M. Oane1, I. N. Mihailescu1, N. Serban1 , C. Oproiu1, G. Florescu2 A theoretical approach concerning the creation of super-thermal hadrons – anti - hadrons pairs using extreme light intensity M. Oane1, I. N. Mihailescu1, N. Serban1 , C. Oproiu1, G. Florescu2 1NATIONAL INSTITUTE FOR LASER, PLASMA AND RADIATION PHYSICS, STR. ATOMISTILOR 409, MAGURELE, ROMANIA 2 SUBSIDIARY OF TECHNOLOGY AND ENGINEERING FOR NUCLEAR PROJECTS, STR. ATOMISTILOR 409, MAGURELE, ROMANIA ABSTRACT In the last years the development of high energy lasers, permit us to study new regimes of laser-matter interaction. The interaction of ultra-intense laser beam with plasma can produce for example, electron-positron. This effect is a relativistic one. In consequence we have to solve non-Fourier heat equations type [1,2,3], which takes into account such effects. At the end we make a brief appreciation in the elegant Kozlowski model [4] in order to establish the laser properties necessary to obtain proton – anti-proton pairs. E-mails: mihai.oane@inflpr.ro or ion.mihailescu@inflpr.ro THE ANALYTICAL MODEL We have : . We may write the non-Fourier equation [1]: . After some algebraically manipulation we have the following relation [2]: where: Using the reverse Laplace transform, we obtain : We may consider [3]: The final results can be express: . RESULTS OF THE THEORETICAL MODEL Fig. 1 The temperature express in MeV versus time for laser plasma irradiation, when relaxation time is equal to pulse time and it is 4fs (using the formalism from [4]) . 1) In the present paper an exact analytical solution was given for laser-solid interaction was given (using the Laplace transform), 2) The second step was to use the previous solution to laser-plasma interaction. We have made “modifications” just in the final formula, 3) We express the temperature in MeV, according to M. Kozlowski and J.M. Kozlowska theory [4]: that the heat can be “quantify in heatons”, which are express in eV. We observe that the energy is high enough to produce electron-positron pairs, for : , 4) Our work is just a “useful” tool for the first investigations necessary to people who work in experimental physics and should be regarded like a semi-classical model, which can be improved or the subject can be “attack” in other way, in order to obtain ”quantum heat equations” [5,6], 5) If we make some elementary algebra we get, for obtaining proton – anti proton pairs the relation: , which until 2020, may be reach by ELI facility at Bucharest. This formula should be regarded as the minimum condition to obtain hadrons – anti-hadrons pairs. [1]. D. D. Joseph and L. Preziosi,( 1989 ),Reviews of Modern Physics, 61 (1), 41 -73, [2]. R. Redheffer, ( 1991 ), Differential equations theory and applications: Jones and Bartlett publishers. Boston, chapters 23 and 24, [3]. R. K. Singh and I. Norayan, ( 1990 ), Physical Review B, Vol. 41, number 13, pg. 8843 – 8859, [4]. M. Kozolowski, I. M. Kozolowska, ( 2001 ), From Quarks to Bulk Matter, Physics the Causal Thermal Phenomena, Hadronic Press, USA, [5]. M. Oane, M. Nemtanu, C. Oproiu, Lasers in Engineering, (2011) ,Vol.21, Nr.3-4, 129-134, [6]. M. Oane, G. Florescu, C. Oproiu, I. N. Mihailescu, Lasers in Engineering, in press, (2011); Vol.21, Nr.5-6.   CONCLUSIONS REFERENCES Acknowledgments: the authors acknowledge with thanks for the financial support of this work by contract NUCLEU/2011 Acknowledgments: the authors acknowledge with thanks for the financial support of this work by the contract NUCLEU/2011.