Abstract
A brief review is given on the controversy and its solution about the fact that the angular momentum vector of protons and that of neutrons in well-deformed nuclei at low total angular momenta have a strong correlation that they are oriented in opposite directions. In a simple two-rotor model in 2-dimensional space, this fact is explained as originating from the quantum mechanical uncertainty relation between the angle and the angular momentum for the relative rotation of the two rotors. As the second topic, a more realistic model consisting of two triaxial rotors in 3-dimensional space coupled with a QQ interaction is employed to investigate a possible shears-band-like collective rotation predicted by T. Otsuka, in which the angle at which the angular momentum of protons and that of neutrons intersect changes continuously from 180° at spin zero toward 0° at high spins within the same rotational band. The probability distributions of the angle between the two angular momenta and the angle between the longest principal axes of two rotors are calculated to examine the participation of the scissors mode in the evolution of the ground rotational band versus spin.
Highlights
We have recently given careful consideration to the meaning of the antiparallel proton and neutron angular momenta at low spins [1]
Ref.[5] argued that the removal of the spurious center-of-mass motion could make the angular momenta of protons and neutrons parallel
In Ref.[1], Otsuka and we have shown that the elimination of the spurious center-of-mass motion does not substantially change the situation in a classical treatment of independent nucleon motions
Summary
We have recently given careful consideration to the meaning of the antiparallel proton and neutron angular momenta at low spins [1]. The principal intention of Ref.[2] was to suggest the possibility that collective rotational excitations are accompanied with a narrowing of the angle between the proton and neutron angular momenta. We calculate the expectation values and the probability distribution of the angle between the angular momenta and the angle between the longest principal axes of rotors These two angles have different kinds of information because of the quantum mechanical uncertainty in the directions of the angular momenta relative to the principal axes of the ellipsoids, and owing to dynamically correlated rotational motions of the two rotors
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