sp-fispact2001 - ENEA AFS Cell

SP-FISPACT2001
A COMPUTER CODE FOR ACTIVATION AND DECAY
CALCULATIONS FOR INTERMEDIATE ENERGIES.
A CONNECTION OF FISPACT WITH MCNPX.
SP-FISPACT2001
UN CODICE PER CALCOLI DI ATTIVAZIONE E
DECADIMENTO PER ENERGIE INTERMEDIE.
CONNETTENDO FISPACT CON MCNPX.
C. Petrovich
ENEA, Bologna, unità ERG-SIEC-FIRE
1

ABSTRACT
The calculation of the number of atoms and the activity of materials following nuclear
interactions at incident energies up to several GeV is necessary in the design of Accelerator
Driven Systems, Radioactive Ion Beam and proton accelerator facilities such as spallation
neutron sources. As well as the radioactivity of the materials, this allows the evaluation of
the formation of active gaseous elements and the assessment of possible corrosion
problems. The particle energies involved here are higher than those used in typical nuclear
reactors and fusion devices for which many codes already exist.
These calculations can be performed by coupling two different computer codes: MCNPX
and SP-FISPACT. MCNPX performs Monte Carlo particle transport up to energies of
several GeV. SP-FISPACT is a modification of FISPACT, a code designed for fusion
applications and able to calculate neutron activation for energies

TABLE OF CONTENTS
1. Introduction ............................................................................... 7
2. Utilization and limitations of SP-FISPACT2001............ ....... 7
3. Calculations with SP-FISPACT2001 ....................................... 9
3.1 Preparation of the outputs of MCNPX .................................................. 9
3.2 Preparation of the preliminary input COLLAPX ................................ 11
3.3 Preparation of the main input ................................................................. 13
4. Warnings .................................................................................... 14
5. Conclusions ................................................................................ 16
APPENDIX A ................................................................................ 17
APPENDIX B ................................................................................. 25
References ...................................................................................... 28
5

1. Introduction
The purpose of this report is to show how to calculate the number of atoms and the activity of
materials following nuclear interactions (at incident energies up to several GeV) by means of
two different computer codes: MCNPX [1] and SP-FISPACT.
These calculations allow the evaluation of the radioactivity of the materials, of the formation
of active gaseous elements as well as the assessment of possible corrosion problems.
This work has been stimulated by projects concerning Accelerator Driven Systems [2] (the
aim being energy production and transmutation of radioactive waste) and Radioactive Ion
Beam facilities [3] and can be applied also to other proton accelerator facilities, such as
spallation neutron sources. In all these systems the particle energies are higher than those used
in typical nuclear reactors and fusion devices (energies up to some GeV instead of energies
under 20MeV) for which many codes already exist.
FISPACT2001 [4] is a code designed for fusion applications and able to calculate activation
caused by neutron fluxes with energies

protons) in a 3-D geometry. Neutron fluxes can thus be calculated and provided as input to
FISPACT for activation calculation for E

SP-FISPACT, together with these cross-sections, stores the „pseudo cross-sections‟ in this file
and, thus, the different utilization of SP-FISPACT with respect to FISPACT concerns only
the way the file COLLAPX is prepared by the input file „collapx.i‟.
See APPENDIX A for the detailed modifications to the subroutines of FISPACT2001 and
APPENDIX B for the definition of the „pseudo cross-section‟.
3. Calculations with SP-FISPACT2001
The procedure for carrying out the calculations is shown in the following page and is
explained here step by step.
3.1 Preparation of the outputs of MCNPX
The MCNPX input file requires the following cards :
- „f4:n‟. This card calculates the volumetric neutron flux. Choose one of the energy group
structures of FISPACT2001 (XMAS, VITAMIN-J, TRIPOLI, see [4]) 2 and, using the card
„e4‟, define the energy bins accordingly.
- „histp‟. This card creates the file „histp‟ (it can be quite a lengthy file). This file is postprocessed
by the code 3 HTAPE3X [1] for calculation of residual nuclei per source proton
after interactions >20MeV.
Two output files are needed from HTAPE3X: the first providing the elastic collisions (this
output file must be called „elast‟), the second providing the residual nuclei after elastic
and inelastic collisions above 20MeV (this ouput file must be called „resid‟):
1. htape3x int=int1 outt=elast
(„int1‟ is the input file for HTAPE3X with the options IOPT=115 and KOPT=2. „elast‟ is the
output containing the elastic collisions).
Here is an example for int1:
Elastic collision
in 25 cells
115,,,,2,25,,,,/
15,20,25,30,44,46,48,52,54,56,58,60,62,64,92,94,96,98,104,
106,108,110,112,114,116
2 The group structures GAM-II and WIMS are not suitable since their highest energy values are respectively 14.9
MeV and 10 MeV.
3 This code belongs to the MCNPX package.
9

output
(with flux

2. htape3x int=int2 outt=resid
(„int2‟ is the input file for HTAPE3X with the options IOPT=108 and KOPT=0. „resid‟ is the
output containing the residual nuclei).
Here is an example for int2:
Residual nuclei
in 25 cells
108,,,,0,25,,,,/
15,20,25,30,44,46,48,52,54,56,58,60,62,64,92,94,96,98,104,
106,108,110,112,114,116
Until now this is just a standard MCNPX procedure.
SP-FISPACT2001 will read the values of „resid‟ (stable and metastable isotopes) and subtract
these values from „elast‟ to obtain the residual nuclei per source proton; finally it will create
the preliminary file COLLAPX with the new pseudo cross-sections.
3.2 Preparation of the preliminary input COLLAPX
The file FLUXES for FISPACT needs to be prepared with the values of the flux spectrum
under 20 MeV as provided by MCNPX.
In order to prepare properly the preliminary input „collapx.i‟ for SP-FISPACT, the user must
specify before the code word COLLAPSE: the value of the flux under 20MeV irradiating the
material, the source proton current used, the material irradiated and the number of atoms of
this material. Five new code words have been introduced for this purpose: CURRENT,
TARGET, ATTARGET, HCOLLAPSE, TCOLLAPSE.
The file collapx.i has to be prepared following these steps:
1. Input the integrated flux under 20MeV using the code word FLUX (this is a standard
FISPACT code word, but it has to be specified also in the preliminary input and not only in
the main input). If activation calculations are needed only above 20MeV then enter in any
case a value of the flux as well as a spectrum of the flux in the file FLUXES. These will be
fictitious values without any consequence for the results. Use a realistic value, such as FLUX
1E15 (see WARNINGS n. 5 at page 14).
Example: if there is a flux under 20MeV of 10 14 neutrons/cm 2 sec, then write: FLUX 1E14.
2. Input the proton current (in mA) used as source particles in MCNPX. Since the results in
MCNPX are, as stated above, provided as residual nuclei per source particle, the value of the
current has to be fixed in order to provide the correct number of residual nuclei per second.
The new code word is CURRENT.
Example: if the proton current of the accelerator is 3mA, then write: CURRENT 3.
11

3. Input the main nuclide which composes the material irradiated in the MCNPX problem.
The isotope must be indicated with the ID number as used internally by FISPACT (see [9] or
the file EAF_INDEX_20010 in the directory „eaf2001‟). It is allowed to input only a single
isotope. If the material is composed of more than one isotope then choose the most abundant.
SP-FISPACT2001 will perform calculations as if all the residual nuclei provided by
HTAPE3X were produced by this isotope.
The new code word is TARGET.
Example: if the material irradiated is natural Pb, Pb 208 can be chosen as representative of the
whole material and write TARGET 1631.
4. Input the number of atoms of the isotope chosen in the above paragraph. The new code
word is ATTARGET.
Example: if there are 1E29 atoms of Pb 208 , then write: ATTARGET 1E29.
5. The standard code word NOERROR (see [4], p. 44) must be used because the error data
for the interactions above 20MeV are not present.
6. Specify one of the following two new code words as alternative to the standard code word
COLLAPSE: TCOLLAPSE or HCOLLAPSE.
-TCOLLAPSE stands for „Total Collapse‟. This code word collapses both the standard
FISPACT cross-sections and the pseudo cross-sections >20MeV. All the values are written in
the file COLLAPX.
Example: if the cross section library in 175 groups is to be used, then: TCOLLAPSE 175.
-HCOLLAPSE stands for „High Collapse‟. This code word collapses only the pseudo crosssection
>20MeV created from MCNPX and not the standard FISPACT2001 cross-section.
This option can be used if only the effects of interactions >20MeV are to be investigated.
Example: HCOLLAPSE 175.
Here is an another example of preliminary input file „collapx.i‟ for an accelerator of 30mA,
providing a flux under 20MeV of 3.43E14 neutrons/cm 2 sec in 4.92E25 atoms of 9 Be. The
energy group VITAMIN-J is used under 20MeV.
FLUX 3.43E14
CURRENT 30
TARGET 15
ATTARGET 4.92E25
NOERROR
TCOLLAPSE 175
FISPACT
* COLLAPSE VITAMIN-J
END
* END OF RUN
/*
12

As in the standard FISPACT procedure prepare the preliminary file arrayx.i and run:
spfisp01 collapx.out
spfisp01 arrayx.out
3.3 Preparation of the main input
The main input is a standard FISPACT input with the following constraints:
1. It is necessary to use the code word FUEL (with the DENSITY code word) and not the
code word MASS.
2. The number of atoms of the material irradiated in MCNPX and specified in the
preliminary input (code word ATTARGET) has to be provided again with the code word
FUEL (it must obviously have the same value).
3. The value of the flux under 20MeV has to be provided again (it must obviously have the
same value).
Here is an example of the main input for the same example as the previous preliminary input:
AINP
FISPACT
*Residual nuclei at all energies
DENSITY 1.8477
FUEL 1
BE9 4.92E25
MIND 1.0E5
FLUX 3.43E14
ATOMS
LEVEL 100 8
TIME 1 YEARS
ATOMS
FLUX 0.
ZERO
TIME 1 HOURS
ATOMS
END
* END
/*
Finally, run:
spfisp01 output
13

4. Warnings
1. Not all the nuclides provided by MCNPX are included in the EAF2001 decay data library
[9] (the missing nuclides are usually neutron-rich nuclides for low Z and neutron-deficient
nuclides for high Z). This follows from the fact that residual nuclei are calculated by MCNPX
by means of physics models while those included in EAF2001 are based on experimental
evaluations. These nuclides are expunged by SP-FISPACT2001 and highlighted in the output
of the collapse process (collapx.out). In the cases analysed they represent 20%-45% of the
total number of nuclides and about 1%-25% of the total residual nuclei production. The
greatest number of expunged nuclei are obtained for high energy fission on U 238 where many
exotic nuclei are produced. Their contribution seems negligible in a first approximation for
spallation processes (6%) but, depending on their decay modes, the activity could be more
considerable. Since most of these data are publicly available (see [10]), the nuclide inventory
in the EAF2001 decay data library could be increased for this purpose.
2. The production of gas nuclides (H 1 , H 2 , H 3 , He 3 , He 4 ) as a consequence of the nuclear
interactions above 20MeV has not yet been implemented.
3. The production of daughter nuclides is proportional to the number of atoms of the parent
nuclides (see equation (1) in APPENDIX B). Therefore, the decrease with time of the amount
of atoms of the initial material causes a decrease in the production of residual nuclei above
20MeV (see the factor Nj(t)/Nj(0) in APPENDIX B). This should be treated as a burn-up
effect but it is usually negligible even for long period of irradiation (Nj(t)/Nj(0) decreases by
0.5% in value for typical cases). The user should check and evaluate the effect for the
problem under investigation.
4. Even if the material irradiated in MCNPX is composed of more than one isotope only a
single isotope must be chosen in SP-FISPACT2001. This does not affect the residual nuclei
production, but the decrease in time of the number of atoms of the initial material turns out to
be approximated. As mentioned above, this effect is usually negligible (although in principle
all the quantities involving the weight of the material irradiated, such as the DOSE RATE, are
thus modified).
5. The pseudo cross-sections created in the file COLLAPX must have a value higher than
~10 -20 (see equation (3), APPENDIX B). Lower values (they should not occur with usual
physical problems) give rise to errors due to the fact that the arrays are treated as single
precision variables. The user is responsible for checking such values.
6. The activity and particle emission (�, �, �) due to the formation of the residual nuclei
described by the physics models (such as residual deexcitation processes) is not included in
the treatment; the duration in time of the whole nuclear interaction process has been
neglected.
7. In the FISPACT main output the values „FLUX‟ and „FLUENCE‟ refer to the values
under 20MeV provided by the user. The values „NUMBER OF FISSION‟ and „HEAT
PRODUCTION‟ and the particle emissions do not include fissions over 20MeV.
8. All the code words concerning uncertainties (such as UNCERTAINTY) are not available.
Also pathway analysis is not a possible option.
9. The highest value of the energy used by FISPACT is 19.64 MeV and the lowest neutron
energy value considered in HTAPE3X is 20MeV. Thus the bin 19.64-20MeV is neglected.
14

10. Benchmarks of MCNPX (physics models at 1GeV) suggest to consider roughly the
degree of accuracy in predicting residual nuclei as a factor of 2 for spallation events and as a
factor of 10 for fission events [6]. This is a general trend, individual isotopes can be
mispredicted even by 2 orders of magnitude. In the range ~20-100MeV the accuracy of the
models is generally worse than above ~100 MeV.
11. FISPACT can treat only trace amounts of actinides that are able to fission because selfshielding
and burn-up effects are not included (see [4], p.11)
15

5. Conclusions
SP-FISPACT2001 makes possible the calculation of the number of atoms and the activity of
materials following nuclear interactions at energies up to several GeV (for energies

APPENDIX A – Fortran Modifications to FISPACT2001
Only one subroutine has been added to FISPACT2001. The subroutine is called spall.f. The
other modifications to the original code only concern the following subroutines:
fmain.f
col069.f
col100.f
col172.f
col175.f
col315.f
The subroutine fmain.f has been modified in order to add five new code words: CURRENT,
TARGET, ATTARGET, HCOLLAPSE, TCOLLAPSE. All of them concern the
preliminary input.
In FISPACT2001 the subroutines col*.f are called by fmain.f (code word COLLAPSE) in
order to create the file COLLAPX according to the desired energy group structure. The
subroutine spall.f is called by the subroutines col*.f (code words TCOLLAPSE and
HCOLLAPSE) for calculations of the pseudo cross-sections for interactions over 20MeV.
Subroutine spall.f
SUBROUTINE SPALL
C C.Petrovich - ENEA
C***************************************************************
C SUBROUTINE FOR CALCULATIONS >20MeV.
C IT USES OUTPUTS PRODUCED BY MCNPX 2.1.5 AND HTAPE3X
C***************************************************************
C
CHARACTER*80 FILES
COMMON /FILES1/ FILES(40)
COMMON /SPAL1/ CPFLUX,CURR,IDTARG,ATTARG
COMMON /SPAL3/ NP2(15000),ND2(15000),ZSEKT(15000),MCP2
DOUBLE PRECISION HISOT(0:300,0:300),ELAS(0:300,0:300),EL,HIS,
* HISOTM(0:300,0:300)
PARAMETER (IS=3000)
INTEGER IZ(IS),IN(IS),IA(IS),IZE(IS),INE(IS),
* IZF(IS),INF(IS),IAF(IS),IZM(IS),INM(IS),IAM(IS),
* ID(IS),IDF(0:300,0:300),IDFM(0:300,0:300)
CHARACTER B*6,C*5,D*3
c Protons per second in 1mA
PROTSC=6.24146E15
17

c Initialisation
NUCLF=0
NUCLH=0
NMET=0
EL=0
HIS=0
PERCF=0
PERCN=0
TOTH=0
TOTF=0
DO 5, I=1,IS
IZ(I)=0
IN(I)=0
IA(I)=0
IZE(I)=0
INE(I)=0
IZF(I)=0
INF(I)=0
IAF(I)=0
IZM(I)=0
INM(I)=0
IAM(I)=0
ID(I)=0
5 CONTINUE
DO 11,I=1,300
DO 10,J=1,300
HISOT(I,J)=0
HISOTM(I,J)=0
ELAS(I,J)=0
IDF(I,J)=0
IDFM(I,J)=0
10 CONTINUE
11 CONTINUE
C
C Read elastic collisions from 'elast' (HTAPE3X output).
C 'mean ' points the end of the file
C
OPEN(1,FILE='elast',STATUS='OLD',FORM='FORMATTED')
DO 25, I=1,IS
READ(1,15) C,D
15 FORMAT(5X,A5,3X,A3)
IF (C.EQ.'mean ') GOTO 30
IF (D.EQ.'n =') THEN
BACKSPACE 1
18

READ(1,20) IZE(I),INE(I),EL
20 FORMAT(8X,I3,6X,I3,3X,D11.5)
IF (IZE(I).EQ.0) IZE(I)=IZE(I-1)
ELAS(IZE(I),INE(I))=EL
END IF
25 CONTINUE
C
C Read residual nuclei (with elastic collisions)
C from 'resid' (HTAPE3X output).
C Then elastic collisions are subtracted.
C 'all z' points the end of the file.
C TOTH: sum of residual nuclei per source particle
C NUCLH: total number of nuclides
C
30 OPEN(2,FILE='resid',STATUS='OLD',FORM='FORMATTED')
DO 35, I=1,IS
READ(2,15) C,D
IF (C.EQ.'all z') GOTO 40
IF (D.EQ.'n =') THEN
BACKSPACE 2
READ(2,20) IZ(I),IN(I),HIS
IF (IZ(I).EQ.0) IZ(I)=IZ(I-1)
IA(I)=IN(I)+IZ(I)
HISOT(IZ(I),IN(I))=HIS-ELAS(IZ(I),IN(I))
TOTH=TOTH+HISOT(IZ(I),IN(I))
IF (HISOT(IZ(I),IN(I)).GT.0) NUCLH=NUCLH+1
ENDIF
35 CONTINUE
C
C Read metastable nuclides from 'resid'
C NMET: Number of metastable nuclides
C which are not only metastable
C
40 READ(2,42) B
42 FORMAT(11X,A6)
IF (B.EQ.'metast') THEN
READ(2,'(/)')
DO 48, I=1,IS
READ(2,45) IZM(I),IAM(I),FRACM
45 FORMAT(2X,I3,2X,I3,27X,D11.5)
IF (IZM(I).EQ.0) GOTO 50
IF (.NOT.FRACM.EQ.1) NMET=NMET+1
INM(I)=IAM(I)-IZM(I)
HISOTM(IZM(I),INM(I))=HISOT(IZM(I),INM(I))*FRACM
19

HISOT(IZM(I),INM(I))=HISOT(IZM(I),INM(I))*(1-FRACM)
48 CONTINUE
ENDIF
GOTO 40
C
C Read nuclides from 'EAF_INDEX_20010' (FISPACT2001)
C to identify material numbers of the nuclides
C provided by HTAPE3X.
C Z,N nuclides are recorded in IDF(Z,N)
C Metastable recorded in IDFM(Z,N)
C
50 OPEN(18,FILE=FILES(18),STATUS='UNKNOWN',IOSTAT=IOS)
DO 55, J=1,1922
READ(18,52,END=60) ID(J),IZF(J),IAF(J),M
52 FORMAT (2X,I4,9X,I3,I3,I1)
INF(J)=IAF(J)-IZF(J)
IF (M.EQ.0) IDF(IZF(J),INF(J))=ID(J)
IF (M.EQ.1) IDFM(IZF(J),INF(J))=ID(J)
55 CONTINUE
C
C Record the pseudo-cross-sections in NP2,ND2,ZSEKT
C (variables used for 'COLLAPX').
C MCP2 and NUCLF count the number of lines
C (nuclides of 'resid' also present
C in the file 'EAF_INDEX_20010' of FISPACT2001).
C The expunged nuclides are written in collapx.out.
C TOTF: Total residual nuclei also present in FISPACT.
C
60 WRITE (6,65)
65 FORMAT (/,' WARNING. The following nuclides produced by HTAPE3X ',
*'have not been accepted by FISPACT2001',/,/,11X,'Z A',/)
DO 80, I=1,IS
IF (HISOT(IZ(I),IN(I)).EQ.0) GOTO 75
IF (IDF(IZ(I),IN(I)).EQ.0) THEN
WRITE(6,70) IZ(I),IA(I)
70 FORMAT (8X,I4,1X,I4)
GOTO 75
ELSE
NUCLF=NUCLF+1
MCP2=MCP2+1
TOTF=TOTF+HISOT(IZ(I),IN(I))
NP2(MCP2)=IDTARG
ND2(MCP2)=IDF(IZ(I),IN(I))
ZSEKT(MCP2)=HISOT(IZ(I),IN(I))*PROTSC*CURR/(ATTARG*CPFLUX)
20

GOTO 75
ENDIF
C Same for metastable nuclides
75 IF (HISOTM(IZ(I),IN(I)).EQ.0) GOTO 80
IF (IDFM(IZ(I),IN(I)).EQ.0) THEN
WRITE(6,77) IZ(I),IA(I)
77 FORMAT (8X,I4,1X,I4,'m')
GOTO 80
ELSE
NUCLF=NUCLF+1
MCP2=MCP2+1
TOTF=TOTF+HISOTM(IZ(I),IN(I))
NP2(MCP2)=IDTARG
ND2(MCP2)=IDFM(IZ(I),IN(I))
ZSEKT(MCP2)=HISOTM(IZ(I),IN(I))*PROTSC*CURR/(ATTARG*CPFLUX)
ENDIF
80 CONTINUE
C
C Adds metastable nuclides (NMET) to the number of nuclides (NUCLH).
C Writes out how many nuclides have been expunged by FISPACT.
C
NUCLH=NUCLH+NMET
NUCLF=NUCLH-NUCLF
TOTF=TOTH-TOTF
PERCN=100*(REAL(NUCLF)/REAL(NUCLH))
PERCR=100*(TOTF/TOTH)
WRITE(6,90) NUCLF,NUCLH,PERCN
90 FORMAT(/,1X,'FISPACT2001 has not accepted ',I4,1X,
*'nuclides out of ',I4,' nuclides produced by HTAPE3X (',
*0PF7.3,'%)')
WRITE(6,95) TOTF,TOTH,PERCR
95 FORMAT(1X,'These correspond to ',1PE10.4,
*' residual nuclei per source particle out of ',
*1PE10.4,' (',0PF7.3,'%)',/)
c
RETURN
END
21

The differences between the two fmain.f subroutines are the following (the line numbers are
indicated):
332a333,340
> c
> c begin >20MeV C.Petrovich
> c
> COMMON /SPAL1 /CPFLUX,CURR,IDTARG,ATTARG
> COMMON /SPAL2 /FLAGCP
> c
> c end >20MeV C.Petrovich
> c
755c763,767
< +*SEQU*GRPC*EAFV*PULS*ENDP*FISY*UNCT*NEWF*CLEA*SPLI&',4)
---
>
+*SEQU*GRPC*EAFV*PULS*ENDP*FISY*UNCT*NEWF*CURR*TARG*ATTA*TCO
L*HCOL*
> +CLEA*SPLI&',4)
> c
> c 20 MeV C.Petrovich. Added in the previous line:
> c *CURR*TARG*ATTA*TCOL*HCOL
775c787,791
< * 1170,1180),J
---
> * 1175,1177,1185,1190,1195,1170,1180),J
> c
> c 20 MeV C.Petrovich. Added in the previous line:
> c 1175,1177,1185,1190,1195,
> c
776a793
> C
1052a1070,1076
> c
> c begin >20MeV C.Petrovich
> c
> CPFLUX=FLUX2
> c
> c end >20MeV C.Petrovich
> c
2403a2428,2456
> c
> c begin >20MeV C.Petrovich
22

c New code words to be input in the preliminary input for collapsing
> c ..........................................................CURR......
> c proton current
> 1175 ICHK=NEWDEC(1)
> CURR=FLDEC(0)
> GO TO 100
> c ..........................................................TARG.....
> c material number
> 1177 ICHK=NEWDEC(1)
> IDTARG=INDEC(0)
> GO TO 100
> c ........................................................ATTARGET...
> c number of atoms of the material number TARG
> 1185 ICHK=NEWDEC(1)
> ATTARG=FLDEC(0)/1E24
> GO TO 100
> c .........................................total collapse...TCOL.....
> c FLAG for collapsing all energies
> 1190 FLAGCP=1
> GO TO 410
> c ..........................................high collapse....HCOL...
> c FLAG for collapsing only interactions >20MeV
> 1195 FLAGCP=2
> GO TO 410
> c
> c end >20MeV C.Petrovich
Since the modifications to the subroutines col*.f are very similar, only the modifications to
the subroutine col175.f are shown.
29,31c29,41
< DIMENSION NUCL(1950),FLUX(176),XSECT(176),ZSECT(24000),
< + ZSEKT(15000),MREAC(114),NP(24000),ND(24000),
< + NP2(15000),ND2(15000),JPAR(1000)
---
> c
> c begin >20MeV C. Petrovich
> c
> c before: DIMENSION NUCL(1950),FLUX(176),XSECT(176),ZSECT(24000),
> c + ZSEKT(15000),MREAC(114),NP(24000),ND(24000),
> c + NP2(15000),ND2(15000),JPAR(1000)
> DIMENSION NUCL(1950),FLUX(176),XSECT(176),ZSECT(24000),
> + MREAC(114),NP(24000),ND(24000),JPAR(1000)
23

COMMON /SPAL3/ NP2(15000),ND2(15000),ZSEKT(15000),MCP2
> COMMON /SPAL2/ FLAGCP
> c
> c end >20MeV C. Petrovich
> c
792a803,815
> c
> c begin >20MeV C. Petrovich
> c FLAGCP>0 for collapsing >20MeV
> c FLAGCP=2 not collapsing IF (FLAGCP.GT.0) THEN
> IF (FLAGCP.EQ.2) M=0
> MCP2=M
> CALL SPALL
> M=MCP2
> ENDIF
> c
> c end >20MeV C. Petrovich
> c
24

APPENDIX B – Definition of ‘pseudo cross-sections’
The number of atoms Ni of the nuclide i produced by the stable nuclide j is governed by the
following equation (without considering fission) 4 :
where:
� is the neutron flux (n cm -2 s -1 )
Nj(t) is the amount of nuclide j at time t
�ij is the reaction cross section for reactions on j producing i (barns).
If there is a fixed number of source particles per second (such as protons in an accelerator)
causing an amount Ni of residual nuclei to be formed in a given material, then the production
of Ni (without decays) is ruled by:
dNi
( t)
dt
where:
„Residual nuclei Ni per source proton‟ is provided by the code HTAPE3X.
The number of „Source protons per sec‟ depends on the current used in the accelerator.
This is the contribution coming from interactions >20MeV to be added in FISPACT2001.
We can define a pseudo cross-section (a fictitious cross-section) such that:
Residual nuclei N
� �
ij
dNi
t)
� ��
ij N j ( t)
�10
dt
( �24
� Residual nuclei N
where:
� is the integral neutron flux under 20MeV (n cm -2 s -1 ).
Nj(0) is the number of atoms of the nuclide j forming the nuclide i at time t=0.
In this way FISPACT will calculate:
4 The complete equation can be found in [4], page 90.
i
i
per source proton * Source protons per sec
per source proton*
Source protons per sec*
10
� * N ( 0)
j
25
(1)
24
(2)
(3)

dNi
( t)
�24
� ��
ij N j ( t)
�10
�
dt
= Residual nuclei Ni per source proton * Source protons per sec * Nj(t)/Nj(0).
If the number of atoms of the initial material remains approximately constant (this is true in
most cases, but the responsibility for checking that is left to the user), then Nj(t)/Nj(0)�1 and
we obtain the desired equation (2).
26

Acknowledgements
K.W. Burn provided fruitful discussions.
Disclaimer
Neither the author nor ENEA accept responsibility for consequences arising from errors in the
present report.
Contact person
Feedback on the use of SP-FISPACT2001 is welcomed. Please contact the author with
comments.
Carlo Petrovich
ENEA
Via M.M.Sole 4, Bologna 40129
Tel. +39-051-6098517
E-mail: carlop@bologna.enea.it
27

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28