M.M.R. Williams

2A Lytchgate Close, South Croydon

Surrey, CR2 0DX, UK

mmrw@nuclear-energy.demon.co.uk

9th November 2000

I recently published an article describing in some detail the problem I encountered when attempting to retrieve some old World war II Canadian Atomic Energy reports. The details of this search may be found in *Progress in Nuclear Energy*, vol. 36, 239-322 (2000). Suffice it to say here that it was with great difficulty and a certain amount of luck that I was able to track down those old Canadian "MT" reports.

As an exercise, and out of genuine interest, I decided to find out how easy it would be to locate some of the old Manhattan District project reports and particularly those referenced in Robert Marshak's famous article "Theory of the slowing down of neutrons by elastic collision with atomic nuclei, " published in* Reviews of Modern Physics*, vol. 19, 185-238 (1947). In this list of references, Marshak mentions A-27 by Gregory Breit and A-25 by Georges Placzek. I once owned a copy of A-25, but it disappeared. It was a delightful article that was in the nature of a review together with original work. I have been unable to get a copy, or, indeed, find out where to get a copy. The National Archives and Records Administration (NARA) and the National Technical Information Service (NTIS) Web sites are less than helpful, and colleagues at Los Alamos have been unable to locate the reports. It is not as though they are classified in any way, so where are they? As with my quest for the Canadian reports, I expected such historic documents to be fully archived and readily accessible. I am sure if these reports were work of art or literature, they would be kept in fully climate-controlled conditions, but it seems that works of science are not so highly valued. I bring this matter to the attention of members of ANS so that they can ponder the way their nuclear heritage is gradually being lost.

Of course, I would be delighted to be proved wrong, and if any reader knows where I can gain ready access to the Manhattan District A series of reports, and also the later AECD and AECU reports, then I would be very pleased indeed.

*M.M.R. Williams*

Emeritus Professor of Nuclear Engineering

University of London, UK

And ANS Fellow

*permission by M.M.R. Williams - Letter to ANS News*

This collection has been made available on CD-ROM to the OECD-Nuclear Energy Agency for general access and dissemination on 29 July 2002.

A note from the compiler of these reports.

M.M.R. Williams: The Development of Nuclear Reactor Theory in the Montreal Laboratory of the National Research Council of Canada (Division of Atomic Energy) 1940-1946. Progress in Nuclear Energy, Vol. 36, No. 3, pp. 239-322, 2000

M.M.R. Williams: Corrigenda and Addenda

If you wish to OBTAIN a COPY of all these reports on CD-ROM, please send a message to CPS

Alvin Weinberg's Comments and historical background (8 September 2000)

**Full list of Montreal Theory Reports**

MT-1 G. Placzek

The Functions of E_{n}(x)=Integral(e^{-xu}u^{-n}du){1,infinity}

MT-4 G. Placzek and G.M. Volkoff

Notes on Diffusion of Neutrons without Change in Energy.

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.

MT-12 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-13 G. Placzek and G.M. Volkoff

A Theorem on Neutron Multiplication

(Canadian Journal of Research, A25 (1947) 276-292)

MT-14 G.M. Volkoff

Analysis of Experimental Data on the Slowing-Down and Thermal Diffusion Lengths in Carbon.

MT-15 P.R. Wallace

Neutron Distribution in Adjoining Piles of Slightly Different Properties.

MT-16 G. Placzek

The Neutron Density Near a Plane Surface, I.

MT-17 R.E. Marshak

On the Slowing Down Length of Neutrons in Water.

MT-18 R.E. Marshak

On The Moments of the Distribution Function of Neutrons Slowed Down in Heavy Elements.

MT-19 R.E. Marshak

On The Slowing Down Length of Neutrons in Mixtures.

(MT-17, 18, 19 in Rev. Mod. Phys. 19(1947)185-238)

MT-20 G. Placzek

Diffusion of Neutrons without Velocity Change. (Not Issued)

MT-21 G.M. Volkoff

Critical Conditions for a Multiplying Spherical Core with an Infinite Reflector of the Same Scattering Properties.

MT-26 J.C. Mark

Milne’s Problem for Anisotropic Scattering.

MT-29 J. LeCaine

Critical Radius of a Strongly Multiplying Sphere Surrounded by a Non-Multiplying Infinite Medium.

MT-30 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-34 P.R. Wallace

Boundary Conditions at Thin Absorbing Shells and Plates.

Annals of Nuclear Energy 2001

MT-35 P.R. Wallace

Neutron Distribution in a Multiplying Exponential Pile with a Plane Source.

MT-38 G.M. Volkoff

Critical Radius of a Multiplying Spherical Core Surrounded by a non-Multplying Reflector of Finite Thickness.

MT-40 E.D. Courant

Production and Consumption of Fissile Materials in One Arrangement of a Producing Unit.

MT-49 R.E. Marshak and W.P. Seidel

Milne’s Problem for a Sphere.

MT-50 J.C. Mark

The Neutron Density Near a Plane surface II.

(Phys Rev 72 (1947) 558-564)

MT-51 G. Placzek

Energy Conversion Factors and Nuclear Constants.

MT-52 R.E. Marshak

Black Utilization. (Not Issued)

MT-53 R.E. Marshak

A Rigorous formula for the slowing down Length in an Element of Arbitrary Mass.

MT-54 R.E. Marshak

On the Slowing Down Length of Neutrons in Water: Supplement to MT-17.

(MT-53 and MT-54 published in Rev. Mod. Phys. 19(1947)185-238)

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-59 E.D. Courant

Measurements in Finite System of the Total Number of Neutrons in an Infinite System.

MT-63 P.R. Wallace

On the Thermal Utilization of Plates in the Presence of Linear Anisotropic Scattering.

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-67 E.D. Courant

Diffusion Equations and Critical Conditions in a Medium with Varying Mean Free Path.

MT-72 F.T. Adler

Theory of the Diffuse Reflection of Neutrons by a Plane Surface of a Semi-infinite Capturing Medium

MT-88 B. Davison

Influence of a Small Black Sphere Upon the Neutron Density In an Infinite Non- Capturing Medium.

(an abridged version can be found in Proc. Phys. Soc. A LXIV, 1951, 881-902.)

MT-89 B.Davison

A remark on the Variational Method.

(Physical Rev. 71(1947)694-697)

MT-91 J. Stewart and G.M. Volkoff

Estimates of Critical Volume of Polymer for Pilot Plant Under Various Conditions.

MT-92 J.C. Mark

The Spherical Harmonic Method, I. (Re-issued as CRT-340)

MT-93 B. Davison

Influence of a Large Black Sphere Upon the Neutron Density in an Infinite Non-Capturing Medium.

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-107 P.R. Wallace

Effect of Scattering on the Capturing Properties of Plates and Spheres.

MT-112 B. Davison

Angular Distribution due to an Isotropic Point Source and Spherically Symmetrical Eigensolutions of the Transport Equation.

(Progress in Nuclear Energy 36, 2000, 323)

MT-118 B. Davison and G.Placzek

Milne’s Problem with Capture and Production.

MT-119 J. LeCaine

Milne's problem with capture II.

(Canadian Journal of Research A28(1950)242)

MT-124 B. Davison

Large Spherical Hole In a Slightly Capturing Medium.

(an abridged version can be found in Proc. Phys. Soc. A LXIV, 1951, 881-902.)

MT-131 J. LeCaine

A Table of Integrals Involving the Functions En(x)

MT-135 B. Davison

Influence of a Large Black Cylinder Upon the Neutron Density in an Infinite Non-Capturing Medium.

(an abridged version can be found in Proc. Phys. Soc. A. LXIV, 1951, 881-902.)

MT-136 B. Davison

Neutron Density at the Centre of a Small Spherical Cavity.

MT-137 E.A. Guggenheim

Compressible flow of perfect gas with heat input distributed symmetrically about middle of channel.

MT-150 M.H.L. Pryce.

The Critical Size of a Multiplying system Surrounded by a Reflector of Different Scattering Properties.

MT-151 M.H.L. Pryce

The Evaluation of the Life Time of a Radioactive Substance from a Small Number of Observations.

MT-164 E.D. Courant

Requirements for the Maintenance of Critical Conditions with Changing Material Constants.

MT-166 E.A.Guggenheim, M.H.L.Pryce and G.M. Volkoff

Thermal Utilization in Some Systems having Axial Symmetry.

MT-169 P.R. Wallace and B. Carlson

Determination of 'f' for spheres.

MT-173 E.D. Courant

On Seeding Depleted Piles.

MT-196 J.M.G. Fell and G.M.Volkoff

Capture of Neutrons by Cylindrical Absorbing Rods Placed Around a Pile.

(Annals of Nuclear Energy, 2001)

MT-197 J.M.G. Fell

A Note on the Temperature Distribution Inside Uranium Rods with Variable Heat Source Density and Variable Conductivity.

MT-199 E.A.Guggenheim and M.H.L.Pryce

Fast Fission in Tubes. (Re-issued as AECL 92)

MT-201 F.T. Adler

Reduction of the Two-Group Model to an Equivalent One-Group Model.

MT-202 (Anon)

Efficiency of Control Rods Absorbing Thermal Neutrons Only. (Not Issued)

MT-207 B.Davison, W.P. Seidel and S.Kushneriuk

Influence of a Small Black Cylinder Upon the Neutron Density in an Infinite Non-Capturing Medium.(Proc. 2nd Canadian Mathematical Congress, Vancouver, B.C. 1949)

MT-208 M.Goldstein and E.A.Guggenheim

Effect of Xenon Poisoning on Uranium-Graphite Piles.

MT-214 B.Davison and S.Kushneriuk

Linear Extrapolation Length for a Black Sphere and a Black Cylinder.

MT-220 E.A. Guggenheim

Thermal Utilization in a System Con-taining Two Moderators. (Re-issued as AECL-63)

MT-221 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-222 F.T. Adler

Efficiency of Control Rods as a function of their Position in a Cylindrical Pile in the One-Group Picture. (Re-issued as AECL 253)

MT-223 E.D.Courant and P.R.Wallace

Fluctuations of the number of Neutrons in a Pile.

(Physical Rev. 72(1947)1037-1048)

MT-232 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-240 H.H. Clayton

Critical Laplacian and Neutron Densities in the NRX Pile.

(Re-issued as AECL 376)

MT-241 H.H. Clayton

Fate of Neutrons in NRX Pile and Production Rates of 49 and 23.

(Re-issued as AECL 377)

MT-242 M.Goldstein, M.Wales, A.S.Lodge

Fast Fission In Tubes: A Numerical Supplement to MT-199.

MT-243 A.S. Lodge

The Temperature Distribution in an Infinite Medium due to a Spatially Uniform Plane Source of Heat

MT-245 B. Davison

Linear Extrapolation Length for the Neutron Density at the Surface of a Large Hollow Cylindrical Shaft

MT-249 J.M.G. Fell

Effect of the Presence of Fast Neutrons on the Utilization of Neutrons by Absorbing Rods Around a Pile.

**Early British Atomic Energy Reports on Reactor Theory**

These reports are the records of work done, either before the Montreal Theory team was set up, or carried out in parallel with it in Britain. In general, the dates are consistent because Davison's work was done in 1943 and 1944 and he did not arrive in Montreal until late 1944. Similarly Pryce's work on criticality was done in 1943 and his name does not appear on Montreal reports until 1945. The other authors either went directly to Los Alamos (e.g. Klaus Fuchs ) or remained in the UK (e.g. Dirac).

MS-1 On the Possibility of a Slow-Neutron Chain Reaction.

R. Peierls (1940)

MS-2 Speed of Reaction in a Chain Reactor with Slow Neutrons.

R. Peierls (1940)

MS-8 The Effect of Expansion of the Sphere.

R. Peierls (1940)

MS-P2a Critical Conditions in Neutron Multiplication.

M.H.L. Pryce (1943)

MS-85 Effect of a Scattering Container on the Critical Radius and Time Constant.

K. Fuchs (1943)

MS-89 A Comparison of the Approximate Methods of Calculating the Critical Size of a Sphere.

A.H. Wilson (1944)

MS-91 A Reduction in Neutron Density Caused by an Absorbing Disc.

T.H.R. Skyrme (1944)

MS-97 The Critical Radius and the Time Constant of a Sphere Embedded in a Spherical Scattering Container.

B. Davison and K. Fuchs (November, 1943)

MS-100 Critical Radius for a Hemisphere with a One-Sided Infinite Container.

B. Davison (November 27, 1944)

MS-102 The Effect of Small Departures from the Spherical Shape upon the Critical Size and Time Constant of a Sphere.

A.H. Wilson (March, 1944)

MS-105 The General Properties of the Transport Equation and its Use in Determining the Multiplication in Bodies Having Spherical Symmetry.

A.H. Wilson (January, 1944)

MS-106 The Effect of Inelastic Scattering on the Multiplication in a Sphere.

A.H. Wilson (January, 1944)

MS-111 The Critical Size and Time Constant of a Spheroid.

H. Fairbrother (June, 1944)

MS-112 Critical Radius of a Hemisphere Completely Surrounded by a Container.

P.D. Preston and B. Davison (July, 1944)

MS-113 The Effect of Anisotropic Scattering on the Multiplication in a Sphere.

A.H. Wilson (July, 1944)

MS-115 A New Method of Determining the Time Constant of a Sphere in a Container.

A.H. Wilson (August, 1944)

MS-D5 (Parts I and II) Approximate Rate of Neutron Multiplication for a Solid of Arbitrary Shape and Uniform Density.

P.A.M. Dirac (1944)

**Some additional reports included are:**

CP-644 The effect of fast fission on k (May 4th, 1943)

H. Castle, H. Ibser, G. Sacher and A.M. Weinberg

LA-756 The Serber-Wilson Method Formulae and Computation Methods.

Bengt Carlson

MDDC-295_LADC-243 Some neutron diffusion problems (September 11, 1946)

R.E. Marshak

MDDC-72 Theoretical Discussion of a Small Homogeneous Enriched Reactor (June 18, 1946)

R.F. Christy

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

C.Mark

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

George Volkoff

**Additional bibliography:**

*"Introduction to the Theory of Diffusion and Slowing Down of Neutrons"* by R.E. Marshak, H. Broks, H. Hurwitz Jr

Nucleonics 1949

May vol 4, No 5, pp10-22

June vol 4, No 6, pp43-49

July vol 5, No 1, pp53-60

August vol 5, No 2, pp59-68

*"Critical conditions in neutron multiplication"*

Proceedings of the Cambridge Philosophical Society, 1939, vol 35, pp 610-615

Last reviewed: 30 May 2011