scholarly journals Is collective motion symmetric in the neutron‐proton degrees of freedom?

1991 ◽  
Author(s):  
Joseph N. Ginocchio ◽  
Amiram Leviatan ◽  
Michael W. Kirson
Keyword(s):  
Degrees Of Freedom ◽  
Collective Motion

COLLECTIVE SPIN BY LINEARIZATION OF THE SCHRÖDINGER EQUATION FOR NUCLEAR COLLECTIVE MOTION

1988 ◽  
Vol 03 (09) ◽  
pp. 859-866 ◽  
Author(s):  
MARTIN GREINER ◽  
WERNER SCHEID ◽  
RICHARD HERRMANN
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
Collective Motion ◽  
First Order ◽  
Energy And Momentum

The free Schrödinger equation for multipole degrees of freedom is linearized so that energy and momentum operators appear only in first order. As an example, we demonstrate the linearization procedure for quadrupole degrees of freedom. The wave function solving this equation carries a spin. We derive the operator of the collective spin and its eigenvalues depending on multipolarity.

MICROSCOPIC SELF-CONSISTENT AND COLLECTIVE MODEL DESCRIPTION OF LOW-ENERGY NUCLEAR STRUCTURE

1989 ◽  
Vol 04 (09) ◽  
pp. 2063-2146 ◽  
Author(s):  
K. HEYDE
Keyword(s):  
Nuclear Structure ◽  
Degrees Of Freedom ◽  
Collective Motion ◽  
Collective Model ◽  
Model Description ◽  
Mixed Symmetry ◽  
Self Consistent ◽  
Closed Shells ◽  
Model Approach

In the present review, an attempt is made to approach the different facets of the nucleus at low excitation energy from both a microscopic, self-consistent and a collective model approach. Some attention is given on how to relate the two “opposite” approaches to nuclear structure. In a final chapter, we discuss some newly appreciated modes in the nucleus that are specific to the proton and neutron degrees of freedom e.g. the study of intruder states near closed shells and the presence of proton-neutron mixed-symmetry collective motion.

SUM RULE FOR MULTISCALE REPRESENTATIONS OF KINEMATICALLY DESCRIBED SYSTEMS

2002 ◽  
Vol 05 (04) ◽  
pp. 409-431 ◽  
Author(s):  
YANEER BAR-YAM
Keyword(s):  
Kinetic Energy ◽  
Degrees Of Freedom ◽  
Collective Motion ◽  
Space Time ◽  
Moment Of Inertia ◽  
Sum Rule ◽  
Effective Moment ◽  
External Frame ◽  
The Moment ◽  
Effective Moment Of Inertia

We derive a sum rule that constrains the scale based decomposition of the trajectories of finite systems of particles. The sum rule reflects a tradeoff between the finer and larger scale collective degrees of freedom. For short duration trajectories, where acceleration is irrelevant, the sum rule can be related to the moment of inertia and the kinetic energy (times a characteristic time squared). Thus, two nonequilibrium systems that have the same kinetic energy and moment of inertia can, when compared to each other, have different scales of behavior, but if one of them has larger scales of behavior than the other, it must compensate by also having smaller scales of behavior. In the context of coherence or correlation, the larger scale of behavior corresponds to the collective motion, while the smaller scales of behavior correspond to the relative motion of correlated particles. For longer duration trajectories, the sum rule includes the full effective moment of inertia of the system in space-time with respect to an external frame of reference, providing the possibility of relating the class of systems that can exist in the same space-time domain.

PARTONIC EQUATION OF STATE IN HIGH-ENERGY NUCLEAR COLLISIONS

2007 ◽  
Vol 16 (03) ◽  
pp. 715-727 ◽  
Author(s):  
NU XU
Keyword(s):  
Equation Of State ◽  
Heavy Ion Collisions ◽  
Degrees Of Freedom ◽  
Collective Motion ◽  
Radial Flow ◽  
Heavy Ion ◽  
High Energy ◽  
Experimental Results ◽  
Nuclear Collisions ◽  
Ion Collisions

After a brief introduction to the physics of high-energy nuclear collisions, we will present recent experimental results that are closely connected to the properties of the matter produced in Au + Au collisions at RHIC. Collective motion with parton degrees of freedom is called partonic collectivity. We will focus on collective observables such as transverse radial flow and elliptic flow. With experimental observations, we will demonstrate that collectivity is developed prior to the hadronic stage in heavy ion collisions at RHIC.

scholarly journals Dynamics of a vibration-driven single disk

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Liyang Guan ◽  
Li Tian ◽  
Meiying Hou ◽  
Yilong Han
Keyword(s):  
Kinetic Energy ◽  
Degrees Of Freedom ◽  
Collective Motion ◽  
Boltzmann Distribution ◽  
Low Frequencies ◽  
Collective Behaviors ◽  
High Frequencies ◽  
Single Disk ◽  
Rotational Motions ◽  
Granular Particles

AbstractGranular particles exhibit rich collective behaviors on vibration beds, but the motion of an isolated particle is not well understood even for uniform particles with a simple shape such as disks or spheres. Here we measured the motion of a single disk confined to a quasi-two-dimensional horizontal box on a vertically vibrating stage. The translational displacements obey compressed exponential distributions whose exponent $$\beta$$ β increases with the frequency, while the rotational displacements exhibit unimodal distributions at low frequencies and bimodal distributions at high frequencies. During short time intervals, the translational displacements are subdiffusive and negatively correlated, while the rotational displacements are superdiffusive and positively correlated. After prolonged periods, the rotational displacements become diffusive and their correlations decay to zero. Both the rotational and the translational displacements exhibit white noise at low frequencies, and blue noise for translational motions and Brownian noise for rotational motions at high frequencies. The translational kinetic energy obeys Boltzmann distribution while the rotational kinetic energy deviates from it. Most energy is distributed in translational motions at low frequencies and in rotational motions at high frequencies, which violates the equipartition theorem. Translational and rotational motions are not correlated. These experimental results show that the random diffusion of such driven particles is distinct from thermal motion in both the translational and rotational degrees of freedom, which poses new challenges to theory. The results cast new light on the motion of individual particles and the collective motion of driven granular particles.

U(6)-Phonon model of nuclear collective motion

2015 ◽  
Vol 24 (05) ◽  
pp. 1550039 ◽  
Author(s):  
H. G. Ganev
Keyword(s):  
Degrees Of Freedom ◽  
Collective Motion ◽  
Pauli Principle ◽  
The Other ◽  
Intrinsic Structure ◽  
Dynamical Group ◽  
Model Interpretation ◽  
State Band ◽  
Phonon Structure ◽  
Phonon Model

The U(6)-phonon model of nuclear collective motion with the semi-direct product structure [HW(21)]U(6) is obtained as a hydrodynamic (macroscopic) limit of the fully microscopic proton–neutron symplectic model (PNSM) with Sp(12, R) dynamical group. The phonon structure of the [HW(21)]U(6) model enables it to simultaneously include the giant monopole and quadrupole, as well as dipole resonances and their coupling to the low-lying collective states. The U(6) intrinsic structure of the [HW(21)]U(6) model, from the other side, gives a framework for the simultaneous shell-model interpretation of the ground state band and the other excited low-lying collective bands. It follows then that the states of the whole nuclear Hilbert space which can be put into one-to-one correspondence with those of a 21-dimensional oscillator with an intrinsic (base) U(6) structure. The latter can be determined in such a way that it is compatible with the proton–neutron structure of the nucleus. The macroscopic limit of the Sp(12, R) algebra, therefore, provides a rigorous mechanism for implementing the unified model ideas of coupling the valence particles to the core collective degrees of freedom within a fully microscopic framework without introducing redundant variables or violating the Pauli principle.

THE NUCLEAR BORN–OPPENHEIMER METHOD APPLIED TO NUCLEAR COLLECTIVE MOTION

2002 ◽  
Vol 11 (03) ◽  
pp. 231-248
Author(s):  
NOUREDINE ZETTILI ◽  
ABDELKRIM BOUKAHIL
Keyword(s):  
Degrees Of Freedom ◽  
Ad Hoc ◽  
Collective Motion ◽  
Collective Model ◽  
Tensor Operator ◽  
Nbo Method ◽  
Inertial Parameters ◽  
Principal Axes ◽  
Selection Of ◽  
Made In

We deal with the application of the nuclear Born–Oppenheimer (NBO) method to the study of nuclear collective motion. In particular, we look at the description of nuclear rotations and vibrations. The collective operators are specified within the NBO method only to the extent of identifying the type of collective degrees of freedom we intend to describe; the operators are then determined from the dynamics of the system. To separate the collective degrees of freedom into rotational and vibrational terms, we transform the collective tensor operator from the lab fixed frame of reference to the frame defined by the principal axes of the system; this transformation diagonalizes the tensor operator. We derive a general expression for the NBO mean energy and show that it contains internal, collective and coupling terms. Then, we specify the approximations that need to be made in order to establish a connection between Bohr's collective model and the NBO method. We show that Bohr's collective Hamiltonian can be recovered from the NBO Hamiltonian only after adopting some rather crude approximations. In addition, we try to understand, in light of the NBO approach, why Bohr's collective model gives the wrong inertial parameters. We show that this is due to two major reasons: the ad hoc selection of the collective degrees of freedom within the context of Bohr's collective model and the unwarranted neglect of several important terms from the Hamiltonian.

Sign in / Sign up

Export Citation Format

Share Document