Radiative-electron-capture-to-continuum cusp in ${\mathrm{U}}^{88+}+{\mathrm{N}}_2$ collisions and the high-energy endpoint of electron-nucleus bremsstrahlung

The radiative electron capture of a target electron into the projectile continuum has been studied for the collision system ${\text{U}}^{88+}+{\text{N}}_2\to {\text{U}}^{88+}+{\left[{\text{N}}_2^{+}\right]}^{*}+e^{-}+\gamma$ at 90 MeV/$\mathrm{u}$. Using a magnetic electron spectrometer, the energy distribution of cusp electrons emitted under an angle of $0^{\circ }$ with respect to the projectile beam and with a velocity close to the projectile velocity has been measured in coincidence with the emitted photons under various observation angles. The experimental results provide a stringent test for the corresponding process in inverse kinematics, namely, the theory of electron-nucleus bremsstrahlung at the high-energy endpoint. For comparison this process is calculated using fully relativistic Dirac wave functions and using semirelativistic Sommerfeld-Maue wave functions.

Figure 1

Layout of the experimental setup at the experimental storage ring ESR with the electron cooler, gas-jet target, electron spectrometer, x-ray detectors, and particle detectors for identification of projectile ionization and capture processes.

Figure 2

Geometry and coordinates in the laboratory system used throughout the paper: The horizontal projectile beam is intersected by the vertical gas-jet target; the angular acceptance of the electron spectrometer as well as the observation angles of the x-ray detectors in the horizontal $xz$-plane is shown.

Figure 3

Electron angular distribution in the projectile frame for different energies of the scattered electron $E_f^{\prime }$ and various photon observation angles ${\vartheta }_{\gamma }$. Here the case is considered of an incoming electron of $E_i^{\prime }=49.58$ keV scattering off the projectile ion with $Z_p=88$ while emitting a photon with energy $E_{\gamma }^{\prime }=E_i^{\prime }-E_f^{\prime }$. Curves are as follows: $E_f^{\prime }=1$ eV (solid), $E_f^{\prime }=10$ eV (short-dashed), $E_f^{\prime }=100$ eV (dotted), $E_f^{\prime }=1$ keV (dot-dashed), and $E_f^{\prime }=10$ keV (long-dashed).

Figure 4

The x-ray energy spectrum observed under ${\vartheta }_{\gamma }=+{90}^{\circ }$ without any coincidence condition (black), (a) in coincidence with a down-charged projectile (green), (b) in coincidence with an up-charged projectile (cyan), (c) in anticoincidence with a charge-changed projectile (blue), and (d) in coincidence with an electron emitted under ${\vartheta }_f=0^{\circ }$ (red).

Figure 5

Experimental and theoretical electron energy distributions at the high-energy endpoint of bremsstrahlung observed under ${\vartheta }_f=0^{\circ }$ for five different photon emission angles ${\vartheta }_{\gamma }$: Dirac theory (solid red line), Sommerfeld-Maue theory multiplied by 2 (dashed green line) for ${\vartheta }_{\gamma }=\pm {90}^{\circ }$. The experimental results (symbols) are normalized to Dirac theory, the same scaling factor is applied to for all five photon angles ${\vartheta }_{\gamma }$.

Figure 6

Photon angular distribution at the high-energy endpoint of electron-nucleus bremsstrahlung, emitted for an electron energy of $E_f^{\prime }=1$ keV. Experimental results (symbols) in comparison with Dirac theory (solid red line), Sommerfeld-Maue theory multiplied by 2 (dashed green line), and a ${sin}^2{\vartheta }_{\gamma }$-like dipole radiation pattern (dotted black line). Top, triple differential cross sections for an electron emission angle of ${\vartheta }_f^{\prime }={180}^{\circ }$; bottom, double differential cross sections integrated over all electron emission angles.