V. Canuto

Hydrogen atom in intense magnetic field

The structure of a hydrogen atom situated in an intense magnetic field is investigated. Three approaches are employed. An elementary Bohr picture establishes a crucial magnetic field strength,Ha≃5×109G. Fields in excess ofHa are intense in that they are able to modify the characteristic atomic scales of length and binding energy. A second approach solves the Schrödinger equation by a combination of variational methods and perturbation theory. It yields analytic expressions for the wave functions and energy eigenvalues. A third approach determines the energy eigenvalues by reducing the Schrödinger equation to a one-dimensional wave equation, which is then solved numerically. Energy eigenvalues are tabulated for field strengths of 2×1010G and 2×1012 G. It is found that at 2×1012 G the lowest energy eigenvalue is changed from −13.6 eV to about −180 eV in agreement with previous variational computations.

Quantum theory of the dielectric constant of a magnetized plasma and astrophysical applications. I. Theory

A quantum mechanical treatment of an electron plasma in a constant and homogeneous magnetic field is considered, with the aim of (a) defining the range of validity of the magnetoionic theory (b) studying the deviations from this theory, in applications involving high densities, and intense magnetic field. While treating the magnetic field exactly, a perturbation approach in the photon field is used to derive general expressions for the dielectric tensor εαβ. The properties of εαβ are explored in the various limits. Numerical estimates on the range of applicability of the magnetoionic theory are given for the case of the ‘one-dimensional’ electron gas, where only the lowest Landau level is occupied.

Thermodynamic approach to the equation of state of a magnetized Fermi gas.

In this paper we have rederived the equations of state for a magnetized Fermi gas by generalizing the physical definition of the pressure. We have also given a simplified derivation of the energy eigenvalues of a free electron in a magnetic field, based on the use of simple harmonic oscillators. Physical interpretations of our results are presented. Possible astrophysical applications are also discussed.

Plasmon neutrinos emission in a strong magnetic field. I - Transverse plasmons

The decay of a longitudinal plasmon into two neutrinos is studied in the presence of a strong magnetic field. Contrary to the transverse case, for longitudinal plasmons the existence of a new mode, entirely dependent on the magnetic field, greatly enhances the energy loss at high densities. Denoting byQHandQ0the neutrino energy losses with and without magnetic field respectively, the situation is as follows: atH≃1011 G andT≥109K,Q0≫105QHfor ϱ<1011g cm−3, WhileQH≫1010Q0for ϱ>1011g cm−3. A second physically interesting feature is the anisotropic character of the energy loss which is highly peaked along the field lines, giving rise to a shorter cooling time in that direction than in any other.

Neutrino luminosity by the ordinary URCA process in an intense magnetic field

The neutrino luminosity by the ordinary URCA process in a strongly magnetized electron gas is computed. General formulae are presented for the URCA energy loss rates for an arbitrary degree of degeneracy. Analytic expressions are derived for a completely degenerate, relativistic electron plasma in the special case of neutron-proton conversion. Numerical results are given for more general cases.The main results are as follows: the URCA energy loss rates are drastically reduced for the regime of great degeneracy by a factor up to 10−3 for Θ≅1, andT9≲10, where Θ=H/Hq,Hq=m2c3/eh=4.414×1013 G. In the non-degenerate regime the neutrino luminosity is enhanced approximately linearly with Θ for the temperature range 1≲T9≲10. Possible applications to white dwarfs and neutron stars are briefly discussed.

Is the Kolmogoroff model applicable to large-scale turbulence?

We discuss the difficulties encountered when the Heisenberg-Kolmogoroff model for turbulence is applied to the large-scale turbulence in: (A) molecular clouds (specifically the velocity vs size relationship) and (B) stars (specifically, the estimate of convective fluxes).A new model for large-scale turbulence is, therefore, needed.

PLASMON NEUTRINOS EMISSION IN A STRONG MAGNETIC FIELD. II. LONGITUDINAL PLASMONS.

The decay of a longitudinal plasmon into two neutrinos is studied in the presence of a strong magnetic field. Contrary to the transverse case, for longitudinal plasmons the existence of a new mode, entirely dependent on the magnetic field, greatly enhances the energy loss at high densities. Denoting byQHandQ0the neutrino energy losses with and without magnetic field respectively, the situation is as follows: atH≃1011 G andT≥109K,Q0≫105QHfor ϱ<1011g cm−3, WhileQH≫1010Q0for ϱ>1011g cm−3. A second physically interesting feature is the anisotropic character of the energy loss which is highly peaked along the field lines, giving rise to a shorter cooling time in that direction than in any other.

Why a variableG

Since a possible time variability ofG has received renewed attention (Wesson and Goodson, 1981), we think it is important to stress a conceptual aspect so far not sufficiently appreciated and which puts the variability ofG in a much wider context. VariableG is a popular but incomplete representation of a much deeper problem:Is the Strong Equivalence Principle (SEP) valid?

Plasmon neutrinos emission in a strong magnetic field

The decay of a longitudinal plasmon into two neutrinos is studied in the presence of a strong magnetic field. Contrary to the transverse case, for longitudinal plasmons the existence of a new mode, entirely dependent on the magnetic field, greatly enhances the energy loss at high densities. Denoting byQHandQ0the neutrino energy losses with and without magnetic field respectively, the situation is as follows: atH≃1011 G andT≥109K,Q0≫105QHfor ϱ<1011g cm−3, WhileQH≫1010Q0for ϱ>1011g cm−3. A second physically interesting feature is the anisotropic character of the energy loss which is highly peaked along the field lines, giving rise to a shorter cooling time in that direction than in any other.