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

2. 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

3. 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.

4. 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
Вид сбоку
Veto-system

5. 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
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;

6. 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 Nn
Ncount
151640
552
40ns

8. 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.

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

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

11. 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
= – 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

12. - 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.

13. 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 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

14. The spectrum of the detected energy releases

15. 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)

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