Quantum Statistical Treatment of Relative Light Intensity of NaI (Pure) Crystal as a Function of Absolute Temperature

Author(s): Joseph Hsu ; William C. Kaiser
Sponsor(s): IEEE Nuclear and Plasma Sciences Society
Publisher: IEEE - Institute of Electrical and Electronics Engineers, Inc.
Publication Date: 1 February 1966
Volume: 13
Page(s): 704 - 715
ISSN (Paper): 0018-9499
ISSN (Online): 1558-1578
DOI: 10.1109/TNS.1966.4324034



Temperature can be employed as a tool to manipulate the internal energy of the excited electrons on the border of the Fermi level of the excited atoms. As a result of temperature decrease, the occupation probability of the excited electrons, obeying the Pauli exclusion principle and Fermi-Dirac distribution function, increases exponentially with the third power of the absolute temperature. "Size Effect" in terms of the total number of the atoms in the crystal can also be elucidated. The equation derived for the relative light intensity of the excited NaI crystal, which is initimately related to the specific heat of the crystal, can be expressed as -H [ 12 π4/5 Nk(T/H)3]TfTi where Ti= initial temperature (° K) Tf final temperature (° K) T = absolute temperature of the crystal (° K) H = proportionality const. (empirical) = 1.88 x 10-9for NaI (3/4" D. ×0.100") N = number of Na atoms in the crystal sample k = Boltzmann's constant = 1.380 x 10-16 erg/° K H = Debye temperature of NaI (° K) Preliminary empirical data at liquid nitrogen temperature (77°K) of NaI (pure) crystal (3/4" D. × 0.100" thickness) indicate an 11-fold increase of the relative light intensity in general agreement with theoretical prediction. The exponential increase of relative light intensity further emphasizes the validity of the highly quantized nature of the energy levels, and that excited electrons in the crystals, or excitons (bound electron -hole pairs) are Fermions strictly obeying the Fermi-Dirac distribution function.