Inversion of neutron/gamma spectra from scintillator measurements J. Köhler a,⇑ , B. Ehresmann a , C. Martin a , E. Böhm a , A. Kharytonov a , O. Kortmann a,c , C. Zeitlin b , D.M. Hassler b , R.F. Wimmer-Schweingruber a a IEAP, Christian Albrechts University, Kiel, Germany b Southwest Research Institute, Department of Space Studies, Boulder, CO, United States c Space Sciences Laboratory, Berkley, CA, United States article info Article history: Received 30 May 2011 Received in revised form 15 July 2011 Available online 4 August 2011 Keywords: Neutron Gamma Mars Inversion abstract The Radiation Assessment Detector (RAD) on-board NASA’s Mars Science Laboratory (MSL) rover will measure charged particles as well as neutron and gamma radiation on the Martian surface. Neutral par- ticles are an important contribution to this radiation environment. RAD measures them with a CsI (Tl) and a plastic scintillator, which are both surrounded by an anticoincidence. The incident neutron/gamma spectrum is obtained from the measurements using inversion methods which often fit a functional behavior, e.g., a power law, to the measured data applying the instrument response function and, e.g., a least-squares method. In situations where count rates are small, i.e., where the stochastic nature of the measurement is evident, maximum likelihood estimates with underlying Poissonian statistics improve the resulting spectra. We demonstrate the measurement and inversion of gamma/neutron spec- tra for a detector concept featuring one high-density scintillator and one high-proton-content scintillator. The applied inversion methods derive the original spectra without any strong assumptions of the func- tional behavior. Instrument response functions are obtained from Monte-Carlo simulations in matrix form with which the instrument response is treated as a set of linear equations. Using the response matri- ces we compare a constrained least-squares minimization, a chi-squared minimization and a maximum likelihood method with underlying Poissonian statistics. We make no assumptions about the incident particle spectrum and the methods intrinsically satisfy the constraint of non-negative counts. We ana- lyzed neutron beam measurements made at the Physikalisch Technische Bundesanstalt (PTB) and inverted the measurement data for both neutron and gamma spectra. Monte-Carlo-generated measure- ments of the expected Martian neutron/gamma spectra were inverted as well, here the maximum like- lihood method with underlying Poissonian statistics produces significantly better results. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Realizing neutron and gamma measurements on-board a space- craft is often difficult due to the limitations of the instruments size and weight. One possible approach is the use of a combination of a high-proton-content and a high-density scintillator material which have different sensitivities for neutrons and gammas. This concept is used in the Radiation Assessment Detector (RAD) which is a part of the Mars Science Laboratory (MSL) mission and will measure the charged particle spectrum up to several 100 MeV/nuc and the neu- tron/gamma particle spectra up to 100 MeV on the surface of Mars. Unlike for stopping charged particles, where the energy deposit equals the particle energy, neutral particles create an energy de- posit which can be randomly distributed and ranging up to their incident energy. Therefore, a measured spectrum does not neces- sarily reflect the energy spectrum of the incoming particles. How- ever, using the measurement and a carefully modeled and calibrated instrument response function, the incoming particle spectrum can be determined by inversion methods. The choice of inversion method is important to ensure its suc- cess. In our case in which we want to measure sometimes low count rates of neutral particles, this aspect is crucial. Because the number of counts may be very low or possibly even zero, the sig- nals must be modeled as a Poissonian process, i.e., using Poissonian statistics. The correct statistical approach is the dominant factor for the investigation of such problems [1–4]. When the uncertainties or noise in the experimental data are distributed with Gaussian statistics the least-squares methods or other variants of chi-square minimization [5–7] can be used for the solution of inverse prob- lems. One can easily show that the least-squares method is a max- imum likelihood estimator of the fitted parameters if the measurements errors are independent and normally (Gaussian) distributed. 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.07.021 ⇑ Corresponding author. Tel.: +49 431 880 3944; fax: +49 431 880 3968. E-mail address: koehler@physik.uni-kiel.de (J. Köhler). Nuclear Instruments and Methods in Physics Research B 269 (2011) 2641–2648 Contents lists available at SciVerse ScienceDirect Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb