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