In this paper, a multi-energy groups of a neutron diffusion equations system is analytically solved by a residual power series method. The solution is generalized to consider three different geometries: slab, cylinder and sphere. Diffusion of two and four energy groups of neutrons is specifically analyzed through numerical calculation at certain boundary conditions. This study revels sufficient analytical description for radial flux distribution of multi-energy groups of neutron diffusion theory as well as determination of each nuclear reactor dimension in criticality case. The generated results are compatible with other different methods data. The generated results are practically efficient for neutron reactors dimension.

Both linear and angular momentum densities of Bessel, Gaussian-Bessel, and Hankel-Bessel lasers are determined. Angular momentum of the three Bessel beams is illustrated at linear and circular polarization. Axial Angular momentum is resolved in particular interpretation: the harmonic order of the physical light momentum. Full Text: PDF References G. Molina-Terriza, J. Torres, and L. Torner, "Twisted photons", Nature Physics 3, 305 - 310 (2007). CrossRef J Arlt, V Garces-Chavez, W Sibbett, and K Dholakia "Optical micromanipulation using a Bessel light beam", Opt. Commun., 197, 4-6, (2001). CrossRef L. Ambrosio and H. Hernández-Figueroa, "Gradient forces on double-negative particles in optical tweezers using Bessel beams in the ray optics regime", Opt Exp, 18, 23 (2010). CrossRef I. Litvin, A. Dudley and A. Forbes, "Poynting vector and orbital angular momentum density of superpositions of Bessel beams", Opt Exp, 19, 18 (2011). CrossRef K Volke-Sepulveda, V Garcés-Chávez, S Chávez-Cerda, J Arlt and K Dholakia "Orbital angular momentum of a high-order Bessel light beam" , JOP B 4 (2). 2002. CrossRef M. Verma, S. Pal, S. Joshi, P. Senthilkumaran, J. Joseph, and H Kandpal, "Singularities in cylindrical vector beams", Jou. of Mod. Opt., 62 (13), 2015. CrossRef R. Borghi, M. Santarsiero, and M. Porras, "Nonparaxial Bessel?Gauss beams", J. Opt. Soc. Am. A, 18 (7) (2011). CrossRef L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian Laser modes", Phys Rev A, 45 (11): 8185-8189 (1992). CrossRef D. Mcglion and K. Dholakia, "Bessel beams: diffraction in a new light", Cont. Phys, 46(1) 15 ? 28. (2005). CrossRef F. Gori, G. Guattari and C. Padovani," Bessel-Gauss Beams", Opt. Commun., 64, 491, (1987). CrossRef V. Kotlyar, A. Kovalev, and A. Soifer, "Hankel?Bessel laser beams" J. Opt. Soc. Am. A, 29 (5) (2012). CrossRef L. Allen and M. Babiker "Spin-orbit coupling in free-space Laguerre-Gaussian light beams", Phys. Rev. A 53, R2937. CrossRef Both linear and angular momentum densities of Bessel, Gaussian-Bessel, and Hankel-Bessel lasers are determined. Angular momentum of the three Bessel beams is illustrated at linear and circular polarization. Axial Angular momentum is resolved in particular interpretation: the harmonic order of the physical light momentum. Full Text: PDF References G. Molina-Terriza, J. Torres, and L. Torner, "Twisted photons", Nature Physics 3, 305 - 310 (2007). CrossRef J Arlt, V Garces-Chavez, W Sibbett, and K Dholakia "Optical micromanipulation using a Bessel light beam", Opt. Commun., 197, 4-6, (2001). CrossRef L. Ambrosio and H. Hernández-Figueroa, "Gradient forces on double-negative particles in optical tweezers using Bessel beams in the ray optics regime", Opt Exp, 18, 23 (2010). CrossRef I. Litvin, A. Dudley and A. Forbes, "Poynting vector and orbital angular momentum density of superpositions of Bessel beams", Opt Exp, 19, 18 (2011). CrossRef K Volke-Sepulveda, V Garcés-Chávez, S Chávez-Cerda, J Arlt and K Dholakia "Orbital angular momentum of a high-order Bessel light beam" , JOP B 4 (2). 2002. CrossRef M. Verma, S. Pal, S. Joshi, P. Senthilkumaran, J. Joseph, and H Kandpal, "Singularities in cylindrical vector beams", Jou. of Mod. Opt., 62 (13), 2015. CrossRef R. Borghi, M. Santarsiero, and M. Porras, "Nonparaxial Bessel?Gauss beams", J. Opt. Soc. Am. A, 18 (7) (2011). CrossRef L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian Laser modes", Phys Rev A, 45 (11): 8185-8189 (1992). CrossRef D. Mcglion and K. Dholakia, "Bessel beams: diffraction in a new light", Cont. Phys, 46(1) 15 ? 28. (2005). CrossRef F. Gori, G. Guattari and C. Padovani," Bessel-Gauss Beams", Opt. Commun., 64, 491, (1987). CrossRef V. Kotlyar, A. Kovalev, and A. Soifer, "Hankel?Bessel laser beams" J. Opt. Soc. Am. A, 29 (5) (2012). CrossRef L. Allen and M. Babiker "Spin-orbit coupling in free-space Laguerre-Gaussian light beams", Phys. Rev. A 53, R2937. CrossRef

The authors wish to insert this additional sentence in the Acknowledgments section