Irradiation history and resulting isotope decay
scheme influence on yttrium sample gamma
activity
S. Kilim1, M. Bielewicz1, A. Polanski1, E. Strugalska-Gola1, M. Szuta1,
A. Wojciechowski1, I. Adam2, M. Kadykov2, V. Pronskikh2, S.Tyutyunnikov2,
V. Wagner3, O.Svoboda3, V.Chilap4
1.
2.
3.
4.
National Centre for Nuclear Research, Otwock-Świerk 05-400, Poland
Joint Institute for Nuclear Research, 141980 Dubna, Russia
Nuclear Physics Institute of CAS, 25068 Rez, Czech Republic
CPTP “Atomenergomash”, Moscow, Russia
Yttrium-89 activation reactions taken into account
Reaction
Y89(n,g)
Y89(n,2n)
Y89(n,3n)
Y89(n,4n)
Y89(n,5n)
Stanislaw Kilim
Produced
Isotope
Y90
T1/2
3.19h
Reaction
Threshold
[MeV]
-6.8570*
Y88
106,65d
11.5
Y87m
13,37h
20.8
γ-line
Energy
[keV]
γ-line
Intensity
[%]
202.51
97.3
479.17
90.74
898.042
93.7
1836.063
99.2
380.79
78
388.53
82.00
484.805
89.7
Y87
79,8h
20.8
Y86
14,74h
32.7
1076.64
82.00
2.68h
42.633
231.67
84.00
4.86h
42.633
231.67
22.8
Y85
Dubna 2012-09
2
A typical formula for isotope production rate
S γ ⋅ 100
N Aσ k
t real λt +
λ k ⋅ t ir
1
≡ Ik =
⋅
⋅
⋅
⋅e
− λ ⋅tir
− λt real
A
m ⋅ ε p ⋅ I γ ⋅ φ ⋅ COI 1 − e
t live
1− e
(
NA – Avogadro’s number
A – sample’s gram atom
σk – reaction channel k cross section
Ik – isotope k production rate per gram
Sγ – gamma peak area
m – activation sample mass [g]
εp – gamma spectrometer efficiency
)(
)
Iγ – correction for gamma line intensity [%]
φ - deuteron fluence
COI – correction for gamma quanta coincidence
λk – isotope decay constant
tir – irradiation time
treal – real time of measurement
tlive – live time of measurement
The formula is based on constant accelerator beam assumption
λ k ⋅ t ir
(1 − e
− λ ⋅tir
)
- correction for irradiation time
Irradiation history – constant beam case
ϕi
- neutrons in pulse i
ϕ i = const =
φ∆t
t ir
Nk(tir) – isotope k nuclei at the EoIr
mN Aσ k φ∆t tir −λk (tir −ti )
N k (t ir ) =
e
∑
A
t ir i =1
mN Aσ k φ
⇒
A t ir
tir
− λk (tir − t )
e
dt
∫
0
mN Aσ k φ
N k (t ir ) =
1 − e −λk tir
A λk t ir
(
N k (t + ) = N k (t ir )e − λk t +
)
Variable beam case
9,0E+09
8,0E+09
7,0E+09
6,0E+09
5,0E+09
4,0E+09
3,0E+09
2,0E+09
1,0E+09
0,0E+00
07:15:55
05:50:00
04:18:47
02:53:05
01:30:43
00:06:04
22:43:42
21:21:29
19:59:07
18:36:35
17:14:11
15:51:05
14:27:57
13:05:43
11:43:09
4 GeV
09:07:04
Beam intensity [d/pulse]
4 GeV deuteron beam run 8-9.03.2011 on Quinta setup
Here the constant beam approximation
can’t be applied! Each pulse contribution
should be calculated separately.
Time [hh:mm:ss]
mN Aσ k
− λ (t
(
)
N k t ir =
ϕ
⋅
e
∑ i
k
A
i
ir
−t i )
Variable beam case
16-17.12.2011 Ed = 4 GeV experiment - "reversed"
Time [hh:mm:ss]
Fluence
t-irr[hh:mm:ss]
14:51:02
16:28:20
18:06:36
19:44:18
21:21:52
22:59:19
00:38:30
02:16:29
03:54:19
Beam
07:10:01
07:39:42
05:58:40
04:17:53
02:37:14
00:56:12
23:14:06
21:33:35
19:53:13
18:12:27
16:31:16
Beam
3,0E+10
2,5E+10
2,0E+10
1,5E+10
1,0E+10
5,0E+09
0,0E+00
05:31:54
Beam
3,00E+10
2,50E+10
2,00E+10
1,50E+10
1,00E+10
5,00E+09
0,00E+00
14:51:02
Beam
16-17.12.2011 Ed = 4 GeV experiment
Time [hh:mm:ss]
3,37E+13
17:31:00
Example irradiation history influence on yttrium isotopes production
Y88
Y87m
Y87
Y86
Y85
Beam run averaged
1,00
1,00
1,00
1,00
1,00
Reversed beam run
1,00
1,18
1,03
1,16
1,83
Real beam run
1,00
0,84
0,97
0,86
0,55
Irradiation history has negligible effect on Y88 production. For Y86 this effect can’t be neglected.
Shorter isotope half life time the irradiation history makes larger effect on measured production.
Residual isotope decay scheme effect on production - Y87
example – constant beam case
87mY
T1/2 = 13.38 hours 380.79 keV
ε+β+
dN1 mN Aσ 1ϕ
=
− λ1 N1
dt
A
t < t irr
dN 2 mN Aσ 2ϕ
=
+ λ1 N 1 − λ 2 N 2
dt
A
9/2+
1.57(10) % <<
ε+β+
98.43(10) %
87Y
1/2-
T1/2 = 79.8 hours
Y87 and Y87m production and decay
1,2E+12
N(tir and t+)
1,0E+12
N1(t)
8,0E+11
N2(t)
6,0E+11
N2direct(t)
N2asympt
4,0E+11
N1+N2direct
2,0E+11
N1(t+)+N2(t+)
0,0E+00
0
10 20
tir
5
15 25 35 45 55 65 75
t+ [h]
dN 1
= −λ1 N1
dt
t + > t irr
dN 2
= λ1 N1 − λ 2 N 2
dt
Residual isotope decay scheme effect on production - Y87
example – constant beam case
87mY
φ (1 − e − λ t
N 1 (t ir ) = mI 1
λ1t ir
T1/2 = 13.38 hours 380.79 keV
)
1 ir
ε+β+
9/2+
1.57(10) % <<
98.43(10) %
(t ) = mI φ (1 − e )
λt
− λ2tir
ε+β+
87Y
N2
1/2-
ir
2
(
T1/2 = 79.8 hours
2 ir
) (
)
 1 − e −λ2tir
e −λ2tir − e −λ1tir 
+ mI 1φ 
−

(
)
λ
t
λ
−
λ
t
2 ir
1
2 ir


Y87 and Y87m production and decay
1,2E+12
N(tir and t+)
1,0E+12
N1(t)
8,0E+11
N2(t)
6,0E+11
N2direct(t)
N2asympt
4,0E+11
N1+N2direct
2,0E+11
N 1 (t + ) = N 1 (t ir )e − λ1t+
N 2 (t + ) = N 2 (t ir )e −λ2t
N1(t+)+N2(t+)
0,0E+00
0
10 20
tir
5
15 25 35 45 55 65 75
t+ [h]
+ N 1 (t ir )
λ1
(λ1 − λ2
() e
− λ2 t +
− e −λ1t+
)
Residual isotope decay scheme effect on production - Y87
example – variable beam case
87mY
ir
N 1 (t ir ) = mI 1 ∑ ϕ i e −λ1 (tir −ti )
T1/2 = 13.38 hours 380.79 keV
ε+β+
9/2+
1.57(10) % <<
ε+β+
i =1
ir
87Y
i =1
1/2-
ir
+ mI 2 ∑ ϕ i e −λ2 (tir −tl )
T1/2 = 79.8 hours
i =1
Y87 and Y87m production and decay
1,2E+12
N(tir and t+)
1,0E+12
N1(t)
8,0E+11
N2(t)
6,0E+11
N2direct(t)
N2asympt
4,0E+11
N1+N2direct
2,0E+11
N1(t+)+N2(t+)
0,0E+00
0
10 20
tir
5
15 25 35 45 55 65 75
t+ [h]
(
)
N 2 (t ir ) = mI 1 ∑ ϕ i 1 − e −λ1 (tir −ti ) e −λ2 (tir −ti )
98.43(10) %
Experiment by experiment illustration
of irradiation history and decay scheme influence
on yttrium isotope production final results
will follow
Experiment QUINTA 2011-03-5-6 2 GeV
Variable beam to constant beam treatment ratio.
1,20E+10
1,00E+10
8,00E+09
6,00E+09
2 GeV
4,00E+09
2,00E+09
Y88
Y87m
Y87
Y86
Y85
1,00
1,09
1,01
1,08
1,56
20:55:01
20:03:21
19:11:26
18:19:54
17:28:15
16:36:36
15:43:36
14:37:58
13:32:14
12:30:49
11:39:09
10:47:46
09:55:17
09:03:14
08:11:34
07:19:31
06:27:59
05:36:28
04:44:57
03:53:02
03:01:31
02:09:35
0,00E+00
Time [h:m:s]
Fluence
t-irr[hh:mm:ss]
1,54E+13
18:50:29
Y87 S2 - axial distr - effect of correctio for Y87m
Y87 S1 - axial distr - effect of correction for Y87m
2,5E-05
2,5E-05
2,0E-05
2,0E-05
R4 S1 no corr.
1,5E-05
R4 S1 corr for Y87m
R8 S1 no corr.
1,0E-05
R8 S1 corr. for Y87m
5,0E-06
0,0E+00
Isotope production
Isotope production
Beam intensity [d/puls]
2 GeV beam run (6.03.2011)
R4 S2 no corr
1,5E-05
R4 S2 corr for Y87m
R8 S2 no corr.
1,0E-05
R8 S2 corr. for Y87m
5,0E-06
0,0E+00
0
1
2
3
4
Axial position [plane number]
5
0
1
2
3
4
5
Axial position [plane number]
Experiment QUINTA 2011-03-8-9 4 GeV
Variable beam to constant beam treatment ratio.
9,0E+09
8,0E+09
7,0E+09
6,0E+09
5,0E+09
4,0E+09
3,0E+09
2,0E+09
1,0E+09
0,0E+00
07:15:55
05:50:00
04:18:47
02:53:05
01:30:43
00:06:04
22:43:42
21:21:29
19:59:07
18:36:35
17:14:11
15:51:05
14:27:57
13:05:43
11:43:09
09:07:04
4 GeV
Time [hh:mm:ss]
Fluence
t-irr[hh:mm:ss]
Y88
Y87m
Y87
Y86
Y85
1,00
1,04
1,01
1,04
0,85
1,50614E+13
22:53:01
Y87 S2 - axial distr - effect of correction for Y87m
Y87 S1 - axial distr - effect of correction for Y87m
5,0E-05
4,5E-05
5,0E-05
4,0E-05
3,5E-05
3,0E-05
4,0E-05
3,5E-05
4,5E-05
R4 S1 no corr
R4 S1 corr for Y87m
2,5E-05
2,0E-05
1,5E-05
1,0E-05
R8 S1 no corr
R8 S1 corr for Y87m
Production
Production
Beam intensity [d/pulse]
4 GeV deuteron beam run 8-9.03.2011 on Quinta setup
R4 S2 no corr
3,0E-05
R4 S2 corr for Y87m
2,5E-05
R8 S2 no corr
2,0E-05
R8 S2 corr for Y87m
1,5E-05
1,0E-05
5,0E-06
5,0E-06
0,0E+00
0,0E+00
0
1
2
3
Plane number
4
5
0
1
2
3
Plane number
4
5
Experiment QUINTA 2011-03-20-21 6 GeV
Variable beam to constant beam treatment ratio.
2,0E+10
1,5E+10
1,0E+10
6 GeV
Y88
Y87m
Y87
Y86
Y85
1,00
1,05
1,01
1,04
1,11
5,0E+09
10:43:40
9:36:08
7:56:00
6:48:27
5:11:54
4:05:17
2:58:49
0:17:12
23:10:23
21:49:48
20:32:22
18:12:59
16:59:55
0,0E+00
Time [hh:mm:ss]
Fluence
t-irr[hh:mm:ss]
2,17E+13
18:35:52
Y87 S1 - axial distr - effect of correction for Y87m
Y87 S2 - axial distr - effect of correction for Y87m
7,0E-05
7,0E-05
6,0E-05
6,0E-05
5,0E-05
R4 S1 no corr
4,0E-05
R4 S1 corr for Y87m
R8 S1 no corr
3,0E-05
R8 S1 corr for Y87m
2,0E-05
5,0E-05
Production
Production
Beam intensity [d/pulse]
6 GeV deuteron beam run 20-21.03.2011 on QUINTA
setup
R4 S2 no corr
4,0E-05
R4 S2 corr for Y87m
3,0E-05
R8 S2 no corr
R8 S2 corr for Y87m
2,0E-05
1,0E-05
1,0E-05
0,0E+00
0
1
2
3
Plane number
4
5
0,0E+00
0
1
2
3
Plane number
4
5
QUINTA experiment 2011-12-14-15 1 GeV
14-15.12.2011 Ed=1 GeV experiment
Variable beam to constant beam treatment ratio.
1,00E+10
Beam
8,00E+09
6,00E+09
Beam
4,00E+09
2,00E+09
Y88
Y87m
Y87
Y86
Y85
1,00
1,01
1,00
1,01
1,06
07:44:49
05:39:22
03:35:04
01:31:08
23:26:51
21:23:09
19:15:21
17:11:33
15:08:18
13:04:08
10:58:55
0,00E+00
Time [hh:mm:ss]
Fluence
t-irr[hh:mm:ss]
6,791E+13
21:07:06
Y87 S1 - axial distr - effect of correction for Y87m
Y87 S2 axial distr - effect of corr. for Y87m
2,5E-06
2,5E-06
2,0E-06
R4 S2 no corr
R4 S1 no corr
1,5E-06
R4 S1 corr for Y87m
R8 S1 no corr.
1,0E-06
R8 S1 corr for Y87m
Production
Production
2,0E-06
5,0E-07
0,0E+00
0,0E+00
1
2
3
Plane number
4
5
R8 S2 no corr
R8 S2 corr for Y87m
1,0E-06
5,0E-07
0
R4 S2 corr for Y87m
1,5E-06
0
1
2
3
Plane num ber
4
5
QUINTA experiment 2011-12-16-17 4GeV
16-17.12.2011 Ed = 4 GeV experiment
07:39:42
05:58:40
04:17:53
02:37:14
00:56:12
23:14:06
21:33:35
19:53:13
18:12:27
16:31:16
Beam
14:51:02
Beam
Variable beam to constant beam treatment ratio.
3,00E+10
2,50E+10
2,00E+10
1,50E+10
1,00E+10
5,00E+09
0,00E+00
Time [hh:mm:ss]
Fluence
t-irr[hh:mm:ss]
Y88
Y87m
Y87
Y86
Y85
1,00
0,84
0,97
0,86
0,55
3,37E+13
17:31:00
Y87 S2 axial distr - effect of correction for Y87m
Y87 S1 axial distr - effect of corr for Y87m
2,5E-05
2,0E-05
R4 S1 no corr
1,5E-05
R4 S1 corr for Y87m
R8 S1 no corr
1,0E-05
R8 S1 corr for Y87m
5,0E-06
2,0E-05
Production
Production
2,5E-05
R4 S2 no corr
R4 S2 corr for Y87m
1,5E-05
R8 S2 no corr
R8 S2 corr for Y87m
1,0E-05
5,0E-06
0,0E+00
0,0E+00
0
1
2
3
Plane number
4
5
0
1
2
3
Plane num ber
4
5
Conclusions
• In case of resulting isotope produced both directly and in decay
chain the effect of decay scheme can be neglected if the
measurement starts later than decaying parent isotope half life time.
• In case of variable beam the irradiation history (beam run) effect
depends on produced isotope half life time. The effect is large for
isotopes with half life time shorter than irradiation time and negligible
for isotopes with the longer one. It is recommended, therefore , not
to apply or apply with care the constant beam approximation while
sample gamma activity working over.
Thank you for attention