Nuclear data evaluation of 206Pb for proton- andneutron-induced reaction in energy region from 20 to200 MeV
Tsuyoshi Kajimoto1 , Nobuhiro Shigyo1 , Kenji Ishibashi1 , Satoshi Kunieda2 ,and Tokio Fukahori212Kyushu University, 744 Nishi-ku, Motooka, Fukuoka 819-0395 Japan
Japan Atomic Energy Agency, Tokai, Naka, Ibaraki 319-1195, Japan

Nuclear data evaluation was carried out for 206 Pb for proton and neutron incidence
in the energy range from 20 to 200 MeV by using the ECIS-96 and the GNASH code.
Evaluated cross sections were compared with mesurement data and the LA150 evaluations.

1

Introduction

The evaluated nuclear data in the intermediate energy range for various nuclei arerequired such technologies as spallation neutron sources, accelerator shielding design, radiation therapy, and space developments. The program for completion of the JENDL HighEnergy File (JENDL-HE)1) is now ongoing under the Japanese Nuclear Data Committee
to meet these needs. The 2007 version of JENDL-HE will be published this year.
In the shielding design of high energy accelerators, lead is one of the important shieldelement. Evaluating nuclear data for lead is necessary to the recent and the future nuclear
technologies. In this work, the evaluation of neutron and proton induced nuclear datafor 206 Pb was performed using the GNASH code system. The evaluations for neutron
incidence were started at 20 MeV that was the upper limit of existing data files for fission
and fusion reactors.
The optical model analysis was carried out as the initial approach. The ECIS-96 code2)
was adopted for the optical model calculation. It was also applied to obtain transmission
coefficients of induced- and outgoing-particles which were required for the statistical model
calculations, and to evaluate elastic- and inelastic- scattering, total and total-reaction
cross sections. The GNASH code3) was used in order to calculate light particle spectraand isotope-production cross sections. The code employed the Hauser-Feshbach model
for statisical decay process, and the exciton model for pre-equilibrium processes.
We made evaluations for such values of total, total-reaction, angular-differential elasticscattering, energy-differential particle-production, and double-differential particle-production
cross sections. The validities of calculated excitation functions for isotope-production
cross sections were also investigated. Present results were compared with the LA1504)
evaluations.

2

Optical model calculation

The optical model is one of the most efficient method to calculate angular-differential
elastic-scattering, total and total reaction cross sections. In the model calculation, theoptical model potential (OMP) parameters were essential to be optimized. They are also

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important values to provide transmission coefficient required in the statical model calculation. Therefore, the optical potential was searched for so as to obtain good descriptionsof measured data. In this work, we assumed the OMP could be described with following
functional froms.
´·³01 †2 †2DISP −λR E †VR = VR + VR E + VR E + VRe
1+01N −Z(−1)Z +1 Cviso
0DISPA
VR + VR³ ´
ZZ 0ρ
E† ,coulA1/32E†
DISP
WV = WV,
2E † + W IDV2·¸
2N − Z −λD E †E†Z 0 +1DISPWD = WD+ (−1)
Cwisoe,22AE † + W IDD+Ccoul†

0 −λSO E
VSO = VSOe,DISPWSO = WSO

¸

(1)
(2)
(3)
(4)

E

†222E † + W IDSO.

(5)

The functions were proposed by Soukhovitskii et al.5) The symbols VR , WV , WD , VSO andWSO correspond to real volume, imaginary volume, imaginary surface, real and imaginary
spin-orbit terms of potential depths in MeV, respectively. The spin-orbit parameters weretaken from those of Koning and Delaroche.6) The parameters A, Z , N and Z 0 are thenumbers of nucleon, proton, neutron in target nucleus and charge-number of projectile
particle, respectively. The E † expresses the relative projectile-energy to the Fermi energy
Ef . The ρcoul stands for the Coulomb term which is written as follows.
³´·†ρcoul = λR VRDISP e−λR E − VR1 − 2VR2 E † 1 +¸
1N −Z
Z 0 +1. (6)(−1)
CvisoA
VR0 + VRDISPThe Woods-Saxon form fR,D,V,SO was utilized to described geometries of the optical potential. The optical potential is described as,·¸dV (r) = −VR fR (r) + i 4WD aD fD (r) − WV fV (r)drµ¶2h̄
1 d+fSO (r) L · σ + VCoul (r) .
(VSO + iWSO )mπ cr dr(7)The symbols L and σ stand for the orbital angular-momentum for the relative motion
and the Pauli matrices of projectile. The VCoul (r) indicates the Coulomb potential.
At first, the OMP parameters were searched for the neutron-incidence interactions.
The initial OMP parameters were taken from the local parameter set proposed by Kunieda et al.7) Parameters VR0−2,DISP , λR,D , WDDISP , and W IDD,V were adjusted so as toobtain acculate descriptions of measured total and elastic scattering differential cross sections. The determined OMP parameters are listed in Table 1. The evaluated total andangular-differential elastic-scattering cross sections are shown together with experimental
data in Figs. 1 and 2, respectively. The characteristic of proton and neutron is analogous except for the Coulomb effects. Therefore, the OMP parameters for proton weredetermined by modifying those for neutron. The determined OMP parameters for proton are also listed in Table 1. Figure 2 gives evaluated proton-induced angular-differential
elastic-scattering cross sections together with measured data. Good agreements were seen
between calculated and experiment data.
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Table 1: OMP parameters used in evaluationof 206 Pb.

VRDISPλR

WDDISPW IDDλDWVDISPW IDVaEf
1010

σ [b]

64810n+Pb, Total

0050

100

150200Incident Neutron Energy [MeV]Fig. 1: Present evaluation and measureddata9) for neutron-induced total cross sections on 206 Pb.
1010

J.C.Ferrer,Pb(1977)
206
N.Olsson, 208Pb(1987)
R.P.Devito, 0Pb(1980)
E.L.Hjort, 0Pb(1990)
M.Ibaraki,Pb(2002)
208
J.Klug 208Pb(2003)
J.H.Osborne,Pb(2004)
Present work

Pb(n, n)

206

2

206

206

0

D.C.Larson, Pb(1980)
0
W.P.Abfalterer, 0Pb(2001)
P.H.Bowen,Pb(1961)
208
R.W.Finlay, 206Pb(1993)
S.F.Hicks, 206Pb(1994)
D.G.Foster,Pb(1971)
LA150
Present work

8neutronproton
−35.3
−39.5
0.02
0.03
0.000145 0.000125
93.28
99.18
0.00450.00445
16.5
15.0
16.0
9.0
0.01850.0155
18.0
17.0
110.0
105.0
0.671
0.671
−8.09
−7.25

VR0
VR1
VR2

10208

206

R.Varner, 206Pb(1986)
J.E.Finck, 208Pb(1983)
H.Sakaguchi, 208Pb(1982)
A.Nadasen, 208Pb(1981)
D.A.Hutcheon,Pb(1988)
Present work

Pb(p, p)810

511.01 MeV (x10 )

6

106

10

4

16.0 MeV (x10 )4

21.6 MeV (x10 )4104

335.0 MeV (x10 )330.0 MeV (x10 )dσ/dΩ [mb/sr]

dσ/dΩ [mb/sr]

102

40.0 MeV (x10 )
210210265.0 MeV (x10 )010155.0 MeV (x10 )180.0 MeV (x10 )01065.0 MeV-210-1-2

75.0 MeV (x10 )10-410-4-3

10155.0 MeV (x10 )-2

96.0 MeV (x10 )121.0 MeV

-6-1

10160.0 MeV (x10 )-4-3

185.0 MeV (x10 )
02040200.0 MeV (x10 )
60

80100 120θcm [degree]

1401601800204060-2

182.0 MeV (x10 )
80100 120θcm [degree]

140160180

Fig. 2: Present evaluations and measured data9) for neutron- and proton-induced angulardifferential elastic-scattering cross sections on 206 Pb.

3The GNASH calculations

The GNASH code was utilized for calculating energy-differential cross sections forthe productions of light-particles (neutron, proton, deuteron, triton, 3 He and α-particle)
and isotope-production cross sections. The code was basically the same one employed in
the LA150 evaluations. In the Mote Carlo simulations for high energy applications, theangular distributions of emission particles are important. Therefore, double-differential
cross sections were also calculated for the emitted particles by using the Kalbach angulardistribution systematics.8)
The exciton model has some adjustable parameters such as the single-particle state2006 Symposium on Nuclear Data

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density parameter g and the average squared matrix element | M |2 . The evaluation of
double-differential cross sections was implemented by adjusting these parameters. The
results deduced in the laboratory frame are compared with available experimental data
and the LA150 evaluations in Fig. 3 for (n, xp) and Fig. 4 for (p, xn) and (p, xp). The
evaluations of isotope-production cross sections are presented together with experimental
data and the LA150 evaluations in Figs. 5 and 6. These results show that the evaluatedcross sections give good agreements with experimental data. However, there was large
discrepancy between evaluated and experimental isotope-production cross sections forsome residual nuclei. One of the reasons might be due to some imperfect descriptions ofthe level density parameters.
0V.Blideanu(2004)(natural data)
LA150
Present work

410o

3o2

V.Blideanu, Pb(2002)
LA150
Present work

410o

3o2o1

20.0 (x10 )20.0 (x10 )30.0 (x10 )40.0 (x10 )
2102

1040.0 (x10 )o1

60.0 (x10 )od σ/dΩ/dE [mb/sr/MeV]o1080.0o

1o-2o-3100.0 (x10 )-210010120.0 (x10 )o-1

70.0 (x10o-2)

o-3)

60.0 (x10 )-21022d σ/dΩ/dE [mb/sr/MeV]

50.0
0110.0 (x10-410-4

140.0 (x10 )

10o-4

160.0 (x10 )
-6

10-6

o

10-4

206

160.0 (x10 )
206

Pb (n, xp) 96.0MeV

020Pb (n, xp) 62.7MeV-8406080

1010001020

proton emission energy [MeV]3040506070

proton emission energy [MeV]Fig. 3: Present evaluations and experimental data9) of double-differential cross sectionsfor (n, xp) reactions on 206 Pb at 96 MeV, and 62.7 MeV.

81020810206

10W.Scobel, Pb(1990)
Present work

Pb(p, xn) 160.3MeVoM.M.Meier, Pb(1989)
LA150
Present workood σ/dΩ/dE [mb/sr/MeV]

3
230 (x10 )22o1o4o3o2o148.0 (x10 )56.0 (x10 )

21069.0 (x10 )010o

82.060 (x10 )

110102o165.0 (x10 )o

75.0

010oooo-2-410-3o-4-3o-4o-5135.0 (x10 )-4oo

115.0 (x10 )106.0 (x10 )10-295.0 (x10 )

10-1o

150

10-1

85.0 (x10 )-295.0 (x10 )

-2

100

3o

55.0 (x10 )
2

102

10

545.0 (x10 )45.0 (x10 )

4101035.0 (x10 )37.5 (x10 )

o

4o

6410o

5o

24.0 (x10 )64o

25.0 (x10 )35.0 (x10 )Pb(p, xn) 113.0MeV

1061072206

o11.0 (x10 )d σ/dΩ/dE [mb/sr/MeV]

510d σ/dΩ/dE [mb/sr/MeV]

8100Pb(2005)
LA150
Present work

Pb(p, xp) 62.9MeV

80.0 (x10 )
610208

A.Guertin,
206

121.0 (x10 )-110020406080

100120neutron emission energy [MeV]-610134.0 (x10 )-610155.0 (x10 )o-810-5

145.0 (x10 )
02040

60-880100120neutron emission energy [MeV]

14016010010203040

506070neutron emission energy [MeV]Fig. 4: Present evaluations and experimental data9) of double-differential cross sectionsfor (p, xn) and (p, xp) reactions on 206 Pb at 113 MeV, 160.3 MeV, and 62.9 MeV.

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206

A.J.Plompen, Pb(2002)
206
P.Reimer, Pb(2001)
Present work

1000

σ [mb]σ [mb]

1

206

206

Pb(n, x)203

Pb(n, x)

203

Hg

100
Hg
206

J.Frehaut, Pb(1980)
Present work

0.1
010203040500510Incident Neutreon Energy [MeV]

15202530Incident Neutreon Energy [MeV]Fig. 5: Present evaluations, experimental data9) of isotope-production cross sections forneutron incidence.
1000

206

206

206

Titarenko, Pb(2004)
206
R.E.Bell, Pb(1956)
LA150
Present work

Titarenko, Pb(2004)
206
C.Deptula,206Pb(1990)
R.E.Bell, Pb(1956)
LA150
Present work

Titarenko,206Pb(2004)
R.E.Bell, Pb(1956)
LA150
Present work

1000

100

202

206

Bi

100

206

Pb(p, x)

204

Bi

100

1050

100

150

200incident proton energy [MeV]

206

Bi

10100Pb(p, x)

σ [mb]

Pb(p, x)σ [mb]σ [mb]

206

1050100incident proton energy [MeV]150

200050100150

200incident proton energy [MeV]Fig. 6: Present evaluations, experimental data9) and LA150 evaluations of isotopeproduction cross sections for proton incidence.

4Summary

The evaluation of cross sections for 206 Pb was performed for neutron- and protoninduced reactions by using the ECIS-96 and the GNASH code. The energy range ofevaluation was from 20 to 200 MeV. The global optical potentials were adopted to allow
the continuous evaluation for the incident energy. The optical model potential parameters
were determined to give good agreements with experimental data of total and angulardifferential elastic scattering cross sections. The GNASH code was used for evaluationsof energy-differential particle-production cross sections and isotope-production cross sections. Double-differential cross-sections of the emitted particles were calculated on thebasis of the Kalbach systematics. Present evaluations were compared with the available experimental data and LA150. Good overall agreements were obtained. However,there was large discrepancy between evaluated and experimental isotope-production crosssections for some residual nuclei.

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Acknowledgments
The authors would like to appreciate technical supports for all the members of Nuclear
Data Center at Japan Atomic Energy Agency.

References
1) T. Fukahori, Y. Watanabe, N. Yoshizawa, F. Maekawa, S. Meigo, C. Konno, N. Yamano, AY Konobeyev, and S. Chiba, J. Nucl. Sci. Technol. Suppl., 2, 25, (2002).
2) J. Raynal, Notes on ECIS94, Report CEA-N-2772, Centre d’Etude de Saclay CEA,Saclay, France (1994).
3) P. G. Young, E. D. Arthur, M. B. Chadwick, in: Workshop on Nuclear Reaction Data
and Nuclear Reactors, Trieste, Italy, 15 April.17 May 1996, p. 227.
4) M. B. Chadwick, P. G. Young, S. Chiba, S. C. Frankle, G. M. Hale, H. G. Hughes, A.
J. Koning, R. C. Little, R. E. MacFarlane, R. E. Prael, et al., Nucl. Sci. Eng., 131,293 (1999).
5) E. Sh. Soukhovitskii, S. Chiba, O Iwamoto, et al., JAERI-Data/Code 2005-002 (2005).
6) A. J. Koning, J. P. Delaroche, Nucl. Phys., A713, 231 (2003).
7) S. Kunieda, S. Chiba, K. Shibata, A. Ichihara, Efrem Sh. Sukhovitskii, published toJ. Nucl. Sci. Technol., 44.
8) C. Kalbach, Phys. Rev. C, 37, 2350 (1988).
9) EXFOR cross section data online at http://www.nea.fr/html/dbdata/x4/welcome.htm

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