Collective rotation

Another interesting case of nuclear rotation occurs in the spherical nuclei. The observation of equally spaced 7-ray transitions implies collective rotation, but such bands have been observed in near spherical 199Pb. It has been suggested that these bands arise by a new type of nuclear rotation, called the shears mechanism. A few... 

In contrast with the chain of coupled oscillators, the translational invariance of a chain of coupled rotors leads not to a continuous spectrum, but to two branches of tunneling states determined by Eqs. (7.83). These states are coherent, whereas the space-localized breather states (7.80) are incoherent. In this respect, the transitions between breather states are similar to thermally activated rotation of a single group, though the number of rotors lying within the breather envelope and participating in the collective motion is greater than unity ( 20). The above discussion of collective rotation, which is based on the paper of Fillaux and Carlile [1990], demonstrates that the spectrum of a chain of coupled rotors is much richer than the spectrum one can expect from the traditional band model. 

Figure 6.8-10 Stokes wings of the collected rotational Raman spectra of N2 and O2 at room temperature using an argon ion laser.

It is considered that several monomeric units are involved in segmental motions which are observed from the spin-lattice relaxation rate. More precisely, it is assumed that collective rotational isomerizations of a small number of succesive monomeric units are converted into a translational random motion of a short segment. An effective friction coefficient of one... 

The alkaline earth atoms—Be, Mg, Ca, Sr, and Ba—are the natural species to consider first. The important question here is whether the states of the two valence electrons are better described by collective, rotation-vibration quantization or by independent-particle quantization. Difficulties with the latter have been discussed.6,86,25 The new issue is whether moleculelike quantization is much more nearly free of its own problems. 

Third, the decay times of the electro-optical responses at dc pulses are systematically lower than those of the responses in the kilohertz range. This is true for polyelectrolytes, as shown by the detailed investigations of Oppermann [16,17], it is also true for the rigid rodlike particles discussed here [58-60]. Assignment of the larger time constants to (collective) rotation is consistent with the fact that translation motions are restricted at higher frequency. 

In Sect. 2.3.1 the shell model of spherical and deformed nuclei was discussed. The model gives a good description of various phenomena observed in the light (A < 80), near double-magic (e.g., around Pb) and well-deformed nuclei (e.g., in the regions 150 < A < 190, A > 220). The shell model is a microscopic nuclear model, i.e., it is formulated at the nucleonic level. At the same time, the application of the model far from magic nuclei leads sometimes to very complicated calculations. Furthermore, many observations clearly show the existence of collective behavior in nuclei (surface vibration, collective rotation), which can be treated in macroscopic framework much more simply. 

Collective rotational states form series, which are called bands. The states belonging to a band are specified by a single intrinsic state. The states of a band only differ in the amount of rotation they carry, i.e., in the value of the angular momentum (i) of the rotational motion. 

High-spin states were observed also in nearly spherical nuclei, e.g., in 4 Gdg3. In this case, the level scheme does not show the regular pattern of collective rotation, and the reduced E2 transition probabilities are close to the Weisskopf unit. The high-spin states are produced by the alignment of individual nucleonic orbits. This is the case of non-collective rotation. The irregularities are related to the occupation of different single-particle states. 

In addition to these two extreme types of rotational motion, a combination of collective and non-collective rotational excitations is also possible. 

The potential energy calculations performed for high-spin states show that some nuclei may again acquire triaxial equilibrium shape before fission, and that may lead to collective rotational states. 

E. Santamato, B. Daino et al.. Collective Rotation of Molecules Driven by the Angular Momentum of Light in a Nematic Film, Phys. Rev. Lett. (1986) 158... 

A well-known nonlinear process taking place in the liquid state of anisotropic molecules is the optical-field induced birefringence (optical Kerr effect ). This nonlinearity results from the reorientation of the molecules in the electric field of a light beam. In the isotropic phase the optical field perturbs the orientational distribution of the molecules. In the perturbed state more molecules are aligned parallel to the electric field than perpendicularly to it and as a consequence the medium becomes birefringent. On the other hand in liquid crystals the orientational distribution of the molecules is inherently anisotropic. The optical field, just as a d.c. electric or magnetic field, induces a collective rotation of the molecules. This process can be described as a reorientation of the director. 

Collective Rotation of Molecules Driven by the Angular Momentum of Light in a Nematic Film... 

Fig. 11 Schematic representation of the angular momenta in the nucleus. On top of an intrinsic excitation with angular momentum I and projection K a collective rotation can be built with orbital angular momentum R. The total angular momentum of the nucleus is J, and all levels in the resulting rotational band have the same K quantum number...

---