This communication is devoted to the study of the cooperative two-photon and four-photon scattering processes between pump field and resonance mode of cavity stimulated by the atomic beams. These collective scattering phenomena between the pump and scattered photons are taking place due to energy transfer between these quantum fields. For the first time was used symmetry SU (2) to describe the quantum of Raman and hyper-Raman laser. The statistical properties of generated photon pairs and connection with the statistic of applied field have been described by using the photons correlation functions. The analytical expressions for two- and four-photon correlations from atom driven in a Raman and hyper-Raman configurations are discussed. The numerical solutions of these equations describe the statistical transformation of N-pump photons into Raman (or hyper-Raman) photon pairs. It is proposed novel two-photon entangled sources, which take into account the coherence and collective phenomena between these states. As the life time of the atom in the cavity is considered smaller than the cooperative scattering time between the pump and Raman modes (or hyper-Raman modes), it is eliminate the atomic variables and focused on the transformation of the pump in Raman mode (or hyper-Raman mode) and vice versa, as a function of the atomic inversion and initially prepared field states. Taking into account the process, that takes place with the absorption (emission) of new quanta, it was introduce the bi-boson operators describing such a quantum transformation between the pump photons into the Raman modes (or hyper-Raman modes). The master equations, in both cases which describes these processes, gives us the possibility to discover the behaviour of quantum fluctuations in nonstationary process of absorption and radiation of pump and hyper-Raman (Raman) photons. The stationary and non-stationary solutions of this master equation in both cases reveal the strong quantum correlation between pump and photons from the cavity. This correlation function gives us the possibility to manipulate with quantum statistics of photons generated in the scattering field as a function of atomic inversion and cavity parameters, like detuning, losses, and quality factor of the cavity.