies
1 i13/2
1609 keV
2 f7/2
896 keV
1 h9/2
0 keV
209
83
Bi126
208Pb
→ 209Bi
Elab = 5 MeV/u
Experimental single-particle energies
γ-spectrum
208Pb
single-hole energies
3 p3/2
898 keV
2 f5/2
570 keV
3 p1/2
0 keV
207
82
Pb125
→ 207Pb
Elab = 5 MeV/u
Experimental single-particle energies
particle states
209Bi
2 f7/2
1609 keV
896 keV
1 h9/2
0 keV
1 i13/2
208
82
209Pb
energy of shell closure:
Pb126
BE(209Bi) BE(208Pb) E(1h9 / 2 )
BE(207Tl ) BE(208Pb) E(3 s1/ 2 )
E 1h9 / 2 E (3 s1/ 2 ) BE( 209Bi) BE( 207Tl ) 2 BE( 208Pb)
4.211MeV
207Tl
207Pb
BE(209Pb) BE(208Pb) E(2 g9 / 2 )
BE(207Pb) BE(208Pb) E(3 p1/ 2 )
hole states
protons
neutrons
E 2 g9 / 2 E (3 p1/ 2 ) BE( 209Pb) BE( 207Pb) 2 BE( 208Pb)
3.432
Level scheme of 210Pb
2846 keV
2202 keV
1558 keV
1423 keV
779 keV
0.0 keV
-1304 keV (pairing energy)
M. Rejmund Z.Phys. A359 (1997), 243
209
82
Pb127
Evolution of nuclear structure
as a funtion of nucleon number
Experimental observables in even-even nuclei
1000
E (41 )
R4 / 2
E (21 )
4+
B ( E2; 41 21 )
400
2+
B ( E2; 21 01 )
0
E ( keV)
0+
Jπ
1
BE 2; J i J f
f M E 2 i
2 Ji 1
2
Systematics of the Te isotopes (Z=52) (Z = 52)
Neutron number
68
70
72
74
76
78
80
82
Val. Neutr. number 14
12
10
8
6
4
2
0
Systematics of the Te isotopes (Z=52) (Z = 52)
2+
0+ 4
1.63
1.59
4+
1.16
1.20
1.10
+ 2+
2+
2+
6+
4+
1.69
1.58
2+
1.28
0.84
0.56
0+
0+
120Te
0+
130Te
134Te
Case of few valence nucleons: lowering of energies, development of multiplets. R4/2 → ~2-2.4
Electric fields of multipoles
d
r
r
(Z = 52)
In general the electric potential due to
an arbitrary charge distribution is
p r '
U r d '
r r'
expansion
1
r ' 4
1
Ym , Y*m ' , '
r r'
2 1 m
0 r
multipole moments
M * , m p r ' r ' Y*m ' , 'd '
m2
4 3 1Z e R0
M
2
,
m
special case: electric quadrupole potential
matrixelement
U r
Y 2,m , 2 M * 2, m
3 4
m 2 5 r
B(E2)-value:
B( E 2; I i I f ) I f M f K f M * 2, m I i M i K i
2
*
Mfm
2