Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

22 Monte Carlo Particle Transport Methods: Neutron and Photon Calculationsand(2.15)The efficiency is trivially the ratio of the circle to the square areas, i.e.,V. - - 0.7854Though the straightforward procedure (2.13) seems to be much simpler than (2.15), inmost computers both the generation of random numbers and the execution of the otherelementary operations of (2.12) are less time consuming than the evaluation of the sine andcosine of an angle.If not a unit vector, but rather a point from the circle area has to be selected then Equation(2.13) should be supplemented byr = max(p,,p 2)(since: p(r) = 2r dr) and x and y should be multiplied by r.In the rejection method Equation (2.14) gives directly the necessary coordinates (thereis no need for normalization), thus its preference to the direct method in Equation (2.12) iseven more obvious.In three dimension the coordinates of a random unit vector are 31Z =(i)x = Vl — w 2 coscpy = Vl — w 2 sincpwhere w is equidistributed on (—1,1) and coscp and sincp can be generated by one of themethods listed above.A point from inside of a sphere can again be selected by the rejection method, wherethe sphere is boxed in a cube. The efficiency here is the ratio of the sphere to the cubevolumes:E = - = 0.5236II. BASIC PHYSICAL QUANTITIESThe reader is assumed to be familiar with the basic physical quantities that are characteristicto particle transport that will be used in the following Chapters of this book. Thereare, however, several quantities which are named differently in different papers (e.g.,fluence, flux, flux density . . . ), or which have equivalent physical interpretations butdifferent names in different contexts (macroscopic cross-section and linear attenuation coefficient).Even a larger variety is found in the use of symbols for a number of terms.Considering all the above arguments it seems appropriate to give a systematic reviewof the basic quantities, their notations, definitions, and symbols as well as the derivation ofthe basic relations between several quantities.The main source of the definitions given in the following sections is the most recentbooklet of the International Commission on Radiation Units and Measurements (ICRU), 13