Alumina sintered body and optical element base substrate

This alumina sintered body: has a plane having a c-plane orientation of at least 5% as found by the Lotgering method using an X ray diffraction profile in a range of 2θ = 20-70° when irradiating with X rays; includes Mg and F; has an Mg/F mass ratio of 0.05-3,500; has an Mg content of 30-3,500 ppm by mass; has a crystal particle diameter of 15-200 µm; and has no more than 250 pores having a diameter of 0.2-0.6 µm when a photograph is viewed in which a 370.0 × 370.0 µm (V × H) field of vision is captured at a magnification of 1,000 times. The volume ratio of pores having a diameter 0.2-0.6 µm, relative to the volume of alumina sintered body, is no more than 130 ppm by volume. This alumina sintered body has a linear transmittance of at least 60% in a wavelength range of 450-1,000 nm, at a thickness of 0.5 mm. In other words, this alumina sintered body has excellent transparency because the linear transmittance is high even if the c-plane orientation is at least 5%.