The Ter-Antonyan functionparameterizes the energy
spectra of primary
cosmic rays in the "knee" region ( eV) by the continuously differentiable function of energy taking into account the rate of change of spectral slope. The function is expressed as:
,
(1)
where is a
scale factor, and are the
asymptoticslopes of the function (or
spectral slopes) in a
logarithmic scale at and respectively for a given energy (the so-called "knee" energy). The rate of change of spectral slopes is set in function (1) by the "sharpness of knee" parameter, . Function (1) was proposed in ANI'98 Workshop (1998)
by Samvel Ter-Antonyan[1]
for both the
interpolation of
primary energy spectra in the energy range 1—100 PeV and the search of
parametrized solutions of
inverse problem to reconstruct primary
cosmic ray energy spectra.[1][2]
Function (1) is also used for the interpolation of observed Extensive
Air Shower spectra in the knee region.[2]
is the “knee” shaping function describing the change of the spectral slope. Examples of for are presented above.
The
rate of change of spectral slope from to with respect to energy () is derived from (1) as:
,
where
,
,
and
is the sharpness-independent spectral slope at the knee energy.
Function (1) coincides with B. Peters[3]
spectra for and
asymptotically approaches the
broken power law of cosmic ray energy spectra for :
,
where
References
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ab
S.V. Ter-Antonyan, L.S. Haroyan (2000). "About EAS size spectra and primary energy spectra in the knee region".
arXiv:hep-ex/0003006. {{
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