Full spectrum analysis with the non-negative least square constraint for laboratory HPGe gamma spectrometry

  • Mai Thanh Man
  • Vu Ngoc Ba
  • Dang Thi Thao My
  • Dang Nguyen Phuong
  • Truong Thi Hong LoanEmail author
  • Ngo Quang Huy


In this work, the full spectrum analysis (FSA) method with the non-negative least square (NNLS) constraint and the Kalman filter were developed for the laboratory HPGe gamma spectrometry. The sensitive spectra of 238U, 232Th and 40K for the HPGe gamma spectrometry were derived from measured gamma spectra of calibration soil samples by using this algorithm. The calculated sensitive spectra have all characteristic gamma lines and a good fit in relative comparison with the respective reference spectra of 238U, 232Th and 40K acquired from measuring the RGU1, RGTh1, RGK1 standard samples. These sensitive spectra were then applied in analyzing the activity concentrations of the 238U, 232Th, 40K radionuclides in soil samples collected at the surveyed area. The results of the activity concentrations were in accordance with the ones determined by the window analysis (WA) method with the most deviations of less than 14%. It proved that our analyzing program using the FSA method with the NNLS constraint gives the reasonable solution of the sensitive spectra matrix, even for HPGe detector which has a high energy resolution and 16 K multi-channel analyzer.


Full spectrum analysis Non negative least square Window analysis Sensitive spectrum HPGe detector Gamma spectrometry 



This research is funded by National Foundation for Science and Technology Development (Nafosted), Vietnam under Grant Number 103.04-2018.61. This research is done at the Nuclear Technique Laboratory (NTLab), VNUHCM - University of Science which was invested by Vietnam National University Ho Chi Minh City, Vietnam.


  1. 1.
    Boson J, Agren G, Johansson L (2008) A detailed investigation of HPGe detector response for improved Monte Carlo efficiency calculations. Nucl Instrum Methods Phys A 587:304–314CrossRefGoogle Scholar
  2. 2.
    Caciolli A, Baldoncini M, Bezzon GP, Broggini C, Buso GP, Callegari I, Colonna T, Fiorentini G, Guastaldi E, Mantovani F, Massa G, Menegazzo R, Mou L, Rossi Alvarez C, Shyti M, Zanon A, Xhixha G (2012) A new FSA approach for in situ γ ray spectroscopy. Sci Total Environ 414:639–645CrossRefGoogle Scholar
  3. 3.
    Crossley DJ, Reid AB (1982) Inversion of gamma ray data for element abundances. Geophysics 47:117–126CrossRefGoogle Scholar
  4. 4.
    Hendriks PHGM, Betti M, Bruzzi L, Mazzotti G (2001) Full-spectrum analysis of natural g-ray spectra. J Environ Radioact 53:365–380CrossRefGoogle Scholar
  5. 5.
    Huy NQ (2010) The influence of deadlayer thickness increase on efficiency decrease for a coaxial HPGe p-type detector. Nucl Instrum Methods Phys A 621:390–394CrossRefGoogle Scholar
  6. 6.
    Laaraiedh M (2012) Implementation of Kalman filter with Python language. IETR Labs, University of Rennes 1, RennesGoogle Scholar
  7. 7.
    Lawson CL, Hanson RJ (1995) Solving least square problems. SIAM, PhiladelphiaCrossRefGoogle Scholar
  8. 8.
    Loan TTH, Phuong DN, Thanh TT, Khanh TA, Nhon MV (2007) Monte-Carlo simulation of HPGe detector response function with using MCNP code. Commun Phys 17(1):59–64Google Scholar
  9. 9.
    Loan TTH, Ba VN, Anh NN, Dao NQ, Man MT, Ngan Thy TH, Yen Hong HT, Thang NV, Hoang TM (2018) Study on soil characteristics in Ben Tre—South Vietnam based on activity concentration distribution of 238U, 232Th, 226Ra, 40 K in depth using laboratory HPGe gamma spectrometry. J Radioanal Nucl Chem 318:1931–1938CrossRefGoogle Scholar
  10. 10.
    Løvborg L, Christiansen EM, Bøtter-Jensen L, Kirkegaard P (1981) Pad facility for the calibration of gamma-ray measurements on rocks. Risø-R-454Google Scholar
  11. 11.
    Mahmood HS, Hoogmoed WB, Van Henten EJ (2011) Estimating soil properties with a proximal gamma-ray spectrometer using windows and full-spectrum analysis methods. In: The second global workshop on proximal soil sensing, Montreal, pp 132–135Google Scholar
  12. 12.
    Mahmood HS, Hoogmoed WB, Van Henten EJ (2013) Proximal gamma-ray spectroscopy to predict soil properties using windows and full-spectrum analysis methods. Sensors 13:16263–16280CrossRefGoogle Scholar
  13. 13.
    Maphoto KP (2004) Determination of natural radioactivity concentrations in soil: a comparative study of windows and full spectrum analysis. Master thesis, University of the Western CapeGoogle Scholar
  14. 14.
    Meijer RJ (1998) Heavy minerals: from ‘Edelstein’ to Einstein. J Geochem Explor 62:81–103CrossRefGoogle Scholar
  15. 15.
    Minty BRS (1992) Airborne gamma-ray spectrometric background estimation using full spectrum analysis. Geophysiscs 57(2):279–287CrossRefGoogle Scholar
  16. 16.
    Newman RT, Lindsay R, Maphoto KP, Mlwilo NA, Mohanty AK, Roux DG, de Meijer RJ, Hlatshwayo IN (2008) Determination of soil, sand and ore primordial radionuclide concentrations by full spectrum analyses of high-purity germanium detector spectra. Appl Radiat Isot 66:855–859CrossRefGoogle Scholar
  17. 17.
    Ortec Industries (2012) Angle 3 software of semiconductor detector efficiency calculation. Ortec Industries, Oak RidgeGoogle Scholar
  18. 18.
    Rodenas J, Pascual A, Zarza I, Serradell V, Ortiz J, Ballesteros L (2003) Analysis of the influence of germanium dead layer on detector calibration simulation for environmental radioactive samples using the Monte Carlo method. Nucl Instrum Methods Phys A 496:390–399CrossRefGoogle Scholar
  19. 19.
    Vidmar T (2010) True coincidence summing corrections CCCC, a deterministic code. Jozef Stefan Institute, LjubljanaGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Nuclear Technique LaboratoryVNUHCM - University of ScienceHo Chi Minh CityVietnam
  2. 2.Nulear Physics Department, Faculty of Physics and Engineering PhysicsVNUHCM - University of ScienceHo Chi Minh CityVietnam
  3. 3.Institute of PhysicsUniversity of FreiburgFreiburg im BreisgauFederal Republic of Germany
  4. 4.Center for Nuclear TechniquesHo Chi Minh CityVietnam
  5. 5.Faculty of MedicineNguyen Tat Thanh UniversityHo Chi Minh CityVietnam

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