Theory of the interaction of the lattice vibrations with the vibrational excitations in solid hydrogen

1970 ◽  
Vol 48 (5) ◽  
pp. 489-501 ◽  
Author(s):  
J. Noolandi ◽  
J. Van Kranendonk
Keyword(s):  
Solid Hydrogen ◽  
The Self ◽  
Order Perturbation ◽  
Lattice Vibrations ◽  
Phonon Coupling ◽  
Phonon Interaction ◽  
Self Consistent ◽  
Vibrational Excitations ◽  
Intramolecular Vibrations ◽  
Quantum Crystals

The theory of the interaction of the vibrational excitations (vibrons) with the lattice vibrations in solid hydrogen is developed. The phonons are treated in the self-consistent harmonic (SCH) approximation appropriate to quantum crystals. The vibron–phonon interaction is expanded in terms of the SCH phonon operators rather than in powers of the displacements of the molecules from their equilibrium positions. First- and second-order perturbation corrections to the vibron energies arising from the vibron–phonon coupling are calculated. The effect of the anharmonicity of the intramolecular vibrations in conjunction with the vibron–phonon coupling is also discussed.

THEORY OF THE INTERACTION BETWEEN THE LATTICE VIBRATIONS AND THE ROTATIONAL MOTION IN SOLID HYDROGEN

1966 ◽  
Vol 44 (2) ◽  
pp. 313-335 ◽  
Author(s):  
J. Van Kranendonk ◽  
V. F. Sears
Keyword(s):  
Rotational Motion ◽  
Zero Point ◽  
Solid Hydrogen ◽  
The Self ◽  
Intermolecular Potential ◽  
Lattice Vibrations ◽  
Energy Effect ◽  
Self Energy ◽  
Blowing Up ◽  
Point Lattice

The effects of the interaction between the rotational motion of the molecules in solid hydrogen and the lattice vibrations, resulting from the anisotropic van der Waals forces, have been investigated theoretically. For the radial part of the anisotropic intermolecular potential an exp–6 model has been adopted. First, the effect of the lattice vibrations, and of the anistropic blowing up of the crystal by the zero-point lattice vibrations, is discussed. The effective anisotropic interaction resulting from averaging the instantaneous interaction over the lattice vibrations is calculated by assuming a Gaussian distribution for the modulation of the relative intermolecular separations by the lattice vibrations. Secondly, the displacement of the rotational levels due to the self-energy of the molecules in the lattice is calculated both classically and quantum mechanically, and the resulting shifts in the frequencies of the rotational transitions in solid hydrogen are given. Finally, the splitting of the rotational levels due to the anisotropy of the self-energy effect is calculated. The theory is applied to the calculation of the asymmetry of the S0(0) triplet in the rotational Raman spectrum of solid parahydrogen, and of the specific heat anomaly in solid hydrogen at low ortho-concentrations.

Electron–Phonon Interaction in Simple Metals: Beyond the Diffraction Model

1974 ◽  
Vol 52 (14) ◽  
pp. 1315-1321 ◽  
Author(s):  
J. P. Perdew ◽  
S. H. Vosko ◽  
R. A. Moore
Keyword(s):  
Exact Solution ◽  
Form Factors ◽  
The Self ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Consistent Field ◽  
Diffraction Model ◽  
Pseudopotential Calculations ◽  
Self Consistent ◽  
Self Consistent Field

The exact solution to the self-consistent field screening problem presented in a previous paper (Moore et al.), reduces in the weak pseudopotential limit to the diffraction model for the electron–phonon matrix element, and in particular to Animalu's expression for the screening of a nonlocal pseudopotential. Systematic corrections to the diffraction model, including local field effects, are presented for a pseudopotential of moderate strength; these corrections are particularly simple when the pseudopotential is local. Local pseudopotential calculations of the anisotropic electron–phonon form factors indicate that corrections to the diffraction model are small in sodium but substantial in lithium.

scholarly journals M1 resonance in Pb208 within the self-consistent phonon-coupling model

2020 ◽  
Vol 102 (6) ◽  
Author(s):  
V. Tselyaev ◽  
N. Lyutorovich ◽  
J. Speth ◽  
P.-G. Reinhard
Keyword(s):  
Coupling Model ◽  
The Self ◽  
Phonon Coupling ◽  
Self Consistent

The thermal decomposition of ammonium perchlorate II. The kinetics of the decomposition, the effect of particle size, and discussion of results

1955 ◽  
Vol 227 (1169) ◽  
pp. 214-228 ◽  
Keyword(s):  
Thermal Decomposition ◽  
The Self ◽  
Lattice Vibrations ◽  
Coupling Constant ◽  
One Dimensional ◽  
Self Consistent ◽  
Second Order Transition ◽  
Consistent Method ◽  
Effect Of Particle Size ◽  
Kinetics Of

Fröhlich has shown that a one-dimensional metal, at absolute zero, can exhibit certain of the properties of a superconductor when the interaction between the lattice vibrations and the electrons is sufficiently strong. The self-consistent method used by him is extended to finite temperatures, and the specific heat is calculated. It is shown that the model exhibits a second-order transition at a temperature which is related to the magnitude of the coupling constant. The approximations demand a coupling constant which is much larger than that of any real metal.

Dynamics and thermodynamics of quantum crystals in the self-consistent phonon theory

1997 ◽  
Author(s):  
Cecylia Malinowska-Adamska ◽  
Piotr Sloma ◽  
Janusz Tomaszewski
Keyword(s):  
The Self ◽  
Self Consistent ◽  
Quantum Crystals ◽  
Phonon Theory
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