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
BE 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
Ym ,   Y*m  ' ,  '

r  r'
2  1 m
 0 r
multipole moments
M * , m    p r '  r ' Y*m  ' ,  'd '
m2

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