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.
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