Spin‐dependent Cyclotron Decay Rates in Strong Magnetic Fields

Abstract

Cyclotron decay and absorption rates have been well studied in the literature, focusing primarily on spectral, angular and polarization dependence. Astrophysical applications usually do not require retention of information on the electron spin state, and these are normally averaged in obtaining the requisite rates. In magnetic fields, higher order quantum processes such as Compton scattering become resonant at the cyclotron frequency and its harmonics, with the resonances being formally divergent. Such divergences are usually eliminated by accounting for the finite lifetimes of excited Landau states. This practice requires the use of spin-dependent cyclotron rates in order to obtain accurate determinations of process rates very near cyclotronic resonances, the phase space domain most relevant for certain applications to pulsar models. This paper develops previous results in the literature to obtain compact analytic expressions for cyclotron decay rates/widths in terms of a series of Legendre functions of the second kind; these expressions can be expediently used in astrophysical models. The rates are derived using two popular eigenstate formalisms, namely that due to Sokolov and Ternov, and that due to Johnson and Lippmann. These constitute two sets of eigenfunctions of the Dirac equation that diagonalize different operators, and accordingly yield different spin-dependent cyclotron rates. This paper illustrates the attractive Lorentz transformation characteristics of the Sokolov and Ternov formulation, which is another reason why it is preferable when electron spin information must be explicitly retained.

Physics of strongly magnetized neutron stars

“…The angular distribution of the photons from annihilation at rest also becomes more anisotropic with increasing field strength, with the peak of emission perpendicular to B , again similar to one-photon annihilation. Similar broadening occurs when the pairs have non-zero momenta parallel to the magnetic field (Kaminker et al 1987, Baring & Harding 1992.…”

“…The kinematic cutoffs occur when | cos θ 2 | = 1, where θ 2 is the angle of the unseen photon. From Baring & Harding (1992).…”

“…Since the photon splitting rate is very sensitive to field strength, its influence grows quickly with increasing field strength with the switch from pair creation to photon splitting being dependent on field geometry. For photons propagating in neutron star dipole magnetic field geometry, photon splitting becomes dominant as an attenuation mechanism for B ′ > ∼ 1 (Baring & Harding 1998). Adler (1971) examined the kinematic selection rules for photon splitting in the weakly dispersive limit and found that only the ⊥→ mode conserved energy and momentum in the magnetized vacuum [another channel, ⊥→ ⊥, is also allowed kinematically, but the rate is suppressed by a factor of order n −1 (see Eq.…”

Electrodynamics of Magnetars. III. Pair Creation Processes in an Ultrastrong Magnetic Field and Particle Heating in a Dynamic Magnetosphere

“…These wave functions are not, however, eigenstates of the electron spin. As a result, physical quantities -such as the decay rate of an electron from a higher Landau state -are not evaluated correctly when one of the initial or final changed particles is in motion parallel to B (see Baring et al 2005 and references therein). We therefore use an alternative form derived by Sokolov & Ternov (1968) and Melrose & Parle (1983a).…”

Dynamics of Spin-12Quantum Plasmas

“…The treatment of charged particles and plasmas using quantum theory has received attention in astrophysical settings, especially in strongly mag-netized environments [32,33]. For example, effects of quantum field theory on the linear response of an electron gas has been analyzed [34], results concerning the spin-dependence of cyclotron decay on strong magnetic fields has been presented [35], and the propagation of quantum electrodynamical waves in strongly magnetized plasmas has been considered [36].…”