Parametric Mössbauer radiation source

Numerous applications of Mössbauer spectroscopy are related to a unique resolution of absorption spectra of resonant radiation in crystals, when the nucleus absorbs a photon without a recoil. However, the narrow nuclear linewidth renders efficient driving of the nuclei challenging, restricting precision spectroscopy, nuclear inelastic scattering and nuclear quantum optics. Moreover, the need for dedicated x-ray optics restricts access to only few isotopes, impeding precision spectroscopy of a wider class of systems. Here, we put forward a novel Mössbauer source, which offers resonant photon flux for a large variety of Mössbauer isotopes with strongly suppressed electronic background. It is based on relativistic electrons moving through a crystal and emitting parametric Mössbauer radiation essentially unattenuated by electronic absorption. As a result, a collimated beam of resonant photons is formed, without the need for additional monochromatization. We envision the extension of high-precision Mössbauer spectroscopy to a wide range of isotopes at accelerator facilities, also using dumped electron beams.

Figure 1

Schematic setup for the generation of PMR in the EAD geometry. The electron beam moves uniformly with velocity $\mathit{v}$ in the $x$ direction. The crystal surface lies in the $x\text{−}y$ plane. $\mathit{g}$ is the reciprocal crystal lattice vector. PMR will be mainly emitted in the direction given by the vector ${\mathit{k}}^{\prime }=-\mathit{k}=-k_0(\sin {\theta }_0\cos {\varphi }_0,\sin {\theta }_0\sin {\varphi }_0,\cos {\theta }_0)$, and thus rapidly leaves the crystal without significant electronic absorption. ${\mathit{k}}_g=\mathit{k}+\mathit{g}$ and ${\theta }_{\mathrm{B}}$ is the Bragg angle. The energy of the PXR is tuned using the angle ${\psi }_0$ between the electron velocity and the projection ${\mathit{g}}_{\perp }$ of $\mathit{g}$ on the crystal surface.

Figure 2

The number of emitted x-ray photons per second as a function of the dimensionless frequency $x=(\omega -{\omega }_0)/(\mathrm{\Gamma }/2)$. The results are averaged over the electron beam parameter distributions, for different transversal widths and divergences of the electron beam, keeping the emittance constant. The figure compares the emission from the (011) reflex of $\alpha$ iron (top left), the (312) reflex of ${\mathrm{Sc}}_2{\mathrm{O}}_3$ (top right), and the (111) reflex of CsF (bottom left). The bottom right panel shows pure PMR emission from the (222) reflection of the InSb crystal. For all panels, we assume an angular spread in the $y$ direction of ${10}^{-3}\mathrm{rad}$. The crystal lengths are chosen as $L=0.5\mathrm{cm}$. Electron parameters are chosen according to the MAMI facility, with energy $E=1000\mathrm{MeV}$, vertical emittance $\epsilon =1.9\times {10}^{-7}$ cm rad, and electron current is $j=100\mu \mathrm{A}$.

Figure 3

Simulation of an absorption spectrum obtained with the PMR source. As a target, a nonenriched ($\eta =0.02$) $\alpha$-iron crystal of thickness $D=5\mu \mathrm{m}$ is assumed. The contrast is determined via the ratio of the electron and the nuclear contributions into the crystal polarizability near the resonance frequency and in the case of $\alpha$-iron $\sim 20$. Other parameters are as in Fig. 2, with $\mathrm{\Delta }a=1.9\times {10}^{-4}\mathrm{cm}$. The electronic “background” is supposed to be removed via temporal gating to obtain the results.