Dynamic Effective Mass Research Articles

Implications of a dynamical effective mass on the nuclear shell model

Phenomenological improvements on the static shell-model potential are proposed by introducing a local effective mass of quasiparticles in the nucleus. The parametrization of m ∗(r)/m includes nonlocal as well as retardation effects in the single-particle self-energy. The model allows for a simultaneous description of average single-particle dynamics close to the Fermi surface as well as features observed far away. We especially emphasize the role of retardation or frequency dependence of the self-energy to enhance high-momentum components in the ground-state wave function of nuclei.

Influence of a dynamical coupling between single particle and collective states on the density distribution of the breathing mode

The effects of a dynamical effective mass in the unperturbed p-h spectrum fof the breathing mode are discussed. Consequences on the transition density of 208Pb are investigated and related to the inelastic scattering cross sections for high energetic α-particles and electrons.

Linear and Nonlinear Electronic Transport in Electron-Phonon Systems: Self-Consistent Approach within the Path-Integral Formalism

The expectation value of the steady-state velocity acquired by an electron interacting with the phonons of a crystal in finite electric and magnetic fields is analyzed quantum mechanically for arbitrary coupling strength, field strengths, and temperature. The rate of loss of momentum by an electron drifting through the crystal in the applied fields is expressed in a form in which the lattice coordinates (the phonons) have been eliminated exactly by path-integral methods. The quadratic influence functional used to simulate the electron-lattice interaction is shown to be derivable from a self-consistent relation for the impedance tensor of the electron in its drifting frame of reference. This eliminates the ambiguity of which influence functional to use in path-integral treatments of electron transport. For zero applied electric and magnetic fields, it is shown that the self-consistency is equivalent to minimizing the free energy of the electron-phonon system at finite temperatures. The Feynman one-oscillator model is discussed in the light of the self-consistency relation. Several important changes are indicated by an approximate self-consistent solution for low temperature. The applied magnetic and electric field problem is briefly discussed. For optical-phonon scattering, it is shown that the cyclotron mass is the same as the dynamic effective mass in the absence of a magnetic field. For the Fr\"ohlich polaron model, it is shown that, because of the influence of the magnetic field on the scattering rate, a longitudinal magnetoresistivity should exist equal to exactly one-half of the transverse value. Finally, two limitations of this general approach are noted and discussed briefly.

Inequalities, instabilities, and renormalization in metals and other fermi liquids

This paper discusses various aspects of microscopic Fermi-liquid theory, with particular emphasis on its application to metals. It is shown that under certain conditions we have the inequalities m∗ 1+ 1 3 F 1 ⩾m, m∗ 1+ 1 12 Z 1 ⩾m The appropriate formulation of the theory is presented for the case that the fermions interact with an arbitrary background (e.g. 3He 4He mixtures). A microscopic proof of the stability conditions is given. The effects of the Coulomb and electron-phonon interaction in metals are treated by completely parallel techniques, and explicit expressions are given for the electronic correlation functions in the limits ω 2> ω D and ω ⪡ ω D. Results for the static properties, etc., are in agreement with the recent work of Prange and Sachs. It is shown that the electron-phonon interaction can only enhance the “dynamic effective mass” m ∗ (1 + 1 3 F 1) , and that the enhancement tends to zero for forward electron-phonon scattering. It is also shown explicitly that phonon effects on the Landau parameters can affect the static properties in the superconducting state even though they cannot in the normal state. The inequalities obtained are compared as far as possible with experiment, and it is shown that the rough value of Z 1 12(≡B 1) recently obtained for Na from CESR experiments is almost certainly not compatible with the optical data. Tentative application is also made to the recently observed Knight shift in superconducting Al.

Acoustic Impedance of Porous Materials

A thorough understanding of the acoustical properties of porous materials is becoming increasingly important because of the wide variety of unusual and important applications in which they are finding use. A simple and useful theory is presented for predicting the normal acoustic impedance of isotropic porous materials in terms of three previously described simple constants, namely, flow resistance, porosity, and effective dynamic mass of the enclosed gas. The variation of normal impedance with angle of incidence for spaced-out or rigidly backed samples is treated. A striking possibility is discussed, namely, that gaseous expansions are isothermal over most of the audiofrequency range in materials made of finely divided particles. Many isotropic acoustical materials appear to fall in this class. This means that an air cavity becomes less stiff to dynamic compression when a very porous finely divided material is added to the cavity than when the material is not present. The results are checked against experimental data. A simple method is described for measuring the porosity P of a material, namely, the ratio of the volume of the air spaces in a material to the total volume of the material.