Lev I. Dorman
       Israel Cosmic Ray Center, affiliated to Tel Aviv University; 
Technion and IZMIRAN; Current address: P.O.Box 2217, Qazrin 12900, ISRAEL
Irina V. Dorman
       Institute of History of Science and Technology, Russian Academy 
of Science, Staropansky 1/5, Moscow 103012, RUSSIA
Jose F. Valdes-Galicia
       Institute of Geofisica of UNAM, Mexico D.F., 04510, MEXICO

We develop our simulation and analytical calculation results of solar neutron propagation in the atmosphere for different initial zenith angles taking into account not only scattering and attenuation but also neutron energy decrease (what leads to increase both of cross-section and scattering angles, what is especially important for small energy solar neutrons). We test the usually used suggestion that solar neutron propagation through the atmosphere of depth H for some initial zenith angle Z of the Sun will be the same as for vertical direction, but for the depth H/cosZ. Our calculations of multi-scattering of neutrons on small angles with attenuation and energy change for different initial zenith angles shows that this suggestion is not correct. Taking into account the neutron energy change shows that with decreasing of solar neutron energy the assymmetry in solar neutron propagation and refraction effect became stronger. We show that during the propagation through the earth's atmosphere the effective zenith angle of solar neutron flux sufficiently decrease. These decreases are especially great for the big initial zenith angles what gives expected solar neutron fluxes many times bigger than in the frame of previous theory of solar neutron propagation. We show also that the optimum direction of solar neutron telescope must be not the direction on the Sun (as for optical telescope), but between the Sun and vertical.