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Register a new userElectric Field Screening by Pairs in the Presence of Returning Positrons
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Shinpei Shibata
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We solve the one-dimensional Poisson equation along a magnetic field line, both analytically and numerically, for a given current density incorporating effects of returning positrons. We find that the number of returning positrons per one primary electrons should be smaller than unity, and the returning of positrons occurs only in a very short braking distance scale. As a result, for realistic polar cap parameters, the accelerating electric field will not be screened out; thus, the model fails to be self-consistent. A previous belief that pair creation with a pair density higher than the Goldreich-Julian density immediately screens out the electric field is unjustified. We suggest some possibilities to resolve this difficulty.
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We study on the self-consistency of the pulsar polar cap model, i.e., the problem of whether the field-aligned electric field is screened by electron-positron pairs that are injected beyond the pair production front. We solve the one-dimensional Poisson equation along a magnetic field line, both analytically and numerically, for a given current density incorporating effects of returning positrons, and we obtain the conditions for the electric-field screening. The formula which we obtained gives the screening distance and the return flux for given primary current density, field geometry and pair creation rate at the pair production front. If the geometrical screening is not possible, for instance, on field lines with a super-Goldreich-Julian current, then the electric field at the pair production front is constrained to be fairly small in comparison with values expected typically by the conventional polar cap models. This is because (1) positive space charge by pair polarization is limited to a small value, and (2) returning of positrons leave pair electrons behind. A previous belief that pair creation with a pair density higher than the Goldreich-Julian density immediately screens out the electric field is unjustified at least for for a super Goldreich-Julian current density. We suggest some possibilities to resolve this difficulty.
The electronic states at graphene-SiO$_2$ interface and their inhomogeneity was investigated using the back-gate-voltage dependence of local tunnel spectra acquired with a scanning tunneling microscope. The conductance spectra show two, or occasionally three, minima that evolve along the bias-voltage axis with the back gate voltage. This evolution is modeled using tip-gating and interface states. The energy dependent interface states density, $D_{it}(E)$, required to model the back-gate evolution of the minima, is found to have significant inhomogeneity in its energy-width. A broad $D_{it}(E)$ leads to an effect similar to a reduction in the Fermi velocity while the narrow $D_{it}(E)$ leads to the pinning of the Fermi energy close to the Dirac point, as observed in some places, due to enhanced screening of the gate electric field by the narrow $D_{it}(E)$
We study the screening of a homogeneous oscillating external electric field $E_0$ in noble-gas atoms using atomic many-body calculations. At zero frequency of the oscillations ($omega=0$) the screened field $E(r)$ vanishes at the nucleus, $E(0)=0$. However, the profile of the field $E(r)$ is complicated, with the magnitude of the field exceeding the external field $E_0$ at certain points. For $omega >0$ the field $E(r,omega)$ strongly depends on $omega$ and at some points may exceed the external field $E_0$ many times. The field at the nucleus is not totally screened and grows with $omega$ faster than $omega^2$. It can even be enhanced when $omega$ comes close to resonance with a frequency of an atomic transition. This field interacts with CP-violating nuclear electric dipole moments creating new opportunities for studying them. The screening of the external field by atomic electrons may strongly suppress (or enhance near an atomic resonance) the low energy nuclear electric dipole transitions.
According to the Schiff theorem, the atomic electrons completely screen the atomic nucleus from an external static electric field. However, this is not the case if the field is time-dependent. Electronic orbitals in atoms either shield the nucleus from an oscillating electric field when the frequency of the field is off the atomic resonances or enhance this field when its frequency approaches an atomic transition energy. In molecules, not only electronic, but also rotational and vibrational states are responsible for the screening of oscillating electric fields. As will be shown in this paper, the screening of a low-frequency field inside molecules is much weaker than it appears in atoms owing to the molecular ro-vibrational states. We systematically study the screening of oscillating electric fields inside diatomic molecules in different frequency regimes,i.e., when the fields frequency is either of order of ro-vibrational or electronic transition frequencies. In the resonance case, we demonstrate that the microwave-frequency electric field may be enhanced up to six orders in magnitude due to ro-vibrational states. We also derive the general formulae for the screening and resonance enhancement of oscillating electric field in polyatomic molecules. Possible applications of these results include nuclear electric dipole moment measurements and stimulation of nuclear reactions by laser light.
The expanded variant of the lectures delivered at the 39th ITEP Winter School in 2011
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