ISO 10645:2022

INTERNATIONAL ISO
STANDARD 10645
Second edition
2022-04
Nuclear energy — Light water reactors
— Decay heat power in non-recycled
nuclear fuels
Énergie nucléaire — Réacteurs à eau légère — Puissance résiduelle
des combustibles nucléaires non recyclés
Reference number
ISO 10645:2022(E)
© ISO 2022

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ISO 10645:2022(E)
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© ISO 2022
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
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Published in Switzerland
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ISO 10645:2022(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and subscripts . 2
4.1 Symbols . 2
4.2 Subscripts . . 3
5 Calculation of decay heat power .3
5.1 General . 3
5.2 Power histogram . 3
5.3 Contribution of fission products . 4
5.4 Contribution of actinides . 6
239 239
5.4.1 Contribution of U and Np . 6
5.4.2 Contribution of other actinides . 7
5.5 Contribution by neutron capture in fission products . 7
134
5.5.1 Contribution of Cs . 7
5.5.2 Contribution of other fission products . 9
5.6 Total decay heat power . 9
Annex A (informative) Example of a calculation.16
Bibliography .20
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ISO 10645:2022(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national Standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 85, Nuclear energy, nuclear technologies,
and radiological protection, Subcommittee SC 6, Reactor technology.
This second edition cancels and replaces the first edition (ISO 10645:1992), which has been technically
revised.
The main changes compared to the previous edition are as follows:
235 238 239 241
— The decay heat curves for U, U, Pu, and Pu are revised using data adopted from the
[1]
American National Standard ANS-5.1-2014 .
— These curves are based on fits to experimental spectroscopic and calorimetric measurements of
5
fission product decay heat at short cooling times less than ~10 seconds, and on measurements and
[2]
simulations for longer times .
— Nuclear data constants are updated to reflect modern evaluated values.
235
— The range of initial U enrichment is extended beyond 4,1 % (mass fraction) to 5 %.
— Burnup range is extended to 62 GWd/t, an increase from 52 GWd/t in the previous 1992 edition.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
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ISO 10645:2022(E)
Introduction
The decay heat power of nuclear fuels is the thermal power produced by radioactive decay of fission and
activation products of the nuclear fuel. Decay heat is one of the contributors to the total heat emitted
from the nuclear fuel during the reactor operation, representing about <7 % of the total heat. As decay
heat continues to be released after shutdown of a nuclear reactor, it is an important physical quantity
for the design of systems in which the decay heat power should be taken into consideration as a heat
source.
This document provides an alternative to dedicated and validated calculation codes, as it provides values
for the local generation of decay heat power as a function of the thermal fuel power during operation.
The values for the fission product component of decay heat are based on fits to measured data for short
5 [2]
cooling times less than ~10 s , and on measurements and computational simulations for longer times.
Values for other components of decay heat are developed to provide conservative estimates. Therefore,
at longer cooling times where fission products represent an increasingly smaller relative contribution
to total decay heat, this document becomes increasing conservative, and alternative methods such as
dedicated computer codes may provide more accurate estimates. The spatial distribution of the energy
conversion into heat, e.g. γ-radiation, is not considered. If required, evaluation of this is left to the user.
The calculation procedure used has the advantage of enabling the estimation of the decay heat power
without the need for a validated dedicated calculation code. Nevertheless, the calculation requires the
fission fractions of each fissile isotope. These values are not given in this document but can be obtained
[3][4]
from literature or computer codes.
The power generated by residual fission induced by delayed neutrons after shutdown and activated
structural materials is not considered in this document. Delayed neutrons are generally negligible
several minutes after core shutdown, and the activated structural materials generally have a minor
effect on the global decay heat. Analyses of delayed neutron heating is configuration specific and may
require more detailed models. Similarly, analysis of structural activation heating requires separate
evaluations.
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INTERNATIONAL STANDARD ISO 10645:2022(E)
Nuclear energy — Light water reactors — Decay heat
power in non-recycled nuclear fuels
1 Scope
This document provides the basis for calculating the decay heat power of non-recycled nuclear fuel of
light water reactors. For this purpose the following components are considered:
— the contribution of the fission products from nuclear fission;
— the contribution of the actinides;
— the contribution of isotopes resulting from neutron capture in fission products.
This document applies to light water reactors (pressurized water and boiling water reactors) loaded
235 238
with a nuclear fuel mixture consisting of U and U. Application of the fission product contribution
to decay heat developed using this document to other thermal reactor designs, including heavy water
reactors, is permissible provided that the other contributions from actinides and neutron capture are
determined for the specific reactor type. Its application to recycled nuclear fuel, like mixed-oxide or
reprocessed uranium, is not permissible.
9
The calculation procedures apply to decay heat periods from 0 s to 10 s.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
decay heat power
thermal power produced by radioactive decay of fission and activation products of the nuclear fuel,
following shutdown of a nuclear fission reactor, excluding prompt radiation emissions
3.2
operating time
entire period of irradiation from the first loading of the considered fuel into the reactor until the final
shutdown and removal of the fuel
3.3
decay time
time elapsing after the operating time (3.2)
3.4
power histogram
approximation of the true continuous variation of power with time, by subdividing the variation into
intervals of constant power output
1
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ISO 10645:2022(E)
4 Symbols and subscripts
4.1 Symbols
Table 1 shows the symbols used in this document.
Table 1 — Symbols
Symbol Quantity Unit
A(t) Factor to be applied to the decay heat power of the fission products P, Unitless
239
for calculating the contribution P of the actinides (excluding U and
A
239
Np)
f (t) Decay heat power of the fission products at time t after a single nuclear (MeV/s)/fission
i
fission of the fissile nuclide i
Δf (t) Standard deviation of f (t) (MeV/s)/fission
i i
F (t ,T ) Decay heat power of the fission products of the fissile nuclide i at time t, (MeV/s)/(fission/s)
i k k
after the irradiation time interval, T , referred to one fission per second
k
ΔF (t ,T ) Standard deviation of F (t) (MeV/s)/(fission/s)
i k k i
H(t) Factor to be applied to the decay heat power of the fission products P, for Unitless
calculating the contribution P from neutron capture in fission products
E
133
(excluding capture in Cs)
th a
P Total thermal power of the fuel during the k time interval T
k k
b
P Contribution of the fissile nuclide i to the thermal power of the fuel dur-
ik
th
ing the k time interval T
k
b
P (t,T) Total decay heat power at time t after the end of operating time, T
N
b
P (t,T) Summed decay heat power on the basis of fission product decays
S
b
ΔP (t,T) Standard deviation of P (t,T)
S S
b
P (t,T) Contribution of fissile nuclide i to the decay heat power P (t,T)
Si S
b
ΔP (t,T) Standard deviation of P (t,T)
Si Si
b
P (t,T) Contribution to the decay heat power due to neutron capture in fission
E
133
products other than Cs
239 239 b
P (t,T) Contribution of actinides U and Np to the decay heat power
B
239 239 b
P (t,T) Contribution of actinides other than U and Np to the decay heat
A
power
134 b
P (t,T) Contribution of Cs to the decay heat power
Cs
Q Total thermal energy released from one nuclear fission of the fissile MeV
i
nuclide i
ΔQ Standard deviation of the thermal energy released from one nuclear MeV
i
fission of the fissile nuclide i
t Decay time (see 5.3 and Figure 1) s
t Time from the end of operating time interval T in the power histogram s
k k
(see Figure 1)
T Operating time (see 5.2 and Figure 1) s
T Duration of operating time interval k in the power histogram (see s
k
Figure 1)
T Operating time minus shutdown intervals s
eff
α Coefficient used for representing the decay heat power of fission prod- (MeV/s)/fission
ij
ucts as the summation of 23 exponential functions
a
Any power unit can be used.
b
Same power unit as P .
k
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ISO 10645:2022(E)
Table 1 (continued)
Symbol Quantity Unit
Coefficient used for representing the standard deviation of the decay (MeV/s)/fission
β
ij
heat power of fission products as the summation of 23 exponential func-
tions
-1
λ Exponent used for representing the decay heat power of fission products s
ij
as the summation of 23 exponential functions
a
Any power unit can be used.
b
Same power unit as P .
k
4.2 Subscripts
235 238 239 241
i Subscript denoting the fissile nuclides U, U, Pu, Pu
j Summation subscript used for representing the decay heat power by a summation of exponential
functions
k Subscript used for enumerating the individual time intervals in the power histogram
m Number of time interval T in the power histogram
k
5 Calculation of decay heat power
5.1 General
To calculate the decay heat power, the following components shall be considered:
235 238 239
— the contribution of the fission products from nuclear fission of the four nuclides U, U, Pu
241 235
and Pu (other fissile nuclides shall be treated as U);
— the contribution of the actinides;
— the contribution of nuclides resulting from neutron capture in fission products.
9
The calculation procedures shall apply to the decay heat power for decay times t between 0 s and 10 s.
Decay heat power from delayed neutron-induced fission and activation in structural materials are not
included in this document and shall be evaluated by the user and appropriately included in any analyses
of decay heat power.
5.2 Power histogram
Generally, the composition and power output of the fuel under consideration are subject to change
during the operating time. This can be taken into account for calculating the decay heat power, by
further subdividing the operating time into intervals of constant power and constant fissile nuclide
fission rate (constant composition, see Figures 1 and A.1). It shall be ensured that the systematic error
introduced by this approximation is taken into account in the estimation of the uncertainty of the
decay heat power. This error can be reduced by making the best possible approximation of the fuel
power at the end of the operating time. The error introduced by the approximation of the power in
the power histogram decreases rapidly with increasing decay time, the accuracy of approximation in
the individual intervals can decrease with increasing distance t of interval k from the decay instant
k
considered. Alternatively, in lieu of performing an uncertainty determination, a conservative calculation
may be performed by using the maximum value of the operating power during the irradiation time in
the reactor and reducing the irradiation time to preserve the burnup. Any conservative calculations
shall be justified by the user.
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ISO 10645:2022(E)
Since a variation in the relative power contributions of the fissile nuclide is less important for the decay
heat power than a variation in the operating power, a rougher scaling is often sufficient for this purpose.
5.3 Contribution of fission products
The contribution P (t,T) of the fission products to the decay heat power is calculated from the individual
S
contributions P (t,T) of the four fissile isotopes using Formula (1).
Si
4
Pt(),,TP= ()tT (1)
SSi
∑
i =1
Each contribution P (t,T) is in turn composed of the summed decay heat powers of the m time intervals
Si
of the power histogram and is calculated as shown in Formula (2).
m m
P
ik
Pt(),,TP= tT = Ft ,T (2)
() ()
∑∑
SSi ik k ik k
Q
i
k ==11k
where
P is the total thermal power released by the fuel during fission;
ik
Q is the total thermal energy released by a single fission;
i
P /Q gives the fission rate of the fissile nuclide i.
ik i
F (t ,T ) is the decay heat power of the fissile nuclide i, referred to one nuclear fission per second, for a
i k k
time interval of duration T and for a decay time t . It is calculated from the energy release f (t) of the
k k i
fission products of a single fission at time t after fission as shown in Formula (3).
T
k
Ft ,Tf=+TT− ′′tTd (3)
() ()
ik k ik k
∫
o
f (t) is calculated as shown in Formula (4) using the coefficients a , λ given in Tables 2, 3, 4, and 5.
i ij ij
23
−λ t
ij
ft = α e (4)
()
i ij
∑
j=1
The following Formula (5) is thus obtained.
23
α
−−λλTt
ij
ij kijk
Ft ,Te=−1 e (5)
()
ik k ( )
∑
λ
ij
j=1
Hence, the contribution P (t,T) of the fission products to the decay heat power is calculated using the
S
Formula (6).
4 m 23
 
α 
P
−−λλTt
 ij 
ik
ij kijk
Pt(),T =−1 ee (6)
  
S ( )
∑∑ ∑
Q λ
 
 i ij 
 
ik==1 11j =
 
Figure 1 illustrates a power histogram with four time intervals of varying power for the fissile nuclide i.
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ISO 10645:2022(E)
Key
X time
Y power
a
Shutdown.
Figure 1 — Power histogram illustration
Thus, for the decay heat power contributions P (t,T), the individual times t are calculated using
Si k
Formula (7).
tt=
1
tt=+T
21
m−1
tt=+ T (7)
m ∑ k
k=1
The relative standard deviation of the decay heat power ΔP /P of the fission products is calculated
Si Si
from the standard deviation ΔF (t ,T ) and the relative standard deviation ΔQ /Q .
i k k i i
The contribution of the fissile nuclide i is calculated using Formula (8).
2
P
m
 
ik
ΔFt ,T
()
2 2
∑ 
ik k
k=1
ΔP ΔQ Q
   
Si i i
 
= + (8)
   
 
P Q P
 SSi   i  i
 
 
The values of Q and ΔQ are given in Table 6.
i i
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ISO 10645:2022(E)
For decay time t ≥ 1 s, the standard deviation ΔF (t ,T ) is calculated using the Formula (9).
k i k k
T
k
′
ΔΔFt(),'Tf=−()TT + tTd (9)
ik k ik k
∫
0
A representation analogous to Formula (4) is adopted to calculate Δf (t) using the following Formula (10).
i
NOTE The values of coefficients λ and β , are given in Tables 2, 3, 4, and 5.
ij ij
23
−λ t
ij
Δft = β e (10)
()
i ij
∑
j=1
Hence, the following Formula (11) is thus obtained.
23
β
 
ij −−λλTt
ij kijk
ΔFt ,Te=−1 e (11)
()  
()
ik k ∑
λ
 
ij
j =1 
For decay times t < 1 s, the standard deviation ΔF (t ,T ) is calculated using the Formula (12).
k i k k
Ft(),T
ik k
ΔΔFt ,T = Ft =1sT, (12)
() ()
ik k ik k
Ft =1sT,
()
ik k
The standard deviation ΔP of the decay heat power of all fission products is calculated using the
S
Formula (13).
4
ΔΔPP= (13)
SS∑ i
i=1
5.4 Contribution of actinides
239 239
5.4.1 Contribution of U and Np
239 239
The decay heat power P (t,T) from U and Np is calculated using the Formula (14).
B
m
P
k
 
Pt,,T = Ft TF+ tT, (14)
() () ()
BU∑ kK Np kk
 
Q
k=1
P /Q is the total fission rate in time interval k and is substituted in Formula (14) as shown in
k
Formula (15).
4
P P
k ik
= (15)
∑
Q Q
i
i=1
For the summation in Formula (14), only the last 20 days of the power histogram need to be considered.
The terms F (t ,T ) and F (t ,T ) in Formula (14) are calculated using Formulae (16) and (17)
U k k Np k k
respectively.
−−λλTt
UUkk
Ft ,TE=−Re1 e (16)
()
()
UUkk
 λ 
λ
Np
−−λλTt
U −λ T −λ t
Np kkNp
U kkkU
Ft ,TE= Re11− ee− − e (17)
()  
() ()
Np kk Np
λλ− λλ−
 
UNp UNp
 
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ISO 10645:2022(E)
where
239
E (= 0,460 MeV) is the mean decay energy of U;
U
239
E (= 0,405 MeV) is the mean decay energy of Np;
Np
-4 -1 239
λ (= 4,926 × 10 s ) is the decay constant of U;
U
-6 -1 239
λ (= 3,405 × 10 s ) is the decay constant of Np;
Np
238
R is the ratio of the neutron capture rate in U to the total fission rate at the end of the oper-
ating time.
If the user does not have values for R, the following approximation, as shown in Formula (18), may be
used.
−0,504
Ra=+0,,974 Ba()0 008 83−× 0,000 726 (18)
0 f 0
where
235
a is the initial enrichment of U (percentage by mass);
0
B is the final burnup of the fuel, in megawatt days per kilogram of initial uranium.
f
Formula (18) was developed for a light water reactor (LWR) spectrum and applies to initial enrichments
between 1,9 % and 5,0 %. It yields conservatively high results.
5.4.2 Contribution of other actinides
239
The contribution P (t,T) of the other actinides resulting from the neutron capture (excluding U and
A
239
Np) is to be stated by the user.
Formula (19)
Pt(),,TA= ()tP ()tT (19)
AS
yields conservatively high results, when using the factors A(t) from Table 7, provided the following
conditions are fulfilled:
— initial enrichment, expressed as percentage by mass, 1,9 % ≤ a ≤ 5,0 %;
0
— burnup, in megawatts days per kilogram of initial uranium, B ≤ 12,5 a ;
f 0
— power density, in kilowatts per kilogram of uranium, S ≥ 5,0 a .
0
5.5 Contribution by neutron capture in fission products
134
5.5.1 Contribution of Cs
134 133
The Cs produced by neutron capture on the fission product Cs can have a significant contribution
8
to the decay heat power, particularly for decay times in the region of 10 s, and is therefore treated
explicitly.
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ISO 10645:2022(E)
The following Formula (20) applies
P
Pt(),,T = Ft()T (20)
Cs Cs
Q
Where Formula (21) defines the value of P/Q
4
P P
i
= (21)
∑
Q Q
i
i=1
and Formula (22) defines Ft(),T .
Cs
−+()λσ φ T −σφT −+()λσ φ T
 
44 3 44
1−ee −e
−λ t
4
Ft,TE=λ y + e (22)
()
 
Cs 4 Cs
λσ+ φσ φλ− +σφ
()
 
 44 3 444 
where
-1 133
y (= 0,068 3 atoms fission ) is the mean Cs cumulative yield per fission;
134
E (= 1,719 MeV) is the mean decay energy of Cs;
Cs
-8 -1 134
λ (= 1,064 × 10 s ) is the decay constant of Cs;
4
-2 -1
ϕ is the total neutron flux in cm s ;
-24 2 l33
σ (= 11,3 × 10 cm ) is the spectrum-averaged (n,γ) cross-section of Cs;
3
-24 2 134
σ (= 10,9 × 10 cm ) is the spectrum-averaged (n,γ) cross-section of Cs.
4
The cross section constants σ and σ were determined for a typical pressurized water reactor (PWR)
3 4
spectrum. When applied to a boiling water reactor (BWR) they yield conservatively high results.
For a power histogram, an effective irradiation time T , an effective neutron flux ϕ and a mean
eff eff
fission rate P/Q are to be used in formulae (20) and (22).
Formula (23) defines T
eff
m
TT=≠forallk withΦ 0 (23)
()
eff ∑ kk
k=1
And Formula (24) defines the effective neutron flux ϕ
eff
m
1
φφ= T (24)
eff ∑ kk
T
eff
k=1
And Formula (25) defines the values of mean fission rate P/Q.
m 4
P
P 1
ik
= T (25)
∑∑ k
QT Q
eff i
k==11i
If no value for neutron flux is available, the following approximation, see Formula (26) can be used.
S
k 13 −−21
φ =×25,c81× 0 ms (26)
()
k
a
eff
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ISO 10645:2022(E)
where
S is the power density, in kilowatts per kilogram of uranium in the fuel;
k
a is the effective enrichment of fissile material which is calculated from the initial enrichment
eff
a , expressed as a percentage by mass.
0
a
0
a =+10, (27)
eff
2
For enrichments and burnups typical of LWRs, ϕ in Formula (26) yields values of P (t,T) which exceed
k Cs
the exact values by up to 5 %. For shorter irradiation times (<25 MWd/kg) the approximate solution
overestimates P (t,T) by up to 15 %.
Cs
5.5.2 Contribution of other fission products
The contribution P (t,T) made to the decay heat power by neutron capture in fission products (except in
E
133
Cs) is to be stated by the user.
The Formula (28)
Pt,,TH= tP tT (28)
() () ()
E S
yields conservatively high results, when using the factors H(t) from Table 8, provided that the following
boundary conditions are fulfilled:
— initial enrichment, expressed as a percentage by mass, 1,9 % ≤ a ≤ 5,0 %;
0
— burnup, in megawatts days per kilogram of uranium, B ≤ 12,5 a ;
f 0
— power density, in kilowatts per kilogram of uranium, S ≥ 5 a .
0
5.6 Total decay heat power
The total decay heat power is calculated using the Formula (29).
Pt,TP= tT,,,+Pt TP+ tT +Pt,,TP+ tT (29)
() () () () () ()
NESB ACs
The error bandwidth ΔP shall be determined from standard deviation ΔP , [see Formula (13)]
N S
associated with the fission product contribution and the uncertainty of the relative thermal power
during operation (ΔP/P) using the Formula (30).
2
ΔP
2
 
ΔΔPt,,Tn= Pt TP+ tT, (30)
()  () ()
 
NNS
 
 P 
where n is the multiple of the standard deviation associated with the chosen confidence level.
The other contributions to the decay heat power P , P , P , and P shall be determined conservatively
B A Cs E
and therefore do not enter into the calculation of the error bandwidth. Using the approximate methods
of this document for these contributions results in conservative estimates of the total decay heat
power. Alternative methods, such as those based on comparisons of code predictions and isotopic
measurements for the main nuclides contributing to each of these decay heat terms, shall be specified,
and justified by the user.
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ISO 10645:2022(E)
235
Table 2 — Coefficients for thermal fission of U
α β
λ
j
MeV/s MeV/s
   
a a
-1 a
(s )
   
 fission   fission 
1 5,280 0E-04 1,227 6E-04 2,721 6E+00
2 6,858 8E-01 2,986 2E-01 1,025 6E+00
3 4,075 2E-01 1,490 1E-02 3,141 9E-01
4 2,193 7E-01 9,636 9E-03 1,178 8E-01
5 5,770 1E-02 1,068 0E-03 3,436 5E-02
6 2,253 0E-02 4,070 5E-04 1,176 2E-02
7 3,339 2E-03 7,872 6E-05 3,606 5E-03
8 9,366 7E-04 1,679 5E-05 1,396 3E-03
9 8,089 9E-04 1,447 4E-05 6,260 8E-04
10 1,957 2E-04 4,372 4E-06 1,892 4E-04
11 3,260 9E-05 5,117 8E-07 5,507 4E-05
12 7,582 7E-06 2,099 7E-08 2,097 1E-05
13 2,518 9E-06 7,925 8E-08 9,994 0E-06
14 4,983 6E-07 9,330 1E-09 2,540 1E-06
15 1,852 3E-07 3,785 5E-09 6,633 2E-07
16 2,659 2E-08 5,400 4E-10 1,228 1E-07
17 2,235 6E-09 4,535 7E-11 2,716 3E-08
18 8,9582E-12 5,5496E-14 3,2955E-09
19 8,5968E-11 1,8015E-12 7,4225E-10
20 2,1072E-14 4,9806E-15 2,4681E-10
21 7,1219E-16 -7,4576E-17 1,5596E-13
22 8,1126E-17 2,5589E-15 2,2573E-14
23 9,4678E-17 -2,4567E-15 2,0503
...