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Neutron Resonances and SAMMY*

Neutron Resonances and SAMMY*. How neutrons interact with matter is a topic of great interest for physicists For example we need to know much about this topic in: Nuclear reactor design Nuclear astrophysics Understanding fundamental nuclear physics Neutron Radiography Medical Physics

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Neutron Resonances and SAMMY*

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  1. Neutron Resonances and SAMMY* • How neutrons interact with matter is a topic of great interest for physicists • For example we need to know much about this topic in: • Nuclear reactor design • Nuclear astrophysics • Understanding fundamental nuclear physics • Neutron Radiography • Medical Physics • Neutron Activation • SAMMY was developed for neutron resonance data analysis by Nancy Larson of the Nuclear Data Group at Oak Ridge National Laboratory and is known world-wide • SAMMY consists of 140,000 lines of Fortran 77 Source Code

  2. What are Neutron Cross Sections and Resolved Energy Regions? • Cross Sections are derived from the transmission of neutrons as they pass through some finite section target at some given angle. e.g. I = I0 e-μx where μ is the linear absorption coefficient. There are many different types of cross sections. e.g. fission cross sections, capture cross sections, etc. • A resolved energy region is a distinct peak in the cross section versus neutron energy curve. If a multitude of individual peaks appear in a spectrum at the same neutron energy you may have an unresolved energy region.

  3. Why was SAMMY Developed • Nuclear theory has not developed to the point where resonance-regions cross sections can be calculated from first principles • Cross sections must be obtained from measured data • Measured data are very voluminous and are not directly useful • Predicted (theoretical data) and experimental data must be compared

  4. A bit more about SAMMY • “In 1980 the multilevel multichannel R-Matrix code was released for use in analysis of neutron induced cross seciton data at the Oak Ridge electron Linear Accelerator”1 • “Since that time SAMMY has evolved to the point where it is now in use around the world for analysis of many different types of data.”…”Corrections for a wide variety of experimental conditions are available for the code”…1 • ”The fitting procedure is Bayes’ method”…1 • SAMMY works for resolved and unresolved resonance regions • R-Matrix code describes what is seen (i.e. the measured cross sections) but does not described what is not seen (i.e. the underlying nuclear physics) 1 excerpts from the Revision 6 Updated Users Guide for SAMMY

  5. The underlying principles of SAMMY • Scattering theory is a mathematically rigorous phenomenological description of what is actually seen in an experiment • R-Matrix theory can be used to parameterize the measurement in terms of interaction radii and boundary conditions, resonance energies, widths, and quantum numbers

  6. Terms used in R-Matrix Theory and Sammy* *Courtesy of Sammy Users Lectures by N.M. Larson

  7. How Neutrons Interact with Matter Neutrons can interact with matter in a number of ways, primarily depending on the neutron energy. (The mechanisms are listed here in (approximate) order of increasing neutron energy.) Elastic scattering Radiative neutron capture Fission reactions Assorted nuclear reactions Inelastic scattering Hadron shower initiation

  8. Courtesy Paul Scherrer Institute at http://neutra.web.psi.ch/What/physic.html

  9. The Energy Classification of neutrons Courtesy Paul Scherrer Institute at http://neutra.web.psi.ch/What/physic.html

  10. Example: Neutrons impinging upon Ni58 • Neutrons are produced (e.g.) by directing a beam of electrons (e.g. produced at the Oak Ridge linear accelerator (ORELA) and directed target of (e.g.) tantalum. The electron beam (and hence the neutron beam) is pulsed; typically on for a few nanoseconds and off for several milliseconds.) • The detector not only records the number of arriving neutrons (compared to the incident neutron beam) but also the time of arrival; i.e. the time the neutrons leave the target (t0) and (t) the time the neutrons arrive at the detector. • Thus by The energy of the neutron can be determined in addition to the transmission factor. In this overall process much data reduction must be done, e.g. background subtraction, detector dead-time corrections, etc.

  11. Experiment (Simplified) I

  12. The ORELA is a powerful electron accelerator-based neutron source located in the Physics Division of Oak Ridge National Laboratory. It produces intense, nanosecond bursts of neutrons, each burst containing neutrons with energies from 10e-03 to 10e08 eV. “The facility consists of a 180-MeV electron accelerator, neutron producing targets, buried and evacuated flight tubes up to 200 m long leading to underground detector locations, a wide variety of sophisticated detectors, and data acquisition and analysis systems. Neutrons are produced by bremsstrahlung from a tantalum radiator.”

  13. ORELA Facility Details

  14. The Nuclear Reaction Process Reaction Figure courtesy of

  15. Overview • The nuclide Y is left in its second excited state • The incident particle brings its EKi to a few nucleons in the target nucleus, the energy is statistically distributed among all the nucleons of the compound nucleus C which is set in the excited state E* = EK + Bi (the incident particle binding energy in the compound nucleus system) • The spontaneous disintegration of this system leads to the emission of particle (e)

  16. Assumptions made in Scattering Theory • Applicability of non-relativistic quantum mechanics • Exclusion of processes in which more than two product nuclei are formed • Exclusion of processes of creation or destruction • A finite separation boundary beyond which no interactions occur

  17. Scattering Theory is couched in terms of channels • A channel is defined as a pair of incoming or outgoing particles described by mass, charge, and spin quantum numbers • The intrinsic spin of the incident neutron is i = ½, positive parity • The intrinsic spin of the nuclide is I (integer of half integer) and parity positive or negative • The relative orbital angular momentum of the neutron-nuclide pair is l, parity is positive for even l and negative for odd l • Intrinsic spins are coupled vectorially to give channel spin s • S is coupled to l to give resonance spin J. • J and parity are conserved in the neutron-nuclide interaction.

  18. Concept of the Channel Radius from R Matrix Theory Figure courtesy of

  19. Steps in the formulation of SAMMY CODE Parameterize the external wave function as Where f has the form derived from Schrodinger’s Eqn Expand the internal radial wave in terms of eigenfunctions whose derivatives are 0 at the boundary Equate the internal and external wave functions and derivatives at the boundary to give the scattering matrix U Where φl is the potential phase shift with A good starting basis for understanding neutron interaction can be obtained from a textbook “The Elements of Neutron Interaction Theory” by Anthony Foderaro, The MIT Press, Cambridge, MASS 1971 ISBN 0 262 06033 7

  20. Approximations are very important • Scattering theory is quite complicated and may involve much computer time despite the advent of newer fast computers. • One example of a approximation in Sammy Code is the Reich Moore (RM) approximation where off diagonal contributions of photon channels are neglected • Reich Moore represents most cross sections well.

  21. With such facilities as ORELA existing in the world today, we will begin our SAMMY Analysis of data. We will start out with a neutron beam impinging on a Sample of element #4 What we know about our fictitious element #4 Element #4 describes a spin-zero nucleus with three spin groups defined, one being l=0, J=0.5 and the other two being l=1, J=0.5 and 1.5. Note that the parity of the l=1 resonances is negative. Only two resonances are defined in the PARameter file, spin group # 2 has no resonances.

  22. An example of two cross sections evaluated by SAMMY so as to give the reader and understanding of the complexity involved Here we have depicted two cross sections, the elastic cross section (above) and a reaction cross section (below) which simply may be descriptive of a nuclear reaction as the capture of a neutron to form a new isotope

  23. Concept of Spin Groups ( Sammy .inp file) Position # 49-50, No. of iterations, default = 2 Alphanumeric Information for Program Options Cross Section (barns) as opposed to transmission data Spin Group numbers

  24. Example of simple SAMMY parameter file (.par file) for target nucleus Spin I = 0 and orbital angular momentum > 0 Test Flags Particle width for Channel 1 (milli-eV Capture width (milli–eV) Resonance energy (eV) Quantum numbers for this group

  25. Graphical Example of SAMMY Data File for run ex004a. Data format is a list of neutron energy(eV), cross section and cross section error There are 152 data points errors ~ +/- 10%

  26. Sammy Run for ex004a In keV +++ data, solid line final SAMMY theoretical calculation, dashed line, zeroth order SAMMY calculation

  27. Behold! SAMMY has generated an output .par file Compare this to the Input .par file here What’s Different? Bayes Theorem needed an estimate! So! How do we improve the SAMMY Fit! Hint! Remember the default is 2 iterations!

  28. SAMMY Run ex004c (5 iterations instead of the default 2) +++ data, solid line final SAMMY theoretical calculation, dashed line, zeroth order SAMMY calculation

  29. Whoops! You just found out in a Phys Rev Letters article that suggests the resonance of Element #4 at 988 eV is a d wave (l= 2). We should re-run the data! In order to do this we will have to add some more spin groups. Sammy .inp file ex004d.inp As Before! Spin Groups are listed here spin groups 4 & 5 (el=2,J=3/2 and el=2,J=5/2) are added Note! Quantum numbers have changed Sammy ex004d.par file

  30. SAMMY Fit with new DATA run ex004d.odf

  31. Sammy Output for Ni58 run no. ex009b Capture Cross Section Neutron Energy (keV) Pluses (ex. Data) solid line (Fit)

  32. Problem: Resonance at 40 keV is not there Resonance missing at 39.955 keV

  33. Better Fit. Wrong resonance energy reported at 40 keV; Resonance energy 39.555 keV! After several Sammy runs we changed the reported resonance energy to 39.555 keV and flagged a fit there to get the final run.

  34. Example of using SAMMY to do background corrections No background corrections included Sammy Calculations Ignore This Raw Data Energy in eV. Note Log Plot.

  35. Same Data. Example of background corrections. Background corrections can include detector drift, detector background, corrections for efficiency, etc. Energy eV

  36. Variation of Radius Test Change the Channel Radius; See what happens if we make it < 10% of original size.

  37. Variation of Radius Size of Channel to < 10% of actual Sammy Run ex011f, Dec. 9, 2003 Poor Fit! Poor Fit! Sammy Fit Raw Data Y axis (Transmission – dimensionless), X axis Energy keV

  38. Doppler Broadening (Effects of Temperature) Sammy Run ex005c 11/12/03 Sammy Fit Data with error bars Sammy Fit Intermediate calculation Raw Data Reported temperature to SAMMY program different from experimental run! Reported temperature to SAMMY program same as experimental run!

  39. Treating Multiple Nuclides in a Sample In a real experiment, the sample usually contains more than one nuclide; sometimes contaminantsare present. Input: Transmission Data through natural silicon oxide taken on the 200 m flight path at ORELA* -- RAW DATA Error Bars not Included

  40. Example of ex012.dat file Bombardment of Si with neutrons (only the beginning and end of the data file) Neutron Energy Transmission Error +/- eV Neutron Energy Transmission Error +/- eV 300003.47 .2292500 .0133873 300026.00 .2215323 .0128452 300048.59 .2302640 .0130915 300071.16 .2328735 .0135787 300093.69 .2419577 .0140825 300116.25 .2345796 .0137422 300138.84 .2305669 .0132813 300161.41 .2259712 .0134183 300183.97 .2277306 .0138025 300206.59 .2469709 .0140359 300229.16 .2206314 .0130591 300251.72 .2348713 .0136783 300274.28 .2379582 .0136706 300296.91 .2330635 .0131666 300319.50 .2206179 .0127233 1795189.75 .5369043 .0092502 1795520.50 .5368451 .0093595 1795851.00 .5323152 .0091588 1796182.00 .5334420 .0092467 1796512.62 .5371031 .0092775 1796843.75 .5376230 .0092792 1797174.62 .5231650 .0091080 1797506.00 .5267552 .0091744 1797837.38 .5498957 .0094703 1798168.50 .5294606 .0091664 1798500.12 .5392026 .0094060 1798831.38 .5358818 .0093329 1799163.12 .5435079 .0094192 1799494.75 .5367498 .0092242 1799826.62 .5133699 .0089948 There are 15736 data elements

  41. Sammy Run ex012aa.odf Full SAMMY Plot of Capture Cross Section 300 – 1800 keV Energy + Raw Data, Smooth Line SAMMY FINAL

  42. Ex012a.inp File for Sammy Si Run (in part, first 7 spin groups Si 28) Sample Element Wt. and Energy Range (CS#2) example ex012: multiple nuclides (Natural Si -- 200 m flight path) Si 27.976928 300000. 1800000. csisrs chi squared is wanted do not suppress any intermediate results generate odf file automatically 300. 200.0000 0.182233 0.0 0.002518 4.20000 0.347162 TRANSMISSION 1 1 1 0.5 0.9223 0.0 Si28 s1/2 1 1 0 0 0.5 0.0 0.0 2 1 0 2 1.5 0.0 1843140.0 2 1 1 -0.5 0.9223 0.0 Si28 p1/2 1 1 0 1 0.5 0.0 0.0 2 1 0 1 0.5 0.0 1843140.0 3 1 1 -1.5 0.9223 0.0 Si28 p3/2 1 1 0 1 0.5 0.0 0.0 2 1 0 1 0.5 0.0 1843140.0 4 1 2 1.5 0.9223 0.0 Si28 d3/2 1 1 0 2 0.5 0.0 0.0 2 1 0 2 0.5 0.0 1843140.0 3 1 0 0 1.5 0.0 1843140.0 5 1 2 2.5 0.9223 0.0 Si28 d5/2 1 1 0 2 0.5 0.0 0.0 2 1 0 2 0.5 0.0 1843140.0 3 1 0 0 2.5 0.0 1843140.0 6 1 2 -2.5 0.9223 0.0 Si28 f5/2 1 1 0 3 0.5 0.0 0.0 2 1 0 3 0.5 0.0 1843140.0 3 1 0 1 2.5 0.0 1843140.0 7 1 2 -3.5 0.9223 0.0 Si28 f7/2 1 1 0 3 0.5 0.0 0.0 2 1 0 3 0.5 0.0 1843140.0 3 1 0 1 2.5 0.0 1843140.0 Sample ID (2 lines) (CS#1) Run Temperature in K degrees, Flight Path Length, etc. (CS#5) Alphanumeric Options (CS#3) Channel Radius, Sample Thickness (CS#7) Indicates data are transmission (CS#8) Resonances Grouped by Nuclide Integer or half integer spin for resonances followed by isotopic abundance for spin group and ground state spin for the target particle (CS#10) Number of Entrance Channels followed by Number of Exit Channels (CS#10) Spin Group Number & If an x appears following, Spin Group is excluded (CS#10)

  43. The input data set (another view) – this slide is just for my own edification

  44. Sammy output for ex012aa.odf natural Si oxide (partial data only 800 – 1100 keV) This area next slide Output Converted to Cross Section σ + are raw data, solid line final SAMMY Dashed line Zeroth order cross section Neutron Energy in keV

  45. Expanded Region in Previous Slide ex012aa.odf file output SAMMY Vertical Axis: Capture Cross Section + Raw Data, Solid Line Sammy Evaluation Par file data 962233.0000 1.6000E+04 7.6614E+07 0 0 0 2 1017777.188 1.0000E+03 7.6192E+04 0 0 0 5 1042856.812 1.0000E+03 9.3370E+05 0 0 0 5 1085169.250 3.6000E+03 7.2794E+04 0 0 0 1 1148103.625 1.0000E+03 3.1469E+03 0 0 0 5 Neutron Energy Range 1000 – 1060 keV

  46. Particle Width for channel 1 Ex012a.par file (first 14 terms) Capture width (milli-eV) -3.6616E+06 1.5877E+053.6985E+09 0 0 1 1 -8.7373E+05 1.0253E+03 1.0151E+02 0 0 1 1 -3.6529E+05 1.0000E+03 3.0406E+01 0 0 0 1 -6.3159E+04 1.0000E+03 4.6894E+01 0 0 0 1 -4.8801E+04 1.0000E+03 9.2496E+00 0 0 0 1 31739.99805 1.0000E+03 1.5667E+01 0 0 0 5 55676.96094 1.5803E+03 6.5331E+05 0 0 0 1 67732.84375 2.5000E+03 2.6589E+03 0 0 0 3 70800.00781 1.0000E+03 2.9617E+01 0 0 0 5 86797.35938 2.5000E+03 7.2618E+02 0 0 0 3 181617.5000 5.6000E+03 3.4894E+07 0 0 0 1 298700.0000 1.0000E+03 9.8860E+03 0 0 0 5 301310.8125 3.6000E+03 2.3548E+03 0 0 0 1 354588.68751.0000E+03 1.4460E+04 0 0 0 5 Quantum numbers for resonance Vary parameters Resonance Energies grouped by nuclide

  47. End of ex012a.par file set shown here RADIUS PARAMETERS FOLLOW 4.13642 4.13642 0-1 1 4 5 4.94372 4.94372 0-1 2 3 6 7 4.40000 4.40000 0-1 8 91011121314151617 4.20000 4.20000 0-11819202122 4.20000 4.20000 0-123242526272829 ISOTOPIC MASSES AND ABUNDANCES FOLLOW 27.976929 1.0000000 .9200 1 1 2 3 4 5 6 7 28.976496 .0467000 .0500 1 8 91011121314151617 29.973772 .0310000 .0200 11819202122 16.000000 1.0000000 .0100000 023242526272829

  48. Important output from ex012aa.lpt file (example sections shown) Isotopic abundance and mass for each nuclide -- Nuclide Abundance Mass Spin groups 1 0.9327 ( 3) 27.9769 1 2 3 4 5 6 7 2 3.8773E-02( 4) 28.9765 8 9 10 11 12 13 14 15 16 17 3 2.1778E-02( 5) 29.9738 18 19 20 21 22 4 1.000 16.0000 23 24 25 26 27 28 29 Disregard this, it is 16O Note! New calculations of isotopic abundance for 28Si, 29Si and 30Si

  49. 28Si, 29Si, and 30Si Bayes Calculation Runs + ++ data, solid line final theoretical cross section (barns) A series of 5 slides ranging from 300 eV to 1800 eV showing 600 eV per slide

  50. 28Si , 29Si, and 30Sis, p, d and f waves

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