Calculating the dose equivalent of coordinate surfaces of the Cartesian geometry: a new analytical method compared with Monte Carlo method

In this paper, an analytical method for calculation of the dose equivalent (DE) of coordinate surfaces of the Cartesian geometry is presented. DE of rectangular surfaces of gamma radiation emitters is calculated. The developed analytical method changes rectangular surface to multiple polar regions by dividing its surface into four types of sectors. By this method, the calculation of the dose is converted into calculation of simple mathematical series. The dose of rectangular shape sources for different gamma radiation emitters at different distances to target is calculated and the results are compared with MCNP code. Results show very good agreement. Advantages of the developed method are: 1—While Monte Carlo techniques usually take time to obtain adequate statistics on small regions, the developed method is independent of statics and therefore performs a very quick calculation (i.e. more than 10⁵ times faster) 2—Usually the trained person is required to calculate the dose with Monte Carlo codes while analytical calculation does not need the trained one. Moreover, analytical methods make possible to perform easily parametric analysis and to reach desired outlet of the dose. Since rectangles with proper size in sufficient numbers can completely reconstruct any surface, therefore, dose of complex surfaces can be calculated using the developed method.