We have developed a collisional radiative model of electron collisional excited x-ray lasers. We calculate the ion abundance and soft x-ray gain for the 4d-4p transition of Ni-like multiple charged ion, in short pulse laser irradiated plasmas. We combine a detailed model using the atomic data calculated by HULLAC code and the averaged model based on the screened hydrogenic approximation. In order to choose a proper set of the levels to be included in the atomic model, investigation of the model dependence of the gain is carried out. The population in the fine structure levels in 3d94s and 3d94f configuration, autoionizing double excited configurations of Ni-like and Cu-like ions are found to cause approximately factor of 2 difference in the soft x-ray gain. The steady-state gain and its dependence on plasma density and temperature are investigated over elements from z equals 45 to 65. The time dependent calculation for a plasma condition corresponds to a thin Ag foil irradiated by tow short laser pulse shows the transient gain which is 40 times greater than the steady state gain.
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