We report the review of the experimental results obtained at the Insti
tute of Laser Engineering, Osaka University, of the sofi; X-ray lasing
in various Ni-like ions whose atomic numbers range from 47(Ag) to 66(
Dy). The lasing wavelengths are between 14 nm and 5 nm. X-ray lasing i
n these materials were obtained when the plasma profiles were properly
controlled in time and space by irradiation of curved slab targets wi
th multiple laser pulses. We also describe the original work of the at
omic physics calculations which provide the transition energies, trans
ition probabilities and other atomic constants for Ni-like ion species
whose atomic numbers range from 36 to 92 calculated with GRASP code (
multi-configuration Dirac Fock code) and YODA code (relativistic disto
rted wave code). Based on these atomic constants, we have calculated t
he kinetics of the population inversion with a simplified rate equatio
n model in conjunction with a one-dimensional hydrodynamic code to fin
d out the desired pumping conditions. We show a possibility for signif
icant improvement in the pumping efficiency with the use of a picoseco
nd laser irradiating a properly configured preformed plasma. Finally,
a simplified estimation of the pumping efficiency is described based o
n the atomic constants and plasma physics issues.