**RSICC CODE PACKAGE MIS-018**

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**1. NAME AND TITLE**

MMRW: Canadian and Early British Energy Reports on Nuclear Reactor Theory (1940-1946).

**2. CONTRIBUTORS**

M.M.R. Williams, South Croydon Surrey, CR2 0DX, UK through the OECD Nuclear Energy Agency Data Bank, Issy-les-Moulineaux, France.

**3. CODING LANGUAGE AND
COMPUTER**

PDF format; many computers (M00018MNYCP00).

**4. NATURE OF PROBLEM
SOLVED**

MMRW is the collection of reports on the beginning and development of nuclear reactor theory in Canada and in the United Kingdom. In this version, the letter by Alvin Weinberg with comments and historical background (8 September 2000) has been added.

**5. METHOD OF SOLUTION**

** **N/A

**6. RESTRICTIONS OR
LIMITATIONS**

** **N/A

**7. TYPICAL RUNNING TIME**

** **N/A

**8. COMPUTER HARDWARE
REQUIREMENTS**

** **N/A

**9. COMPUTER SOFTWARE
REQUIREMENTS**

Adobe Acrobat Reader can be used to access the files in Portable Data Format (.pdf).

**10. REFERENCES**

** 10a.
Included Documentation**

- G. Placzek: The Functions of En(x)=Integral(e-xuu-ndu){1,infinity} (MT-1).

- G. Placzek and G.M. Volkoff: Notes on Diffusion of Neutrons without Change in Energy. (MT-4).

- P.R. Wallace and J. LeCaine: Elementary Approximation in the Theory of Neutron Diffusion (Nucleonics 4(2),30-35, 4(3), 48-67, 1949) (MT-12).

- G.M. Volkoff: Analysis of Experimental Data on the Slowing-Down and Thermal Diffusion Lengths in Carbon (MT-14).

- P.R. Wallace: Neutron Distribution in Adjoining Piles of Slightly Different Properties (MT-15).

- G. Placzek: The Neutron Density Near a Plane Surface, I. (MT-16).

- R.E. Marshak: On the Slowing Down Length of Neutrons in Water. (MT-17).

- R.E. Marshak: On The Moments of the Distribution Function of Neutrons Slowed Down in Heavy Elements. (MT-18).

- R.E. Marshak: On The Slowing Down Length of Neutrons in Mixtures. (MT-19).

- G.M. Volkoff: Critical Conditions for a Multiplying Spherical Core with an Infinite Reflector of the Same Scattering Properties. (MT-21).

- J.C. Mark: Milne's Problem for Anisotropic Scattering. (MT-26).

- J. LeCaine: Critical Radius of a Strongly Multiplying Sphere Surrounded by a Non-Multiplying Infinite Medium. (MT-29).

- J. LeCaine and G.M. Volkoff: Application of 'Synthetic' Kernels to the Study of Critical Conditions in a Multiplying Sphere with an Infinite Reflector. (MT-30).

- P.R. Wallace: Boundary Conditions at Thin Absorbing Shells and Plates. (MT-34).

- P.R. Wallace: Neutron Distribution in a Multiplying Exponential Pile with a Plane Source. (MT-35).

- G.M. Volkoff: Critical Radius of a Multiplying Spherical Core Surrounded by a non-Multplying Reflector of Finite Thickness (MT-38).

- E.D. Courant: Production and Consumption of Fissile Materials in One Arrangement of a Producing Unit. (MT-40).

- R.E. Marshak and W.P. Seidel: Milne's Problem for a Sphere. (MT-49).

- R.E. Marshak: A Rigorous formula for the slowing down Length in an Element of Arbitrary Mass. (MT-53).

- R.E. Marshak: On the Slowing Down Length of Neutrons in Water: Supplement to MT-17. (MT-54).

- E.D. Courant: Measurements in Finite System of the Total Number of Neutrons in an Infinite System (MT-59).

- P.R. Wallace: On the Thermal Utilization of Plates in the Presence of Linear Anisotropic Scattering (MT-63).

- E.D. Courant: Diffusion Equations and Critical Conditions in a Medium with Varying Mean Free Path (MT-67).

- F.T. Adler: Theory of the Diffuse Reflection of Neutrons by a Plane Surface of a Semi-infinite Capturing Medium (MT-72).

- B. Davison: Influence of a Small Black Sphere Upon the Neutron Density In an Infinite Non- Capturing Medium. (MT-88).

- J. Stewart and G.M. Volkoff: Estimates of Critical Volume of Polymer for Pilot Plant Under Various Conditions (MT-91).

- J.C. Mark: The Spherical Harmonic Method, I. (MT-92).

- B. Davison: Influence of a Large Black Sphere Upon the Neutron Density in an Infinite Non-Capturing Medium. (MT-93).

- P.R. Wallace: Effect of Scattering on the Capturing Properties of Plates and Spheres. (MT-107).

- B. Davison: Angular Distribution due to an Isotropic Point Source and Spherically Symmetrical Eigensolutions of the Transport Equation. (MT-112).

- B. Davison and G.Placzek: Milne's Problem with Capture and Production. (MT-118).

- B. Davison: Large Spherical Hole In a Slightly Capturing Medium. (MT-124).

- J. LeCaine: A Table of Integrals Involving the Functions En(x) (MT-131).

- B. Davison: Influence of a Large Black Cylinder Upon the Neutron Density in an Infinite Non-Capturing Medium. (MT-135).

- B. Davison: Neutron Density at the Centre of a Small Spherical Cavity. (MT-136).

- E.A. Guggenheim: Compressible flow of perfect gas with heat input distributed symmetrically about middle of channel. (MT-137).

- M.H.L. Pryce: The Critical Size of a Multiplying system Surrounded by a Reflector of Different Scattering Properties. (MT-150).

- M.H.L. Pryce: The Evaluation of the Life Time of a Radioactive Substance from a Small Number of Observations. (MT-151).

- E.D. Courant: Requirements for the Maintenance of Critical Conditions with Changing Material Constants. (MT-164).

- E.A.Guggenheim, M.H.L.Pryce and G.M. Volkoff: Thermal Utilization in Some Systems having Axial Symmetry. (MT-166).

- P.R. Wallace and B. Carlson: Determination of 'f' for spheres. (MT-169).

- E.D. Courant: On Seeding Depleted Piles. (MT-173).

- J.M.G. Fell and G.M.Volkoff: Capture of Neutrons by Cylindrical Absorbing Rods Placed Around a Pile. (MT-196).

- J.M.G. Fell: A Note on the Temperature Distribution Inside Uranium Rods with Variable Heat Source Density and Variable Conductivity. (MT-197).

- E.A.Guggenheim and M.H.L.Pryce: Fast Fission in Tubes. (MT-199).

- F.T. Adler: Reduction of the Two-Group Model to an Equivalent One-Group Model. (MT-201).

- B.Davison, W.P. Seidel and S.Kushneriuk: Influence of a Small Black Cylinder Upon the Neutron Density in an Infinite Non-Capturing Medium. (MT-207).

- M.Goldstein and E.A.Guggenheim: Effect of Xenon Poisoning on Uranium-Graphite Piles. (MT-208).

- B.Davison and S.Kushneriuk: Linear Extrapolation Length for a Black Sphere and a Black Cylinder (MT-214).

- E.A. Guggenheim: Thermal Utilization in a System Con-taining Two Moderators. (MT-220).

- V.H. Rumsey and G.M.Volkoff: Diffusion Theory Expressions for the Thermal Utilization Factor f in Cells with Slab, Cylindrical and Spherical Geometry (MT-221).

- F.T. Adler: Efficiency of Control Rods as a function of their Position in a Cylindrical Pile in the One-Group Picture. (MT-222).

- B. Davison: Influence of an Air Gap Surrounding a Small Black Sphere upon the Linear Extrapolation Length of the Neutron Density in the Surrounding Medium. (MT-232).

- H.H. Clayton: Critical Laplacian and Neutron Densities in the NRX Pile. (MT-240).

- H.H. Clayton: Fate of Neutrons in NRX Pile and Production Rates of 49 and 23. (MT-241).

- M.Goldstein, M.Wales, A.S.Lodge: Fast Fission In Tubes: A Numerical Supplement to MT-199. (MT-242).

- A.S. Lodge: The Temperature Distribution in an Infinite Medium due to a Spatially Uniform Plane Source of Heat (MT-243).

- B. Davison: Linear Extrapolation Length for the Neutron Density at the Surface of a Large Hollow Cylindrical Shaft (MT-245).

- J.M.G. Fell: Effect of the Presence of Fast Neutrons on the Utilization of Neutrons by Absorbing Rods Around a Pile. (MT-249).

- R. Peierls: On the Possibility of a Slow-Neutron Chain Reaction. (1940) (MS-1).

- R. Peierls: Speed of Reaction in a Chain Reactor with Slow Neutrons. (1940) (MS-2).

- R. Peierls: The Effect of Expansion of the Sphere. (1940) (MS-8).

- M.H.L. Pryce: Critical Conditions in Neutron Multiplication. (1943) (MS-P2a).

- K. Fuchs: Effect of a Scattering Container on the Critical Radius and Time Constant. (1943) (MS-85).

- A.H. Wilson: A Comparison of the Approximate Methods of Calculating the Critical Size of a Sphere. (1944) (MS-89).

- B. Davison and K. Fuchs: The Critical Radius and the Time Constant of a Sphere Embedded in a Spherical Scattering Container. (Nov.1943) (MS-97).

- B. Davison: Critical Radius for a Hemisphere with a One-Sided Infinite Container. (Nov. 1944) (MS-100).

- A.H. Wilson: The Effect of Small Departures from the Spherical Shape upon the Critical Size and Time Constant of a Sphere. (March 1944) (MS-102).

- A.H. Wilson: The General Properties of the Transport Equation and its Use in Determining the Multiplication in Bodies Having Spherical Symmetry. (Jan. 1944) (MS-105).

- A.H. Wilson: The Effect of Inelastic Scattering on the Multiplication in a Sphere. (Jan. 1944) (MS-106).

- H. Fairbrother: The Critical Size and Time Constant of a Spheroid. (June 1944) (MS-111).

- P.D. Preston and B. Davison: Critical Radius of a Hemisphere Completely Surrounded by a Container. (July 1944) (MS-112).

- A.H. Wilson: A New Method of Determining the Time Constant of a Sphere in a Container. (Aug. 1944) (MS-115).

- P.A.M. Dirac: Approximate Rate of Neutron Multiplication for a Solid of Arbitrary Shape and Uniform Density, Parts I and II (1944) (MS-D5).

- H. Castle, H. Ibser, G. Sacher and A.M. Weinberg: The effect of fast fission on k (May 4th, 1943) (CP-644).

- Bengt Carlson: The Serber-Wilson Method Formulae and Computation Methods. (LA-756).

- R.E. Marshak: Some neutron diffusion problems. (September 11, 1946) (MDDC-295_LADC-243).

- R.F. Christy: Theoretical Discussion of a Small Homogeneous Enriched Reactor. (June 18, 1946) (MDDC-72).

- C.Mark: Terms in an Expansion of the Wiener-Hopf Solution of Milne's Equation for Small Values of the Argument (October 25, 1943) (TPI-5).

- George Volkoff: TL-1 to TL-6 Volkoff Lectures on Reactor Physics, 1944.

- A.H. Wilson: The Effect of Anisotropic Scattering on the Multiplication in a Sphere. (July 1944) (MS-113).

- G. Placzek: Energy Conversion Factors and Nuclear Constants (MT-51).

- T.H.R. Skyrme: A Reduction in Neutron Density Caused by an Absorbing Disc. (1944) (MS-91).

- Letter by Alvin Weinberg with comments and historical background (8 September 2000).

**10b. Background References**

MT-5 G. Placzek and W.P. Seidel, Milne's Problem in Transport Theory. (Physical Review, 72 (1947) 550-555).

MT-6 G. Placzek, The Angular Distribution of neutrons Emerging from a Plane Surface. (Physical Review, 72(1947)556-558).

MT-7 G. Placzek, Boundary Conditions in Elementary Diffusion Theory. (Not issued).

MT-13 G. Placzek and G.M. Volkoff, A Theorem on Neutron Multiplication (Canadian Journal of Research, A25 (1947) 276-292).

MT-20 G. Placzek, Diffusion of Neutrons without Velocity Change. (Not Issued).

MT-50 J.C. Mark, The Neutron Density Near a Plane surface II. (Phys Rev 72 (1947) 558-564).

MT-52 R.E. Marshak, Black Utilization. (Not Issued).

MT-55 R.E. Marshak, The Application of Variational Theory to the Determination of Asymptotic Neutron Densities. (Phys Rev 71 (1947) 688-693).

MT-56 J.C. Mark, Constants and Expansions of Wiener-Hopf Method. (Not Issued).

MT-65 G. Placzek, Report on Research in Theoretical Physics Feb. to July 15/44. (Not Issued).

MT-66 F.T. Adler and J.C. Mark, Milne's Problem with Capture. (Not Issued).

MT-89 B. Davison, A remark on the Variational Method. (Physical Rev. 71(1947)694-697).

MT-97 J.C. Mark, The Spherical Harmonic Method, II. (Re-issued as CRT-338). Also AECL-490 (1958).

MT-106 P.R. Wallace, Moments of the Angular Distribution in the Asymptotic Region (Canadian Journal of Research A26(1948)99-114).

MT-119 J. LeCaine, Milne's problem with capture II. (Canadian Journal of Research A28(1950)242).

MT-202 (Anon), Efficiency of Control Rods Absorbing Thermal Neutrons Only. (Not Issued).

MT-223 E.D. Courant and P.R. Wallace, Fluctuations of the number of Neutrons in a Pile. (Physical Rev. 72(1947)1037-1048).

**11. CONTENTS OF CODE
PACKAGE**

The MMRW package is transmitted on CD and includes 92 PDF files.

**12. DATE OF ABSTRACT**

June 2013.

**KEYWORDS:** ANGULAR
DISTRIBUTION, LEGACY, SLOWING**-**DOWN, TEMPERATURE DISTRIBUTION, THERMAL
UTILIZATION