- Email: [email protected]
Extension of TALYS to 1 GeV
Available online at www.sciencedirect.com
Nuclear Data Sheets 118 (2014) 187–190 www.elsevier.com/locate/nds
Extension of TALYS to 1 GeV A.J. Koning,1, ∗ D. Rochman,1 and S.C. van der Marck1 1
Nuclear Research and Consultancy Group NRG, 1755 ZG Petten, The Netherlands
One of the latest features of the TALYS nuclear reaction model code is described: the extension to higher energies. The Koning-Delaroche optical model potential from 2003 has been extended by two simple terms for the volume real and imaginary potentials. The resulting predictions have been tested against available experimental data above 200 MeV and now seem to provide reasonable results up to about 1 GeV. By means of logarithmic binning of the multiple decay scheme in TALYS it is now also possible to calculate non-elastic channels at higher energies. Emission spectra have not yet been validated, but preliminary results for residual production cross sections are shown.
I.
INTRODUCTION
Many nuclear data evaluations and related validation methods revolve around TALYS. TALYS is software for the analysis and prediction of nuclear reactions that involve neutrons, photons, protons, deuterons, tritons, 3 Heand alpha-particles, and formally for target nuclides of mass 5 and heavier, while results are expected to be reasonable for masses heavier than 20. To achieve this, a suite of nuclear reaction models has been implemented into a single code system. This enables to evaluate nuclear reactions from the unresolved resonance range up to intermediate energies. TALYS is extensively used for both basic and applied science. At the time of this writing, TALYS has been used in more than 600 different publications since its initial release in 2004. Fig.1 shows a classification of these papers. An extensive description of TALYS and the nuclear data evaluation and validation software built around it has recently been published[1]. Therefore, we restrict ourselves here to a recent important feature: extension to higher energies. II.
TALYS EXTENSION TO 1 GEV
An interesting question is: at what incident energy does TALYS finally fail to produce reasonable results? The formal limit of TALYS-1.4 is 250 MeV, and this limit was set because the KD03 optical model potential [2] that lies at the base of most calculations is known to perform well up to about 200 MeV and reasonably up to about 250 MeV. If we want to extend this limit to higher energies,
∗
Corresponding author: [email protected]
http://dx.doi.org/10.1016/j.nds.2014.04.033 0090-3752/2014 Published by Elsevier B.V.
we need to worry about, at least, 4 possible aspects: • The optical model potential needs to be extended to higher energies, such that the non-elastic cross section provides a reasonable overall scaling factor for all partial channels • The exciton model for pre-equilibrium reactions needs to be valid up to a certain energy. Fortunately, in other studies and reaction codes, it has been verified that the exciton model can be applied up to quite high energies. Moreover, a multiple preequilibrium scheme up to any order of emission is present in TALYS, so that the available phase space is at least correctly estimated. • We should be aware of the fact that at some point the omission of reaction mechanisms will perturb the prediction of the other channels, in terms of reaction competition. examples are pion production and multifragmentation. • In a deterministic code such as TALYS, it is clear that an equidistant exciton energy grid for multiple Hauser-Feshbach decay is no longer appropriate. Therefore, in the current working version of TALYS, this has indeed been generalized to logarithmically spaced energy bins for all residual nuclides in the reaction chain. This also gives better numerical precision at lower incident energies. The best strategy is then to make sure that TALYS is computationally robust until an energy as high as possible, and to let physical arguments and performance against measurement decide at which energy the validity of TALYS is breaking down. In the next release version of TALYS, the energy limit will be 1 GeV. In this paper, we will address the first issue in the list above.
Extension of TALYS . . .
NUCLEAR DATA SHEETS
A.J. Koning et al.
FIG. 1. Worldwide use of TALYS per year and per application area.
A.
Next, c can be determined by requiring that the highenergy potential is equal to that of the low energy expression Eq. (1) at the joining energy
Optical Model Extension to 1 GeV
To be able to predict the total, elastic and non-elastic cross sections up to 1 GeV, the KD03 OMP [2] has been phenomenologically extended. It is emphasized here that this was just done to test at which energy the validity of TALYS in predicting other (residual) cross section will fail. We are well aware of the fact that the usual Schr¨ odinger picture of the OMP is valid up to about 180 MeV, and should then be taken over by a Dirac approach. Nevertheless, a functional form was be constructed which leaves all KD03 parameter values below a joining energy EJ , at or around 200 MeV, unaltered while smoothly extending the energy dependence above EJ . This was only applied to the real, VV , and imaginary, WV , volume parts of the potential. For that, the KD03 OMP for neutrons below EJ reads [2]
VV (EJ ) = V∞ + (VV (Efn ) − V∞ ) exp(−c(EJ − Efn )), (5) giving c=−
WV (E) = w3n
v4n (E − Efn )3 ] (E − Efn )2 , (E − Efn )2 + (w2n )2 (1) is the Fermi energy. For VV , we assume that the where exponential decrease should continue beyond EJ . After all, the KD03 form of Eq. (1) for VV is just a Taylor expansion of the exponential function, in which we gave ourselves the freedom to alter the individual coefficients v1 , etc. Also, following studies like [3, 4], we assume that it converges to a negative value V∞ . Hence, the form chosen for E > EJ is VV (E) = V∞ + b. exp(−c(E −
b=
− V∞ .
VV (E) =
+ d,
(7)
(EJ − Efn )4 (EJ − Efn )4 + (w4n )4
(8)
In sum, we have the following simple extension of the KD03 OMP for E > EJ VV (E) = V∞ + (VV (Efn ) − V∞ ) E − Efn VV (EJ ) − V∞ × log( ) , × exp EJ − Efn VV (Efn ) − V∞
(2)
WV (E) = WV (EJ ) − w3n
(3)
Hence V∞ +(VV (Efn )−V∞ ) exp(−c(E−Efn )).
(E − Efn )4 + (w4n )4
d = WV (EJ ) − w3n
We determine the new parameters b and c by calculating the value at E = Efn , giving VV (Efn )
(E − Efn )4
where we find that a power of 4, instead of the usual 2, gives a better description of experimental data. Also here, a parameter d was added to ensure a value exactly equal to KD03 at EJ , i.e. at E = EJ we have
Efn
Efn )).
(6)
For WV it is expected that at high energies new absorption channels, such as pion production, emerge and that WV will show another smooth increase as function of energy. Hence, the form of WV for E > EJ is
VV (E) = v1n [1 − v2n (E − Efn ) + v3n (E − Efn )2 − WV (E) = w1n
1 VV (EJ ) − V∞ ). log( (EJ − Efn ) VV (Efn ) − V∞
+ w3n
(4) 188
(EJ − Efn )4
(EJ − Efn )4 + (w4n )4
(E − Efn )4 . (E − Efn )4 + (w4n )4
(9)
Extension of TALYS . . .
NUCLEAR DATA SHEETS
Neutron total cross section
Proton non−elastic cross section
5000
2500 TALYS Finlay (1993) Finlay (1993) Abfalterer (2001)
3000
197
TALYS EXFOR 2000
Cross section [mb]
4000
Cross section [mb]
A.J. Koning et al.
Au
2000
1500
197
Au
1000
93
93
Nb
Nb
1000
500 27
27
Al
0
0
100
200
300
400 500 600 Energy [MeV]
700
800
900
1000
0
0
100
200
300
400 500 600 Energy [MeV]
700
Al
800
900
1000
FIG. 2. High energy neutron total and proton non-elastic cross sections.
which joins smoothly with the KD03 expression of Eq. (1) for E < EJ . The following, preliminary, values were obtained from a fit to neutron total and proton non-elastic cross sections up to 1 GeV EJ V∞ w3n w4n
= = = =
Angular distributions and emission spectra have not yet been investigated, but Fig. 3 shows some preliminary results for residual production cross sections.
200. −30. 25. − 0.0417A 250.
III.
CONCLUSIONS
The nuclear data evaluation system built around TALYS is progressing in two main directions: a) automation of nuclear data evaluation, including smooth connection between the Resolved Resonance Region (RRR), Unresolved Resonance Region (URR) and fast range, processing and validation, for increased performance of the TENDL nuclear data library and new uncertainty methods to improve uncertainty propagation for nuclear systems, and b) extended capabilities of the TALYS code itself, such as extension to 1 GeV, medical isotope production and increased flexibility for data fitting to enable production of better quality nuclear data libraries. Here we have described the latter.
(10) In Eq. (9), VV (Efn ), VV (EJ ) and WV (EJ ) are obtained from Eq. (1). The above extension and parameters also hold for incident protons. Fig. 2 shows a few examples of total and non-elastic cross sections up to 1 GeV, obtained with above parameterization. It can be concluded that while the predictive power of the KD03 OMP for neutron total cross sections below 200 MeV was claimed to be within 2%, this claim needs to be relaxed somewhat at higher energies where, at the moment, this deviation can amount to about 5%.
This extension has been implemented in TALYS to enable complete nuclear reaction calculations up to 1 GeV.
Acknowledgements: The authors are indebted to Dr. J.-C Sublet (CCFE) for useful suggestions. This work was funded by Dutch ministry of Economic Affairs, the EU FP7 Fission project ANDES, and the Fusion for Energy FPA-168 project.
[1] A.J. Koning and D. Rochman, Nucl. Data Sheets 113, 2841 (2012). [2] A.J. Koning and J.P. Delaroche, Nucl. Phys. A713, 231 (2003).
[3] S. Typel, O. Riedl, H.H. Wolter, Nucl. Phys. A709, 299 (2002). [4] S. Chiba et al., in Meet. on the nucleon nucleus opt. model up to 200 MeV, Bruyeres-le-Chatel (1996).
B.
Reaction Calculations
189
Extension of TALYS . . .
NUCLEAR DATA SHEETS nat
Pb(p,x)
202
Pb(p,x)
TALYS Gloris(2001) Kuhnhenn(2001) Kuhnhenn(2001) Aleksandrov(1996) Gloris(1996) Damdinsuren(1989)
40 30 20 10
50 40 30 20 10
10
100 nat
0
1000
Pb(p,x)
10
100 nat
Pb TALYS Alexandrov(1997)
Pb(p,x)
203
Bi TALYS Kuhnhenn(2001)
600
60
Cross section [mb]
Cross section [mb]
1000
Energy [MeV]
198
70
50 40 30 20
500 400 300 200 100
10 10
100
0
1000
1
10
Energy [MeV] nat
100
1000
Energy [MeV]
32
nat
Fe(p,x) P
3.5
TALYS Korteling(1970)
3 2.5 2 1.5 1
51
Fe(p,x) Cr
TALYS AlAbyad(2009) Sisterson(2006) Fassbender(1999) Neumann(1999) Gloris(1998) Michel(1997) Schiekel(1996) Michel(1995) Aleksandrov(1990) Aleksandrov(1989) Michel(1989) Barchuk(1987) Michel(1983) Michel(1980)
200
Cross section [mb]
Cross section [mb]
Tl TALYS Titarenko(2011) Titarenko(1996)
Energy [MeV]
0
202
60
Cross section [mb]
50
Cross section [mb]
208
Tl
60
0
A.J. Koning et al.
150
100
Michel(1979) Schoen(1979) Orth(1976) Perron(1976) Perron(1976) Walton(1976) Weigel(1975) Brodzinski(1971) Cline(1971) Cline(1971) Rayudu(1968) Williams(1967) Honda(1964) Rayudu(1964)
50
0.5 100
0
1000
1
10
Energy [MeV] nat
52
nat
Fe(d,x) Mn TALYS Hermanne(2000) ZhaoWenrongg(1995)
180
100
1000
Energy [MeV] Fe(d,x)
52m
Mn TALYS Clark(1969)
100
Cross section [mb]
Cross section [mb]
160 140 120 100 80 60 40
80 60 40 20
20 0
1
10
100
1000
Energy [MeV]
0
1
10
100
Energy [MeV]
FIG. 3. Residual production cross sections for various projectile and target combinations.
190
1000
Nuclear Data Sheets 118 (2014) 187–190 www.elsevier.com/locate/nds
Extension of TALYS to 1 GeV A.J. Koning,1, ∗ D. Rochman,1 and S.C. van der Marck1 1
Nuclear Research and Consultancy Group NRG, 1755 ZG Petten, The Netherlands
One of the latest features of the TALYS nuclear reaction model code is described: the extension to higher energies. The Koning-Delaroche optical model potential from 2003 has been extended by two simple terms for the volume real and imaginary potentials. The resulting predictions have been tested against available experimental data above 200 MeV and now seem to provide reasonable results up to about 1 GeV. By means of logarithmic binning of the multiple decay scheme in TALYS it is now also possible to calculate non-elastic channels at higher energies. Emission spectra have not yet been validated, but preliminary results for residual production cross sections are shown.
I.
INTRODUCTION
Many nuclear data evaluations and related validation methods revolve around TALYS. TALYS is software for the analysis and prediction of nuclear reactions that involve neutrons, photons, protons, deuterons, tritons, 3 Heand alpha-particles, and formally for target nuclides of mass 5 and heavier, while results are expected to be reasonable for masses heavier than 20. To achieve this, a suite of nuclear reaction models has been implemented into a single code system. This enables to evaluate nuclear reactions from the unresolved resonance range up to intermediate energies. TALYS is extensively used for both basic and applied science. At the time of this writing, TALYS has been used in more than 600 different publications since its initial release in 2004. Fig.1 shows a classification of these papers. An extensive description of TALYS and the nuclear data evaluation and validation software built around it has recently been published[1]. Therefore, we restrict ourselves here to a recent important feature: extension to higher energies. II.
TALYS EXTENSION TO 1 GEV
An interesting question is: at what incident energy does TALYS finally fail to produce reasonable results? The formal limit of TALYS-1.4 is 250 MeV, and this limit was set because the KD03 optical model potential [2] that lies at the base of most calculations is known to perform well up to about 200 MeV and reasonably up to about 250 MeV. If we want to extend this limit to higher energies,
∗
Corresponding author: [email protected]
http://dx.doi.org/10.1016/j.nds.2014.04.033 0090-3752/2014 Published by Elsevier B.V.
we need to worry about, at least, 4 possible aspects: • The optical model potential needs to be extended to higher energies, such that the non-elastic cross section provides a reasonable overall scaling factor for all partial channels • The exciton model for pre-equilibrium reactions needs to be valid up to a certain energy. Fortunately, in other studies and reaction codes, it has been verified that the exciton model can be applied up to quite high energies. Moreover, a multiple preequilibrium scheme up to any order of emission is present in TALYS, so that the available phase space is at least correctly estimated. • We should be aware of the fact that at some point the omission of reaction mechanisms will perturb the prediction of the other channels, in terms of reaction competition. examples are pion production and multifragmentation. • In a deterministic code such as TALYS, it is clear that an equidistant exciton energy grid for multiple Hauser-Feshbach decay is no longer appropriate. Therefore, in the current working version of TALYS, this has indeed been generalized to logarithmically spaced energy bins for all residual nuclides in the reaction chain. This also gives better numerical precision at lower incident energies. The best strategy is then to make sure that TALYS is computationally robust until an energy as high as possible, and to let physical arguments and performance against measurement decide at which energy the validity of TALYS is breaking down. In the next release version of TALYS, the energy limit will be 1 GeV. In this paper, we will address the first issue in the list above.
Extension of TALYS . . .
NUCLEAR DATA SHEETS
A.J. Koning et al.
FIG. 1. Worldwide use of TALYS per year and per application area.
A.
Next, c can be determined by requiring that the highenergy potential is equal to that of the low energy expression Eq. (1) at the joining energy
Optical Model Extension to 1 GeV
To be able to predict the total, elastic and non-elastic cross sections up to 1 GeV, the KD03 OMP [2] has been phenomenologically extended. It is emphasized here that this was just done to test at which energy the validity of TALYS in predicting other (residual) cross section will fail. We are well aware of the fact that the usual Schr¨ odinger picture of the OMP is valid up to about 180 MeV, and should then be taken over by a Dirac approach. Nevertheless, a functional form was be constructed which leaves all KD03 parameter values below a joining energy EJ , at or around 200 MeV, unaltered while smoothly extending the energy dependence above EJ . This was only applied to the real, VV , and imaginary, WV , volume parts of the potential. For that, the KD03 OMP for neutrons below EJ reads [2]
VV (EJ ) = V∞ + (VV (Efn ) − V∞ ) exp(−c(EJ − Efn )), (5) giving c=−
WV (E) = w3n
v4n (E − Efn )3 ] (E − Efn )2 , (E − Efn )2 + (w2n )2 (1) is the Fermi energy. For VV , we assume that the where exponential decrease should continue beyond EJ . After all, the KD03 form of Eq. (1) for VV is just a Taylor expansion of the exponential function, in which we gave ourselves the freedom to alter the individual coefficients v1 , etc. Also, following studies like [3, 4], we assume that it converges to a negative value V∞ . Hence, the form chosen for E > EJ is VV (E) = V∞ + b. exp(−c(E −
b=
− V∞ .
VV (E) =
+ d,
(7)
(EJ − Efn )4 (EJ − Efn )4 + (w4n )4
(8)
In sum, we have the following simple extension of the KD03 OMP for E > EJ VV (E) = V∞ + (VV (Efn ) − V∞ ) E − Efn VV (EJ ) − V∞ × log( ) , × exp EJ − Efn VV (Efn ) − V∞
(2)
WV (E) = WV (EJ ) − w3n
(3)
Hence V∞ +(VV (Efn )−V∞ ) exp(−c(E−Efn )).
(E − Efn )4 + (w4n )4
d = WV (EJ ) − w3n
We determine the new parameters b and c by calculating the value at E = Efn , giving VV (Efn )
(E − Efn )4
where we find that a power of 4, instead of the usual 2, gives a better description of experimental data. Also here, a parameter d was added to ensure a value exactly equal to KD03 at EJ , i.e. at E = EJ we have
Efn
Efn )).
(6)
For WV it is expected that at high energies new absorption channels, such as pion production, emerge and that WV will show another smooth increase as function of energy. Hence, the form of WV for E > EJ is
VV (E) = v1n [1 − v2n (E − Efn ) + v3n (E − Efn )2 − WV (E) = w1n
1 VV (EJ ) − V∞ ). log( (EJ − Efn ) VV (Efn ) − V∞
+ w3n
(4) 188
(EJ − Efn )4
(EJ − Efn )4 + (w4n )4
(E − Efn )4 . (E − Efn )4 + (w4n )4
(9)
Extension of TALYS . . .
NUCLEAR DATA SHEETS
Neutron total cross section
Proton non−elastic cross section
5000
2500 TALYS Finlay (1993) Finlay (1993) Abfalterer (2001)
3000
197
TALYS EXFOR 2000
Cross section [mb]
4000
Cross section [mb]
A.J. Koning et al.
Au
2000
1500
197
Au
1000
93
93
Nb
Nb
1000
500 27
27
Al
0
0
100
200
300
400 500 600 Energy [MeV]
700
800
900
1000
0
0
100
200
300
400 500 600 Energy [MeV]
700
Al
800
900
1000
FIG. 2. High energy neutron total and proton non-elastic cross sections.
which joins smoothly with the KD03 expression of Eq. (1) for E < EJ . The following, preliminary, values were obtained from a fit to neutron total and proton non-elastic cross sections up to 1 GeV EJ V∞ w3n w4n
= = = =
Angular distributions and emission spectra have not yet been investigated, but Fig. 3 shows some preliminary results for residual production cross sections.
200. −30. 25. − 0.0417A 250.
III.
CONCLUSIONS
The nuclear data evaluation system built around TALYS is progressing in two main directions: a) automation of nuclear data evaluation, including smooth connection between the Resolved Resonance Region (RRR), Unresolved Resonance Region (URR) and fast range, processing and validation, for increased performance of the TENDL nuclear data library and new uncertainty methods to improve uncertainty propagation for nuclear systems, and b) extended capabilities of the TALYS code itself, such as extension to 1 GeV, medical isotope production and increased flexibility for data fitting to enable production of better quality nuclear data libraries. Here we have described the latter.
(10) In Eq. (9), VV (Efn ), VV (EJ ) and WV (EJ ) are obtained from Eq. (1). The above extension and parameters also hold for incident protons. Fig. 2 shows a few examples of total and non-elastic cross sections up to 1 GeV, obtained with above parameterization. It can be concluded that while the predictive power of the KD03 OMP for neutron total cross sections below 200 MeV was claimed to be within 2%, this claim needs to be relaxed somewhat at higher energies where, at the moment, this deviation can amount to about 5%.
This extension has been implemented in TALYS to enable complete nuclear reaction calculations up to 1 GeV.
Acknowledgements: The authors are indebted to Dr. J.-C Sublet (CCFE) for useful suggestions. This work was funded by Dutch ministry of Economic Affairs, the EU FP7 Fission project ANDES, and the Fusion for Energy FPA-168 project.
[1] A.J. Koning and D. Rochman, Nucl. Data Sheets 113, 2841 (2012). [2] A.J. Koning and J.P. Delaroche, Nucl. Phys. A713, 231 (2003).
[3] S. Typel, O. Riedl, H.H. Wolter, Nucl. Phys. A709, 299 (2002). [4] S. Chiba et al., in Meet. on the nucleon nucleus opt. model up to 200 MeV, Bruyeres-le-Chatel (1996).
B.
Reaction Calculations
189
Extension of TALYS . . .
NUCLEAR DATA SHEETS nat
Pb(p,x)
202
Pb(p,x)
TALYS Gloris(2001) Kuhnhenn(2001) Kuhnhenn(2001) Aleksandrov(1996) Gloris(1996) Damdinsuren(1989)
40 30 20 10
50 40 30 20 10
10
100 nat
0
1000
Pb(p,x)
10
100 nat
Pb TALYS Alexandrov(1997)
Pb(p,x)
203
Bi TALYS Kuhnhenn(2001)
600
60
Cross section [mb]
Cross section [mb]
1000
Energy [MeV]
198
70
50 40 30 20
500 400 300 200 100
10 10
100
0
1000
1
10
Energy [MeV] nat
100
1000
Energy [MeV]
32
nat
Fe(p,x) P
3.5
TALYS Korteling(1970)
3 2.5 2 1.5 1
51
Fe(p,x) Cr
TALYS AlAbyad(2009) Sisterson(2006) Fassbender(1999) Neumann(1999) Gloris(1998) Michel(1997) Schiekel(1996) Michel(1995) Aleksandrov(1990) Aleksandrov(1989) Michel(1989) Barchuk(1987) Michel(1983) Michel(1980)
200
Cross section [mb]
Cross section [mb]
Tl TALYS Titarenko(2011) Titarenko(1996)
Energy [MeV]
0
202
60
Cross section [mb]
50
Cross section [mb]
208
Tl
60
0
A.J. Koning et al.
150
100
Michel(1979) Schoen(1979) Orth(1976) Perron(1976) Perron(1976) Walton(1976) Weigel(1975) Brodzinski(1971) Cline(1971) Cline(1971) Rayudu(1968) Williams(1967) Honda(1964) Rayudu(1964)
50
0.5 100
0
1000
1
10
Energy [MeV] nat
52
nat
Fe(d,x) Mn TALYS Hermanne(2000) ZhaoWenrongg(1995)
180
100
1000
Energy [MeV] Fe(d,x)
52m
Mn TALYS Clark(1969)
100
Cross section [mb]
Cross section [mb]
160 140 120 100 80 60 40
80 60 40 20
20 0
1
10
100
1000
Energy [MeV]
0
1
10
100
Energy [MeV]
FIG. 3. Residual production cross sections for various projectile and target combinations.
190
1000