Table Of ContentXXV European Cosmic Ray Symposium, Turin, Sept. 4-9 2016 1
Measurement of the muon-induced neutron seasonal modulation with LVD
N. Yu. Agafonova on behalf of the LVD Collaboration
Institute for Nuclear Research RAS, prospekt 60-letiya Oktyabrya 7a, Moscow, Russia
Cosmic ray muons with the average energy of 280 GeV and neutrons produced by muons are
detectedwiththeLargeVolumeDetectoratLNGS.Wepresentananalysisoftheseasonalvariation
of the neutron flux on the basis of the data obtained during 15 years. The measurement of the
seasonal variation of the specific number of neutrons generated by muons allows to obtaine the
variation magnitude of of the average energy of the muon flux at the depth of the LVD location.
The source of the seasonal variation of the total neutron flux is a change of the intensity and the
7 average energy of themuon flux.
1
0
2
I. INTRODUCTION forming 7 levels and 5 column.
n Muons passing throughthe LVD generate hadronic
a As it is known, there is seasonal variation of the and electromagnetic showers, which include neutrons
J
muon flux at the sea level and underground [1]. The produced in πA (hadronic showers) and γA (elec-
7 variationiscausedbythetemperatureandbarometric tromagnetic showers) interactions. The neutrons are
1
effects associatedwith the increase ofthe atmosphere slowed down in a scintillation counters and captured
] altitude insummeranddecreaseofitinwinter. Tem- by protons (n+p→d+γ, Eγ =2.2 MeV) or by iron
E perature effect infuences the muon production in the nuclei (n+Fe→Fe+γ, where the summed average
H π/K- decays, barometric effect influences the muon energyΣEγ is about8 MeV). The neutronlifetime in
. decays. For high-energy muons, which we detect at scintillatorisabout200microseconds. Thetriggerfor
h 3650 m w.e. underground there is a positive temper- theneutrondetectionistheenergyreleaseinacounter
p
- ature effect. It is associated with the fact that far more than 50 MeV. Trigger opens the time gate of 1
o underground penetrate, mainly, muons from pions of ms for detection of γ-quanta at energy threshold of
r the first generation, the number of which increases 0.5 MeV.
t
s when the atmosphere density of the upper layers (at
a
[ the altitude ∼ 20 km) falls due to expansion of the
atmosphere. III. DATA ANALYSIS
1
Measurementsofthe muonintensity variationdeep
v
undergroundwereperformedbyexperimentsMACRO We analyzed the whole available data set with the
0
2 [2], MINOS [3], AMANDA [4], LVD [5], IceCube [6], detector in its final configuration, starting in 1 Jan-
6 Borexino [7]. uary 2001 and ending in October 2016.
4 In the LVD papers [5], [8] the seasonal modulation We have chosen good inner counters in all three
0 of the muon intensity and the variation of the neu- towers. We have selected from muon data counters
1. trons produced by muons in the LVD material were hittingbymuontrigger(Etr >50MeV,0<ttr <250
0 presented. The variation amplitude of the muon flux ns). In hitting counters we search for gamma-quanta
7 intensityIµ =1.5%andphaseφ=185±15weremea- pulses at the energy from 1.5 to 12 MeV within time
1 suredduring8yearsofobservations. Moreover,itwas window50-350µs. Thesepulses(N )areproduced
tot
:
v obtained that the amplitude of the neutron number by neutrons and background.
i variation is higher than the muon intensity modula- In the analysis of neutron seasonal variation, we
X
tion amplitude almost 10 times as much in Ref.[9]. used the value N /N (specific number of muon-
n tr
r The purpose of this work is to determine more accu- induced neutrons), where N is the number of neu-
a n
rately the magnitude of amplitude and phase of the trons detected in a counter and N is the number of
tr
muon-induced neutron seasonalmodulation. triggers(number of muons crossing a counter). Using
this value we can determine the variation amplitude
without taken into account the LVD acceptance, the
II. LVD DESCRIPTION neutron detection efficiency, and data gaps for short-
term shutdown of counters.
TheLVD(LargeVolumeDetector)islocatedinun-
dergroundlaboratoryin GranSasso(Italy)atthe av-
erage depth of hHi = 3650 m w.e. [10]. The LVD is IV. DETERMINATION OF THE VARIATION
multipurpose experiment, whose the main goal is the AMPLITUDE OF THE NUMBER OF THE
search for neutrino flux from the stellar core gravita- MUON-INDUCED NEUTRONS
tional collapse. According to this program, the de-
tector works since 1992 [11]. The LVD consists of We used two methods to determine the variation
3
3 towers containing 840 scintillation 1.5 m counters amplitude. These are the Epoch folding method and
eConf C16-09-04.3
2 XXV European Cosmic Ray Symposium, Turin, Sept. 4-9 2016
χχ22 // nnddff 443399..66 // 118888
m
nor1.6 AA 00..11002255 ±± 00..000088228877
)
Ntr pphhaassee 77..446677 ±± 00..11559944
/n
N
( 1.4
1.2
1
0.8
0.6
0.4
0 20 40 60 80 100 120 140 160 180
Month
FIG. 1: The temporal behaviour of the value Nn/Ntr. The curve is the best fit with function f(t) = A×cos(2π(t−
φ)/T)+1. Parameters A and φ are free, T = 12 months.
the Residual method. χχ22 // nnddff 88..339977 // 1100
)Ntrnorn 1.1 AApphh aa ss ee 00..007777 666677..99 ±±77 6600 ..±±00 000088..225544667733
A. Epoch folding method /Nn
(1.05
Muon events in the inner LVD counters during 15
1
years(190 month) of observations were analyzed. We
determinedthe number N for a counterduring each
tr 0.95
monthandthenumberN ofneutronswithin50-350
n
µs.
0.9
Toavoidbackgroundwe assumethatallpulses N
bg
within time interval of 450 - 750 µs are due to back- 0 2 4 6 8 10 12
Progressive month
ground and number of background pulses within in-
terval of 50 - 350 µs is equal to the N number.
bg
The specific number of muon-induced neutrons FIG.2: Superpositionofthemeanmonthly(Nn/Ntr)norm
values. The fitting curve is function f(t) = 1 + A ×
N /N =(N −N )/N , where N =N +N ,
n tr tot bg tr tot n bg cos(2π(t−φ)/T). Parameter T = 12 months is fix. Pa-
was determined for each month. In Figure 1 the
rameters A and φ are free.
N /N values are normalized per average year value
n tr
<N /N >.
n tr
TheEpochfoldingmethodallowstoobtaintheam-
plitude modulation δN /N and phase φ with suffi-
n n
cient accuracy. To do this annual data for the fifteen
years of observations are superposed on one another.
The result of the procedure is presented in Figure 2.
When fitting the histogram on Figure 2 by the equa-
tion N(t)=1+δN /N ×cos(2π(t−φ)/T) for fixed The resulting phase is φ = 7.0±0.4(stat)±0.5(sys)
n n
T =12monthsitwasobtainedδN /N =7.7±0.8%. month.
n n
eConf C16-09-04.3
XXV European Cosmic Ray Symposium, Turin, Sept. 4-9 2016 3
obtained.
V. THE MODULATION AMPLITUDE δE OF
THE AVERAGE MUON ENERGY AT THE
DEPTH OF 3650 M W.E.
Thenumberofneutronsgeneratedbymuonfluxde-
scribed by dependence N ∝ E0.78 [12], where E is
n µ µ
the average energy of the muon flux. Thus, the neu-
tron number increasing in summer can be expressed
as: (N +δN )/N =((E +δE )/E )0.78.
n n n µ µ µ
Substituting the measured value δN /N = 0.077
n n
(the value determined by two methods), we obtained
(δE /E )(1+0.077)1/0.78−1≈0.10. So,the average
µ µ
energy of the muon flux at the LVD depth increases
by 10% in summer.
Consequently, the flux of muon-induced neutrons
undergoes seasonal variation under the influence of
two factors: a) change of muon intensity, b) change
FIG. 3: Time distribution of the gamma-quantum pulses of muon average energy. The factor b) is dominant.
within 50−550µs for winter (upper panel) and summer Thus,themodulationamplitudeδΦ ofthetotalneu-
n
(lower panel) months. The fitting curve is f(t) = N0 × tron flux Φ is δΦ = (1+δI )×(1+δN )−1 =
exp(−t/τ)+B. 1.015×1.07n7−1=n0.093, i.e. δµΦ (I ,N )=n9.3%.
n µ n
B. Residual method
VI. CONCLUSION
Largestatisticsallowstodeterminewithgoodaccu-
The seasonal variation of muon-induced neutrons
racythenumberofmuon-inducedneutrons,whichare
per muonwasfound onthe basisofdata for 15years.
produced during summer and winter months. To do
this, we use the time distribution of gamma-quantum The measured characteristics of the neutron varia-
pulses in the energy range 1 −12 MeV in the time tion indicate seasonal variation in the average energy
interval of 50−550µs after the muon trigger for 45 of muons at the LVD depth with amplitude of 10%,
summer months (June, July, August) and 45 winter i.e. Eµ =280±28 GeV.
months (December, January, February). Previously it was assumed that the flux of cosmo-
Time distributions were approximated using law genic neutrons is proportional to the amplitude of
Nn(t) = N0 × exp(−t/τ) + B, where τ = 170 µs muon intensity variation 1.5%. We have shown that
is exponent of gamma-quantum distribution, B is the neutron flux has an amplitude of seasonal varia-
a constant depending on the background conditions tionin6timesmore,becausetheaveragemuonenergy
of counters, N0 × τ is the total number neutrons also varies with the amplitude of ∼10%.
(Figure 3). It was found that the specific num-
ber of neutrons per a counter for summer months
is Nn/Ntsr = 111814/18695762 = 5.98×10−3 , and Acknowledgments
N /Nw = 90143/17597826= 5.12×10−3 for winter
n tr
months.
This work was supported by the Russian Founda-
The variation amplitude (δN /N ) was defined
n n tion for Basic Research (project No. 15-02-01056 a)
as half a difference between the neutron specific
and the program of investigations of the Presidium
number in summer (s) and winter (w), divided
of Russian Academy of Sciences High Energy Physics
by the average value: δN /N = 0.5(Ns/Ns −
n n n tr and Neutrino Astrophysics.
Nw/Nw)/0.5(Ns/Ns + Nw/Nw). The value
n tr n tr n tr
δN /N = 0.077±0.002 (stat.) ± 0.016 (sys.) was
n n
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