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All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Collisional excitation of electron Landau levels in strong magnetic fields

The cross sections for the excitation and deexcitation of the quantized transverse energy levels of an electron in a magnetic field are calculated for electron-proton and electron-electron collisions in light of the importance of the cross sections for studies of X-ray pulsar emission. First-order matrix elements are calculated using the Dirac theory of the electron, thus taking into account relativistic effects, which are believed to be important in accreting neutron stars. Results for the collisional excitation of ground state electrons by protons are presented which demonstrate the importance of proton recoil and relativistic effects, and it is shown that electron-electron excitations may contribute 10 to 20% of the excitation rate from electron-proton scattering in a Maxwellian plasma. Finally, calculations of the cross section for electron-proton small-angle scattering are presented which lead to relaxation rates for the electron velocity distribution which are modified by the magnetic field, and to a possible increase in the value of the Coulomb logarithm.

Langer, S. H.↗
NASA NTRS1972

Quantum limit studies in single crystal and pyrolytic graphite

The occupied regions of momentum space in graphite are confined to elongated volumes near the hexagonal Brillouin zone edges. The elongation is along the hexagonal axis (c-axis), so that cross sectional areas perpendicular to that axis are very small. When magnetic fields are applied parallel to the c-axis, only the n = 0 Landau levels remain below the Fermi energy for fields above 7 tesla. The energy bands in graphite can be described by a set of seven parameters (including the Fermi energy as a parameter). In a quantizing magnetic field the Landau levels are described by a secular equation determined by diagonalizing the Hamiltonian. A major feature for the levels along the Brillouin zone edge is that the n = 0 Landau level for electrons is independent of magnetic field, while that for holes is field-dependent.

Woollam, J. A.↗
NASA NTRS1974

Quantum limit studies in single-crystal and pyrolytic graphite

The occupied regions of momentum space in graphite are confined to very elongated volumes near the hexagonal Brillouin zone edges. The elongation is along the hexagonal axis (c axis) so that cross-sectional areas perpendicular to that axis are very small. Hence, when magnetic fields are applied parallel to the c axis only the n = 0 Landau levels remain below the Fermi energy for fields above 7 T (Woollam, 1971). The energy bands in graphite can be described by a set of seven parameters (McClure, 1971) (including the Fermi energy as a parameter). In a quantizing magnetic field the Landau levels are described by a secular equation determined by diagonalizing the Hamiltonian (McClure, 1960). A major unusual feature for the levels along the Brillouin zone edge is that the n = 0 Landau level for electrons is independent of magnetic field, while that for holes is field dependent.

Woollam, J. A.↗
NASA NTRS1992

X-ray suppression in gamma-ray bursts through resonant Compton scattering

An X-ray that scatters with an electron in the first Landau level of a strong magnetic field is converted into a gamma ray. This process has a resonant cross section at X-ray energies and is therefore highly likely to occur even when the first Landau level is sparsely populated. Converted X-rays are cyclotron absorbed, maintaining the equilibrium between the cyclotron photon density and the population of the first Landau level. By suppressing a neutron star's black body emission, this mechanism can produce a gamma-ray burst with a low X-ray flux.

Brainerd, J. J.↗
NASA NTRS1991

Radiative widths and splitting of cyclotron lines in superstrong magnetic fields

The radiative line widths of the Landau levels in a superstrong magnetic field are calculated and simple analytic expressions and fits are given for these which are valid over a wide range of the principal quantum number and the magnetic field strength. If QED corrections are not taken into account, all levels but the first are doubly degenerate, corresponding to the two possible spin projections. However, the interaction with the QED vacuum removes this degeneracy, leading to an energy splitting of each level which exceeds the radiative linewidth for low Landau levels if the magnetic field is not too large (B is less than approximately 10 exp 13 G). Estimations are presented of the splitting in various limits as a function of field strength and Landau number. The possibility of observing this splitting in accreting X-ray pulsars and in gamma-ray bursters is discussed.

Pavlov, G. G.↗
NASA NTRS1986

Compton scattering in strong magnetic fields

The relativistic cross section for Compton scattering by electrons in strong magnetic fields is derived. The results confirm and extend earlier work which has treated only transitions to the lowest or first excited Landau levels. For the teragauss field strengths expected in neutron star magnetospheres, the relative rates for excited state transitions are found to be significant, especially for incident photon energies several times the cyclotron frequency. Since these transitions must result in the rapid emission of one or more cyclotron photons as well as the Compton-scattered photon, the scattering process actually becomes a photon 'splitting' mechanism which acts to soften hard photon spectra, and also provides a specific mechanism for populating higher Landau levels in the electron distribution function. The results should be significant for models of gamma-ray bursters and pulsating X-ray sources.

Daugherty, Joseph K.↗
NASA NTRS1972

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

A quantum mechanical treatment of an electron plasma in a constant and homogeneous magnetic field is considered, with the aim of (1) defining the range of validity of the magnetoionic theory (2) 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. 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.

Canuto, V.↗
NASA NTRS1976

Magnetic field generated resistivity maximum in graphite

In zero magnetic field, B, the electrical resistivity, rho(O,T) of highly oriented pyrolytic (polycrystalline) graphite drops smoothly with decreasing T, becoming constant below 4 K. However, in a fixed applied magnetic field B, the resistivity rho(B,T) goes through a maximum as a function of T, with larger maximum for larger B. The temperature of the maximum increases with B, but saturates to a constant value near 25 K (exact T depends on sample) at high B. In single crystal graphite a maximum in rho(B,T) as a function of T is also present, but has the effects of Landau level quantization superimposed. Several possible explanations for the rho(B,T) maximum are proposed, but a complete explanation awaits detailed calculations involving the energy band structure of graphite, and the particular scattering mechanisms involved.

Wollam, J. A.↗
NASA NTRS1976

Magnetic field generated resistivity maximum in graphite

In a zero magnetic field, the electrical resistivity of highly oriented pyrolytic (polycrystalline) graphite drops smoothly with decreasing temperature, becoming constant below 4 K. However, in a fixed applied magnetic field, the resistivity goes through a maximum as a function of temperature, with a larger maximum for a larger field intensity. The temperature of the maximum increases with field intensity, but saturates to a constant value near 25 K (the exact temperature depends on the sample) at high intensity. In single-crystal graphite, a maximum in resistivity as a function of temperature is also present, but has the effects of Landau level quantization superimposed. Several possible explanations for the resistivity maximum are proposed, but a complete explanation awaits detailed calculations involving the energy band structure of graphite, and the particular scattering mechanisms involved.

Woollam, J. A.↗
NASA NTRS1983

Pair Production near Threshold in Pulsar Magnetic Fields

In pulsar polar cap models, curvature radiation gamma rays produce e(+)e(-) pairs in the strong magnetic fields near the surface of the neutron star. While these gamma rays have energies E sub gamma mc(2), they also propagate at very small angles to the fields, such that the threshold condition, E gamma 2mc(2)/sin theta is just barely satisfied when they pair produce. Threshold effects on the pair production attenuation coefficient, which are due to the discreteness of the e(+)e(-) Landau states, must therefore be considered when computing the mean free paths of curvature radiation photons in pulsar magnetic fields. These effects, which are not incorporated in the asymptotic expression for the attenuation coefficient, have some interesting consequences for pulsar models. Since pair production is suppressed near threshold, the photon mean free paths are longer than previously thought. In magnetic fields approximately 6x10 approximately G, the pairs tend to be produced in the ground state Landau level and will not synchrotron radiate. Since synchrotron radiation is an essential ingredient in the electromagnetic cascades which produce low energy pairs above the acceleration region, pulsars with very high magnetic fields may not produce many pairs.

Harding, A. K.↗
NASA NTRS1984

Magnetic flare model of gamma-ray bursts

The thermal synchrotron (TS) interpretation of gamma-ray burst continuum spectra requires an emission region which is hot, optically thin, and possessed of a super-Eddington flux of 10 to the 30 ergs/sq cm per sec for a 10-km neutron star. In order to maintain a pair population close to the Maxwellian, the collision excitation rate into higher Landau levels must exceed the cyclotron decay rates. Even if collective processes whose rates are close to the electron plasma frequency, or scattering by heavy ions, are invoked, a particle density of 10 to the 25th/cu cm is still needed. Both hypotheses point in the direction of a dense but thin emitting sheet, to whose structure attention is presently given together with the generation, propagation and coupling of the electromagnetic energy fluxes. A flare-like model can account for most of gamma ray bursts' general features.

Liang, E. P.↗
NASA NTRS1983

Pair production near threshold in pulsar magnetic fields

In Pulsar polar cap models, curvature radiation gamma-rays produce e(+) e(-) pairs in the strong magnetic fields near the surface of the neutron star. While these gamma rays havea energies E sub gamma mc(2), they also propagate at very small angies to the fields, such that the threshold condition, E gamma 2mc(2)/sin theta is just barely satisfied when they pair produce. Threshold effects on the pair production attenuation coefficient, which are due to the discreteness of the e(+) e(-) Landau states, must therefore be considered when computing the mean free paths of curvature radiation photons in pulsar magnetic fields. These effects, which are not incorporated in the asymptotic expression for the attenuation coefficient, have some interesting consequences for pulsar models. Since pair production is suppressed near threshold, the photon mean free paths are longer than previously thought. In magnetic fields greater than approximately 6 x 10 to the 12th G, the pairs tend to be produced in the ground state Landau level and will not synchrotron radiate. Since synchrotron radiation is an essential ingredient in the eiectromagnetic cascades which produce low energy pairs above the acceleration region, pulsars with very high magnetic fields may not produce many pairs.

Harding, A. K.↗
NASA NTRS1985

Soft X-ray production by photon scattering in pulsating binary neutron star sources

A new mechanism is proposed as a source of soft (less than 1 keV) radiation in binary pulsating X-ray sources, in the form of photon scattering which leaves the electron in an excited Landau level. In a plasma with parameters typical of such sources, the low-energy X-ray emissivity of this mechanism far exceeds that of bremsstrahlung. This copious source of soft photons is quite adequate to provide the seed photons needed to explain the power-law hard X-ray spectrum by inverse Comptonization on the hot electrons at the base of the accretion column.

Bussard, R. W.↗
NASA NTRS1986

One- and two-photon Compton scattering in strong magnetic fields

Calculations are made of the Compton scattering cross section in a very strong magnetic field, such as encountered in pulsars, for arbitrary photon and electron energies. The effect of the vacuum polarization in the weak-field limit is included as well as the plasma polarizability. Radiative transitions between any pair of Landau levels are included as well as two-photon scattering. The latter process, due to the presence of the cyclotron resonance, becomes comparable to nonresonant one-photon scattering when excited final states are allowed, and acts as a source of photons which is more important than bremsstrahlung at low plasma densities.

Bussard, R. W.↗
NASA NTRS1989

Cyclotron scattering lines in gamma-ray burst spectra

If cyclotron scattering, rather than absorption, is responsible for the line features observed recently in two gamma-ray burst spectra (Murakami et al., 1988), then the second and higher harmonics are due to resonant scattering events that excite the electron to Landau levels above the ground state. Here, relativistic Compton scattering cross sections are used to estimate the expected ratio of third to second harmonics in the presence of Doppler broadening. At the field strength (1.7 TG) required to give first and second harmonics at 19 keV and 38 keV, there should be no detectable third harmonic in the spectrum.

Harding, Alice K.↗
NASA NTRS1991

Magnetic two-photon scattering and two-photon emission - Cross sections and redistribution functions

The magnetic two-photon scattering cross section is discussed within the framework of QED, and the corresponding scattering redistribution function for this process and its inverse, as well as the scattering source function are calculated explicitly. In a similar way, the magnetic two-photon emission process which follows the radiative excitation of Landau levels above ground is calculated. The two-photon scattering and two-photon emission are of the same order as the single-photon magnetic scattering. All three of these processes, and in optically thick cases also their inverses, are included in radiative transport calculations modeling accreting pulsars and gamma-ray bursters. These processes play a prominent role in determining the relative strength of the first two cyclotron harmonics, and their effects extend also to the higher harmonics.

Alexander, S. G.↗
NASA NTRS1992

On the continuum radiation of gamma-ray bursts

I describe the qualitative features of a model for gamma-ray bursts assuming that they are produced by galactic neutron stars. The model is based on the assumption that electrons are continuously accelerated high up in the magnetosphere to relativistic energies and large pitch angles. These electrons emit a self-absorbed synchrotron spectrum at energies greater than mc-squared and, as a result, lose all of the energy associated with their motion perpendicular to the magnetic field. They thus slide along the field lines hitting the high density crust where by collision with ions acquire non-zero pitch angle (or are excited to higher Landau levels) and emit either cyclotron or bremsstrahlung photons.

Petrosian, Vahe↗