scholarly journals Crystal Field Effects in S-state Ions Due to Exchange Polarization

1976 ◽  
Vol 29 (3) ◽  
pp. 177 ◽  
Author(s):  
DJ Newman
Keyword(s):  
Crystal Field ◽  
Electron Correlation ◽  
Ground State ◽  
Matrix Elements ◽  
Open Shells ◽  
The Matrix ◽  
New Type ◽  
Relationship Of ◽  
The Relationship ◽  
Exchange Polarization

It is shown that the matrix elements of the tensor operators describing a new type of crystal field can be calculated using the properties of the spin ~ quasi-spin transformation. The relationship of this field to electron correlation in open shells is clarified, and its contribution to the ground state splittings of S-state ions is discussed

scholarly journals Терагерцовая спектроскопия магнитоэлектрика HoAl-=SUB=-3-=/SUB=-(BO-=SUB=-3-=/SUB=-)-=SUB=-4-=/SUB=-

2022 ◽  
Vol 130 (1) ◽  
pp. 59
Author(s):  
А.М. Кузьменко ◽  
В.Ю. Иванов ◽  
А.Ю. Тихановский ◽  
А.Г. Пименов ◽  
А.М. Шуваев ◽  
...  
Keyword(s):  
Crystal Field ◽  
Excited States ◽  
Ground State ◽  
Theoretical Study ◽  
Low Frequency ◽  
Local Symmetry ◽  
Matrix Elements ◽  
The Matrix ◽  
Excitation Conditions ◽  
Ground Multiplet

Experimental and theoretical study of submillimeter (terahertz) spectroscopic and magnetic properties of the rare-earth aluminum borate HoAl3(BO3)4 were performed at temperatures 3–300 K. In the transmittance spectra a number of resonance lines were detected at frequencies 2–35 cm–1 for different radiation polarizations. These modes were identified as transitions between the lower levels of the ground multiplet of the Ho3+ ion split by the crystal field, including both transitions from the ground state to the excited ones and transitions between the excited states. The established excitation conditions of the observed modes and the simulation of the spectra made it possible to separate the magnetic and electric dipole transitions and to determine the energies of the corresponding states, their symmetry, and the matrix elements of the transitions. Low-frequency lines that do not fit into the established picture of the electron states of Ho3+ were also found; these lines, apparently, correspond to the ions with the distorted by defects local symmetry of the crystal field.

Zero-field splitting calculations. Part II. Tabulation of the reduced matrix elements of the irreducible double tensor operators

1976 ◽  
Vol 54 (12) ◽  
pp. 1228-1233 ◽  
Author(s):  
R. Chatterjee ◽  
M. R. Smith ◽  
H. A. Buckmaster
Keyword(s):  
The Other ◽  
Tensor Operator ◽  
Zero Field ◽  
Matrix Elements ◽  
Zero Field Splitting ◽  
Field Splitting ◽  
The Matrix ◽  
The Many ◽  
Relationship Of ◽  
The Relationship

The many-electron reduced matrix elements of the double tensor operator [Formula: see text] are tabulated for the pn, dn and fn configurations. These tables have been calculated from the Racah formalism and form an extension of the tabulations given by Nielson and Koster for K2 = 1. The relationship of this tensor with the other double tensors and the calculation of the matrix elements is summarized. See Chatterjee et al for an application.

scholarly journals Oculomotor activity parameters of the operator in the P300 brain computer interface and similar stimulus situations

2015 ◽  
Vol 8 (4) ◽  
pp. 134-144
Author(s):  
I.A. Basyul
Keyword(s):  
Average Length ◽  
Brain Computer Interface ◽  
Computer Interface ◽  
Similar Stimulus ◽  
The Matrix ◽  
Relationship Of ◽  
The Relationship ◽  
Visual Fixations ◽  
Oculomotor Activity ◽  
Stimulus Environment

Hypotheses about the relationship of the processes of visual perception and variations of the task in an identical stimulus environment was tested. The following tasks were tested: 1) a simple observation of the illuminations of the character in the matrix; 2) counting the number of highlights; 3) monitoring of the target symbol highlights and typing text with the P300 BCI. In a group of 14 people showed that the highest average length of visual fixation and the lowest dispersion of fixation observed for the second type of task. Statistically significant differences in the level of dispersion of visual fixations found between 1-2 and 1-3 modes; differences between the modes for the duration of fixations are at trends. Significant differences in the number of visual fixations on the target symbols wasn’t detected. The overall conclusion is the high perspective of pairing methodology brain-computer interface on the P300 wave with eye tracking to optimize the characteristics of the stimulus in the BCI environment. The differences in the parameters of oculomotor activity between the tasks reflect the level of attention concentration in the target symbols of the P300 BCI

Research on the Method of Circumferential Spring Dual Mass Flywheel Damper Matching with Diesel Engine

2009 ◽  
Vol 419-420 ◽  
pp. 65-68
Author(s):  
Zheng Feng Jiang ◽  
Lei Chen
Keyword(s):  
Diesel Engine ◽  
Torsional Vibration ◽  
Torsional Stiffness ◽  
Vibration Damper ◽  
Passenger Car ◽  
Inertia Coefficient ◽  
New Type ◽  
Working Principle ◽  
Relationship Of ◽  
The Relationship

As a new type of torsional vibration damper, a Dual Mass Flywheel (DMF) has different configuration and working principle from the traditional clutch. Focusing on the problem of matching DMF with a diesel engine, the relationship of circumferential spring dual mass flywheel (CS-DMF) and gearbox is analyzed based on a multi-freedom model, and then the methods of gearbox selection, rotary inertia coefficient ascertain and optimization of torsional stiffness are proposed in this paper. The methods have been applied to a CS-DMF matching with a passenger car with diesel engine. Modal simulation and torque fluctuating experiment show the CS-DMF has excellent damping performance.

scholarly journals The Nonlinear Dispersion Relation and the Relationship of the Forming Soliton Area to the Evolution of Pulsars

1987 ◽  
Vol 125 ◽  
pp. 461-461 ◽  
Author(s):  
Mao Xinjie ◽  
Tong Yi
Keyword(s):  
Electric Field ◽  
Ground State ◽  
Nonlinear Effects ◽  
Electric Polarization ◽  
Nonlinear Dispersion ◽  
Hydrogen Atoms ◽  
Nonlinear Dispersion Relation ◽  
Relationship Of ◽  
The Relationship ◽  
The Universe

Based on Zakharov's equations, Karpman et al. claimed that there were solitons in the magnetosphere. According to the model proposed by Goldreich and Julin, there is a strong induced electric field in the magnetosphere. It seems that we should include the nonlinear effects of the electric field on the polarization of hydrogen atoms if there really are some hydrogen atoms spreading in the magnetosphere of the pulsar. Assuming the magnetosphere is symetric, therefore the electric polarization of hydrogen atoms is of the form P=χ(1)E +χχE3. We treat χ(1) and χ(2) as scalars because most hydrogen atoms in the universe are in the ground state and χ(3) is much smaller than χ(1).

scholarly journals Triaxiality in the odd-A nuclei 109−117I studied through a microscopic rotationparticle coupling

2018 ◽  
Vol 178 ◽  
pp. 02030
Author(s):  
Swati Modi
Keyword(s):  
Systematic Study ◽  
Coming Out ◽  
Ground State ◽  
Rotor System ◽  
Matrix Elements ◽  
Triaxial Deformation ◽  
The Matrix

A systematic study of ground state spectrum with the triaxial deformation γ for odd-A Iodine isotopes 109−117I is carried out with the nonadiabatic quasiparticle approach. The rotation-particle coupling is accomplished microscopically such that the matrix elements of a particle-plus-rotor system are written in terms of the rotor energies. The 5/2+ state is confirmed as ground state for odd-A 111−117I and also coming out as lowest in energy for 109I.

The 12 C(γ, 3α) reaction energy levels of 8 Be and 12 C

1955 ◽  
Vol 228 (1174) ◽  
pp. 376-396 ◽  
Keyword(s):  
Ground State ◽  
Energy Levels ◽  
Electric Quadrupole ◽  
Angular Distributions ◽  
Reaction Energy ◽  
Reaction Proceeds ◽  
Γ Ray ◽  
Relationship Of ◽  
The Relationship ◽  
Α Particles

The mechanism of the 12 C(γ, 3α) reaction, for γ-ray energies, E γ , up to about 40 MeV, has been determined from a study of over 2500 stars in nuclear emulsions. The study includes investigation of the angular distributions and correlations of the α-particles. The reaction is initiated mainly by electric-dipole and electric-quadrupole γ-ray interaction, the former being unexpectedly strong when E γ < 20 MeV. For E γ < 25 MeV the reaction proceeds mainly by transitions to the ground-state of 8 Be (spin J = 0), and to 2⋅95 ± 0⋅10 MeV ( J = 2) and 4⋅0 ± 0⋅1 MeV ( J = 2 or 4) levels of 8 Be. Transitions to levels near 6, 10 and 15 MeV (all J = 0, 2 or 4) become predominant when 25 MeV ≤ E γ <26 MeV. For E γ ≥ 26 MeV, most transitions lead to 16⋅8 ± 0⋅2 MeV ( J = 2) and 17⋅6 ± 0⋅2 MeV ( J = 2, possibly 0) levels, and possibly to a further 16⋅4 ± 0⋅2 MeV ( J = 0 or 2) level, levels which have not been detected in other reactions. The reaction mechanism is interpreted in terms of competing modes of decay of a compound nucleus, demonstrating the strong influence of the isotopic spins ( T ) of the levels of 12 C and 8 Be involved. For example, the 2 + levels of 12 C involved when 16 MeV ≤ E γ <20 MeV are (unexpectedly) found to have T = 1, and the 16⋅8 and 17⋅6 MeV levels of 8 Be are also found to have T = 1. The relationship of the 12 C (γ, 3α) reaction to other 12 C photodisintegration reactions (including some new reactions established during the present experiments) is discussed.

scholarly journals Quaternion treatment of the relativistic wave equation

1937 ◽  
Vol 162 (909) ◽  
pp. 145-154 ◽  
Keyword(s):  
Wave Function ◽  
Wave Equation ◽  
Linear Functions ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Formal Representation ◽  
The Matrix ◽  
Scalar Products ◽  
Relationship Of ◽  
The Relationship

A set of matrices can be found which is isomorphic with any linear associative algebra. For the case of quaternions this was first shown by Cayley (1858), but the first formal representation was made by Peirce (1875, 1881). These were two-matrices, and the introduction of the four-row matrices of Dirac and Eddington necessitated the treatment of a wave function as a matrix of one row (as columns). Quaternions have been used by Lanczos (1929) to discuss a different form of wave equation, but here the Dirac form is discussed, the wave function being taken as a quaternion and the four-row matrices being linear functions of a quaternion. Certain advantages are claimed for quaternion methods. The absence of the distinction between outer and scalar products in the matrix notation necessitates special expedients (Eddington 1936). Every matrix is a very simple function of the fundamental Hamiltonian vectors α, β, γ , so that the result of combination is at once evident and depends only on the rules of combination of these vectors. At all stages the relationship of the different quantities to four-space is at once visible. The Dirac-Eddington matrices, the wave equation and its exact solution by Darwin, angular momentum operators, the general and Lorentz transformation, spinors and six-vectors, the current-density four-vector are treated in order to exhibit the working of this method. S and V for scalar and vector products are used. Quaternions are denoted by Clarendon type, and all vectors are in Greek letters.

scholarly journals The Pivotal Meaning and Its Relationship with Derivation Al Tahqiq fe AlQuran Al-Kareem. A Sample (Scrutinizing Words in Glorious Quran: A Sample)

2018 ◽  
Vol 212 (1) ◽  
pp. 211-240
Author(s):  
Assist. Prof. Dr. Khamis Abdullah Al-Timimy. ◽  
Dr. Haider Shnawa Faisal Al-zaidi.
Keyword(s):  
New Type ◽  
Points Of View ◽  
The Difference ◽  
Central Meaning ◽  
Relationship Of ◽  
The Relationship

The Paper has tackled the pivotal meaning, its relationship with derivation, and its types. The paper starts with defining the pivotal meaning and the ways of its formation, then mentioning the difference between the pivotal meaning and central meaning with revealing the most significant points of view anciently and recently. The researcher has defined derivation mentioning the essential views that have said about it with providing on adequate exposure to Mustafawi's remarks concerning derivation and hid unique achievement in this field i.e. adding a new type of derivation which he calls "extractive derivation". The researcher has also tackled about the relationship of the pivotal meaning with types of derivation represented by: small, big, the biggest, and magnificent. Keeping in mind that derivation is a linguistic procedure which cannot be restricted in specific limits in addition to the fact that its relation with the pivotal meaning is divergent depending on the type of derivation. 

DOMINANCE OF LONG DISTANCE EFFECTS IN THE KL-KS MASS DIFFERENCE

1990 ◽  
Vol 05 (19) ◽  
pp. 1477-1483 ◽  
Author(s):  
K. TERASAKI ◽  
S. ONEDA
Keyword(s):  
Asymptotic Behavior ◽  
Vector Meson ◽  
Ground State ◽  
Mass Shell ◽  
Mass Difference ◽  
Matrix Elements ◽  
Long Distance ◽  
Distance Effects ◽  
Intermediate States ◽  
The Matrix

It is argued that the asymptotic behavior of the matrix elements of Hw involving on-mass-shell ground-state mesons with infinite momenta, which were instrumental in explaining the |ΔI|=1/2 rule in the K→ππ decays, actually implies [Formula: see text]. The long distance effects (contributions of PS and vector meson poles and ππ intermediate states) may reproduce the observed KL−Ks mass difference, consistent with the |ΔI|=1/2 rule. Its estimate is however sensitive to the η-η′-… mixing.

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