  The actual theoretical research investigates the resonant high-energy
spontaneous bremsstrahlung of ultrarelativistic electrons with considerable
energies in the field of a nucleus and a quasimonochromatic laser wave. Under
the resonant conditions within the laser field the intermediate virtual
electron transforms into the real particle. As a result, the accomplished
analysis defines that the polar emission angle characterizes the frequency of a
spontaneous photon. The study derives the expressions for the resonant
differential cross-sections of the represented processes that realize
simultaneous registration of the frequency and radiation angle in correlation
to the momentum of the initial electron (for the channel A) and of the final
electron (for the channel B) of the spontaneous photon with absorption of $r$
wave photons ($r = 1, 2, 3,... $ - the number of a resonance). Additionally,
the distribution of the resonant differential cross-section as a function of
the angle of the spontaneous photon emission for the higher numbers of
resonance ($r = 2, 3,... $) delineates a dependency with a sharp peak maximum
that coordinates to the particle radiation at the most probable frequency. To
summarize, the accomplished work represents that the resonant differential
cross-section acquires considerable magnitude. Thus, for the first resonance of
the channel A the resonant differential cross-section attains the $\sim
10^{12}$ order of a magnitude, and for the third resonance of the channel B
$\sim 10^5$ order of a magnitude (in the units of $\alpha Z^2 r_e^2$). Finally,
numerous scientific facilities with specialization in pulsed laser radiation
(SLAC, FAIR, XFEL, ELI, XCELS) may experimentally verify the constructed model
calculations.
