Linearly Modulated OSL in K\(_{3}\)Na(SO\(_{4}\))\(_{2}\):Eu\(^{3+}\) Phosphor Irradiated With 48 MeV Li\(^{3+}\) and 85 MeV C\(^{6+}\) Swift Heavy Ions Beam

K\({}_{3}\)Na(SO\({}_{4}\))\({}_{2}\):Eu\({}^{3+}\) shows OSL when irradiated with swift heavy ion beams of Li\({}^{3+}\) and C\({}^{6+}\) at different fluences. The micro sample is prepared through solid state diffusion method along with its counter parts of ball milled (7 days) nanophosphor and co-precipitated nanophosphor samples. The material was characterized by XRD to confirm its formation in a single phase. Comparison of the experimental data with that of the data available in the literature (JCPDS data file \#74 0398) shows formation of a single hexagonal phase, with the space group P3 m1. Study on the particle size effect shows that particle size in the 75--106 \(\mu\)m rangeis more suitable for the linearly modulated-optically stimulated luminescence (LM-OSL) dosimetry in micro form. Dosimetric properties of the phosphor material using LM-OSL technique for blue light stimulation (\(\lambda=470\) nm and \(t=120$\) seconds) show that it is highly sensitive in the linear dose range. Here in this paper, we tried to find a relationship between detrapping probabilities and photoionization cross section using curve fitting (deconvolution) method. We also calculated and converted the fluence into doses using SRIM software. Data are presented indicating that the LM-OSL peak is composed of three overlapping components originating from populated traps with optical cross sections of 10\({}^{-17}\)-10\({}^{-18}\) cm\({}^{2}\). It was found that micro and ball milled nanophosphor Carbon ion beam irradiated samples dominates the photoionization cross section as compared with lithium ion irradiated samples, but co-precipitated sample is dominant in lithium irradiated samples. Which infers about the different trapping level formation and also recombination processes involved during the preparation and in readouts of samples.