Arqueros, F

CERN Document Server

29th International Cosmic Ray Conference Pune (2005) 7, 267270Dependence of the Air-Fluorescence Yield on Electron EnergyF. Arqueros, F. Blanco and M. OrtizDepartamento de F·sica At·omica, Molecular y Nuclear, Facultad de Ciencias F·sicas, Universidad Complutense,E-28040 Madrid, SpainPresenter: F. Arqueros (arqueros@gae.ucm.es), spa-arqueros-F-abs2-he14-oralThe air fluorescence yield from electrons is related with several molecular parameters according to well estab-lished relationships. Experimental cross sections available in the literature in combination with theoretical dataon Franck-Condon factors and branching ratios can be used for the calculation of the fluorescence yield as afunction of the electron energy in a wide interval (keV - GeV).1. IntroductionAir fluorescence is a well established technique for the detection of ultra-high energy cosmic rays [1]. Inparticular, fluorescence telescopes are a key tool for the energy calibration of the Pierre Auger Observatory [2].In order to achieve a precise calibration, accurate values of the fluorescence yield of air excited by electronsare required. This need has promoted a number of experiments for the measurement of this parameter in thewavelength interval 300 - 420 nm [3]. In this interval, fluorescence arises from the First Negative System ofN  (B X  ) and the Second Positive System of N  (C 	B 	  ) which will be called 1N and 2PSystems respectively.Not being available yet direct measurements at low energy, the corresponding yield are usually inferred byextrapolating high energy values, assuming that the efficiency for the generation of fluorescence is proportionalto the stopping power which follows the well known Bethe-Bloch formula. As far as we know, this assumptionhas not yet been established neither experimentally nor theoretically. In this paper the dependence of thefluorescence yield with the electron energy is studied using a combination of both, molecular properties andexperimental results on the related cross sections.2. Fluorescence Yield and Stopping PowerThe fluorescence yield for a molecular band  is defined as the number of fluorescence photons emitted in themolecular transition  per electron and unit path length. At very low pressure  ﬀﬂﬁ ﬃ ﬂﬁ ,where  is the number of molecules per unit volume, ﬁ  is the excitation cross section for the  level, ﬃ is the branching ratio (i.e. the ratio between the partial  ! and total  ! radiative transition probabilities)and ﬁ" is the so-called optical cross section for the transition #$% . As is well known the excitation crosssections ﬁ" are also proportional to the Franck-Condon factors &')(  , defined as the overlapping integrals ofthe vibrational wavefunctions of the ground and the excited levels. The relationﬁ*ﬁ*+,+&')(&')(+ﬃﬃ+-+(1)allows the calculation of any optical cross section from data on a measured transition (e.g.  /. 0" /. ).At high pressure, collisional quenching plays an important role and the fluorescence yield can be expressed by268 F. Arqueros, F. Blanco and M. Ortiz1325476 ﬀﬂﬁ 88:94<;4(2)where 4 is the pressure for which the probability of collisional quenching equals that of radiative de-excitation.The stopping power = (i.e. the energy loss of an electron per unit length of traversed matter due to bothexcitation and ionization processes) can be accurately predicted for energies above 10 keV by the well knownBethe-Bloch formula. On the other hand, a cross section ﬁ?> , proportional to the stopping power, can be definedby means of = ﬀ@Aﬁ"> where @ is the Bethe parameter (average energy released per collision).The fluorescence efficiency B  , defined as the fraction of deposited energy which is emitted as photons ofthe CDE band, is related with the stopping power byB 32F476 G  1 =G Fﬁ  @Eﬁ*>88:94<;4(3)Note that only a fraction of the energy loss is converted in excitation to the level v of interest, not because ofinternal processes (as often stated), but due to other allowed direct excitation channels.3. The First Negative system of N HThe 1N System has been studied by many authors. In particular many measurements of the optical cross sectionﬁ+,+ corresponding to the strongest band at 391.4 nm are available in the literature. At high energy, the crosssection for the excitation of the 1N upper level follows a Born-Bethe relativistic law [4].ﬁI JLKNMPO<QJMPO28J6JR(4)whereJis the relativistic speed and,  and Q are constants. For any function following the behavior ofequation (4), a plot of ﬁJversus S  MTO 2J6MTO28J6J(Fano plot) should be a straight line. In figure1 a significant set of the available experimental results have been represented on a Fano plot. A linear fit of thedata over 300 eV predicts a cross section in reasonable agreement with the measurements of Hirs et al. [5].The Born-Bethe function shown in the figure seems to provide us with a reliable value of ﬁ?+-+ in a wide energyrange. The cross section for other bands can be easily obtained using relation (1).On the other hand, it can be easily checked that the stopping power is not linear in a Fano plot. This resultshould not be surprising since ﬁU takes into account only one of the many inelastic processes involved in ﬁL> .4. The Second Positive system of N HMany authors have studied the excitation of the 2P System. Experiments carried out on pure nitrogen at lowelectron energy (GWV1keV) and low pressure (a few mTorr or lower), show a fastGYXdependence of thefluorescence light (expected from the optically-forbidden nature of the involved transition). For comparison,1N System exhibits a much slower (logE)/E dependence. Taking into account that, at 1keV energies, theobserved 2P fluorescence at low pressure is about three orders of magnitude less intense than that from the1N system, a simple extrapolation would predict that the 2P fluorescence should be completely negligible at30keV energies and above (compared to 1N System). On the contrary, experiments carried out at high energiesDependence of the Air-Fluorescence ... 269Figure 1. Optical cross section Z\[][ of the 1N system. Left: Available experimental data in a Fano plot together with aBorn-Bethe t. Right: Optical cross section versus electron energy. The Bethe Block function is shown for comparison.(up to 1GeV) show that 2P fluorescence even dominates over the 1N system. The experiments of this secondgroup, mainly devoted to study the fluorescence emission of air, have been performed at much higher pressures(ranging from a few Torr up to 1 atm).Obviously, other processes take place in the excitation of neutral nitrogen. Very recently a model has beenproposed [6] which explains these discrepancies. This model takes into account that each ionization processreleases at least one low energy electron for which both the inelastic ﬁL^P_a`cb and the 2P excitation cross sectionsare very large resulting, for these secondary electrons, in very small mean free paths and large contribution tofluorescence.An apparent optical cross section ﬁed,fcan be calculated [6] which turns out to depend on the quantity g =ﬁ*^P_a`cbFh ( h is the size of the interaction region). In figure 2, the result for the strongest band of the 2P System(337.1 nm) has been represented against the electron energy for several h values together with availableexperimental data. Measurements at very low pressure and very low energy show a maximum of the crosssection at about 20 eV with a fast decrease with energy as predicted by the model. In the limiting case ofhjiki 1 (high pressure experiments) the model predicts an apparent cross section given byﬁld,f2G6/ﬁ"2G69Vﬁ*ﬁ^T_A`cbimﬁ"^Pn,_2G6 (5)where ﬁ"^on3_ is the cross section for all ionization processes. As shown in the figure, experimental results at highpressure and high energy are in very good agreement with the model.5. ConclusionsThe optical cross sections for emission of air fluorescence light induced by electrons have been obtained for awide energy range using both molecular properties and available experimental results. Optical cross sectionsfor 1N system follow the Born-Bethe law. A model which takes into account the contribution of secondaryelectrons provides the apparent cross section of the 2P system up to high electron energy.270 F. Arqueros, F. Blanco and M. OrtizFigure 2. Apparent optical cross section Z"p,q[][for 2P system of N r versus electron energy as predicted by the model ofref. [6] for several sut values (continuous lines). Data deduced from measurements of Nagano et al. ( v ) and Kakimotoet al. ( w ) at high pressure are in good agreement with the model. This model also accounts for experimental results at lowpressure ( x , y ). See [6] for more details.At high pressure the fluorescence yield can be inferred from these optical cross sections by evaluation of thequenching effect. In a realistic atmosphere, collision of excited molecules with the various quenchers (N  , O  ,contaminants) has to be properly determined taking into account a possible dependence of the quenching crosssection on energy collision (i.e. temperature).The application of the above methods for the evaluation of the air fluorescence yield in a wide energy range isin progress and the results will be published soon.6. AcknowledgementsThis work has been funded by the Spanish Ministerio de Ciencia y Tecnologia (ref.: FPA03-08733-C02-01).References[1] R.M. Baltrusaitis et al., Nucl. Instrum. Meth. Phys. Res. A 240 (1985) 410; T. Abu-Zayyad et al., Nucl.Instrum. Meth. Phys. Res. A 450 (2000) 253.[2] J. Abraham et al., Nucl. Instrum. Meth. Phys. Res. A 523 (2004) 5095. See other contributed papers ofthe Pierre Auger Observatory in this conference.[3] F. Kakimoto et al., Nucl. Instrum. Meth. Phys. Res. A 372 (1996) 244; M. Nagano et al., Astropart. Phys.20 (2003) 293; M. Nagano et al., Astropart. Phys. 22 (2004) 235; http://www.auger.de/events/air-light-03/; http://lappweb.in2p3.fr/IWFM05/[4] M. Inokuti, Rev. Mod. Phys. 43 (1971) 297.[5] M.N. Hirsh, E. Poss, P.N. Eisner, Phys. Rev. A 1 (1970) 1615.[6] F. Blanco and F. Arqueros: The role of secondary electrons in some experiments determining fluorescenceemission from Nitrogen C 	levels (Phys.Lett.A in press).

Dependence of the Air-Fluorescence Yield on Electron Energy

Abstract

Similar works

Full text

Available Versions

CERN Document Server