Reporting of response function of
a TOF - spectrometer
EC – JRC – IRMM
SG – 36, 23 – 05 -2012, WPEC, NEA Paris
Time-of-flight technique
Target- moderator
assembly
Detector
L
pulsed
e- - beam
Sample
T0
Ts
tm = (Ts – T0) + to
L
v
tm


1
E  mnc 
 1
 1  (v / c)2



2
Response of TOF-spectrometer
Target- moderator
assembly
pulsed
e- - beam
Detector
L
v
Sample
T0
Ts
tm = (Ts – T0) + to
t = tm – ( tt +td )
v
L
t
Response of TOF-spectrometer
v=
v

v
L
t
t 2
t
2

L2

E  m c 2 (  -1)

E
v
 (   1)
E
v
L2
L
v
 L ( 1 mm)
 t
• Initial burst width
T0
• Time jitter detector & electronics
Ts
• Neutron transport in target - moderator tt
• Neutron transport in detector
td
T0
Ts
t = tm – ( tt +td )
Response of TOF-spectrometer
v=
v

v
L
t
t 2
t
2

L2

E  m c 2 (  -1)

E
v
 (   1)
E
v
L2
L
v
 L ( 1 mm)
 t
• Initial burst width
T0
• Time jitter detector & electronics
Ts
• Neutron transport in target - moderator tt
• Neutron transport in detector
td
T0
Ts
t = tm – ( tt +td )
Probability distribution of tt : GELINA
10
0
0.01 - 0.02 eV
1 - 2
eV
1 - 2 keV
100 - 125 keV
-2
x 10
-3
R(tt,E)
x 10
10
-1
10
-2
10
-3
10
-1
x 10
-3
10
-2
-1
0
10
10
Time, tt / s
10
1
10
2
Flaska et al.,NIM , A531, 394 (2004)
Characteristics of P(tt) for GELINA
2
2
10
10
Most propable
Average
1
1
10
Width / s
tt / s
10
0
10
-1
10
0
10
-1
10
-2
10
-2
-3
10
10
10
FWHM
2.35 x 
0.5
1.6 / (E / 1 eV)
-3
-2
10
-1
10
0
1
2
3
4
10 10 10 10 10
Neutron Energy / eV
5
10
-2
10
-1
10
0
1
2
3
4
10 10 10 10 10
Neutron Energy / eV
5
10
Equivalent distance : Lt = v tt
dL t
dt t
1 5 eV
100 - 500 eV
1000 - 2000 eV
6000 - 8000 eV
10000 - 20000 eV
60000 - 80000 eV
0.4
Probability desinsity
P(t t ,En )  P'(L t (t t ) , En )
0.3
1 - 5 eV
0.4
0.2
0.3
0.2
2 cm
L  2cm
0.1
0.1
0.0
0.0
0
5
0
2
10
15
Distance / cm
4
6
20
8
10
25
Response function R’(L,En)
0
1 5 eV
100 - 500 eV
1000 - 2000 eV
6000 - 8000 eV
10000 - 20000 eV
60000 - 80000 eV
-1
10
-2
10
-3
10
1 5 eV
100 - 500 eV
1000 - 2000 eV
6000 - 8000 eV
10000 - 20000 eV
60000 - 80000 eV
0.4
Probability desinsity
Probability desinsity
10
0.3
0.2
0.3
0.2
0.1
-4
0
5
10
15
Distance / cm
20
25
0.0
2 cm
0.1
0.0
10
1 - 5 eV
0.4
0
5
0
2
10
15
Distance / cm
4
6
20
8
10
25
Resolution : experimental verification
206
/ Barn
Capture
n) / barn
(Yield /Yield
40
FWHM = 3.89 eV
R = 3.25 eV
D = 2.24 eV
Gt = 0.34 eV
56
Pb(n,)
Exp
RSA (REFIT)
Resolution (Coceva)
2
20
1
0
3.34
0
3.35
3.36
3.37
Neutron Energy / keV
Fe(n,)
FWHM =
42.88 eV
R =
D =
Gt =
42.29 eV
6.84 eV
1.96 eV
34.1
Exp.
RSA (REFIT)
Resolution (Coceva)
34.2
34.3
Neutron Energy / keV
34.4
Characteristics of P(Lt) for GELINA
8
20
18
Target equivalent distance
Moderated beam
o
Flight path : 0
Most probable
Average
Width / cm
Eq. Distance / cm
10
6
4
16
14
Target equivalent distance
Moderated beam
o
Flight path : 0
FWHM
2.35 
12
10
8
2
6
4
0
-2
-1
0
1
2
3
4
10 10 10 10 10 10 10
Neutron Energy / eV
2
0
-2
-1
0
1
2
3
4
10 10 10 10 10 10 10
Neutron Energy / eV
5
10
How to report data in energy : use average or most probable equivalent distance ?
Report data in time-of-flight
5
10
Characteristics of P(Lt) : analytical
1 5 eV
100 - 500 eV
1000 - 2000 eV
6000 - 8000 eV
10000 - 20000 eV
60000 - 80000 eV
Probability desinsity
0.4
0.3
P(t t ,En )  P'(L t (t t ) , En )
dL t
dt t
 Between 0.5 eV and 2000 eV:
1 - 5 eV
0.4
0.2
0.2
0.1
to moderation process and
2 cm
0.1
0.0
0.0
R’(Lt,En) dominated by 2 due
L  2cm
0.3
0
5
0
2
10
15
Distance / cm
4
6
20
8
almost independent of En
10
25
 Above 1 keV : more complex
TOF – response : analytical - MCNP
GELINA L = 12.5 m and 18o
103Rh(n,)
-3
2
4
Analytical (REFIT)
MCNP
Exp.
Analytical (REFIT)
MCNP
1
3
10
Yield
Probability density
10
0
10
-1
2
1
10
-2
10
x 10
0
5
10
15
Distance / cm
20
25
0
3620
3630
Neutron Energy / eV
TOF – response : analytical - MCNP
GELINA L = 60 m and 9o
56Fe(n,)
-3
2
1.4
10
1.2
Exp.
Analytical (REFIT)
MCNP
1
10
1.0
Yield
Probabilty density
Analytical (REFIT)
MCNP
x 10
0
10
0.8
0.6
0.4
-1
10
0.2
-2
10
0
5
10
15
Distance / cm
20
25
0.0
34100
34200
Neutron energy / eV
34300
Impact of response function
Response function
10
8
1.0
E = 100 eV at 10 m (GELINA)

 -distribution
Gauss (FWHM = 130 ns)


Gauss
Transmission
P(t)
R = 180 meV
6
4
0.8
0.6
2
0
-0.2
0.0
0.2
Time-of-flight / s
0.4
98
0.4
99
100
101
102
Energy / eV
Er =
100
eV
Er
=
(99.963 ± 0.002) eV
Gn =
10 meV
Gn
=
(9.97 ± 0.02 ) meV
G =
100 meV
G
=
(85.2 ± 4.4) meV
Lithium-glass scintillator : P(Ld)
6Li(n,t)
En = 10 eV
1
10
Response / (1/cm)
Scintillator + PMT
MCNP
REFIT
0
10
-1
10
-2
10
-3
10
0
1
2
3
4
Distance / cm
Low energy :
High energy :
6Li(n,t)
Li-glass
H(n,n)H Plastic scintillator
Reporting response of TOF-spectrometers
 Many emails, no specific suggestions
 GELINA :
• MC response : per configuration P(Lt,E) dim. 120 x 35
• 5 angles
 How to proceed?
• Recommendations for EXFOR
− TOF-response
− Transmission detectors