3. Results and discussion

In Figure 5.1 the doubly differential cross-sections are shown for bremsstrahlung in collisions of U⁹⁰⁺ with N₂ and Ar target electrons at observation angles 132^o and 90^o, respectively. The experimental data are compared to the predictions of the relativistic Born approximation calculations with Elwert correction factor, and to the rigorous relativistic calculations. The latter were obtained using relativistic independent particle approximation which takes into account the exact scattering electron wave-functions in a static potential, and include the lowest non-zero term in the interaction between the emitted photon field with the electron [2]. It is evident that both models underestimate the experimental data for photon energies up to the vicinity of the end-point of the bremsstrahlung spectra. It should be recognized that for He-like projectiles an additional x-ray continuum associated with the excitation process to the 2S₀ state of the projectile contributes to the observed x-ray spectra. The characteristic K$\alpha$ and K$\beta$ radiation seen in Fig. 5.1 is due to the Coulomb excitation to the P states of U⁹⁰⁺. In contrast, the collisionally excited 2S states, decay by succesive emission of two-photons (2E1) which is manifested as an x-ray continuum stretching from photon energy equal zero to approximately the energy of the K$\alpha_2$ transition in U⁹⁰⁺. This de-excitation mode can alter slightly the shape of the observed x-ray continua. However, the end-point energy region of bremsstrahlung is not affected by the two-photon transitions, while simultaneously, here the systematic uncertainties of the absolute experimental cross sections are smallest. This energy domain is in particular sensitive to the final state Coulomb interaction, since high energy x-rays originate from collisions where final kinetic electron energy is small as compared to the electron-nucleus interaction. For these photon energies the calculations based on the Born-approximation generally fail to predict the experimental data. This failure is connected to the fact that Born approximation utilizes a power expansion in series of Z $\alpha/\beta_f$ (Z is here the charge of the scattering center, $\alpha$ is fine structure constant and $\beta_f$ is final electron velocity in units of the speed of the light). It is apparent from Fig. 5.1 that rigorous calculations lead to a better agreement with experimental data for doubly differential bremsstrahlung cross-sections at the end-point energy region. This demonstrates the importance of rigorous non-perturbative treatment of the electron - electromagnetic field interaction for bremsstrahlung in the domain of strong Coulomb potentials.