Birks' law

Birks' law[1][2] (named after British physicist John B. Birks)[3] is an empirical formula for the light yield per path length as a function of the energy loss per path length for a particle traversing a scintillator, and gives a relation that is not linear at high loss rates.

Overview

The relation is:

where L is the light yield, S is the scintillation efficiency, dE/dx is the energy loss of the particle per path length, and kB is Birks' constant, which depends on the material. kB is 0.126 mm/MeV for polystyrene-based scintillators[4] and 1.26–2.07 × 10−2 g/(MeV cm2) for polyvinyltoluene-based scintillators.[5]

Birks speculated that the loss of linearity is due to recombination and quenching effects between the excited molecules and the surrounding substrate. Birks' law has mostly been tested for organic scintillators. Its applicability to inorganic scintillators is debated. A good discussion can be found in Particle Detectors at Accelerators: Organic scintillators.[6] A compilation of Birks' constant for various materials can be found in Semi-empirical calculation of quenching factors for ions in scintillators.[7][8] A more complete theory of scintillation saturation, that gives Birks' law when only unimolecular de-excitation is included, can be found in a paper by Blanc, Cambou, and De Laford.[9]

References
  1. Birks, J.B. (1951). "Scintillations from Organic Crystals: Specific Fluorescence and Relative Response to Different Radiations". Proc. Phys. Soc. A64 (10): 874–877. Bibcode:1951PPSA...64..874B. CiteSeerX 10.1.1.205.7427. doi:10.1088/0370-1298/64/10/303.
  2. Birks, J.B. (1964). The Theory and Practice of Scintillation Counting. London: Pergamon.
  3. A Tribute to Professor John B Birks - LSC International Home
  4. Leverington, B.L.; Anelli; Campana; Rosellini (1970). "A 1 mm Scintillating Fibre Tracker Readout by a Multi-anode Photomultiplier". arXiv:1106.5649v2 [physics.ins-det].
  5. Torrisi, L. (October 2000). "Plastic scintillator investigations for relative dosimetry in proton-therapy". Nuclear Instruments and Methods in Physics Research Section B. 170 (3–4): 523–530. Bibcode:2000NIMPB.170..523T. doi:10.1016/S0168-583X(00)00237-8.
  6. Johnson, Kurtis. "Particle Detectors at Accelerators: Organic scintillators" (PDF).
  7. Tretyak, V.I. (2010). "Semi-empirical calculation of quenching factors for ions in scintillators". Astroparticle Physics. 33 (1): 40–53. arXiv:0911.3041. Bibcode:2010APh....33...40T. doi:10.1016/j.astropartphys.2009.11.002.
  8. Nyibule, S. (2014). "Birks' scaling of the particle light output functions for the EJ 299-33 plastic scintillator". Nuclear Instruments and Methods in Physics Research Section A. 768: 141–145. Bibcode:2014NIMPA.768..141N. doi:10.1016/j.nima.2014.09.056.
  9. Blanc, D.; Cambou, F.; De Lafond, Y.G. (1962). C. R. Acad. Sci. Paris. 254: 3187. Missing or empty |title= (help)


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