Abstract
We study neutral fermions pair creation with anomalous magnetic moment from the vacuum by time-independent magnetic-field inhomogeneity as an external background. We show that the problem is technically reduced to the problem of charged-particle creation by an electric step, for which the nonperturbative formulation of strong-field QED is used. We consider a magnetic step given by an analytic function and whose inhomogeneity may vary from a “gradual” to a “sharp” field configuration. We obtain corresponding exact solutions of the Dirac-Pauli equation with this field and calculate pertinent quantities characterizing vacuum instability, such as the differential mean number and flux density of pairs created from the vacuum, vacuum fluxes of energy and magnetic moment. We show that the vacuum flux in one direction is formed from fluxes of particles and antiparticles of equal intensity and with the same magnetic moments parallel to the external field. Backreaction to the vacuum fluxes leads to a smoothing of the magnetic-field inhomogeneity. We also estimate critical magnetic field intensities, near which the phenomenon could be observed.
Highlights
From the vacuum by stationary inhomogeneous electric fields of constant direction
We study neutral fermions pair creation with anomalous magnetic moment from the vacuum by time-independent magnetic-field inhomogeneity as an external background
We study a mechanism that explains the creation of neutral fermion pairs with anomalous magnetic moments from the vacuum by inhomogeneous magnetic fields
Summary
We present general considerations on the Dirac-Pauli equation with inhomogeneous magnetic fields. The problem of neutral fermion pair production with well-defined values of the complete set of commuting operators px, pz, Πz, R [whose eigenvalues are (px, pz, ω, s)] can be technically reduced to the problem of charged-particle production with well-defined energy, transversal momentum, and spin polarization [whose eigenvalues are (px, pz, p0, σ)] It should be remarked, though, that the production of charged particles is possible only in cases of critical potential steps, whose magnitudes obey the inequality U (D)(+∞) − U (D)(−∞) > 2m. It is important to emphasize both sets of solutions exist provided the quantum numbers n obey the conditions [sπs (L/R)]2 > πx2 These inequalities ensure the nontriviality of DP spinors with real asymptotic momenta pL and pR in remote areas and impart consequences to the quantization of the theory, as shall be discussed below. We use results obtained in the latter work, taking into account relation between eqs. (2.9) and (2.12); see appendix A for in- and out-solutions of the DP equation with the field (2.24)
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