In the present paper, a net effective gain of multi-pumping Raman amplifier in  ultra-wavelength division multiplexing (UW-WDM) and  ultra long-haul (ULH) optical communication systems has been modeled and parametrically investigated over wide ranges of affecting parameters, taking into account the polarization effect. N_R pumps are processed with or without equal spectral spacing. The effective fiber core area, the gain coefficients and the amplified spontaneous emission power ASE (as a measure of the minimum detectable power) are calculated over the operating wavelength. The above three quantities are cast in simple polynomial forms. The average net Raman gain, the on-off Raman gain, the signal-to-noise ratio at the effective length has been investigated also. The obtained results are employed to find the average repeater spacing over the spectral range under the processing. It is concluded that for repeater spacing, the total injected Raman powers are the vital factor rather than the number of amplifiers, while for the gain spectral width, the number of amplifiers is the vital factor. The central wavelength of the subset of channels that propagates in a link indicates the order of link. The total number of links in the core determines the ultimate values of different effects.