How do nuclei rotate?

5. Appearance of bands

Deformed mean field solutions

zJiz e )( axis-z about the Rotation R

This is clearly the case for a well deformed nucleus.Deformed nuclei show regular rotational bands.Spherical nuclei have irregular spectra.

n.orientatiodifferent

of states theseall of ionsuperposita is state rotational The

.energy same thehave )( | states field mean All

peaked.sharply is 1|||

.but

|R

|R

RRRR

z

z

zzzz hhHH

deformed

Er163

spherical

Pb200

Dynucleus

medsuperdefor thefrom rays - 152

Pbnucleus

spherical thefrom rays - 199

E2 radiation

M1 radiation

Magnetic rotation

Shears mechanism

Most of interaction is dueto polarization of the core.

TAC calculations describethe phenomenon.

TAC

Measurements confirmed the length of the parallelcomponent of the magnetic moment.

Antimagnetic rotation

Ferromagnet Anti-Ferromagnet

Magnetic rotor Antimagnetic rotor

58106

48Cd

Magnetic rotor Antimagnetic rotor

small B(E2) (deformation)

large B(M1) (transversal no B(M1) (transversal magnetic moment ) magnetic moment)

decreases with I

decreases with I

sequence 2

symmetry )(

ΔIz R

sequence 1

symmetry )( no

ΔIz R

Substantial moment of inertia

2

2)2(

)(100

)2( ebMeVEB

Band termination

],[],[ 2/112/112/9lki hhglik

termination

5810951 Sb

6011151 Sb

The nature of nuclear rotational bands

The experimentalist’s definition of rotational bands:

Requirements for the mean field:

norientatio peaked.sharply is 1||| |Rz

smoothness 1. toclose is 1|)1(|)(| DII

deformation super normal weak

axes ratio (

1:2 (0.6) 1:1.5 (0.3) 1:1.1 (0.1)

mass 150 180 200

1 1/2 1/7

2 4 20

4 8 20

60 30 8

D 0.005 0.03 0.05

rig /)2(

irrot /)2(

][o

][J

4,, 2 J

R

Rrigirrot

Terminating bands

Classical periodic orbits in a deformed potential

Summary

• Breaking of rotational symmetry does not always mean substantial deviation of the density distribution from sphericity.

• Magnetic rotors have a non-spherical arrangement of current loops. They represent the quantized rotation of a magnetic dipole.

• The angular momentum is generated by the shears mechanism.

• Antimagnetic rotors are like magnetic ones, without a net magnetic moment and signature symmetry.

• Bands terminate when all angular momentum of the valence nucleons is aligned.

• The current loops of the valence orbits determine the current pattern and the moment of inertia.