XVIth International Workshop on
Quantum Systems in
Chemistry and Physics
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Blackbody, synchrotron radiation, bremsstrahlung and plasmon analyzed by Tsallis nonextensive entropy
Jun Kawai, Abbas Alshehabi, Hiroyuki Iwasaki, Koretaka Yuge, Ágnes Nagy*
Kyoto University, Department of Materials Science and Engineering,
Sakyo-ku, Kyoto 606-8501, Japan
*Debrecen University, H-4010 Debrecen, Hungary
Manne Siegbahn once wrote that “the curve (bremsstrahlung from X-ray tube) rises abruptly on the short wave-length side. In this respect the curve differs fundamentally from the curve for the radiation of a ‘black’ body, though otherwise the curves have an external resemblance”[1]. Blackbody and bremsstrahlung or synchrotron radiation are similar in their overall spectral shape but a minor difference exists [2-4]. The Planck’s blackbody equation is expressed through the Tsallis nonextensive entropy [5]: N(E)=1/[(1+(q-1)x)1/(q-1)-1], where N is the number of photons, x=E/kT, and q the Tsallis parameter [6,7]. When q->1 , the above equation becomes Plank’s blackbody equation. We have fitted Eqn.(1) to a synchrotron radiation (relativistic bremsstrahlung) and when q=1.05 the agreement is best and satisfactory as shown in Fig. 1. The parameter q >1 means the long-range correlation due to nonextensitivity. The blackbody is ideal gas of photons without interaction, but the photons are weakly interacting each other for the synchrotron radiation.
Similarly the plasmon energy loss peaks when Si is irradiated by e.g., 1500 eV electron beam, decays exponentially from the 1st loss to the higher orders. The deviation from the exponential decay is also expressed by the Tsallis q parameter, which indicate the intrinsic and extrinsic paths of the plasmon energy loss processes.
exp(-E/kT)appears in physical chemistry, and the deviation from exponential could be interpreted by the long range interaction through the Tsallis parameter q.

References
[1] M. Siegbahn, “The Spectroscopy of X-Rays”, transl. G. A. Lindsay, Oxford Univ. Press, London, 1925, p. 206.
[2] J. Kawai, H. Ishii, Spectrochim. Acta, Part B, 60, 1586 (2005).
[3] J. Kawai, H. Ishii, Radiation Phys. Chem., 75, 1716 (2006).
[4] T. Tanigaki, J. Kawai, X-Ray Spectrom., 36, 321 (2007).
[5] C. Tsallis, Introduction to Nonextensive Statistical Mechanics, Springer (2009).
[6] Q. A. Wang, A. Le Mehaute, Phys. Lett. A, 242, 301 (1998).
[7] S. Martnez, F. Pennini, A. Plastino, C. J. Tessone, Physica A, 309, 85 (2002).









Figure 1. Comparison of synchrotron radiation (dotted)and blackbody radiation (solid line) with q=1.05.

Figure 2. Plasmon energy loss spectra.



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