The nuclear scissors mode from various aspects

Three methods to describe collective motion, random phase approximation (RPA), Wigner function moments (WFM) and the Green’s Function (GF) method are compared in detail and their physical content analyzed on an example of a simple model, the harmonic oscillator with quadrupole-quadrupole residual interaction. It is shown that they give identical formulae for eigenfrequencies and transition probabilities of all collective excitations of the model, including the scissors mode, which is the subject of our special attention. The exact relation between the RPA and WFM variables and the respective dynamical equations is established. The transformation of the RPA spectrum into the one of WFM is explained. The very close connection of the WFM method with the GF one is demonstrated. The normalization factor of the “synthetic” scissors state and its overlap with physical states are calculated analytically. The orthogonality of the spurious state to all physical states is proved rigorously. A differential equation describing the current lines of RPA modes is established and the current lines of the scissors mode analyzed as a superposition of rotational and irrotational components.     

Collective motion from various aspects

Three methods to describe collective motion, the Random Phase Approximation (RPA), Wigner Function Moments (WFM), and Green’s Function (GF) methods, are compared in detail and their physical content analyzed in the example of a simple model, a harmonic oscillator with quadrupole-quadrupole residual interaction. It is shown that they give identical formulae for eigenfrequencies and transition probabilities of all collective excitations of the model. The exact relation between the RPA and WFM variables and the respective dynamical equations is established. The transformation of the RPA spectrum into one of WFM is explained. The very close connection of the WFM method with the GF method is demonstrated. A differential equation describing the current lines of RPA modes is established and the current lines of the scissors mode are analyzed as a superposition of rotational and irrotational components. The orthogonality of the spurious state to all physical states is proved rigorously. The text was submitted by the author in English.     

Low-collective scissors mode

Realistic microscopic RPA calculations for¹⁵⁶Gd with a deformed Woods-Saxon mean field, quadrupole-quadrupole, spin-spin and symmetry-restoring residual interactions show that the purely collective scissors mode of the two-rotor model is fragmented over orbital isovector 1⁺ states, lying at 2–7 MeV. The strongest experimentally observed magnetic dipole state is interpreted as performing a low-collective scissors-type of geometrical motion. This conclusion evolves from the identification of the above state with the strongest RPA excitation, which reproduces well the experimental energy,B(M1) value and (e, e′) form factor, has the largest overlap with the scissors state and can be represented as a low-collective scissors type vibration.     

From conventional (neutron-proton) nuclear scissors to spin nuclear scissors

Investigations of the nuclear scissors mode in the frame of the Wigner Function Moments (WFM) method leading to the discovery of the new types of the nuclear collective motion are reviewed. It is demonstrated how the generalization of WFM method to take into account spin degrees of freedom allows one to reproduce all earlier described qualitative features of the conventional (neutron-proton) nuclear scissors (deformation dependence of the energy and transition probabilities, connection with isovector GQR implying the Fermi surface deformation, flows) and allows one to reveal a variety of new collective modes: isovector and isoscalar spin scissors, the relative motion of the orbital angular momentum and spin, isovector and isoscalar spin-vector GQR, spin-flip excitations.     

Wigner Function Moments versus RPA in a simple model

Two complementary methods to describe the collective motion, RPA and Wigner Function Moments (WFM) method, are compared using an example of a simple model—harmonic oscillator with quadrupole-quadrupole residual interaction. It is shown that they give identical formulas for eigenfrequencies and transition probabilities of all collective excitations of the model, including the scissors mode, which is a subject of our special attention. The exact relation between the variables of the two methods and the respective dynamical equations is established. The transformation of the RPA spectrum into the WFM one is explained. The text was submitted by the authors in English.     

The Nuclear Spin Scissors Mode—Theory and Experiment

A new type of nuclear collective motion—the spin scissors mode—was predicted seven years ago. Promising signs of its existence in ²³²Th were found. We perform a systematic analysis of experimental data on M1 excitations in rare earth nuclei to find traces of the spin scissors mode in this area. Obvious signs of its existence will be demonstrated. We propose new criteria to attribute the observed 1⁺ states to the scissors mode, entailing that the agreement of the experimental data with the results of our calculations and with the sum rules is improved substantially.     

Development of finite fluctuations in local density, velocity, and temperature for real fluids

Analytical expressions for large-scale finite local fluctuations of temperature and collective velocity valid for all states of real fluids are presented. Models for the probability distribution of finite density and temperature fluctuations are proposed. It is demonstrated that a fluctuating fluid consists of two fractions. The basic properties of the fractions are established, and the role of each faction in the makeup of the physical and chemical properties of the fluid is specified. It is shown that the development of large-scale finite fluctuations is not an inherent feature of the critical state: it is characteristic of a wide range of states of real fluids.     

On the validity of the cranking model for 2+-vibrations

The relation of the cranking model to more fundamental methods of determining the generator of a collective state is investigated for the quadrupole case. We are able to show that the heuristic procedure starting with an adiabatic change in the nuclear deformation and splitting the cranking operator according to main quantum number selection rules approximates the true collective states very well. However, for the low-lying collective state the analytic form of the cranking term is completely different from any type of scaling ansatz.     

Rotational states and interacting bosons

Rotational states are investigated in terms of the interacting boson model. A ground-state rotational band is built from a shell-model many-nucleon system. It is shown that the S and D collective nucleon pairs play dominant roles in low-spin states of the band and that this S-D dominance is broken in high-spin states. The intrinsic hamiltonian is constructed from the effective nucleon-nucleon interaction used in the shell model calculation and the intrinsic state of the rotational band is shown to be comprised primarily of S and D pairs. We introduce a λ boson which is a linear combination of s, d and higher angular momentum bosons, and the boson intrinsic state is given by the λ boson condensate state. The s and d bosons constitute approximately 90 % of the λ boson, and the boson intrinsic state reproduces very well the energy and the intrinsic quadrupole moment of the nucleon intrinsic state. The s-d boson hamiltonian is constructed from the S and D pairs, while effects of non S-D pairs are also included by renormalization of the boson hamiltonian. The renormalization is made by using the λ boson. The s-d boson quadrupole operator is derived similarly. The boson hamiltonian and quadrupole operator thus derived reproduce well the exactly calculated values for low-spin states of the rotational band, although the accuracy decreases in high-spin states. It is shown that the IBM possesses the same physical picture of the rotational states as the Nilsson scheme with pairing correlations. It is therefore concluded that the IBM is capable of describing low-lying rotational states.     

Correlated Nucleon Pair Model and Microscopic Basis of Interacting Boson

An earlier work dealing with low-lying collective states in nuclei is revised and improved. Correlated and independent nucleon S and D pairs properly modified so that they behave approximately like bosons are constructed in terms of which a model space for lowlying collective states is defined, and a microscopic basis for IBM is thus set up. All dynamical variables can also be "bosonized", i.e., expressed in terms of these "bosons" but with statedependent coefficients or operators to incorporate their state dependence in model space.     

Laser control of collective spontaneous emission

The collective spontaneous emission of a pair of two coupled three-level radiators in vacuum is investigated in the presence of a possibly intense laser field. The parameters describing the collective interaction along with the population and decay rates of all involved dressed states are shown to be controllable by the applied laser field. In particular, all populations of the collective system may be transferred at will in a reversible way into a subradiant state, allowing effective storage and manipulation of the quantum system.     

Virtual-Excitation Induced High-Dimensional State Transfer in a Quantum Network

We propose a scheme for quantum state transfer within the high-dimensional state subspaces between any two nodes in a quantum network. The states are encoded in the collective ground states of multiple atoms. The transfer processes are controlled by only applying external laser pulses. The prominent feature of the scheme is that the state transfer of any dimension can be achieved through virtually coupling all the excitations of the total system.     

Shell model theory of elastic scattering of nucleons by deformed nuclei

The escape width originating from a collective rotational state as a doorway state is calculated in the framework of the shell model theory of nuclear reactions. The rotational states are constructed by Yoccoz-Peierls angular momentum projection from deformed intrinsic states which are described by BCS wave functions. For some rare earth nuclei it is shown that there result escape widths of the order of magnitude of 20–100 keV.     

Robust and fragile Werner states in the collective dephasing

We investigate the concurrence and Bell violation of the standard Werner state or Werner-like states in the presence of collective dephasing. It is shown that the standard Werner state and certain kinds of Werner-like states are robust against the collective dephasing, and some kinds of Werner-like states is fragile and becomes completely disentangled in a finite-time. The threshold time of complete disentanglement of the fragile Werner-like states is given. The influence of external driving field on the finite-time disentanglement of the standard Werner state or Werner-like states is discussed. Furthermore, we present a simple method to control the stationary state entanglement and Bell violation of two qubits. Finally, we show that the theoretical calculations of fidelity based on the initial Werner state assumption well agree with previous experimental results.     

Quantum computing with collective ensembles of multilevel systems

We propose a new physical approach for encoding and processing of quantum information in ensembles of multilevel quantum systems, where the different bits are not carried by individual particles but associated with the collective population of different internal levels. One- and two-bit gates are implemented by collective internal state transitions taking place in the presence of an excitation blockade mechanism, which restricts the population of each internal state to the values zero and unity. Quantum computers with 10-20 bits can be built via this scheme in single trapped clouds of ground state atoms subject to the Rydberg excitation blockade mechanism, and the linear dependence between register size and the number of internal quantum states in atoms offers realistic means to reach larger registers.     

动态关联和110Cd的集体态

提出了动态关联的概念,并用这种关联讨论了¹¹⁰Cd的集体态. 同时还考虑了该核素中的g玻色子自由度,并在sdf玻色子的框架下讨论了它的八极态.     

Nuclear scissors with pairing and continuity equation

The coupled dynamics of the isovector and isoscalar giant quadrupole resonances and low-lying modes (including scissors) is studied with the help of the Wigner-function-moment method generalized to take into account pair correlations. Equations of motion for collective variables are derived on the basis of the time-dependent Hartree-Fock-Bogoliubov equations in the harmonic-oscillator model with quadrupole—quadrupole residual interaction and a Gaussian pairing force. Special care is taken of the continuity equation. The text was submitted by the authors in English.