of Neutrons produced by The Energy Spectrum of Neutrons produced by Cosmic Ray Muons in LVD.

Детектор большого объема Гран Сассо, Италия Длина 22.7 м Ширина 13.2 м Высота 10 м Масса железа 1020 т Объем сцинтиллятора 1260 м3 Масса сцинтиллятора 1008 т Число сцинт. счетчиков 840 Число PMTs (ФЭУ) 2520 Глубина 3300 м.в.э. Средняя энергия мюонов 280 ГэВ

Assumptions: The pulses at energy > 10 MeV in the temporal range 0 – 0.25 s after t-muon in counters of d-volume are the neutron energy releases. These pulses are produced by a single neutron (in correspondence with data on neutron yield from muons a probability for 2 neutrons is 3%). The neutrons come out from t-column and pass through d-volume are isotropic in 2. Horizontal gaps between the d-volume counters weekly change the efficiency of a fast neutron detection. The role of Fe at determination of the spectrum and the flux of fast neutrons is insignificant.

Geometry L=7 L=6 L=5 L=4 L=3 L=2 L=1 1 2 3 4 5 6 7 8 9 10 d-volume Target column Geometry Вид сверху C=1 C=2 C=3 C=4 C=5 L=7 L=6 L=5 L=4 L=3 L=2 L=1 1 2 3 4 5 6 7 8 9 10 Вид сбоку Veto-system

T- criterea L=7 L=6 D- criterea L=5 L=4 L=3 L=2 L=1 Selection of vertical muons crossing target column а) E50 MeV in counters of L=1 and L=7; b) E>50 MeV L=3 & 4 or L=4 & 5 or L=3 & 5; c) Amount of triggering counters with E50MeV Ntr 5 C=1 C=2 C=3 C=4 C=5 L=7 L=6 L=5 L=4 L=3 L=2 L=1 1 2 3 4 5 6 7 8 9 10 D- criterea Selection of neutron events а) Amount of counters in d–volume N4 b)  Ei350MeV in counters of d-volume c) Should be no events with E>100 MeV in counters on the same vertical – to exclude parallel muon crossing d-volume а) in veto counters should be no events with E>100 MeV;

L=7 L=6 L=5 L=4 L=3 L=2 L=1 Ncount 1 2 3 4 5 6 7 8 9 10 C=1 C=2 C=3 C=4 C=5 L=7 L=6 L=5 L=4 L=3 L=2 L=1 1 2 3 4 5 6 7 8 9 10 Nn Ncount 151640 552 40ns

1 2 3 4 5 6 7 8 9 10

Distribution of neutron stoppings over half column (hc) The half column containing neutron stop is a last one from t-column where a neutron pulse appears. -a transmittance of the LVD matter for fast neutrons, =0.779 – best fit of the neutron stopping distribution. In such a case, at the mean neutron range in LVD matter Ln=12m*0.59=7.1 m the average neutron pass length in hc is lhc=1.8 m.

The coefficient k2 takes into account the number of operating counters in target column (~54 from 60) - the fast neutron detection efficiency

Calculations using previous formula. t s 1d 2d 3d 4d 5d 6d 1 1.7 2.7 3.7 4.4 5.4 6.4 7.1 8.1 9.1 m Calculations using previous formula.

The neutron flux at energy 20< Tn< 450MeV The neutron flux from the target column surface producing by a vertical muon in target column - the area of the neutron emitting surface of target column = 151640 – total amount of vertical muons crossing target column = 5400 – total amount of neutrons - the neutron flux from the target column surface, producing by the total flux passing t-c - average number of counters in target column - average number of counters in target column crossing by vertical muons

- the neutron flux from the target column surface, producing by the total flux of muons passing t-c G = 63 м2 sr – the geometric factor of target column for the total muon flux.

Configurations of data set (variants of choice of t-column) C=1 C=2 C=3 C=4 C=5 L=7 L=6 L=5 L=4 L=3 L=2 L=1 1 2 3 4 5 6 7 8 9 10 n Configurations of data set (variants of choice of t-column) C=1 C=2 C=3 C=4 C=5 L=7 L=6 L=5 L=4 L=3 L=2 L=1 1 2 3 4 5 6 7 8 9 10

The spectrum of the detected energy releases

The distributions of the neutron energy releases in SC at fixed Tn. Tn=20 MeV Tn=100 MeV Tn=180 MeV Tn=260 MeV Tn=60 MeV Tn=140 MeV Tn=220 MeV Tn=300 MeV The correspondence between Tn and a neutron energy En in scintillator; Black squares – MonteCarlo simulation at quenching, Red circles – without quenching, Green circles – calculations using the SHIELD code (Nikolay Sobolevskiy)

The differential energy spectrum of neutrons Фn ( Tn ) Фn , m-2 s-1 (10MeV)-1