《A PRACTICAL MANUAL ON THE Monte Carlo Method for random walk problems》求取 ⇩

CHAPTER Ⅰ．BASIC PRINCIPLES1

1．General nature of the problem1

2．Outline of procedure1

3．Production of random numbers4

4．The fundamental principle of Monte Carlo4

5．Application of the principle8

CHAPTER Ⅱ．THE SOURCE ROUTINE11

1．Introduction11

2．Particle parameters12

3．Remarks on units15

4．Space co-ordinates for source particles16

(a)Uniform source on an annulus of radii R017

(b)Uniform source in a spherical shell17

(c)Parallel-beam source incident on lateral cylindrical surface,or on a sphere18

(d)Isotropic point source external to cylinder18

5．Direction co-ordinates for source particles19

(a)Isotropic source;u,v,w direction cosine19

(b)The cosine distribution19

(c)Isotropic and cosine sources in spherically symmetric systems20

(d)Isotropic point source external to cylinder21

(e)General distribution in half of direction-space22

(f)A prejudiced source23

6．Energy of source particles24

7．Other source parameters24

8．Source for α-type calculations25

CHAPTER Ⅲ．THE MAIN FREE PATH AND TRANSMISSION27

1．The cross section concept27

2．The mean free path28

3．An example29

4．＇Small＇systems and transmission30

5．The＇forced first collision＇routine31

6．Remark on the device in spherical problems32

7．The transmission in subsequent history34

8．Prejudiced first collision in＇large＇systems34

CHAPTER Ⅳ．THE COLLISION OR ESCAPE ROUTINE37

1．Introduction37

2．A routine for the spherical shell39

3．Reorienation formulas for the spherical shell40

4．Flux problems in spherical geometry42

5．A routine for the finite cylinder43

6．The finite cylindrical shell with central hole43

7．The spherical shell in absolute space46

8．Slab geometry47

9．Problems run in cycles of time △r49

CHAPTER Ⅴ．THE COLLISION ROUTINE FOR NEUTRONS52

1．Introduction52

2．Capture and selection of the type of collision52

3．Elastic collisions in general56

4．The differential elastic scattering cross section63

5．A routine for elastic scattering64

6．Differential elastic cross section for the laboratory system68

7．A weight device for elastic scattering70

8．Fission71

9．Inelastic(n-n)collisions in general74

10．Inelastic(n-n)collisions on heavy nuclei77

11．Inclastic(n-n)collision with Maxwell distribution77

12．A combined transfer matrix for fissionable nuclei79

13．Collisions shattering a nucleus80

14．The(n-2n)reaction in deuterium84

15．An(n-2n)reaction on heavy nuclei86

16．Capture in a small zone87

17．Capture by a＇point＇detector89

18．Remarks on thermal neutrons90

19．Remark on determination of photon sources92

CHAPTER Ⅵ．PHOTON COLLISIONS94

1．Introduction94

2．Basic concepts and constants94

3．Compton collisions95

4．The Klein-Nishina differential cross section98

5．The photon energy distribution and Compton cross section99

6．Photoelectric effect and pair production100

CHAPTER Ⅶ．DIRECTION PARAMETERS AFTER COLLISION103

1．Introduction103

2．Formulas for the final direction cosines103

3．Subroutine for the final direction cosines107

4．Final direction w in slab or spherically symmetric case107

5．Scattering isotropic in the laboratory system109

CHAPTER Ⅷ．TERMINAL CLASSIFICATION110

1．Introduction110

2．Classification of escapes on number of collisions110

3．Energy and angle distributions of escape110

CHAPTER Ⅸ．REMARKS ON COMPUTATION117

1．Sealing117

2．Debugging117

3．Special subroutines118

(a)A random number routine118

(b)Shifted random numbers119

(c)A logarithm routine119

(d)The expontial exp(-x/y)121

(e)A cosine routine122

4．A Monte Carlo device for √r124

5．A Monté Carlo device for the cosine of an equi-distributed angle125

CHAPTER Ⅹ．STATISTICAL CONSIDERATIONS128

1．The limit theorem in the Bernoulli case128

2．Application to the terminal ratios129

3．The central limit theorem131

4．Application to problems using weights132

5．Illustrative examples133

APPENDIX．SUMMARY OF CERTAIN PROBLEMS RUN ON MANIAC I141

Introduction141

Problem 1．Compton collisions in a spherical shell142

Problem 2．Compton collisions in a solid sphere142

Problem 3．Neutrons in a spherical shell142

Problem 4．Energy independent scattering in a cylinder143

Problem 5．Energy dependent scattering in a cylinder143

Problem 6．Cylindrical shell with parallel source144

Problem 7．14 MeV neutrons in a cylindrical shell144

Problem 8．Cylindrical shell with point source146

Problem 9．A scintillation counter147

Problem 10．A＇long counter＇147

Problem 11．A problem connected with neutrino detection148

Problem 12．An α determination149

Problem 13．Neutron flux in air149

Problem 14．Escape distribution from a carbon slab150

Problem 15．Escape distribution from a spherical shell150

Problem 16．A rocket motor150

Problem 17．Photon diffusion in a reactor152

Problem 18．A thick Zr target problem152

Problem 19．A thick C target problem153

Problem 20．Heavy water experiment153