Mathematical calculation of energy spectrum of x ray by computer, (1)

The purpose of this paper is to examine a few problems in mathematics acceptable by the computer for calculating energy spectrum of X ray. These are the following: 1. The estimation of the mass attenuation and the mass energy-absorption coefficients except the reprinted coefficients 2. The solution of normal equations about X-ray energy spectrum As the functional relationship between the photon energy and the coefficients of various materials can be approximated by the polynomials, the unknown coefficients can be estimated using these polynomials. The close agreement between the reprinted and the estimated coefficients was obtained for the range from 10 to 300 KeV. The normal equations can be solved directly by using the various methods of SSL (Gauss-elimination, sweep out, Gauss-Seidel). However, as the specific energy spectrum of X ray, we can not give a clear physical interpretation for irregular curve Therefore, for solving the normal equations, we shall apply to the Gauss-Seidel technique with an initial value in place of the above-mentioned SSL methods, and details will be reported at a next paper. (author)