1. Nitrogen fluorescence yield in dependence on atmospheric conditions Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft B. Keilhauer 1, J. Blümer 1,2, R. Engel 2, H. O. Klages 2 (1) Universität Karlsruhe, Institut für Experimentelle Kernphysik (2) Forschungszentrum Karlsruhe, Institut für Kernphysik Fluorescence Efficiency - measurements and calculations Fluorescence Yield at sea level dependence on altitude dependence on relative humidity

2. Fluorescence Efficiency needs efficiency at each wavelength λ without collisional quenching measurements - interpolation to zero pressure (e.g. Bunner, 1967) relative calculations - combination of radiative transition probabilities radiative life times apparent exitation cross sections

3. with air taken to be a two-component gas Fluorescence Efficiency

4. Results for 2P system (only excerpt) Relative calculations are scaled to the strongest emission of measurements.

5. Fluorescence Light  mainly e ± of EAS excites N 2 molecules in air  18 strong emission bands in 2P system between 300 and 400 nm  1 strong emission band in 1N system between 300 and 400 nm  only contributions < 1% from Argon  even less from Oxygen ⇒ Fluorescence Yield with assumption

6. Fluorescence Yield at sea level (only excerpt) p and T at sea level of US Standard atmosphere air with 78.8 % N 2 and 21.1 % O 2 0.85 MeV electron as exciting particle ⇒ dE/dX = 0.1677 MeV/kg·m -2

7. Fluorescence Yield at sea level

8. Relative comparison of 19 band systems

9. Bunner (1967) Davidson & O‘Neil (1964) Nagano et al. ( 2004) Waldenmaier (2006) this work with Bunner constants this work with Morozov et al. constants this work with Gilmore et al., Fons et al. constants sum of λ = (300 – 400) nm 3.001(3.490)(3.698)(3.429)3.6723.653(3.438) sum of all Nagano - wavelengths 2.798(3.405)3.698(3.429)3.4603.438(3.283) sum of all Nagano - wavelengths above 320 nm 2.5743.4043.149(2.905)3.2203.159(2.957) sum of all Nagano - wavelengths above 320 nm, without 1N 2.2932.9512.847(2.646)2.9062.8442.957 sum of all 2P ( ν' = 0, 1) without 333.9 nm, plus 1N 2.746(3.338)3.4553.4293.4063.383(3.253)

10. Bunner (1967) Davidson & O‘Neil (1964) Nagano et al. ( 2004) Waldenmaier (2006) this work with Bunner constants this work with Morozov et al. constants this work with Gilmore et al., Fons et al. constants sum of λ = (300 – 400) nm 3.001(3.490)(3.698)(3.429)3.6723.653(3.438) sum of all Nagano - wavelengths 2.798(3.405)3.698(3.429)3.4603.438(3.283) sum of all Nagano - wavelengths above 320 nm 2.5743.4043.149(2.905)3.2203.159(2.957) sum of all Nagano - wavelengths above 320 nm, without 1N 2.2932.9512.847(2.646)2.9062.8442.957 sum of all 2P ( ν' = 0, 1) without 333.9 nm, plus 1N 2.746(3.338)3.4553.4293.4063.383(3.253) non-wavelength dependent results Kakimoto et al. (1996) FY (300-400nm) at sea level = 3.275 HiRes Coll. (2005) FY (300-400nm) per charged particle in EAS = 5.0 assumes average dE/dX of 0.22 MeV/kg m -2 ⇒ FY at sea level = 3.811 ⇒ with altitude-dependence ≈ 3.6 - 3.7

11. Altitude dependence this work: with Nagano et al. (2004): Kakimoto et al. (1996):

12. Altitude dependence for some wavelengths

13. Altitude dependence

14. Seasonal and Altitude dependence for Auger

15. Seasonal and Altitude dependence - rel. difference to US-StdA -

16. Humidity dependence US-StdA with relative humidity = 100 % Morozov et al. (2005) measured collisional cross-section for 2P, ν' = 0, 1 ⇒ reduction of FY 337nm by about20 % at sea level 5 % at 4 km a.s.l. 0.3 % at 8 km a.s.l. Waldenmaier (2006) measured collisional cross-section for 2P, ν' = 0, 1 and 1N, ν' = 0 at 20 °C ⇒ reduction at sea level by 21.7 % for 2P, ν' = 0 19.6 % for 2P, ν' = 1 10.0 % for 1N, ν' = 0 for realistic conditions reduction by about 5 - 10 % at ground 1 - 3 % at 4 km a.s.l.

17. Summary FY-calculations agree quite well with measurements from Davidson & O‘Neil (1964), Nagano (2004), and Waldenmaier (2006) results from Bunner (1967) and Kakimoto (1996) are lower by 18 % and 11 %, respectively value used by HiRes collab. (2005) slightly higher (4 %) if no altitude dependence is applied parameterizations for altitude dependence for wavelength range 300 – 400 nm agree well with calculations increase of FY (photons/m) from 0 km to 8 km a.s.l. by 7 % seasonal dependence in the order of 3 % water vapor reduces FY due to additional quenching  paper published in Astropart. Phys. 25, pp. 259-268, (2006), or astro-ph/0511153