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ANALYSIS OF DOPPLER-BROADENED PEAK IN THERMAL NEUTRON INDUCED 10B(n,α γ)7Li REACTION USING HYPERGAM

  • Choi, Hee-Dong (Department of Nuclear Engineering, Seoul National University) ;
  • Jung, Nam-Suk (Department of Nuclear Engineering, Seoul National University) ;
  • Park, Byung-Gun (Department of Nuclear Engineering, Seoul National University)
  • Published : 2009.02.28

Abstract

The line shape functions for the Doppler-broadened gamma ray spectrum are considered in the $^{10}B(n,{\alpha}{\gamma})^7Li$ reaction occurring in a surrounding medium where the excited $^7Li$ nucleus is slowed down and stopped before decay. The phenomenological form of the stopping power was used for the broadening effect. Convolution with the detailed response of a germanium detector is taken into consideration for the simplest case of solely electronic stopping. A numerical study for the analysis of $^{10}B$ by thermal neutron capture is conducted by performing a parametric search and fitting the measured spectrum in a least-squares approach. In comparison with the previous numerical approach using the same analysis, the computational speed is increased and reliable information concerning the stopping power of the medium is obtained while estimating the uncertainty. Implementation of the routine analysis of $^{10}B$ is facilitated on a recent version of the gamma ray spectrum analysis package HyperGam.

References

  1. W. Neuwirth, W. Pietsch, K. Richter and U. Hauser, “On the Invalidity of Bragg's Rule in Stopping Cross Sections of Molecules for Swift Li Ions”, Z. Physik A, 275, 215 (1975) https://doi.org/10.1007/BF01409287
  2. H. O. U. Fynbo, “Doppler Broadened $\gamma$-lines from Exotic Nuclei”, Nucl. Instr. and Meth. B, 207, 275 (2003) https://doi.org/10.1016/S0168-583X(03)00570-6
  3. V. Brudanin, V. Egorov, T. Filipova, A. Kachalkin, V. Kovalenko, A. Salamatin, Yu. Shitov, I. $\breve{S}$tekl, S. Vassiliev, V. Vorobel, Ts. Vylov, I. Yutlandov, Sh. Zaparov, J. Deutsch, R. Prieels, L. Grenacs, J. Rak and Ch. Brian$\varsigma$on, “Measurement of the Induced Pseudoscalar Form Factor in the Capture of Polarized Muons by Si Nuclei”, Nucl. Phys. A, 587, 577 (1995) https://doi.org/10.1016/0375-9474(95)00052-3
  4. J. F. Ziegler and J. P. Biersack, The Stopping and Range of Ions in Solids, Pergamon Press, New York (1985)
  5. J. Lindhard, M. Scharff and H. E. Schi$\phi$tt, “Range Concepts and Heavy Ion Ranges (Notes on Atomic Collisions, II)”, Kong. Dansk. Vid. Selsk. Mat.-Fys. Medd., 33, 14 (1963)
  6. M. Magara and C. Yonezawa, “Decomposition of Prompt Gamma-ray Spectra Including the Doppler-broadened Peak for Boron Determination”, Nucl. Instr. and Meth. A, 411, 130 (1998) https://doi.org/10.1016/S0168-9002(98)00303-9
  7. M. K. Kubo and Y. Sakai, “A Simple Derivation of the Formula of the Doppler Broadened 478 keV gamma ray Lineshape from $^{7+}Li$and Its Analytical Application”, J. Nucl. Radiochem. Sci., 1, 83 (2000) https://doi.org/10.14494/jnrs2000.1.83
  8. G. W. Phillips and K. W. Marlow, “Automatic Analysis of Gamma-ray Spectra from Germanium Detectors”, Nucl. Instr. and Meth., 137, 525 (1976); G. W. Phillips and K.W. Marlow, Program HYPERMET for Automatic Analysis of Gamma-Ray Spectra from Germanium Detectors, NRL Memorandum Report 3198, Naval Research Laboratory, Washington D.C., USA, (1976)
  9. R.M. Lindstrom, “Reference Material Certification by Prompt-Gamma Activation Analysis”, Fresenius J. Anal. Chem., 360, 322 (1998) https://doi.org/10.1007/s002160050702
  10. J. W. Olness and E. K. Warburton, “Studies of $F^{18}$ from the $O^{16}$($He^{3}$,p$\gamma$)$F^{18}$ Reaction”, Phys. Rev., 151, 792 (1966) https://doi.org/10.1103/PhysRev.151.792
  11. L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge (1966).
  12. S. Baechler, P. Kudejova, J. Jolie, J.-L. Schenker and N. Stritt, “Prompt Gamma-ray Activation Analysis for Determination of Boron in Aqueous Solutions”, Nucl. Instr. and Meth. A, 488, 410 (2002) https://doi.org/10.1016/S0168-9002(02)00466-7
  13. R. B. Firestone, V. S. Shirley, C. M. Baglin, S. Y. Frank Chu and J. Zipkin, Table of Isotopes, $8^{th}$ ed., John Wiley & Sons Inc., New York, (1996)
  14. L. Szentmikl$\acute{o}$si, K. Gm$\acute{e}$ling and Zs. Révay, “Fitting the Boron Peak and Resolving Interferences in the 450-490 keV Region of PGAA Spectra”, J. Radioanal. Nucl. Chem., 271, 447 (2007) https://doi.org/10.1007/s10967-007-0229-7
  15. M. J. Puska and R. M. Nieminen, “Theory of Positrons in Solids and on Solid Surfaces”, Rev. Mod. Phys., 66, 841 (1994) https://doi.org/10.1103/RevModPhys.66.841
  16. A. Z. Schwarzschild and E. K. Warburton, “The Measurement of Short Nuclear Lifetimes”, Ann. Rev. Nucl. Sci., 18, 265 (1968) https://doi.org/10.1146/annurev.ns.18.120168.001405
  17. S. H. Byun, G. M. Sun and H. D. Choi, “Prompt Gamma Activation Analysis of Boron in Reference Materials using Diffracted Polychromatic Neutron Beam”, Nucl. Instr. and Meth. B, 213, 535 (2004) https://doi.org/10.1016/S0168-583X(03)01626-4
  18. W. Neuwirth, U. Hauser and E. Kühn, “Energy Loss of Charged Particles in Matter: I. Experimental Method and Velocity Dependence of the Energy Loss of Lithium Ions”, Z. Physik, 220, 241 (1969) https://doi.org/10.1007/BF01394701
  19. B.A. Moftah, E. Gete, D.F. Measday, D.S. Armstrong, J. Bauer, T.P. Gorringe, B.L. Johnson, B. Siebels and S. Stanislaus, “Muon Capture in $^{28}Si$ and $g_{p}$/$g_{a}$”, Phys. Lett. B, 395, 157 (1997) https://doi.org/10.1016/S0370-2693(97)00081-6
  20. E. K. Warburton, J. W. Olness, K. W. Jones, C. Chasman, R. A. Ristinen and D. H. Wilkinson “Lifetime Determinations for Nuclei A=10, 11, and 12 from Gamma-Ray Doppler Shifts”, Phys. Rev., 148, 1072 (1966) https://doi.org/10.1103/PhysRev.148.1072
  21. S. H. Byun, G. M. Sun and H.D. Choi, “Development of a Prompt Gamma Activation Analysis Facility Using Diffracted Polychromatic Neutron Beam”, Nucl. Instr. and Meth. A, 487, 521 (2002) https://doi.org/10.1016/S0168-9002(02)00394-7
  22. Y. Sakai, M. K. Kubo, C. Yonezawa, H. Matsue and M. Jimbo, “Determination of Degradation Constants of Energetic $^{7+}Li$ Ion in Liquid Media Using a Thin Boron Film on Silicon Wafer”, J. Nucl. Radiochem. Sci., 2, 1 (2001) https://doi.org/10.14494/jnrs2000.2.1
  23. Y. Sakai, C. Yonezawa, M. Magara, H. Sawahata and Y. Ito, “Measurement and Analysis of the Line Shape of Prompt gamma rays from Recoiling $^{7+}Li$ Produced in the $^{10}B$(n, $\alpha$)$^{7}Li$ Reaction”, Nucl. Instr. and Meth. A, 353, 699 (1994) https://doi.org/10.1016/0168-9002(94)91755-8
  24. G.M. Sun, C.S. Park and H.D. Choi, “Doppler-broadened boron peak analysis by using a modified spectral decompositon algorithm”, J. Radioanal. Nucl. Chem., 278, 637 (2008) https://doi.org/10.1007/s10967-008-1301-7
  25. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, Inc., New York (1970)
  26. W. Gander and W. Gautschi, Adaptive Quadrature- Revisited, Report 306, Departement Informatik, ETH Z$\ddot{u}$rich (1998)
  27. P. Asoka-Kumar, M. Alatalo, V. J. Ghosh, A. C. Kruseman, B. Nielsen and K. G. Lynn, “Increased Elemental Specificity of Positron Annihilation Spectra”, Phys. Rev. Lett., 77, 2097 (1996) https://doi.org/10.1103/PhysRevLett.77.2097
  28. E. K. Warburton, J. W. Olness and A. R. Poletti, “Nuclear Structure of Na22. I. Gamma-Ray Correlations and Lifetime Measurements for Levels of Eex<3.1 MeV”, Phys. Rev., 160, 938 (1967). https://doi.org/10.1103/PhysRev.160.938
  29. C. S. Park, H. D. Choi, G. M. Sun and J. H. Whang, “Status of Developing HPGe gamma ray Spectrum Analysis Code HYPERGAM”, Prog. in Nucl. Energy, 50, 389 (2008) https://doi.org/10.1016/j.pnucene.2007.11.022
  30. U. Hauser, W. Neuwirth, W. Pietsch and K. Richter, 'On the Determination of Collision Cross Sections by Nuclear Doppler Shift', Z. Physik, 269, 181 (1974) https://doi.org/10.1007/BF01669060
  31. E. K. Warburton, D. E. Alburger and D. H. Wilkinson, “Lifetime of the $Be^{10}$ 3.37-MeV Level. I. Experiment”, Phys. Rev., 129, 2180 (1963) https://doi.org/10.1103/PhysRev.129.2180
  32. Yu. Shitov, V. Egorov, Ch. Briançon, V. Brudanin, J. Deutsch, T. Filipova, C. Petitjean, R. Prieels, T. Siiskonen, J. Suhonen, Ts. Vylov, V. Wiaux, I. Yutlandov and Sh. Zaparov, "Doppler-broadening of Gamma Rays Following Muon Capture: Search for Scalar Coupling", Nucl. Phys. A, 699, 917 (2002) https://doi.org/10.1016/S0375-9474(01)01284-2
  33. T. A. E. C. Pratt, “The Range-Effect in the Gamma- Neutrino Angular Correlation Experiment”, Nucl. Instr. and Meth. 66, 351 (1968) https://doi.org/10.1016/0029-554X(68)90283-8
  34. S. Wolfram, The Mathematica Book, $5^{th}$ ed., Wolfram Media (2003)
  35. T. K. Alexander and J. S. Forster, Advances in Nuclear Physics, Vol. 10, (Eds.) M. Baranger and E. Vogt, Plenum Press, New York (1978)
  36. W. Neuwirth, W. Pietsch, K. Richter and U. Hauser, “Electronic Stopping Cross Sections of Elements and Compounds for Swift Lithium Ions”, Z. Physik A, 275, 209 (1975) https://doi.org/10.1007/BF01409286
  37. H. G. B$\ddot{o}$rner and J. Jolie, “Sub-picosecond Lifetime Measurements by Gamma Ray Induced Doppler Broadening”, J. Phys. G: Nucl. Part. Phys., 19, 217 (1993) https://doi.org/10.1088/0954-3899/19/2/006
  38. K. G. Lynn, J. R. MacDonald, R. A. Boie, L. C. Feldman, J. D. Gabbe, M. F. Robbins, E. Bonderup and J. Golovchenko, “Positron-Annihilation Momentum Profiles in Aluminum: Core Contribution and the Independent-Particle Model”, Phys. Rev. Lett., 38, 241 (1977) https://doi.org/10.1103/PhysRevLett.38.241

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