MHfSH I M m By!IB Eg© V-: ^H m 0**-*Ci. Ban SCud rail ft*«li ^H .. -rn »s M ^-> : mKt NBS TECHNICAL NOTE 576 Computer Code for the Calculation of Thermal Neutron Absorption in Spherical and Cylindrical Neutron Sources — NATIONAL BUREAU OF STANDARDS 1 The National Bureau of Standards was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measure- ment system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Center for Computer Sciences and Technology, and the Office for Information Programs. 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JO u UNITED STATES DEPARTMENT OF COMMERCE Maurice H. Stans, Secretary NATIONAL BUREAU OF STANDARDS,* Lewis M. Branscornb, Director » * o NBS TECHNICAL NOTE 576 ISSUED MAY 1971 Nat. Bur. Stand. (U.S.), Tech. Note 576, 25 pages (May 1971) CODEN: NBTNA Computer Code for the Calculation of Thermal Neutron Absorption in Spherical and Cylindrical Neutron Sources V. Spiegel, Jr. and W. M. Murphey Nuclear Radiation Division Institute for Basic Standards National Bureau of Standards Washington, D.C. 20234 ^ °F % \mj' °<">eM of NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be listed or referred to in the open literature. For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C, 20402. (Order by SD Catalog No. C 13.46:576). Price 35 cents. Stock No. 0303 0851 Abstract A computer code has been written in FORTRAN IV for the calculation of thermal neutron absorption in spherical and cylindrical neutron sources. The formalism of the cal- culation, the structure of the computer code, a listing of the code, and some sample results are presented. The com- parison of the results of this calculation to experiment appears elsewhere (l). Key words: Manganous sulfate bath calibration of neutron sources; neutron; neutron standards. 11 Computer Code for the Calculation of Thermal Neutron Absorption in Spherical and Cylindrical Neutron Sources V. Spiegel, Jr. and William M. Murphey 1. INTRODUCTION This calculation has been carried out in connection with a program to reduce the uncertainties in the corrections applied to the manganous sulfate bath calibration of neutron sources (2,3). The correction considered here is to account for the reduction of the manganese activity due to the loss of thermalized neutrons absorbed in the neutron source itself. The source may be composed of up to three cladding and one, possibly fissionable, core material. The calculation is carried out in a single interaction approximation, i.e., the effects of elastic and inelastic scattering of thermal neutrons are neglected. This approximation is adequate because the neutrons are in thermal equilibrium and because the cor- rection which is applied to the calibration is small (typi- cally Y% or less). Two cases are available. The first is for a spherically symmetric source and the second is for a cylindrically symmetric source. Each consists of a core and up to three cladding layers. The thicknesses of the ends and side of a cladding cylinder may all be different. A measure- ment or knowledge of the thermal -neutron flux at the source location is required. The thermal -neutron flux is assumed to be isotropic, which enables one to carry out the computation as a sum of mono-directional fluxes from different directions. All integrations are performed with Weddle's formula (4). 2. DESCRIPTION OF THE CALCULATION Part I. The probability of neutron loss for a given neutron direction and position. If the source materials are labeled A, B, C, and D from the inside out, then the probability of a thermal neutron interacting in passing through the source is 2 £ - Saa(t)-Ebb(t)- cc(t)- dd(t) where a(t) is the thickness of "A" material for this parti- cular direction and location of passing through the source, b(t) is the total thickness of "B" material, etc., and "t" denotes any particular path through the source. The E's are £ the appropriate macroscopic cross sections, a being the sum of Present address is: Technical Analysis Division, Institute for Applied Technology, National Bureau of Standards, Washington, D.C 20234. the absorption and fission cross sections for the "A" material, 2 being the absorption cross section for the "B" material, etc. The probability of fission in the fissionable material is given by E "E a(t) , , af , a w -(V^^V^^V^)}d c ^ . \ P (t) (l-e )(e ) f »_i£ (2) S a where d»(t) is the thickness of the "D" layer passed in this direction and location going from the outside into the MA" material, c'(t) the thickness of the "C" layer passed in going into the source, etc., and zaf is the macroscopic fission cross section of material "A". Part II. Case 1. A spherically symmetric source. In this case the probability of neutron disappearance for a neutron striking the source is given by R 2Tiy p(y) dy % (3) TT R2 where R is the outer radius of the source and y is the per- pendicular distance from the center of the source to the path through it. The probability of fission is similarly ,R 2TTy P (y) dy 'o f Pf « (4) 2 TTR The probability of loss of neutrons from the bath per neutron striking the source