n several research areas , such as ICF and astrophysics the knowledge of the interaction between the radiation and plasma is essential In these plasmas the calculation of its radiation properties is a difficult task due to the huge number of levels and transitions involved ,even for low Z plasmas such as carbon plasma. Most of work in this field was developed under LTE conditions and the calculation of opacity is very important although it is very complex Because Carbon may be used as dupants in the ablator of target in ICF, The knowledge of their opacities is crucial, we have calculated the opacity by using analytical and numerical calculations. To calculate the opacity needs to know the atomic energy level ,oscillator strength ,line profiles and atomic level populations .Under the local thermodynamic equilibrium (LTE) conditions ,the level populations can be acquired to solve Boltzmann – Saha equation . To calculate the other part efficiently, we have to resort to the average ion model, especially for the calculation of the atomic level populations .Refer to the our work, we calculate the opacity and its Plank and Rosseland mean values ,of hot and dense plasma at a given temperature and density. The average ion model is employed to calculate the allowed maximum value of principle quantum number nmax, which can be used to terminate the summation foIr the calculation of the partition function in the saha equation under LTE conditions. Pn is the occupation number calculated by average ion model in bound-free part of equation number. In this model, the plasma is considered to be composed of average atom. These atoms are inter-independence and electro neutral inside the atomic cell the electronic density is consist of bound electronic density and free one. The bound-free cross section can be calculated from quantum mechanically procedure or from Kramer´s formula. Finally, the free-free spectrum has been obtained employing the Kramer’s formula for the cross section (corrected by the gaunt factor).

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