- Email: [email protected]
Experimental studies of positive and negative atmospheric muons with a cosmic rays telescope
Astroparticle Physics 24 (2005) 183–190 www.elsevier.com/locate/astropart
Experimental studies of positive and negative atmospheric muons with a cosmic rays telescope M. Bahmanabadi a
a,*
, M. Khakian Ghomi b, F. Sheidaei
a
Department of Physics, Sharif university of Technology, P.O. Box 11365–9161, Tehran, Iran b Institute for Advanced Studies in Basic Sciences, P.O.Box 1159, Zanjan 45195, Iran Received 26 January 2005; received in revised form 12 June 2005; accepted 14 June 2005 Available online 14 July 2005
Abstract An experiment has been developed for the measurement of the muon charge ratio (ratio of positive to negative muons) in the cosmic ray flux in energy range 0.236–0.242 GeV. The muon charge ratio is found to be 1.35 ± 0.10 with a mean zenith angle of 32 ± 5. Meanwhile, the distributions of muons in zenith (h) and azimuth angles have been studied. A cosn h distribution with n = 1.95 ± 0.13 has been obtained. An asymmetry has been observed in East–West directions because of geomagnetic field. 2005 Elsevier B.V. All rights reserved. PACS: 96.40.Tv; 96.40.Kk; 14.60.Pq Keywords: Cosmic rays; Atmospheric muons; Muon charge ratio
1. Introduction Our Earth is continuously bombarded by primary cosmic ray particles. The primary cosmic rays hitting the top of the EarthÕs atmosphere are almost all protons or heavier atomic nuclei. These primary cosmic rays highly interact with the * Corresponding author. Tel.: +98216164501; fax: +98216005410. E-mail address: [email protected] (M. Bahmanabadi).
EarthÕs atmosphere and produce copious quantities of secondary particles. The most common secondary particles are baryons and mesons. Atmospheric muons mainly originate from the decay of charged pions and kaons. ACR þ AAir ! p ; p0 ; K ; other hadrons; p ! l þ ml ðml Þ 100% s0 ¼ 26 ns; K ! l þ ml ðml Þ 63.5% s0 ¼ 12 ns.
ð1Þ
Muons have a much longer lifetime than pions. A muon at rest has a mean lifetime about s0 = 2.197 ls. They do not interact very much at
0927-6505/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.astropartphys.2005.06.005
184
M. Bahmanabadi et al. / Astroparticle Physics 24 (2005) 183–190
all, and can penetrate through the air fairly easily arrive at the surface of the Earth. Muons mostly decay into electrons or positrons and their related neutrinos as following reactions: lþ ! eþ þ me þ ml ; l ! e þ me þ ml .
ð2Þ
The muon charge ratio, R = l+/l, is important in giving information about ‘‘the atmospheric neutrino problem’’, and for ‘‘the properties of hadronic interactions’’. A rough adding of the flavors in the decay chains lead to the ratio: Rm ¼
ml þ ml ¼ 2; me þ me
ð3Þ
but the ratio which observed by Kamiokande [1,2] is significantly lower than the expected value 2 [3,4]. This anomaly has been explained in terms of neutrino oscillations (ml ! ms) [1]. At the low energy range of muons (1 GeV), the muon charge ratio directly relates to the numbers of electronic neutrinos and antineutrinos lþ =l ¼ me =me [4], and since the interaction of neutrinos and antineutrinos with matter do in different ways [5], the muon charge ratio can be important for the response of neutrino detectors. Therefore for exact analysis of the experiments related to the ratio Rm, it is necessary precise knowledge of the contribution of each neutrino flavor. On the other hand the muon charge ratio provides important information on the interactions of the primary cosmic rays with nuclei in the atmosphere. Thus in addition to the particle physics aspects there are further perspectives of muon charge ratio studies which prepare a general knowledge of our environment. Meanwhile, since arrival directions of cosmic rays are essentially isotropic, the atmospheric flux of muons originating from the decay of charged pions and kaons produced by cosmic ray interactions in the atmosphere, is nearly isotropic as well. Nevertheless at lower muon energies it is influenced by the magnetic field of Earth. Thus a detailed understanding of the asymmetries of the fluxes of positive and negative muons is indispensable for doing reliable calculations of the atmospheric neutrino flux. The muon charge ratio is a quantity rather sensitive to effects of the geomagnetic field. Most of the
previous measurements, for obtaining the muon charge ratio, have been carried out using magnetic deflection to determine the muon charge with simultaneous determinations of the energy [6–8]. The other experimental approach is the method of delayed coincidences [9,10]. The magnetic spectrometers are difficult to use for very low energy, due to the large percentage of electrons present in the secondary cosmic rays and different acceptances for positive and negative particles. To avoid the difficulties and the systematic errors of magnetic spectrometers we use the second method which is based on the different interactions of positive and negative muons with matter. A cosmic rays telescope has been constructed for measuring the muon charge ratio at Sharif University of Technology in Tehran (3543 0 N, 5120 0 E). We used the second method for determination of muon charge ratio. The elevation of the site is 1200 m above sea level (890 g cm2). The purpose of the experiment is the investigation of the zenithal and azimuthal dependence of the muon charge ratio and as a consequence the mean muon charge ratio is determined.
2. The method When negative and positive muons are stopped in matter, they have different behaviors. The main idea of the delayed coincidence method is based on these behaviors. When positive muons are stopped in scintillator or any other material, they decay (Eq. (2)) or may form muonium (a hydrogen-like atom l+e), by the reaction lþ þ X ! ðlþ e Þ þ X þ .
ð4Þ
where X is any available molecule. However, the branching ratio for the mode (4) is only 1 part in 1010 [11], so that muonium formation does not effect on the decay rate appreciably. But for negative muons there is an alternative reaction in the presence of matter. The host atom captures the negative muon and forms a ‘‘muonic atom’’ [12]. Since muon is about 200 times more massive than electron, its orbit can be very close to the nucleus and can often be captured by the nucleus. In fact the negative muon interact with atomic nuclei
M. Bahmanabadi et al. / Astroparticle Physics 24 (2005) 183–190
according to the reaction l + p ! n + ml. Practically the entire energy liberated in this process is carried off by the neutrino and no signal will be produced in the detector. As a result the mean negative muon lifetime becomes 1=sl ¼ Kc þ 1=s0 , where Kc is the capture probability and s0 the decay lifetime for a free muon. The nuclear capture rate is proportional to Z4 and so becomes significant for sufficiently high Z atoms. Table 1 shows the mean life time and the decay probability of negative muon in some elements [13]. Thus, the muon charge ratio can be extracted from the measured decay curve, which is a superposition of the different lifetimes of negative muons in scintillator and the absorber material as well as positive muons. If there are no non-random backgrounds, the expected time spectrum is of the form " dN Nt 1 ¼ RS 0 expðt=s0 Þ dt s0 Rþ1 # X 1 þ S j expðt=sj Þ ; ð5Þ sj j where index 0 stands for positive muons, while the index j(1, 2, 3, . . .) indicates the negative muons decaying in the different absorber materials, R = l+/l represents the muon charge ratio, Nt is the total number of two muons, and the parameters S0 and Sj include the stopping powers of different materials, the decay probability for the negative muons and the efficiencies to detect the resulting electron or positron, which are determined by Monte-Carlo simulation. We can split Sj in S j ¼ S 0j P jdecay ;
ð6Þ
Table 1 Mean life time and decay probability of negative muon in some elements
Vacuum Carbon Oxygen Aluminum Silicon Lead
Mean life time (ns)
Decay probability (%)
2197.03 ± 0.04 2026.3 ± 1.5 1795.4 ± 2 864.0 ± 1 756.0 ± 1 75.4 ± 1
100.00 92.15 81.57 39.05 34.14 2.75
185
where only S 0j s are determined from the simulation and decay probabilities, P jdecay , are taken from Table 1. In order to reduce the number of free parameters of the fit, the mean life time and the probability of decay are extracted from Table 1. By fitting Eq. (5) on our experimental data, Nt and R are obtained.
3. Description of the telescope and experimental setup Configuration of the telescope and all detectors, modules and necessary connections for this experiment are summarized in Fig. 1. The telescope consists of three scintillators (100 · 14 · 1 cm3) placed on top of each other. The spacing of the top and bottom scintillators is 283 cm, and of the middle and bottom scintillators is 10 cm. A 7 cm thick aluminum block was placed between the middle and bottom scintillators. Its operation is initiated when an incoming muon passes through the top and middle scintillators. The generated signals from the PMTs are amplified in one stage (·10) with a fast amplifier (CAEN N412). Then the signals are connected to an 8-channel fast discriminator (CAEN N413A) which was operated at a fixed level of 20 mV. Each channel of the discriminator has two outputs; one of them is connected to a logic unit (CAEN N405) with a gate width of 150 ns. The output of the logic unit is connected to the start input of a TAC(ORTEC 566) by a 10 m cable. The stopped muon in the aluminum or the bottom scintillator decays at some later time (Fig. 1). The neutrinos from the decay leave the scintillator without any further effect. The electron (positron) leaves an ionization serial in the bottom scintillator, and as a consequence, the decay of the muon causes another signal. This pulse through the amplifier and discriminator is sent to the stop input of the TAC. Then the output of TAC which was set to a full scale of 10 ls is fed into a multichannel analyzer (MCA) via an analog to digital converter (ADC) unit. The time interval (Dt) between the start and stop signals is a measure of the muon lifetime. The cable to the start input of the TAC is approximately 10 m longer than the cable to the stop input. In its normal state, the
186
M. Bahmanabadi et al. / Astroparticle Physics 24 (2005) 183–190
Fig. 1. Configuration of the telescope and its electronic circuit.
TAC is ready to accept only a start pulse. It ignores the stop pulse, and the start pulse starts a timing run. The delay of the start pulse relative to the stop pulse by the 10 m of additional cable assures that the stop input is no longer activated when the pulse gets to the start input. The 10 m cable extension subtracts approximately 50 ns from the time recorded, but does not change the shape of the spectrum stored and the mean lifetime obtained from the slope of the spectrum. Our cosmic ray telescope is suitable for the measurement of zenith or azimuthal angular dependence of muon intensities, since it moves toward various directions. The geometrical acceptance
solid angle of the telescope is approximately 26 cm2 sr.
4. Experimental measurements and results We measured the decay spectrum of muons for 12 directions including the North, West, South and East and in the zenith angles of 20 ± 10, 40 ± 10, and 60 ± 10. The energy range of muons is 0.236–0.242 GeV. The measurements cover a total period of 1152 h. To compare the decay spectrum of different directions we changed direction of the telescope while all the rest of the
M. Bahmanabadi et al. / Astroparticle Physics 24 (2005) 183–190
setup (including distances of scintillators, voltages, thresholds, etc.) were kept untouched and equal exposure times were used. Fig. 2 shows the data obtained of different directions. By fitting the decay curve (Eq. (5)) on the data, Nt and R were determined. Note that Eq. (5) assumes we are able to view the entire muon decay spectrum, whereas the circuit logic of the present experiment forces us to blank out the first 30 channels (0.3 ls) of the muon spectrum. The omission of these few channels weights slightly the positive muon component which has the longer lifetime. Thus we have a small systematic error in the use of Eq. (5). On the other hand, there is another exponential which is due to the background from random coincidences. Nevertheless, due to the long lifetime of this exponential, the background is approximately uniformly distributed in the time window of 10 ls. Fig. 3 shows background subtracted.
187
Table 2 shows the muon charge ratio, R, obtained from the fitting for different directions. For all spectra the fit regression is more than 96%. Fig. 4 shows the differential zenith angle distribution of muons (Nt). The zenith angle distribution can be represented by IðhÞ ¼ Ið0Þcosn h with n = 1.95 ± 0.13. Azimuthal angular dependence of muons can be shown in the positive excess of muons in each azimuthal angle. We define the positive excess as follows: Positive excess ¼
Nþ N ; Nþ þ N
ð7Þ
where N+ and N show the number of positive and negative muons. The errors have been obtained by the following equation: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 r¼ þ N þ2 N þ N þ N 2 . ð8Þ ðN þ N Þ2
Fig. 2. Muon decay spectrum obtained of the different directions.
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M. Bahmanabadi et al. / Astroparticle Physics 24 (2005) 183–190
Fig. 3. Subtracted background of Fig. 2.
Table 2 The muon charge ratio, R, calculated for different directions
h = 20 h = 40 h = 60
North
West
South
East
1.26 1.32 1.62
1.43 1.67 1.73
1.27 1.34 1.48
1.22 1.24 1.11
The muon positive excess at various azimuthal angles is presented in Fig. 5, in the zenith angles 20 ± 10, 40 ± 10, and 60 ± 10. The error bars show the statistical errors only. The results show a pronounced East–West effect in the low energy range, which is consistent with other previous results [14]. The reduction of the positive excess in the east direction in relation to the west, in the low energy range is thought to be caused by the geomagnetic effect. The azimuthal anisotropy, A = (RW RE)/(RW + RE), (with RW and RE being the values
Fig. 4. The zenith angular dependence of muons.
M. Bahmanabadi et al. / Astroparticle Physics 24 (2005) 183–190
189
of the muon charge ratio measured in the west and east direction) is 0.12 in the energy range 0.236– 0.242 GeV, with a mean zenith angle 32 ± 5. From the present measurement results, we obtain R = 1.35 ± 0.10 with the calculated mean zenith angle 32 ± 5. The muon charge ratio results in the energy range up to 10 GeV from the various experiments have been compiled in Fig. 6 [15]. Our result has been shown with light circle. Our experiment has been done at 1200 m a.s.l. (Xv = 890 g cm2), while the rest of the muon charge ratio results in Fig. 6 are from sea level. But our measurements are with a mean zenith angle of h = 32 ± 5, so that the corresponding slant depth is X ’ X v =cos h ¼ 1049 g cm2 . Hence the muon charge ratio obtained of this experiment is comparable with those from sea level.
5. Conclusions
Fig. 5. The azimuthal angular dependence of the positive excess of muon for various zenith angles.
A cosmic ray telescope has been installed at Sharif University of Technology in Tehran for study of positive and negative atmospheric muons. By applying the method of delayed coincidences, we determined the charge ratio of cosmic ray muon in energy range 0.236–0.242 GeV. Our measurements indicate a muon charge ratio value of 1.35 ± 0.10 with a mean zenith angle of 32 ± 5. An East–West effect is observed at low energy,
Fig. 6. Some selected measurements on the muon charge ratio in the energy range up to 10 GeV [15]. Light circle shows our measurement.
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M. Bahmanabadi et al. / Astroparticle Physics 24 (2005) 183–190
which is due to the geomagnetic field. The East– West effect can be shown by the anisotropy quantity A = (RW RE)/(RW + RE) which has been found to be 0.12 in the energy range 0.236– 0.242 GeV. The zenith angle of the arrival direction of muons obeys a cosn h law with n = 1.95 ± 0.13 in this energy range.
[2] [3] [4] [5] [6] [7] [8] [9]
Acknowledgement This research has been partly supported by Grant No. NRCI 1853 of National Research Council of Islamic Republic of Iran.
[10] [11] [12] [13]
References [1] Y. Fukuda et al., Phys. Lett. B 436 (1998) 33, Phys. Rev. Lett. 81, 1562.
[14] [15]
K.S. Hirata et al., Phys. Lett. B 205 (1988) 416. T.K. Gaisser, T. Stanev, Phys. Rev. D 38 (1998) 85. M. Honda et al., Phys. Rev. D 52 (1995) 4985. P. Lipari, Astropart. Phys. 1 (1995) 195. G. Tarle et al., in: Proc. 25th ICRC, Durban, South Africa, vol. 6, 1997, p. 321. G. Basini et al., in: Proc. 22nd ICRC, Dublin, Ireland, vol. 4, 1991, p. 544. S.A. Stephens, R.L. Golden, in: Proc. 20th ICRC, Moscow, Russia, vol. 6, 1987, p. 173. I.M. Brancus et al., in: Proc. 27th ICRC, Hamburg, Germany, HE2, 2001, p. 1187. C.P Achenbach, J.H. Cobb, in: Proc. 27th ICRC, Hamburg, Germany, HE2, 2001, p. 1313. V.W. Hughes, T. Kinoshita, Muon Physics, in: V.W. Hughes, C.S. Wu (Eds.), Academic Press, 1977, p. 89. J. Hufner, F. Scheck, C.S. Wu, Muon Physics, in: V.W. Hughes, C.S. Wu (Eds.), Academic Press, 1977. T. Suzuki, D.F. Measday, J.P. Roalsvig, Phys. Rev. C 35 (1987) 2212. S. Tsuji et al., Proc. 26th ICRC, Salt Lake City, Utah, USA, vol. 2, 1999, p. 52. B. Volpescu et al., Report FZKA 6071, Forschungszentrum Karlsruhe, 1998.
Experimental studies of positive and negative atmospheric muons with a cosmic rays telescope M. Bahmanabadi a
a,*
, M. Khakian Ghomi b, F. Sheidaei
a
Department of Physics, Sharif university of Technology, P.O. Box 11365–9161, Tehran, Iran b Institute for Advanced Studies in Basic Sciences, P.O.Box 1159, Zanjan 45195, Iran Received 26 January 2005; received in revised form 12 June 2005; accepted 14 June 2005 Available online 14 July 2005
Abstract An experiment has been developed for the measurement of the muon charge ratio (ratio of positive to negative muons) in the cosmic ray flux in energy range 0.236–0.242 GeV. The muon charge ratio is found to be 1.35 ± 0.10 with a mean zenith angle of 32 ± 5. Meanwhile, the distributions of muons in zenith (h) and azimuth angles have been studied. A cosn h distribution with n = 1.95 ± 0.13 has been obtained. An asymmetry has been observed in East–West directions because of geomagnetic field. 2005 Elsevier B.V. All rights reserved. PACS: 96.40.Tv; 96.40.Kk; 14.60.Pq Keywords: Cosmic rays; Atmospheric muons; Muon charge ratio
1. Introduction Our Earth is continuously bombarded by primary cosmic ray particles. The primary cosmic rays hitting the top of the EarthÕs atmosphere are almost all protons or heavier atomic nuclei. These primary cosmic rays highly interact with the * Corresponding author. Tel.: +98216164501; fax: +98216005410. E-mail address: [email protected] (M. Bahmanabadi).
EarthÕs atmosphere and produce copious quantities of secondary particles. The most common secondary particles are baryons and mesons. Atmospheric muons mainly originate from the decay of charged pions and kaons. ACR þ AAir ! p ; p0 ; K ; other hadrons; p ! l þ ml ðml Þ 100% s0 ¼ 26 ns; K ! l þ ml ðml Þ 63.5% s0 ¼ 12 ns.
ð1Þ
Muons have a much longer lifetime than pions. A muon at rest has a mean lifetime about s0 = 2.197 ls. They do not interact very much at
0927-6505/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.astropartphys.2005.06.005
184
M. Bahmanabadi et al. / Astroparticle Physics 24 (2005) 183–190
all, and can penetrate through the air fairly easily arrive at the surface of the Earth. Muons mostly decay into electrons or positrons and their related neutrinos as following reactions: lþ ! eþ þ me þ ml ; l ! e þ me þ ml .
ð2Þ
The muon charge ratio, R = l+/l, is important in giving information about ‘‘the atmospheric neutrino problem’’, and for ‘‘the properties of hadronic interactions’’. A rough adding of the flavors in the decay chains lead to the ratio: Rm ¼
ml þ ml ¼ 2; me þ me
ð3Þ
but the ratio which observed by Kamiokande [1,2] is significantly lower than the expected value 2 [3,4]. This anomaly has been explained in terms of neutrino oscillations (ml ! ms) [1]. At the low energy range of muons (1 GeV), the muon charge ratio directly relates to the numbers of electronic neutrinos and antineutrinos lþ =l ¼ me =me [4], and since the interaction of neutrinos and antineutrinos with matter do in different ways [5], the muon charge ratio can be important for the response of neutrino detectors. Therefore for exact analysis of the experiments related to the ratio Rm, it is necessary precise knowledge of the contribution of each neutrino flavor. On the other hand the muon charge ratio provides important information on the interactions of the primary cosmic rays with nuclei in the atmosphere. Thus in addition to the particle physics aspects there are further perspectives of muon charge ratio studies which prepare a general knowledge of our environment. Meanwhile, since arrival directions of cosmic rays are essentially isotropic, the atmospheric flux of muons originating from the decay of charged pions and kaons produced by cosmic ray interactions in the atmosphere, is nearly isotropic as well. Nevertheless at lower muon energies it is influenced by the magnetic field of Earth. Thus a detailed understanding of the asymmetries of the fluxes of positive and negative muons is indispensable for doing reliable calculations of the atmospheric neutrino flux. The muon charge ratio is a quantity rather sensitive to effects of the geomagnetic field. Most of the
previous measurements, for obtaining the muon charge ratio, have been carried out using magnetic deflection to determine the muon charge with simultaneous determinations of the energy [6–8]. The other experimental approach is the method of delayed coincidences [9,10]. The magnetic spectrometers are difficult to use for very low energy, due to the large percentage of electrons present in the secondary cosmic rays and different acceptances for positive and negative particles. To avoid the difficulties and the systematic errors of magnetic spectrometers we use the second method which is based on the different interactions of positive and negative muons with matter. A cosmic rays telescope has been constructed for measuring the muon charge ratio at Sharif University of Technology in Tehran (3543 0 N, 5120 0 E). We used the second method for determination of muon charge ratio. The elevation of the site is 1200 m above sea level (890 g cm2). The purpose of the experiment is the investigation of the zenithal and azimuthal dependence of the muon charge ratio and as a consequence the mean muon charge ratio is determined.
2. The method When negative and positive muons are stopped in matter, they have different behaviors. The main idea of the delayed coincidence method is based on these behaviors. When positive muons are stopped in scintillator or any other material, they decay (Eq. (2)) or may form muonium (a hydrogen-like atom l+e), by the reaction lþ þ X ! ðlþ e Þ þ X þ .
ð4Þ
where X is any available molecule. However, the branching ratio for the mode (4) is only 1 part in 1010 [11], so that muonium formation does not effect on the decay rate appreciably. But for negative muons there is an alternative reaction in the presence of matter. The host atom captures the negative muon and forms a ‘‘muonic atom’’ [12]. Since muon is about 200 times more massive than electron, its orbit can be very close to the nucleus and can often be captured by the nucleus. In fact the negative muon interact with atomic nuclei
M. Bahmanabadi et al. / Astroparticle Physics 24 (2005) 183–190
according to the reaction l + p ! n + ml. Practically the entire energy liberated in this process is carried off by the neutrino and no signal will be produced in the detector. As a result the mean negative muon lifetime becomes 1=sl ¼ Kc þ 1=s0 , where Kc is the capture probability and s0 the decay lifetime for a free muon. The nuclear capture rate is proportional to Z4 and so becomes significant for sufficiently high Z atoms. Table 1 shows the mean life time and the decay probability of negative muon in some elements [13]. Thus, the muon charge ratio can be extracted from the measured decay curve, which is a superposition of the different lifetimes of negative muons in scintillator and the absorber material as well as positive muons. If there are no non-random backgrounds, the expected time spectrum is of the form " dN Nt 1 ¼ RS 0 expðt=s0 Þ dt s0 Rþ1 # X 1 þ S j expðt=sj Þ ; ð5Þ sj j where index 0 stands for positive muons, while the index j(1, 2, 3, . . .) indicates the negative muons decaying in the different absorber materials, R = l+/l represents the muon charge ratio, Nt is the total number of two muons, and the parameters S0 and Sj include the stopping powers of different materials, the decay probability for the negative muons and the efficiencies to detect the resulting electron or positron, which are determined by Monte-Carlo simulation. We can split Sj in S j ¼ S 0j P jdecay ;
ð6Þ
Table 1 Mean life time and decay probability of negative muon in some elements
Vacuum Carbon Oxygen Aluminum Silicon Lead
Mean life time (ns)
Decay probability (%)
2197.03 ± 0.04 2026.3 ± 1.5 1795.4 ± 2 864.0 ± 1 756.0 ± 1 75.4 ± 1
100.00 92.15 81.57 39.05 34.14 2.75
185
where only S 0j s are determined from the simulation and decay probabilities, P jdecay , are taken from Table 1. In order to reduce the number of free parameters of the fit, the mean life time and the probability of decay are extracted from Table 1. By fitting Eq. (5) on our experimental data, Nt and R are obtained.
3. Description of the telescope and experimental setup Configuration of the telescope and all detectors, modules and necessary connections for this experiment are summarized in Fig. 1. The telescope consists of three scintillators (100 · 14 · 1 cm3) placed on top of each other. The spacing of the top and bottom scintillators is 283 cm, and of the middle and bottom scintillators is 10 cm. A 7 cm thick aluminum block was placed between the middle and bottom scintillators. Its operation is initiated when an incoming muon passes through the top and middle scintillators. The generated signals from the PMTs are amplified in one stage (·10) with a fast amplifier (CAEN N412). Then the signals are connected to an 8-channel fast discriminator (CAEN N413A) which was operated at a fixed level of 20 mV. Each channel of the discriminator has two outputs; one of them is connected to a logic unit (CAEN N405) with a gate width of 150 ns. The output of the logic unit is connected to the start input of a TAC(ORTEC 566) by a 10 m cable. The stopped muon in the aluminum or the bottom scintillator decays at some later time (Fig. 1). The neutrinos from the decay leave the scintillator without any further effect. The electron (positron) leaves an ionization serial in the bottom scintillator, and as a consequence, the decay of the muon causes another signal. This pulse through the amplifier and discriminator is sent to the stop input of the TAC. Then the output of TAC which was set to a full scale of 10 ls is fed into a multichannel analyzer (MCA) via an analog to digital converter (ADC) unit. The time interval (Dt) between the start and stop signals is a measure of the muon lifetime. The cable to the start input of the TAC is approximately 10 m longer than the cable to the stop input. In its normal state, the
186
M. Bahmanabadi et al. / Astroparticle Physics 24 (2005) 183–190
Fig. 1. Configuration of the telescope and its electronic circuit.
TAC is ready to accept only a start pulse. It ignores the stop pulse, and the start pulse starts a timing run. The delay of the start pulse relative to the stop pulse by the 10 m of additional cable assures that the stop input is no longer activated when the pulse gets to the start input. The 10 m cable extension subtracts approximately 50 ns from the time recorded, but does not change the shape of the spectrum stored and the mean lifetime obtained from the slope of the spectrum. Our cosmic ray telescope is suitable for the measurement of zenith or azimuthal angular dependence of muon intensities, since it moves toward various directions. The geometrical acceptance
solid angle of the telescope is approximately 26 cm2 sr.
4. Experimental measurements and results We measured the decay spectrum of muons for 12 directions including the North, West, South and East and in the zenith angles of 20 ± 10, 40 ± 10, and 60 ± 10. The energy range of muons is 0.236–0.242 GeV. The measurements cover a total period of 1152 h. To compare the decay spectrum of different directions we changed direction of the telescope while all the rest of the
M. Bahmanabadi et al. / Astroparticle Physics 24 (2005) 183–190
setup (including distances of scintillators, voltages, thresholds, etc.) were kept untouched and equal exposure times were used. Fig. 2 shows the data obtained of different directions. By fitting the decay curve (Eq. (5)) on the data, Nt and R were determined. Note that Eq. (5) assumes we are able to view the entire muon decay spectrum, whereas the circuit logic of the present experiment forces us to blank out the first 30 channels (0.3 ls) of the muon spectrum. The omission of these few channels weights slightly the positive muon component which has the longer lifetime. Thus we have a small systematic error in the use of Eq. (5). On the other hand, there is another exponential which is due to the background from random coincidences. Nevertheless, due to the long lifetime of this exponential, the background is approximately uniformly distributed in the time window of 10 ls. Fig. 3 shows background subtracted.
187
Table 2 shows the muon charge ratio, R, obtained from the fitting for different directions. For all spectra the fit regression is more than 96%. Fig. 4 shows the differential zenith angle distribution of muons (Nt). The zenith angle distribution can be represented by IðhÞ ¼ Ið0Þcosn h with n = 1.95 ± 0.13. Azimuthal angular dependence of muons can be shown in the positive excess of muons in each azimuthal angle. We define the positive excess as follows: Positive excess ¼
Nþ N ; Nþ þ N
ð7Þ
where N+ and N show the number of positive and negative muons. The errors have been obtained by the following equation: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 r¼ þ N þ2 N þ N þ N 2 . ð8Þ ðN þ N Þ2
Fig. 2. Muon decay spectrum obtained of the different directions.
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M. Bahmanabadi et al. / Astroparticle Physics 24 (2005) 183–190
Fig. 3. Subtracted background of Fig. 2.
Table 2 The muon charge ratio, R, calculated for different directions
h = 20 h = 40 h = 60
North
West
South
East
1.26 1.32 1.62
1.43 1.67 1.73
1.27 1.34 1.48
1.22 1.24 1.11
The muon positive excess at various azimuthal angles is presented in Fig. 5, in the zenith angles 20 ± 10, 40 ± 10, and 60 ± 10. The error bars show the statistical errors only. The results show a pronounced East–West effect in the low energy range, which is consistent with other previous results [14]. The reduction of the positive excess in the east direction in relation to the west, in the low energy range is thought to be caused by the geomagnetic effect. The azimuthal anisotropy, A = (RW RE)/(RW + RE), (with RW and RE being the values
Fig. 4. The zenith angular dependence of muons.
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of the muon charge ratio measured in the west and east direction) is 0.12 in the energy range 0.236– 0.242 GeV, with a mean zenith angle 32 ± 5. From the present measurement results, we obtain R = 1.35 ± 0.10 with the calculated mean zenith angle 32 ± 5. The muon charge ratio results in the energy range up to 10 GeV from the various experiments have been compiled in Fig. 6 [15]. Our result has been shown with light circle. Our experiment has been done at 1200 m a.s.l. (Xv = 890 g cm2), while the rest of the muon charge ratio results in Fig. 6 are from sea level. But our measurements are with a mean zenith angle of h = 32 ± 5, so that the corresponding slant depth is X ’ X v =cos h ¼ 1049 g cm2 . Hence the muon charge ratio obtained of this experiment is comparable with those from sea level.
5. Conclusions
Fig. 5. The azimuthal angular dependence of the positive excess of muon for various zenith angles.
A cosmic ray telescope has been installed at Sharif University of Technology in Tehran for study of positive and negative atmospheric muons. By applying the method of delayed coincidences, we determined the charge ratio of cosmic ray muon in energy range 0.236–0.242 GeV. Our measurements indicate a muon charge ratio value of 1.35 ± 0.10 with a mean zenith angle of 32 ± 5. An East–West effect is observed at low energy,
Fig. 6. Some selected measurements on the muon charge ratio in the energy range up to 10 GeV [15]. Light circle shows our measurement.
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which is due to the geomagnetic field. The East– West effect can be shown by the anisotropy quantity A = (RW RE)/(RW + RE) which has been found to be 0.12 in the energy range 0.236– 0.242 GeV. The zenith angle of the arrival direction of muons obeys a cosn h law with n = 1.95 ± 0.13 in this energy range.
[2] [3] [4] [5] [6] [7] [8] [9]
Acknowledgement This research has been partly supported by Grant No. NRCI 1853 of National Research Council of Islamic Republic of Iran.
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