- Email: [email protected]
Temperature-dependent quenching of UV fluorescence of N2
ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Temperature-dependent quenching of UV fluorescence of N2 M.M. Fraga a,, A. Onofre a, L. Pereira a, N. Castro a, F. Veloso a, F. Fraga a, R. Ferreira Marques a, M. Pimenta b, A. Policarpo a a b
LIP-Coimbra and Departamento de Fı´sica, Universidade de Coimbra, 3004-516 Coimbra, Portugal LIP/IST, Av. Elias Garcia 14, 1100-149 Lisboa, Portugal
a r t i c l e in fo
abstract
Available online 20 August 2008
The detection of fluorescence radiation produced in the atmosphere by the extensive air showers (EAS) generated by the interaction of incoming ultra high energy cosmic rays (UHECR) with the air molecules, is a technique that is being used by several experiments like Hires and Auger. This emission results from 2 þ the radiative de-excitation of the N2 C3 Pu and Nþ 2 B Su molecular states (2P and 1N systems, respectively) that can also be deactivated by two body collisions with molecules in their ground states. The efficiency of this electronic quenching depends on the nature of the quencher, the gas density and the gas temperature. In this work, an analysis of the quenching mechanisms is presented with particular emphasis on their temperature dependence. The quenching rate constant for 2P ð0; 0Þ band is found to decrease with increasing temperature. All data were corrected for geometrical factors and for the temperature dependence of the response of the optical system elements. & 2008 Elsevier B.V. All rights reserved.
Keywords: Cosmic rays Nitrogen scintillation Air fluorescence Quenching cross-sections
1. Introduction The air fluorescence detection technique is particularly suitable for the detection of Ultra High Energy Cosmic Rays (UHECR) with energies above 1019 eV, a very interesting and challenging problem of contemporary astrophysics. At this energy scale, the Greisen–Zatsepin–Kuzmin (GZK) [1] effect (known as the GZK-cutoff) should lead to a suppression of cosmic rays with energies above 5 1019 eV, if they are of extragalactic origin. The fact that Agasa [2] and HiRes [3] experiments have produced results that are conflicting both on the shape of the high energy end of the spectrum and on the location of spectral features, possibly due to discrepant energy scales, led to the development of new high statistics experiments, like Auger [4] with improved detection capabilities for UHECR. When a cosmic ray enters the atmosphere it loses energy in the collisions along its path and produces an air-shower. A small fraction of the cosmic ray energy loss (5 105 ) appears as ultraviolet (UV) light, known as air fluorescence, that results from the radiative de-excitation of molecular nitrogen. This light is emitted isotropically in the wavelength region between 280 and 420 nm and consists of two systems of vibrational transitions: the second positive system (2P) of the N2 molecule, (the C3 Pu ; v0 ! B3 Pg ; v00 transitions) and the first negative system (1N) of the
Corresponding author. Tel.: +351 239833465; fax: +351 239822358.
E-mail address: margarida@fis.uc.pt (M.M. Fraga). 0168-9002/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2008.08.046
2 þ 2 þ nitrogen ion, Nþ 2 , (the B Su ! X Sg transitions). The integrated intensity of the fluorescence light is a direct measure of the energy loss, from which the cosmic ray primary energy can be reconstructed. This technique is of utmost importance for the precise determination of the cosmic ray energy, and needs to be studied under very well controlled conditions at lab. In this work we study the fluorescence light yield from nitrogen, as a function of pressure and temperature, using a-particles from an 241Am radioactive source. The choice of a-particles instead of an electron source will not matter in terms of the effects that are being investigated in this paper as described below.
2. The nitrogen primary scintillation The structure of the light spectrum emitted by the molecular nitrogen can be studied using energetic a-particles as the excitation source. As the a-particle travels through gaseous nitrogen, at a given pressure and temperature, it loses energy along its path in ionization and excitation collisions. Spin conservation rules forbid direct excitation from the ground state 3 N2 (X 1 Sþ g ) to N2 (C Pu ) or to any other triplet electronic state. Tatischeff [5] found that the specific excitation (the number of excitations per mm) leading to the C3 Pu state was nearly proportional to the specific ionization (number of ion pairs created per mm) in most of the track of 4.3 MeV a-particles in nitrogen. However, at the end of the track a considerable increase
ARTICLE IN PRESS 76
M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
of the excitation over ionization was found, possibly due to the direct excitation of the C3 Pu state by Heþ. The probability of creating a Heþ ion increases as the energy of a-particle goes down and the lower the energy is, the more efficient will become the excitation of the C3 Pu state. Since this effect is difficult to include in our simulation code, we limit the gas density to values where the a-particle ranges are larger than the chamber dimensions. The main channel for the excitation of the N2 ðC3 Pu ) state will thus be by collisions with the primary and secondary electrons produced in the gas by the a-particle. The energy distribution of the primary electrons was calculated using the Rudd model for proton ionization [6] and the Z 2eff scaling of Ziegler et al. [7], and it is shown in Fig. 1a for three different a-particle energies. For comparison, the energy distribution function of the secondary electrons produced by 1 keV electrons is also shown. The mean energies of the primary electrons are indicated for each case. To check the consistency of our results, the total ionization crosssection was also calculated (see Fig. 1b) and compared with experimental data available in the literature [8,9]. A good agreement is obtained in the energy range between 0.6 and 5 MeV. Below 600 keV, a small deviation (o2:5s) is observed. Since the electron impact cross-sections for the excitation of the N2 C3 Pu vibrational levels (v0 ¼ 0; 1; 2) peak at low energies (15 eV) [10,11], and almost vanish for energies above 300 eV, the
Fig. 2. Band profiles for the 2P system of N2 between 310 and 360 nm, for T ¼ 300 K. Vibrational transitions (v0 ; v00 ) are indicated on the spectrum.
type of primary particle should not affect the pressure and temperature dependence of the 2P light yield. The 2nd positive system of N2 consists of a series of bands corresponding to the different C3 Pu ; v0 ! B3 Pg ; v00 vibrational transitions (with v0 ¼ 0; 1; 2; . . . and v00 ¼ 0; 1; 2; . . .). The rotational structure of each band reflects the population distribution among the different rotational levels of the upper state and the line strengths for each allowed transition. The band profiles were estimated [12] for different gas temperatures and for a very low gas pressure, where collisional effects are negligible. The histogram obtained with a bin width of 0.1 nm, at room temperature, is shown in Fig. 2. The relative intensities of the different bands were also obtained from Ref. [12].
3. Kinetic model It has been generally accepted in air fluorescence studies that the only excitation channel of the C3 Pu ; v0 states is by direct electron impact excitation from the ground molecular state: v0
ke
3 0 N2 ðX 1 Sþ g ; vÞ þ e ! N2 ðC Pu ; v Þ
(1)
i.e., vibrational relaxation and population from the upper E state are neglected. The de-excitation proceeds either by two body collisions (electronic quenching), kqv0
N2 ðC3 Pu ; v0 Þ þ N2 ðX 1 Sþ g ; vÞ ! N2 þ N2
(2)
or by photon emission, Av0 v00
N2 ðC3 Pu ; v0 Þ ! N2 ðB3 Pg ; v00 Þ þ hn.
(3)
In the steady-state condition, the number of excited molecules, per unit volume, in the vibrational state v0 is given by N2 ðCÞv0 ¼ ne tv0 C v0
Fig. 1. (a) Energy distribution function of the primary electrons produced by aparticles. The solid curve represents the energy distribution of the secondary electrons produced by 1 keV electron. (b) Ionization cross-section by a-particles.
(4)
where N and ne are the gas density (in number of molecules per v0 unit volume) and the electron density, C v0 ¼ ke N represents the excitation rate of vibrational state v0 (v0 ¼ 0–4) by electron impact and tv0 is the corresponding effective lifetime. The effective lifetime of level v0 depends on the natural lifetime t0v0 of the state
ARTICLE IN PRESS M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
and on the collisional de-excitation rate, i.e., 1
¼
tv0
1
t0v0
þ kqv0 N
(5)
here kqv0 is the electronic quenching rate constant for collisions with nitrogen molecules in their ground states. The natural lifetime, t0v0 , is related to the Einstein coefficients Av0 v00 for the (v0 ,v00 ) transition by 1
t0v0
¼
X
Av0 v00 ¼ Av0 .
(6)
v00
The light yield for the v0 ! v00 transition (in terms of number of photons per unit energy deposited) can be expressed as Y v0 v00 ¼ Av0 v00 tv0 Y 0v0
(7)
Y 0v0
¼ ne C v0 =Av0 ge is the intrinsic fluorescence yield (number where of photons emitted per deposited energy, in the absence of collisions) and ge is the energy deposited per unit volume. In this case, the reciprocal of the light yield for the ðv0 ; v00 Þ band increases linearly with pressure, according to 1 Av0 kv0 ¼ 1þ P (8) 0 Y v0 v00 Av0 Av0 v00 Y v0 with 1 1
kv0 ðhPa
s
Þ ¼ 2:471 1016 kqv0 ðcm3 s1 Þ
(9)
for T ¼ 293 K. The ratio of the slope to the intercept of the linear fit gives the kv0 =Av0 ratio. The reciprocal of this value has the dimensions of a pressure and is known as the characteristic pressure p0v0 . Calo and Axtmann [13] and Dilecce et al. [14] proposed the addition of a vibrational relaxation mechanism for the deexcitation of the C3 Pu ðv0 40Þ states, according to N2 ðC3 Pu ; v0 Þ þ N2 ðX 1 Sþ g ; vÞ kv0 w00
3
! N2 ðC Pu ; w00 ov0 Þ þ N2 ðX
(10) 1
Sþ g ; wÞ.
This means that besides direct excitation from the ground state, there is also a pressure-dependent population channel leading to the C3 Pu ðv0 ¼ 0Þ state. In spite of this mechanism, the reciprocal of the light yield for the 2P(0,0) band is still a linear function of P, and the ratio of the slope to the intercept of the linear fit to the experimental data yields a value that is estimated to be very similar to the real value of p00 (6–9% lower) [15]. The simplified kinetic model described above is, therefore, a useful and valid approximation and will be used in this work to describe the pressure and temperature dependence of the light yield.
77
corresponds to the mean velocity of the molecules in the gas for a given temperature T, kB is the Boltzmann constant, m the reduced mass of the two colliding partners, and x ¼ =kB T. The integral term has the dimensions of a cross-section, the quenching crosssection, and determines the temperature dependence of the quenching rate constant. In the hard sphere model the quenching cross-section is simply given by
sAB ¼ pðr A þ rB Þ2
(14)
with r A and r B representing the radii of the colliding partners A and B. This value is normally taken as an upper value of the quenching cross-section and when the experimental values approach sAB the quencher is considered an efficient quencher. The efficiency of quenching and the temperature variation of the quenching rate constants depend on the interactions occurring during the collision. Several models have been proposed but none of them is able to predict all the experimental results. In general, when repulsive forces are important the rate constant increases with T. When long range attractive forces play the main role the rate constants are expected to decrease with increasing T. Models based solely on multipole attractive forces predict an inverse power law for the temperature dependence of the quenching cross-sections. For example, for the case of two non-polar colliding molecules, the dispersion forces are expected to dominate the long range interaction and sT 1=3 . For ion–molecule reactions sT 1=2 and therefore the rate constant is not expected to vary with the temperature. However, for the 2 quenching of Nþ 2 ðB SÞ by N2 a power law of the type kq ¼ 0:32 aT was found [17]. Belikov et al. [17] suggested that 2 quenching of Nþ 2 ðB SÞ by N2 proceeds through the formation of a complex with a probability P. If this is the case, when the temperature is lowered both the probability of the complex formation and the lifetime of the complex should increase with the consequent increase of the quenching rate. This mechanism has also been proposed for some neutral–neutral reactions [18] and seems to be favored when collisions involve high-energy electronic states. To our knowledge, there are no published experimental or theoretical data regarding the temperature dependence of the collisional de-activation of the different vibrational states of N2 ðC3 Pu Þ by N2, O2 and H2 O (the most important quenchers of the C state in air). A study of the temperature dependence of the main 2P and 1N band intensities has been reported [19] but it only refers to the combined effect of N2 and O2 on the collisional deactivation of the N2 ðC3 Pu Þ state. Gru¨n and Schopper’s measurements [20] of the temperature dependence of the 2P luminescence in pure nitrogen and in Ar=N2 mixtures, showed a decrease of the total light yield with the temperature.
4. Temperature dependence of the quenching rate constant 5. Experimental setup The quenching rate constant is given as the average of the vsR ðvÞ over a thermal distribution of molecular velocities, i.e. Z kq ðTÞ ¼ vsR ðvÞf ð~ vÞ d~ v (11) where v is the relative velocity, sR ðvÞ is the collisional crosssection for a given relative velocity and f ð~ vÞ is the Maxwell–Boltzmann distribution function of velocities. This expression can also be expressed in terms of the collision energy, , as [16] sffiffiffiffiffiffiffiffiffiffiffi Z 8kB T (12) xsR ex dx ¼ hvisðTÞ kq ðTÞ ¼
pm
hvi ¼
1=2 8kB T
pm
(13)
Setup I: The detection chamber, a stainless steel chamber (with diameter f ¼ 50 mm and width h ¼ 30 mm) is coupled to two XP2020Q photomultipliers (PM1 and PM2) through fused silica windows (Fig. 3a). The chamber is inserted in a cooling unit which only allows the temperature to change from 300 down to 250 K. In order to reduce the photomultipliers temperature gradient, PM1 and PM2 are housed in cylindrical PVC tubes (covered with black foam) which isolate them from the inside of the cooling unit. A Melles–Griot interference filter (IF) (with center wavelength lc ¼ 340 nm, Dl ¼ 10 nm and peak transmission of 31%) is placed between the chamber and PM2 to isolate the 0–0 band (peaking at 337.1 nm) (see Fig. 3a). At the top of the chamber a 12:5 mm mylar window allows the a-particles from a non-collimated 241Am source to get inside the
ARTICLE IN PRESS 78
M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
Cooling unit
counting mode at the same positive applied voltages as in setup I. The signals from each PMT are amplified, sent to a discriminator and counted. The dark counting rates are measured periodically for both photomultipliers by interposing a shutter in the beam path. This setup can also be used to investigate the influence of temperature on the photomultiplier response. In this case, the amplified signals of the photomultipliers are sent to a multichannel analyzer (Canberra 35+) to obtain the single electron spectra.
αs
PM2
PM1
6. Temperature dependence of the photomultiplier response
IF
C.Unit
Interference filter
PM1
MONOC
PM2 OF Cooling unit
LAMP
BS
Fig. 3. (a) Experimental setup I, used to study the fluorescence light yield as a function of pressure and temperature using a-particles as excitation source; (b) setup II, used to characterize the response of the photomultipliers and interference filters.
chamber (Fig. 3a). The a-source is placed in a small secondary chamber that can be evacuated during the measurements to prevent energy losses outside the main chamber. The chamber is evacuated with a diffusion pump for several hours prior to each gas filling. The gas used was N2 from Air Liquide, 99.999% pure. Once the working pressure is obtained, the chamber is closed and the cooling cycle initiated. A pressure sensor (SETRA 216) and two temperature probes (PT100) are used to control and measure the pressure and temperature inside and outside the chamber. The PMT signals are set into coincidence after adequate amplification and discrimination. The coincidence counting rate is recorded with a data acquisition program, FluDaq, developed with Labview. This program also allows the remote control of the temperature inside the cooling unit and the readout of the pressure sensor and temperature probes during each temperature cycle. All the data are corrected for the accidental coincidence counting rate. Setup II: In order to characterize the response of the IF a second setup was assembled (see Fig. 3b). The IF is placed in a copper housing and mounted at the axis of a step motor inside the cooling unit. One temperature probe is attached to the body of PM2, close to the photocathode window. Two other probes, one attached to the copper housing of the filter, measure the temperature inside the cooling unit. The light beam from the deuterium lamp is attenuated with a combination of neutral filters and split into two beams: the one used as a reference is further attenuated and detected by PM1; the other beam passes through a monochromator (Jobin-Yvon, H20 FUV), is directed to the filter through an optical fiber (OF) with a collimating lens and it is detected by the second photomultiplier. The step motor position and the selection of wavelength are controlled externally with a PC. Both photomultipliers work on the single photon
It is well known that the dark count rate is reduced when the temperature within the PMT housing is decreased. The signal counting rate also changes due to the combined effect of the temperature dependence of both the multiplier gain and the photocathode sensitivity [21]. Both effects can be measured independently [22] from the analysis of the single electron response (SER) of the photomultiplier. The shape of the SER remains unchanged but there is a shift of the peak position (corresponding to 1 photoelectron). The ratio of the relative gain shift to the corresponding temperature variation is defined as the multiplier gain coefficient. This coefficient is expected to be independent of the photon wavelength and, for the photomultiplier under study, is negative (the gain increases as temperature decreases) and equal to 0:18%= (Fig. 4). The associated uncertainty is estimated to be of the order of 20%. The relative variation of the integral of the counts of the single electron spectra is used to define the cathode spectral sensitivity coefficient, ak ðlÞ, that is mostly independent of the wavelength, except near the long wavelength limit where it can change significantly [21]. The sum extends from a lower channel ci , in the valley of the SER, such that the ratio ci =cpeak remains constant over the temperature range under study, up to a channel cf corresponding to 4 times the peak channel. The total number of counts is corrected in each case with the counting rate of the reference photomultiplier to take into account possible fluctuations of the lamp. The cathode spectral sensitivity coefficient, measured for l ¼ 337 nm, is very low as expected [21] and equal to ð0:04 0:02Þ%= .
Fig. 4. Relative variation of multiplier gain as a function of temperature. Variations are calculated relative to room temperature (24 C). Symbols correspond to two different runs.
ARTICLE IN PRESS M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
79
The variation in the counting rate as given by the counter is a measure of the combined effects of gain shift and spectral sensitivity variation since the lower level of the discriminator is kept constant during all the measurements. The combined coefficient, also known as the anode sensitivity coefficient, aA , is in our experimental conditions given by ð0:10 0:05Þ%=.
7. Response of the IF The central wavelength, lc , of the transmission curve of an IF depends on the angle of incidence, y, according to sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin2 y 0 (15) lc ¼ lc 1 2 n
l0c and n being the central wavelength at normal incidence and the effective refractive index of the IF relative to air [23], respectively. However, this expression is only valid for small angles ðyo15 Þ while in our chamber the mean angle of incidence is around 30 in setup I. The transmission of the IF was measured, at room temperature, as a function of wavelength for different angles of incidence (Fig. 5a) and as a function of the angle of incidence for fixed values of wavelength (Fig. 5b). All the values were corrected for the dark counts and for the dependence on the wavelength of the light emitted by the lamp, IðlÞ. Repeated measurements assured the consistency of the data and allowed the estimation of the associated uncertainties. The transmission of the filter was also measured as a function of wavelength, for normal incidence, for different temperatures. The results show that as the temperature is lowered the central wavelength shifts towards lower wavelengths with Dlc =DT ¼ ð0:012 0:003Þ nm= (Fig. 6). The counting rate at the maximum of the transmission curve increases by 0:09%= with an uncertainty of 30%. The dependence of the transmission on the angle of incidence was also measured for different temperatures. The results are consistent with those obtained at room temperature within the experimental uncertainty.
8. Monte Carlo simulation A GEANT4 [24] simulation of the setup was developed in order to estimate the correcting factor for each experimental point (for a given pressure P and temperature T). The a-particles are emitted from the source along a direction selected at random, cross the mylar window, and get into the chamber with a mean energy Ei ¼ 3:8 MeV. UV photons are emitted isotropically along the track with an energy distribution given by the characteristic band profile calculated for the working temperature T (see Section 2). Some of the photons will cross the fused silica window, the filter and eventually reach the photocathode of the photomultiplier. The purpose of this simulation is to compute the mean number of photons, Nph arriving at the photocathode of the photomultiplier per a-particle. For this reason it is necessary to have a careful description of the different materials and optical interfaces the photons may encounter along their paths. One of the most important components of the optical system is the IF since its transmission strongly depends on the incidence angle and photon wavelength, as shown in the previous section. The convolution of transmission of the filter with the angular distribution of the UV photons leads to a narrow angular distribution of the photons reaching the PMT that does not depend on the gas density. In Fig. 7 the distributions of the angles
Fig. 5. (a) Transmission of the IF as a function of wavelength for different angles of incidence. (b) Transmission of the IF as a function of the angle of incidence for different wavelengths. All curves were obtained at room temperature and are normalized to the transmission at 337.1 nm and normal incidence.
Fig. 6. Central wavelength of the IF versus temperature. Different symbols correspond to data obtained in different days.
ARTICLE IN PRESS 80
M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
dn=dT, is positive and of the order of 1:4 105 = for 300 nmolo400 nm [25]. This implies a relative variation of the refractive index of about 0.05% for a temperature variation of 50 K. The variation of the transmission of the fused silica windows with the temperature was shown to be negligible in our experimental conditions as expected. However, this may not be always the case as pointed out by Erdman and Zipf [26].
9. Experimental results and discussion 9.1. Pressure dependence In order to validate the GEANT4 simulation and the reliability of the correction factors, we studied the pressure dependence, at room temperature, of the light yield corresponding to the 337.1 nm band of the 2nd positive system of N2 . The coincidence rate is corrected for the accidental coincidences and divided by the correction factor Nph as calculated by the GEANT4 simulation R¼
R0 ¼ gðlÞnA00 t0 Nph ðP; T; Ei Þ
(16)
where n is the number of a-particles entering the chamber per second, g represents the efficiency of the coincidence circuit and ðlÞ gives the detection efficiency of the optical system at room temperature (including the quantum efficiency of the photocathode of the photomultiplier, the transmission of the filter at the maximum of the curve and windows transmission). The reciprocal of R is expected to increase with the pressure according to (see Eq. (8)) 1 k0 ¼a 1þ P (17) R A0 where a is a constant dependent on the experimental conditions. The variation of 1=R is shown in Fig. 8 as a function of pressure normalized at 293 K. The error bars represent only the statistical errors. A linear fitting to the data allows the calculation of the ratio of the quenching rate constant to the Einstein coefficient as explained in Section 3. In Table 1, our value is compared with data obtained by other authors and there is a good agreement.
Fig. 7. (a) Angular distribution of the photons arriving at the filter; (b) Angular distribution of the photons collected by the PMT. The filling gas is N2 (336 hPa for 296 K).
of incidence at the filter and at the photomultiplier window are shown, as given by the simulation code. The influence of temperature on the filter transmission is also accounted for in the simulation. The uncertainties on the various factors that may affect the temperature dependence of the correction factor (anode sensitivity coefficient, filter transmission curves, bands profile and temperature of the different optical components) contribute with a total uncertainty of less than 5% at 254 K. The change of the refractive index of fused silica with temperature is linear over the temperature range between 273 and 970 K and the average thermal coefficient of refractive index,
Fig. 8. Reciprocal of the light yield (337.1 nm band) versus pressure.
ARTICLE IN PRESS M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
Table 1 Quenching rate constant, intrinsic lifetime and characteristic pressure for the N2 ðC3 Pu ; v0 ¼ 0Þ state 1
k0 (104 hPa
2.9670.25 2.6270.12 2.870.3 3.1670.12 3.2170.05 –
ns1 )
t (ns)
p00 ¼ A0 =k0 (hPa)
Ref.
41.772.1 3176 36.170.7 40.571.3 4272 –
81.376.6 123724 98711 7874 7474 110727
[27] [28] [14] [13] [29] Present work
81
temperature T, can be expressed in terms of effective lifetime trt 0 and characteristic pressure p0rt 0 both measured at room temperature T rt , as " # trt0 Rrt prt T b ¼ 1 þ 0rt R t00 p0 T rt
(20)
with b ¼ a þ 0:5. prt is the filling pressure (at room temperature). A least square fitting to the Rrt =R values for each gas density produce similar values of b, with a mean value of 0:37 0:15. This value implies that both the quenching rate and the quenching cross-section decrease with increasing temperature. The fitting curves are also represented in Fig. 9. To our knowledge there are no experimental results on the temperature dependence of the quenching cross-sections for the vibrational states of the C3 Pu state of N2 by nitrogen molecules. Within the experimental uncertainty, good agreement was found between the values of k0 =A0 (or p0rt 0 ) from the temperature study and other published values. The negative temperature dependence of the cross-section suggests that the main interaction during the collision involve long range forces and probably that an intermediate complex is formed. Calo and Axtmann [13] studied the de-excitation of the C3 Pu ; v0 ¼ 1 state and argued that it deactivates in two ways (by electronic quenching and vibrational relaxation) via the intermediate formation of the same complex molecule (N4 ). However, they could not find any experimental evidence or theoretical justification of this process. Further studies are needed in order to clarify the quenching mechanism not only by nitrogen molecules but also by oxygen and water vapor molecules. Studies in dry air [19] reveal a slight increase of the 2P(0,0) band light yield with decreasing temperature, in apparent disagreement with our data. However, since oxygen is a much more efficient quencher for the 2P emissions than N2 [28,29], the temperature dependence of the 2P(0,0) light yield in dry air is expected to be dominated by the temperature dependence of the rate constant for the deactivation of the C3 Pu ; v0 ¼ 0 state by the O2 molecules. 10. Conclusions
Fig. 9. Corrected coincidence rate as a function of temperature for the 2P(0,0) band of N2 . The pressures at room temperature are indicated for each case. The error bars represent only the statistical uncertainties.
9.2. Temperature dependence The temperature dependence of the 337.1 nm band in nitrogen was studied for different values of the gas density (kept constant during the cooling cycle). The measured R values (Eq. (16)) are represented in Fig. 9 as a function of T for two different values of gas density. They show a similar behavior, i.e., the 2P(0,0) band light yield decreases with the temperature. The quenching rate constant (in cm3 s1 ) may be written (see Eq. (12)) as pffiffiffi kq0 ¼ s0 T T a (18) assuming that the quenching cross-section follows a power law
s / Ta.
(19)
The ratio of the corrected coincidence rate (Eq. (16)) measured at room temperature to the corrected coincidence rate measured at
Detailed measurements, on the temperature dependence of 2P(0,0) band light yield in pure nitrogen, showed that the electronic quenching rate decreased with increasing temperature. Further studies for other molecular bands of the 2P and 1N system in N2 and dry air are underway in an attempt to clarify the mechanisms involved. This is particularly important for the air fluorescence detection of high energy cosmic rays but it is also relevant for the modeling of Earth’s middle and upper atmosphere.
Acknowledgments This work was supported by the Portuguese FCT under projects POCTI/FP/63440/2005 and POCTI/ FP/63913/2005.
References [1] K. Greisen, Phys. Rev. Lett. 16 (1966) 748; G. Zatsepin, V. Kuzmin, J. Exp. Theor. Phys. Lett. 4 (1966) 78. [2] K. Shinozaki, AGASA Collaboration, Nucl. Phys. B (Proc. Suppl.) 151 (2006) 3. [3] R.W. Springer, HiRes Collaboration, Nucl. Phys. B (Proc. Suppl.) 138 (2005) 307. [4] J. Abraham, Auger Collaboration, et al., Nucl. Instr. and Meth. A 523 (2004) 50. [5] I. Tatischeff, J. Chem. Phys. 52 (1970) 503. [6] M.E. Rudd, Phys. Rev. A 38 (1988) 6129. [7] J.F. Ziegler, J.M. Manoyan, Nucl. Instr. and Meth. B 35 (1988) 215.
ARTICLE IN PRESS 82
M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
[8] L.J. Puckett, G.O. Taylor, D.W. Martin, Phys. Rev. A 178 (1969) 271. [9] E.S. Solov’ev, R.N. Il’in, V.A. Oparin, N.V. Fedorenko, Sov. Phys. J. Exp. Theor. Phys. 18 (1966) 342. [10] M. Zubek, J. Phys. B At. Mol. Opt. Phys. 27 (1994) 573. [11] D.J. Burns, F.R. Simpson, J.W. McConkey, J. Phys. B At. Mol. Phys. 2 (1969) 52. [12] G. Hartmann, P.C. Johnson, J. Phys. B 11 (1978) 1597. [13] J.M. Calo, R.C. Axtmann, J. Chem. Phys. 54 (1971) 1332. [14] G. Dilecce, P.F. Ambrico, S. De Benedictis, Chem. Phys. Lett. 431 (2006) 241. [15] A. Morozov et al., Proceedings of the 5th Fluorescence Workshop, Nucl. Instr. and Meth. A 597 (2008) 105. [16] S.N. Levine, Quantum Mechanics of Molecular Rate Processes, Clarendon Press, Oxford, 1969. [17] A.E. Belikov, O.V. Kusnetsov, R.G. Sharafutdinov, J. Chem. Phys. 102 (1995) 2792. [18] K.L. Steffens, D.R. Crosley, J. Chem. Phys. 112 (2000) 9427.
[19] M. Ave, et al., AIRFLY Collaboration, Proceedings of the 5th Fluorescence Workshop, Nucl. Instr. and Meth. A 597 (2008) 50. [20] A.E. Gru¨n, E. Schopper, Z. Naturforschg. 9A (1954) 134. [21] Photonis, PHOTOMULTIPLIER TUBES: Principles & applications, 2002 hhttp:// www.photonis.com/products/photomultiplier-tubes/application_booki. [22] A.S. Singh, A.G. Wright, IEEE Trans. Nucl. Sci. NS-34 (1987). [23] Melles Griot, hhttp://www.mellesgriot.com/pdf/0013.25-13.29.pdfi. [24] GEANT4-a simulation toolkit, Nucl. Instr. and Meth. A 506 (2003) 250. [25] T. Toyoda, M. Yabe, J. Phys. D Appl. Phys. 16 (1983) L97. [26] P.W. Erdman, E.C. Zipf, Appl. Opt. 27 (1988) 3318. [27] A. Morozov, et al., Eur. Phys. J. D 33 (2005) 207. [28] H. Brunet, These du doctorat, Univ. Paul Sabatier, Toulouse, France, 1973. [29] S.V. Pancheshnyi, S.M. Starikovskaia, A.Yu. Starikovskii, Chem. Phys. 262 (2000) 349.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Temperature-dependent quenching of UV fluorescence of N2 M.M. Fraga a,, A. Onofre a, L. Pereira a, N. Castro a, F. Veloso a, F. Fraga a, R. Ferreira Marques a, M. Pimenta b, A. Policarpo a a b
LIP-Coimbra and Departamento de Fı´sica, Universidade de Coimbra, 3004-516 Coimbra, Portugal LIP/IST, Av. Elias Garcia 14, 1100-149 Lisboa, Portugal
a r t i c l e in fo
abstract
Available online 20 August 2008
The detection of fluorescence radiation produced in the atmosphere by the extensive air showers (EAS) generated by the interaction of incoming ultra high energy cosmic rays (UHECR) with the air molecules, is a technique that is being used by several experiments like Hires and Auger. This emission results from 2 þ the radiative de-excitation of the N2 C3 Pu and Nþ 2 B Su molecular states (2P and 1N systems, respectively) that can also be deactivated by two body collisions with molecules in their ground states. The efficiency of this electronic quenching depends on the nature of the quencher, the gas density and the gas temperature. In this work, an analysis of the quenching mechanisms is presented with particular emphasis on their temperature dependence. The quenching rate constant for 2P ð0; 0Þ band is found to decrease with increasing temperature. All data were corrected for geometrical factors and for the temperature dependence of the response of the optical system elements. & 2008 Elsevier B.V. All rights reserved.
Keywords: Cosmic rays Nitrogen scintillation Air fluorescence Quenching cross-sections
1. Introduction The air fluorescence detection technique is particularly suitable for the detection of Ultra High Energy Cosmic Rays (UHECR) with energies above 1019 eV, a very interesting and challenging problem of contemporary astrophysics. At this energy scale, the Greisen–Zatsepin–Kuzmin (GZK) [1] effect (known as the GZK-cutoff) should lead to a suppression of cosmic rays with energies above 5 1019 eV, if they are of extragalactic origin. The fact that Agasa [2] and HiRes [3] experiments have produced results that are conflicting both on the shape of the high energy end of the spectrum and on the location of spectral features, possibly due to discrepant energy scales, led to the development of new high statistics experiments, like Auger [4] with improved detection capabilities for UHECR. When a cosmic ray enters the atmosphere it loses energy in the collisions along its path and produces an air-shower. A small fraction of the cosmic ray energy loss (5 105 ) appears as ultraviolet (UV) light, known as air fluorescence, that results from the radiative de-excitation of molecular nitrogen. This light is emitted isotropically in the wavelength region between 280 and 420 nm and consists of two systems of vibrational transitions: the second positive system (2P) of the N2 molecule, (the C3 Pu ; v0 ! B3 Pg ; v00 transitions) and the first negative system (1N) of the
Corresponding author. Tel.: +351 239833465; fax: +351 239822358.
E-mail address: margarida@fis.uc.pt (M.M. Fraga). 0168-9002/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2008.08.046
2 þ 2 þ nitrogen ion, Nþ 2 , (the B Su ! X Sg transitions). The integrated intensity of the fluorescence light is a direct measure of the energy loss, from which the cosmic ray primary energy can be reconstructed. This technique is of utmost importance for the precise determination of the cosmic ray energy, and needs to be studied under very well controlled conditions at lab. In this work we study the fluorescence light yield from nitrogen, as a function of pressure and temperature, using a-particles from an 241Am radioactive source. The choice of a-particles instead of an electron source will not matter in terms of the effects that are being investigated in this paper as described below.
2. The nitrogen primary scintillation The structure of the light spectrum emitted by the molecular nitrogen can be studied using energetic a-particles as the excitation source. As the a-particle travels through gaseous nitrogen, at a given pressure and temperature, it loses energy along its path in ionization and excitation collisions. Spin conservation rules forbid direct excitation from the ground state 3 N2 (X 1 Sþ g ) to N2 (C Pu ) or to any other triplet electronic state. Tatischeff [5] found that the specific excitation (the number of excitations per mm) leading to the C3 Pu state was nearly proportional to the specific ionization (number of ion pairs created per mm) in most of the track of 4.3 MeV a-particles in nitrogen. However, at the end of the track a considerable increase
ARTICLE IN PRESS 76
M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
of the excitation over ionization was found, possibly due to the direct excitation of the C3 Pu state by Heþ. The probability of creating a Heþ ion increases as the energy of a-particle goes down and the lower the energy is, the more efficient will become the excitation of the C3 Pu state. Since this effect is difficult to include in our simulation code, we limit the gas density to values where the a-particle ranges are larger than the chamber dimensions. The main channel for the excitation of the N2 ðC3 Pu ) state will thus be by collisions with the primary and secondary electrons produced in the gas by the a-particle. The energy distribution of the primary electrons was calculated using the Rudd model for proton ionization [6] and the Z 2eff scaling of Ziegler et al. [7], and it is shown in Fig. 1a for three different a-particle energies. For comparison, the energy distribution function of the secondary electrons produced by 1 keV electrons is also shown. The mean energies of the primary electrons are indicated for each case. To check the consistency of our results, the total ionization crosssection was also calculated (see Fig. 1b) and compared with experimental data available in the literature [8,9]. A good agreement is obtained in the energy range between 0.6 and 5 MeV. Below 600 keV, a small deviation (o2:5s) is observed. Since the electron impact cross-sections for the excitation of the N2 C3 Pu vibrational levels (v0 ¼ 0; 1; 2) peak at low energies (15 eV) [10,11], and almost vanish for energies above 300 eV, the
Fig. 2. Band profiles for the 2P system of N2 between 310 and 360 nm, for T ¼ 300 K. Vibrational transitions (v0 ; v00 ) are indicated on the spectrum.
type of primary particle should not affect the pressure and temperature dependence of the 2P light yield. The 2nd positive system of N2 consists of a series of bands corresponding to the different C3 Pu ; v0 ! B3 Pg ; v00 vibrational transitions (with v0 ¼ 0; 1; 2; . . . and v00 ¼ 0; 1; 2; . . .). The rotational structure of each band reflects the population distribution among the different rotational levels of the upper state and the line strengths for each allowed transition. The band profiles were estimated [12] for different gas temperatures and for a very low gas pressure, where collisional effects are negligible. The histogram obtained with a bin width of 0.1 nm, at room temperature, is shown in Fig. 2. The relative intensities of the different bands were also obtained from Ref. [12].
3. Kinetic model It has been generally accepted in air fluorescence studies that the only excitation channel of the C3 Pu ; v0 states is by direct electron impact excitation from the ground molecular state: v0
ke
3 0 N2 ðX 1 Sþ g ; vÞ þ e ! N2 ðC Pu ; v Þ
(1)
i.e., vibrational relaxation and population from the upper E state are neglected. The de-excitation proceeds either by two body collisions (electronic quenching), kqv0
N2 ðC3 Pu ; v0 Þ þ N2 ðX 1 Sþ g ; vÞ ! N2 þ N2
(2)
or by photon emission, Av0 v00
N2 ðC3 Pu ; v0 Þ ! N2 ðB3 Pg ; v00 Þ þ hn.
(3)
In the steady-state condition, the number of excited molecules, per unit volume, in the vibrational state v0 is given by N2 ðCÞv0 ¼ ne tv0 C v0
Fig. 1. (a) Energy distribution function of the primary electrons produced by aparticles. The solid curve represents the energy distribution of the secondary electrons produced by 1 keV electron. (b) Ionization cross-section by a-particles.
(4)
where N and ne are the gas density (in number of molecules per v0 unit volume) and the electron density, C v0 ¼ ke N represents the excitation rate of vibrational state v0 (v0 ¼ 0–4) by electron impact and tv0 is the corresponding effective lifetime. The effective lifetime of level v0 depends on the natural lifetime t0v0 of the state
ARTICLE IN PRESS M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
and on the collisional de-excitation rate, i.e., 1
¼
tv0
1
t0v0
þ kqv0 N
(5)
here kqv0 is the electronic quenching rate constant for collisions with nitrogen molecules in their ground states. The natural lifetime, t0v0 , is related to the Einstein coefficients Av0 v00 for the (v0 ,v00 ) transition by 1
t0v0
¼
X
Av0 v00 ¼ Av0 .
(6)
v00
The light yield for the v0 ! v00 transition (in terms of number of photons per unit energy deposited) can be expressed as Y v0 v00 ¼ Av0 v00 tv0 Y 0v0
(7)
Y 0v0
¼ ne C v0 =Av0 ge is the intrinsic fluorescence yield (number where of photons emitted per deposited energy, in the absence of collisions) and ge is the energy deposited per unit volume. In this case, the reciprocal of the light yield for the ðv0 ; v00 Þ band increases linearly with pressure, according to 1 Av0 kv0 ¼ 1þ P (8) 0 Y v0 v00 Av0 Av0 v00 Y v0 with 1 1
kv0 ðhPa
s
Þ ¼ 2:471 1016 kqv0 ðcm3 s1 Þ
(9)
for T ¼ 293 K. The ratio of the slope to the intercept of the linear fit gives the kv0 =Av0 ratio. The reciprocal of this value has the dimensions of a pressure and is known as the characteristic pressure p0v0 . Calo and Axtmann [13] and Dilecce et al. [14] proposed the addition of a vibrational relaxation mechanism for the deexcitation of the C3 Pu ðv0 40Þ states, according to N2 ðC3 Pu ; v0 Þ þ N2 ðX 1 Sþ g ; vÞ kv0 w00
3
! N2 ðC Pu ; w00 ov0 Þ þ N2 ðX
(10) 1
Sþ g ; wÞ.
This means that besides direct excitation from the ground state, there is also a pressure-dependent population channel leading to the C3 Pu ðv0 ¼ 0Þ state. In spite of this mechanism, the reciprocal of the light yield for the 2P(0,0) band is still a linear function of P, and the ratio of the slope to the intercept of the linear fit to the experimental data yields a value that is estimated to be very similar to the real value of p00 (6–9% lower) [15]. The simplified kinetic model described above is, therefore, a useful and valid approximation and will be used in this work to describe the pressure and temperature dependence of the light yield.
77
corresponds to the mean velocity of the molecules in the gas for a given temperature T, kB is the Boltzmann constant, m the reduced mass of the two colliding partners, and x ¼ =kB T. The integral term has the dimensions of a cross-section, the quenching crosssection, and determines the temperature dependence of the quenching rate constant. In the hard sphere model the quenching cross-section is simply given by
sAB ¼ pðr A þ rB Þ2
(14)
with r A and r B representing the radii of the colliding partners A and B. This value is normally taken as an upper value of the quenching cross-section and when the experimental values approach sAB the quencher is considered an efficient quencher. The efficiency of quenching and the temperature variation of the quenching rate constants depend on the interactions occurring during the collision. Several models have been proposed but none of them is able to predict all the experimental results. In general, when repulsive forces are important the rate constant increases with T. When long range attractive forces play the main role the rate constants are expected to decrease with increasing T. Models based solely on multipole attractive forces predict an inverse power law for the temperature dependence of the quenching cross-sections. For example, for the case of two non-polar colliding molecules, the dispersion forces are expected to dominate the long range interaction and sT 1=3 . For ion–molecule reactions sT 1=2 and therefore the rate constant is not expected to vary with the temperature. However, for the 2 quenching of Nþ 2 ðB SÞ by N2 a power law of the type kq ¼ 0:32 aT was found [17]. Belikov et al. [17] suggested that 2 quenching of Nþ 2 ðB SÞ by N2 proceeds through the formation of a complex with a probability P. If this is the case, when the temperature is lowered both the probability of the complex formation and the lifetime of the complex should increase with the consequent increase of the quenching rate. This mechanism has also been proposed for some neutral–neutral reactions [18] and seems to be favored when collisions involve high-energy electronic states. To our knowledge, there are no published experimental or theoretical data regarding the temperature dependence of the collisional de-activation of the different vibrational states of N2 ðC3 Pu Þ by N2, O2 and H2 O (the most important quenchers of the C state in air). A study of the temperature dependence of the main 2P and 1N band intensities has been reported [19] but it only refers to the combined effect of N2 and O2 on the collisional deactivation of the N2 ðC3 Pu Þ state. Gru¨n and Schopper’s measurements [20] of the temperature dependence of the 2P luminescence in pure nitrogen and in Ar=N2 mixtures, showed a decrease of the total light yield with the temperature.
4. Temperature dependence of the quenching rate constant 5. Experimental setup The quenching rate constant is given as the average of the vsR ðvÞ over a thermal distribution of molecular velocities, i.e. Z kq ðTÞ ¼ vsR ðvÞf ð~ vÞ d~ v (11) where v is the relative velocity, sR ðvÞ is the collisional crosssection for a given relative velocity and f ð~ vÞ is the Maxwell–Boltzmann distribution function of velocities. This expression can also be expressed in terms of the collision energy, , as [16] sffiffiffiffiffiffiffiffiffiffiffi Z 8kB T (12) xsR ex dx ¼ hvisðTÞ kq ðTÞ ¼
pm
hvi ¼
1=2 8kB T
pm
(13)
Setup I: The detection chamber, a stainless steel chamber (with diameter f ¼ 50 mm and width h ¼ 30 mm) is coupled to two XP2020Q photomultipliers (PM1 and PM2) through fused silica windows (Fig. 3a). The chamber is inserted in a cooling unit which only allows the temperature to change from 300 down to 250 K. In order to reduce the photomultipliers temperature gradient, PM1 and PM2 are housed in cylindrical PVC tubes (covered with black foam) which isolate them from the inside of the cooling unit. A Melles–Griot interference filter (IF) (with center wavelength lc ¼ 340 nm, Dl ¼ 10 nm and peak transmission of 31%) is placed between the chamber and PM2 to isolate the 0–0 band (peaking at 337.1 nm) (see Fig. 3a). At the top of the chamber a 12:5 mm mylar window allows the a-particles from a non-collimated 241Am source to get inside the
ARTICLE IN PRESS 78
M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
Cooling unit
counting mode at the same positive applied voltages as in setup I. The signals from each PMT are amplified, sent to a discriminator and counted. The dark counting rates are measured periodically for both photomultipliers by interposing a shutter in the beam path. This setup can also be used to investigate the influence of temperature on the photomultiplier response. In this case, the amplified signals of the photomultipliers are sent to a multichannel analyzer (Canberra 35+) to obtain the single electron spectra.
αs
PM2
PM1
6. Temperature dependence of the photomultiplier response
IF
C.Unit
Interference filter
PM1
MONOC
PM2 OF Cooling unit
LAMP
BS
Fig. 3. (a) Experimental setup I, used to study the fluorescence light yield as a function of pressure and temperature using a-particles as excitation source; (b) setup II, used to characterize the response of the photomultipliers and interference filters.
chamber (Fig. 3a). The a-source is placed in a small secondary chamber that can be evacuated during the measurements to prevent energy losses outside the main chamber. The chamber is evacuated with a diffusion pump for several hours prior to each gas filling. The gas used was N2 from Air Liquide, 99.999% pure. Once the working pressure is obtained, the chamber is closed and the cooling cycle initiated. A pressure sensor (SETRA 216) and two temperature probes (PT100) are used to control and measure the pressure and temperature inside and outside the chamber. The PMT signals are set into coincidence after adequate amplification and discrimination. The coincidence counting rate is recorded with a data acquisition program, FluDaq, developed with Labview. This program also allows the remote control of the temperature inside the cooling unit and the readout of the pressure sensor and temperature probes during each temperature cycle. All the data are corrected for the accidental coincidence counting rate. Setup II: In order to characterize the response of the IF a second setup was assembled (see Fig. 3b). The IF is placed in a copper housing and mounted at the axis of a step motor inside the cooling unit. One temperature probe is attached to the body of PM2, close to the photocathode window. Two other probes, one attached to the copper housing of the filter, measure the temperature inside the cooling unit. The light beam from the deuterium lamp is attenuated with a combination of neutral filters and split into two beams: the one used as a reference is further attenuated and detected by PM1; the other beam passes through a monochromator (Jobin-Yvon, H20 FUV), is directed to the filter through an optical fiber (OF) with a collimating lens and it is detected by the second photomultiplier. The step motor position and the selection of wavelength are controlled externally with a PC. Both photomultipliers work on the single photon
It is well known that the dark count rate is reduced when the temperature within the PMT housing is decreased. The signal counting rate also changes due to the combined effect of the temperature dependence of both the multiplier gain and the photocathode sensitivity [21]. Both effects can be measured independently [22] from the analysis of the single electron response (SER) of the photomultiplier. The shape of the SER remains unchanged but there is a shift of the peak position (corresponding to 1 photoelectron). The ratio of the relative gain shift to the corresponding temperature variation is defined as the multiplier gain coefficient. This coefficient is expected to be independent of the photon wavelength and, for the photomultiplier under study, is negative (the gain increases as temperature decreases) and equal to 0:18%= (Fig. 4). The associated uncertainty is estimated to be of the order of 20%. The relative variation of the integral of the counts of the single electron spectra is used to define the cathode spectral sensitivity coefficient, ak ðlÞ, that is mostly independent of the wavelength, except near the long wavelength limit where it can change significantly [21]. The sum extends from a lower channel ci , in the valley of the SER, such that the ratio ci =cpeak remains constant over the temperature range under study, up to a channel cf corresponding to 4 times the peak channel. The total number of counts is corrected in each case with the counting rate of the reference photomultiplier to take into account possible fluctuations of the lamp. The cathode spectral sensitivity coefficient, measured for l ¼ 337 nm, is very low as expected [21] and equal to ð0:04 0:02Þ%= .
Fig. 4. Relative variation of multiplier gain as a function of temperature. Variations are calculated relative to room temperature (24 C). Symbols correspond to two different runs.
ARTICLE IN PRESS M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
79
The variation in the counting rate as given by the counter is a measure of the combined effects of gain shift and spectral sensitivity variation since the lower level of the discriminator is kept constant during all the measurements. The combined coefficient, also known as the anode sensitivity coefficient, aA , is in our experimental conditions given by ð0:10 0:05Þ%=.
7. Response of the IF The central wavelength, lc , of the transmission curve of an IF depends on the angle of incidence, y, according to sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin2 y 0 (15) lc ¼ lc 1 2 n
l0c and n being the central wavelength at normal incidence and the effective refractive index of the IF relative to air [23], respectively. However, this expression is only valid for small angles ðyo15 Þ while in our chamber the mean angle of incidence is around 30 in setup I. The transmission of the IF was measured, at room temperature, as a function of wavelength for different angles of incidence (Fig. 5a) and as a function of the angle of incidence for fixed values of wavelength (Fig. 5b). All the values were corrected for the dark counts and for the dependence on the wavelength of the light emitted by the lamp, IðlÞ. Repeated measurements assured the consistency of the data and allowed the estimation of the associated uncertainties. The transmission of the filter was also measured as a function of wavelength, for normal incidence, for different temperatures. The results show that as the temperature is lowered the central wavelength shifts towards lower wavelengths with Dlc =DT ¼ ð0:012 0:003Þ nm= (Fig. 6). The counting rate at the maximum of the transmission curve increases by 0:09%= with an uncertainty of 30%. The dependence of the transmission on the angle of incidence was also measured for different temperatures. The results are consistent with those obtained at room temperature within the experimental uncertainty.
8. Monte Carlo simulation A GEANT4 [24] simulation of the setup was developed in order to estimate the correcting factor for each experimental point (for a given pressure P and temperature T). The a-particles are emitted from the source along a direction selected at random, cross the mylar window, and get into the chamber with a mean energy Ei ¼ 3:8 MeV. UV photons are emitted isotropically along the track with an energy distribution given by the characteristic band profile calculated for the working temperature T (see Section 2). Some of the photons will cross the fused silica window, the filter and eventually reach the photocathode of the photomultiplier. The purpose of this simulation is to compute the mean number of photons, Nph arriving at the photocathode of the photomultiplier per a-particle. For this reason it is necessary to have a careful description of the different materials and optical interfaces the photons may encounter along their paths. One of the most important components of the optical system is the IF since its transmission strongly depends on the incidence angle and photon wavelength, as shown in the previous section. The convolution of transmission of the filter with the angular distribution of the UV photons leads to a narrow angular distribution of the photons reaching the PMT that does not depend on the gas density. In Fig. 7 the distributions of the angles
Fig. 5. (a) Transmission of the IF as a function of wavelength for different angles of incidence. (b) Transmission of the IF as a function of the angle of incidence for different wavelengths. All curves were obtained at room temperature and are normalized to the transmission at 337.1 nm and normal incidence.
Fig. 6. Central wavelength of the IF versus temperature. Different symbols correspond to data obtained in different days.
ARTICLE IN PRESS 80
M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
dn=dT, is positive and of the order of 1:4 105 = for 300 nmolo400 nm [25]. This implies a relative variation of the refractive index of about 0.05% for a temperature variation of 50 K. The variation of the transmission of the fused silica windows with the temperature was shown to be negligible in our experimental conditions as expected. However, this may not be always the case as pointed out by Erdman and Zipf [26].
9. Experimental results and discussion 9.1. Pressure dependence In order to validate the GEANT4 simulation and the reliability of the correction factors, we studied the pressure dependence, at room temperature, of the light yield corresponding to the 337.1 nm band of the 2nd positive system of N2 . The coincidence rate is corrected for the accidental coincidences and divided by the correction factor Nph as calculated by the GEANT4 simulation R¼
R0 ¼ gðlÞnA00 t0 Nph ðP; T; Ei Þ
(16)
where n is the number of a-particles entering the chamber per second, g represents the efficiency of the coincidence circuit and ðlÞ gives the detection efficiency of the optical system at room temperature (including the quantum efficiency of the photocathode of the photomultiplier, the transmission of the filter at the maximum of the curve and windows transmission). The reciprocal of R is expected to increase with the pressure according to (see Eq. (8)) 1 k0 ¼a 1þ P (17) R A0 where a is a constant dependent on the experimental conditions. The variation of 1=R is shown in Fig. 8 as a function of pressure normalized at 293 K. The error bars represent only the statistical errors. A linear fitting to the data allows the calculation of the ratio of the quenching rate constant to the Einstein coefficient as explained in Section 3. In Table 1, our value is compared with data obtained by other authors and there is a good agreement.
Fig. 7. (a) Angular distribution of the photons arriving at the filter; (b) Angular distribution of the photons collected by the PMT. The filling gas is N2 (336 hPa for 296 K).
of incidence at the filter and at the photomultiplier window are shown, as given by the simulation code. The influence of temperature on the filter transmission is also accounted for in the simulation. The uncertainties on the various factors that may affect the temperature dependence of the correction factor (anode sensitivity coefficient, filter transmission curves, bands profile and temperature of the different optical components) contribute with a total uncertainty of less than 5% at 254 K. The change of the refractive index of fused silica with temperature is linear over the temperature range between 273 and 970 K and the average thermal coefficient of refractive index,
Fig. 8. Reciprocal of the light yield (337.1 nm band) versus pressure.
ARTICLE IN PRESS M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
Table 1 Quenching rate constant, intrinsic lifetime and characteristic pressure for the N2 ðC3 Pu ; v0 ¼ 0Þ state 1
k0 (104 hPa
2.9670.25 2.6270.12 2.870.3 3.1670.12 3.2170.05 –
ns1 )
t (ns)
p00 ¼ A0 =k0 (hPa)
Ref.
41.772.1 3176 36.170.7 40.571.3 4272 –
81.376.6 123724 98711 7874 7474 110727
[27] [28] [14] [13] [29] Present work
81
temperature T, can be expressed in terms of effective lifetime trt 0 and characteristic pressure p0rt 0 both measured at room temperature T rt , as " # trt0 Rrt prt T b ¼ 1 þ 0rt R t00 p0 T rt
(20)
with b ¼ a þ 0:5. prt is the filling pressure (at room temperature). A least square fitting to the Rrt =R values for each gas density produce similar values of b, with a mean value of 0:37 0:15. This value implies that both the quenching rate and the quenching cross-section decrease with increasing temperature. The fitting curves are also represented in Fig. 9. To our knowledge there are no experimental results on the temperature dependence of the quenching cross-sections for the vibrational states of the C3 Pu state of N2 by nitrogen molecules. Within the experimental uncertainty, good agreement was found between the values of k0 =A0 (or p0rt 0 ) from the temperature study and other published values. The negative temperature dependence of the cross-section suggests that the main interaction during the collision involve long range forces and probably that an intermediate complex is formed. Calo and Axtmann [13] studied the de-excitation of the C3 Pu ; v0 ¼ 1 state and argued that it deactivates in two ways (by electronic quenching and vibrational relaxation) via the intermediate formation of the same complex molecule (N4 ). However, they could not find any experimental evidence or theoretical justification of this process. Further studies are needed in order to clarify the quenching mechanism not only by nitrogen molecules but also by oxygen and water vapor molecules. Studies in dry air [19] reveal a slight increase of the 2P(0,0) band light yield with decreasing temperature, in apparent disagreement with our data. However, since oxygen is a much more efficient quencher for the 2P emissions than N2 [28,29], the temperature dependence of the 2P(0,0) light yield in dry air is expected to be dominated by the temperature dependence of the rate constant for the deactivation of the C3 Pu ; v0 ¼ 0 state by the O2 molecules. 10. Conclusions
Fig. 9. Corrected coincidence rate as a function of temperature for the 2P(0,0) band of N2 . The pressures at room temperature are indicated for each case. The error bars represent only the statistical uncertainties.
9.2. Temperature dependence The temperature dependence of the 337.1 nm band in nitrogen was studied for different values of the gas density (kept constant during the cooling cycle). The measured R values (Eq. (16)) are represented in Fig. 9 as a function of T for two different values of gas density. They show a similar behavior, i.e., the 2P(0,0) band light yield decreases with the temperature. The quenching rate constant (in cm3 s1 ) may be written (see Eq. (12)) as pffiffiffi kq0 ¼ s0 T T a (18) assuming that the quenching cross-section follows a power law
s / Ta.
(19)
The ratio of the corrected coincidence rate (Eq. (16)) measured at room temperature to the corrected coincidence rate measured at
Detailed measurements, on the temperature dependence of 2P(0,0) band light yield in pure nitrogen, showed that the electronic quenching rate decreased with increasing temperature. Further studies for other molecular bands of the 2P and 1N system in N2 and dry air are underway in an attempt to clarify the mechanisms involved. This is particularly important for the air fluorescence detection of high energy cosmic rays but it is also relevant for the modeling of Earth’s middle and upper atmosphere.
Acknowledgments This work was supported by the Portuguese FCT under projects POCTI/FP/63440/2005 and POCTI/ FP/63913/2005.
References [1] K. Greisen, Phys. Rev. Lett. 16 (1966) 748; G. Zatsepin, V. Kuzmin, J. Exp. Theor. Phys. Lett. 4 (1966) 78. [2] K. Shinozaki, AGASA Collaboration, Nucl. Phys. B (Proc. Suppl.) 151 (2006) 3. [3] R.W. Springer, HiRes Collaboration, Nucl. Phys. B (Proc. Suppl.) 138 (2005) 307. [4] J. Abraham, Auger Collaboration, et al., Nucl. Instr. and Meth. A 523 (2004) 50. [5] I. Tatischeff, J. Chem. Phys. 52 (1970) 503. [6] M.E. Rudd, Phys. Rev. A 38 (1988) 6129. [7] J.F. Ziegler, J.M. Manoyan, Nucl. Instr. and Meth. B 35 (1988) 215.
ARTICLE IN PRESS 82
M.M. Fraga et al. / Nuclear Instruments and Methods in Physics Research A 597 (2008) 75–82
[8] L.J. Puckett, G.O. Taylor, D.W. Martin, Phys. Rev. A 178 (1969) 271. [9] E.S. Solov’ev, R.N. Il’in, V.A. Oparin, N.V. Fedorenko, Sov. Phys. J. Exp. Theor. Phys. 18 (1966) 342. [10] M. Zubek, J. Phys. B At. Mol. Opt. Phys. 27 (1994) 573. [11] D.J. Burns, F.R. Simpson, J.W. McConkey, J. Phys. B At. Mol. Phys. 2 (1969) 52. [12] G. Hartmann, P.C. Johnson, J. Phys. B 11 (1978) 1597. [13] J.M. Calo, R.C. Axtmann, J. Chem. Phys. 54 (1971) 1332. [14] G. Dilecce, P.F. Ambrico, S. De Benedictis, Chem. Phys. Lett. 431 (2006) 241. [15] A. Morozov et al., Proceedings of the 5th Fluorescence Workshop, Nucl. Instr. and Meth. A 597 (2008) 105. [16] S.N. Levine, Quantum Mechanics of Molecular Rate Processes, Clarendon Press, Oxford, 1969. [17] A.E. Belikov, O.V. Kusnetsov, R.G. Sharafutdinov, J. Chem. Phys. 102 (1995) 2792. [18] K.L. Steffens, D.R. Crosley, J. Chem. Phys. 112 (2000) 9427.
[19] M. Ave, et al., AIRFLY Collaboration, Proceedings of the 5th Fluorescence Workshop, Nucl. Instr. and Meth. A 597 (2008) 50. [20] A.E. Gru¨n, E. Schopper, Z. Naturforschg. 9A (1954) 134. [21] Photonis, PHOTOMULTIPLIER TUBES: Principles & applications, 2002 hhttp:// www.photonis.com/products/photomultiplier-tubes/application_booki. [22] A.S. Singh, A.G. Wright, IEEE Trans. Nucl. Sci. NS-34 (1987). [23] Melles Griot, hhttp://www.mellesgriot.com/pdf/0013.25-13.29.pdfi. [24] GEANT4-a simulation toolkit, Nucl. Instr. and Meth. A 506 (2003) 250. [25] T. Toyoda, M. Yabe, J. Phys. D Appl. Phys. 16 (1983) L97. [26] P.W. Erdman, E.C. Zipf, Appl. Opt. 27 (1988) 3318. [27] A. Morozov, et al., Eur. Phys. J. D 33 (2005) 207. [28] H. Brunet, These du doctorat, Univ. Paul Sabatier, Toulouse, France, 1973. [29] S.V. Pancheshnyi, S.M. Starikovskaia, A.Yu. Starikovskii, Chem. Phys. 262 (2000) 349.