Emission of twisted photons by a scalar charge in a strong magnetic field

We consider the emission of a photon by a scalar charged particle in a constant and uniform magnetic field. In contrast to the conventional approach with both photon and outgoing charge being assumed to be detected, we study the case where only the state of the charge is measured and investigate the properties of the emitted photon. The background magnetic field is taken into account exactly in the calculations and the charge is described by relativistic Landau states. It is shown that the emitted photon state represents a twisted Bessel beam, with total angular momentum given by $\ell-\ell'$, where $\ell$ and $\ell'$ are angular momentum quantum numbers of the initial and final charged particle, respectively. The majority of photons emitted by unpolarized charges, especially in the hard X-ray and $\gamma$-ray range and in critical and sub-critical magnetic fields, as compared to the Schwinger value of $H_c = 4.4\times 10^9$ T, turn out to be twisted with $\ell-\ell'\gtrsim 1$ for non-relativistic charged particles and with $\ell-\ell' \gg 1$ for ultra-relativistic ones. Also, it is found that the radiation intensity of the twisted photons grows with the initial charge momentum $p_z$ along the magnetic field and saturates at $|p_z| \sim 10-50\, mc$, with $m$ being the mass of the charge.