- Email: [email protected]
Production and multiplication of neutrons in lead targets induced by protons above 1 GeV
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 562 (2006) 747–749 www.elsevier.com/locate/nima
Production and multiplication of neutrons in lead targets induced by protons above 1 GeV Vladimir I. Yurevicha,, Robert M. Yakovlevb, Ratmir G. Vassilkovc, Vadim A. Nikolaevb, Vladimir G. Lyapinb, Igor O. Tsvetkovb a Joint Institute for Nuclear Research, Joliot Ccurie 6, Dubna 141980, Russia V.G. Khlopin Radium Institute, 2nd Murinsky Av. 28, St. Petersburg 194021, Russia c Moscow Radio-Engineering Institute of RAS, Warshavskoye chaussee 132, Moscow 113519, Russia b
Available online 2 March 2006
Abstract The results on neutron production in various lead targets obtained in measurements with 1–3.7 GeV proton beam by the TOF and threshold detector methods are given. It is shown that the modified Moving Source Model is a good tool for fitting of the neutron doubledifferential cross-section above 0.5 GeV with approximately constant temperature parameters. Analysis of available experimental data shows a saturation effect for the neutron multiplicity in the reaction Pbðp; nxÞ with the proton energy. For the extended lead target 20 diam: 60 cm secondary nuclear interactions in the target give a large and increasing with energy contribution to the neutron yield. For this target the mean neutron multiplicity per unit of proton energy has a broad maximum in a range 1–2 GeV. The same function but for the kinetic energy of neutrons continues to grow with the beam energy due to increasing of the average energy of neutrons. This phenomenon could be used for further multiplication of neutrons in a target-blanket system. r 2006 Elsevier B.V. All rights reserved. PACS: 25.40.Qa; 25.40.Sc; 28.20.v; 29.30.Hs Keywords: GeV protons; Lead targets; Neutron production; Moving source model; Neutron multiplicity
1. Introduction There are various important applications of neutron sources based on high-current accelerators with highenergy proton beam. Heavy metal targets are usually applied for the conversion of the proton kinetic energy to the neutron radiation, and Pb or Pb–Bi targets are often used for this purpose. A systematic experimental study of neutron production in various lead targets by 1–3.7 GeV protons was performed at the Dubna synchrophasotron for many years. The neutron double-differential cross-section and yields were measured by TOF method with thin ð10 10 0:6 cmÞ and two thick (8 8 8 and 20 diam: 20 cm) lead targets in a wide energy range from 0:3 to 500 MeV in angular interval 30 –150 . The spatial-energy distribuCorresponding author. Tel.: +7 096 216 3841; fax: +7 096 216 5894.
E-mail address: [email protected] (V.I. Yurevich). 0168-9002/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2006.02.038
tion of neutrons emitted from an extended lead target 20 diam: 60 cm was studied by the threshold detector method with a set of fission and fragmentation threshold detectors. Some results were earlier reported in Refs. [1–4]. In this paper, an analysis of experimental data on the neutron double-differential cross-section, neutron multiplicity, and neutron multiplication is presented. 2. Neutron double-differential cross-section Some available TOF results on the double-differential cross-section of neutron production in the reaction Pbðp; nxÞ for proton energies above 500 MeV were analyzed in the framework of modified Moving Source Model (MSM). The MSM includes four moving sources corresponding to main processes of the nuclear system decay with the neutron emission. These processes are (1) the collision of beam proton with one or a few nucleons mainly in the peripheral region of target nucleus, (2) the cascade in
ARTICLE IN PRESS V.I. Yurevich et al. / Nuclear Instruments and Methods in Physics Research A 562 (2006) 747–749
the central collision where many nucleons are involved in creation of an initial hot source, (3) the decay of this hot nuclear system by the fragmentation and (4) the deexcitation of the remnant by the neutron evaporation. Finally, an expression used in our analysis is !, ) ( 4 X d2 s E þ m pbi cos y ¼ pAi exp m Ti dEdO ð1 b2i Þ1=2 i¼1 (1)
100 T1
T2 10 T, MeV
748
T3 T4
where the neutron momentum is calculated as
1
p ¼ ðE 2 þ 2EmÞ1=2 ,
3. Mean neutron multiplicity in reaction The mean neutron multiplicity M was estimated by integration of Eq. (1) with found parameters over the
d2σ/dEdΩ, mb MeV-1 sr-1
7
10
30°(×104)
106
60°(×103)
105
90°(×102)
104
120°(×10)
103
150°
10
35 30 25 20 15 10 M20 5
0.5
1.0
1.5 2.0 Ep , GeV
2.5
3.0
3.5
Fig. 3. A dependence of the mean neutron multiplicities for all neutrons and neutrons with E420 MeV ðM 20 Þ on the proton energy for the reaction Pbðp; nxÞ: ’, our result; &, [5–10]; , [11]; , [13]; n, [16,17]; m, [18] (corrected on high-energy neutron leakage), , [19,20], the solid curve—our fit, the dashed curve—the Cugnon’s formula [15].
102 101 100
1
1 Ep , GeV
Fig. 2. The temperature parameters of the MSM sources found by the fitting of our ðÞ and the LANL ðÞ, KEK ðmÞ and ITEP ð’; .Þ results for the reaction Pbðp; nxÞ at different proton energies.
0 0.0
108
10-1
0.1 0.1
M, neutrons/interaction
E is the kinetic energy of neutron in lab. system (MeV), m – the neutron rest mass (MeV), y – the angle of emitted neutron in lab. frame. There are three parameters for each source: the amplitude Ai , the temperature T i and the velocity bi ¼ V i =c. A result of the fitting to our experimental data is shown in Fig. 1. The same fitting procedure was used for description of the neutron double-differential cross-section for the reaction Pbðp; nxÞ obtained by groups from LANL [5–10], KEK [11] and ITEP [12,13] at various proton energies. It is clearly seen in Fig. 2 that with increasing of the proton energy the temperatures of the sources become constant with values of T 1 ¼ 75 8, T 2 ¼ 21 2, T 3 ¼ 4:7 0:2, and T 4 ¼ 1:65 0:15 MeV. It is interesting to note that in recent studies of the intermediate-mass fragment (IMF) emission in central collisions of light-mass projectiles with heavy nuclei two components with different temperatures closed to the values found for T 2 and T 3 were observed. Probably, this fact means the same origin of the neutron and IMF sources.
10 E, MeV
100
1000
Fig. 1. A result of the neutron double-differential cross-section fitting for the reaction Pbðp; nxÞ at E p ¼ 2 GeV (measurement with 6-mm target).
neutron energy and the solid angle. The reaction crosssection of 1695 mb calculated with the code [14] was used. We obtained that M ¼ 21:8 3:4 neutrons per nuclear interaction of the 2-GeV proton with lead nucleus. The energy dependence of the mean neutron multiplicity was studied on a base of some available experimental results shown in Fig. 3. The fitting to these data gave an expression M ¼ 39ð1 expð0:22E p ÞÞ0:55 ,
(2)
ARTICLE IN PRESS V.I. Yurevich et al. / Nuclear Instruments and Methods in Physics Research A 562 (2006) 747–749
4. Mean neutron multiplicity for lead targets Values of the mean neutron multiplicity obtained for the studied lead targets are given in Table 1. A comparison of these data with the HERMES code prediction [19,20] made for some different lead targets shows a good agreement between our and the calculated results. The mean neutron multiplicity increases with the target dimension because of the neutron multiplication by secondary nuclear interactions inside a lead target. 5. Neutron multiplication in extended target The energy dependence of the neutron multiplication phenomenon for the extended lead target is shown in Fig. 4 where the mean neutron yield Y and the mean yield of neutrons produced in the primary p–Pb interactions Y 1 are presented. The energy dependence of Y 1 was calculated on a base of formula (2). The relative contribution of the primary interactions falls with the proton energy. But the contribution of the secondary interactions to the neutron production increases, and at 3 GeV it becomes about two times higher than in the first process. 6. Choice of beam energy for neutron production For the extended lead target the mean number of neutrons per unit of the proton energy has a maximum between 1 and 2 GeV and falls a bit at higher energies. At the same time the obtained experimental data show that a ratio of the mean kinetic energy of neutrons E kin to the proton energy slowly increases with the beam energy. The energy coming to the neutron production including the energy of neutron separation has the same tendency. A reason of this effect is a growing of the neutron average energy with the beam energy.
Table 1 The mean neutron multiplicities per beam proton interaction for the studied lead targets and two proton energies. For the target 20 diam: 60 cm the mean neutron yield per incident proton is given E p (GeV)
2.0 2.55
Target (cm) 10 10 0:6
888
21:8 3:4
25:6 3:8
20 diam: 20
20 diam: 60
41:4 6:2
44:2 5:3 63:5 7:6
100
80 Y, neutrons/incident proton
where E p is the proton energy in GeV. This dependence is closed to the Cugnon’s formula [15] as it shown in Fig. 3. Also the mean multiplicity of neutrons with energies above 20 MeV is presented in the same figure. Analysis of the experimental data shows that the mean kinetic energy of neutrons in the reaction Pbðp; nxÞ takes about 31% of the beam proton energy in GeV range.
749
60
40 Y1 20
0
0
1
2 Ep , GeV
3
4
Fig. 4. The neutron yield per incident proton Y and the primary interaction contribution Y 1 as functions of the proton energy for the lead target 20 diam: 60 cm: , our data; , [18] (corrected on high-energy neutron leakage), n, [21,22]; the solid curve—the HERMES code prediction [19].
It means that further multiplication of neutrons, for instance in a blanket placed around the extended lead target, probably could shift the maximum of the value Y =E p to a higher energy range. Thus, the question about the optimal proton energy for the neutron production has to be considered for a target-blanket system because of the neutron multiplication effect out of a target. References [1] R.G. Vassilkov, V.I. Yurevich, in: Proceedings of ICANS-XI, KEK, Tsukuba, 22–26 October 1990; KEK Report 90-25, 1991, p. 340. [2] V.A. Nikolaev, et al., in: Proceedings of ICANS-XI, KEK, Tsukuba, 22–26 October 1990; KEK Report 90-25, 1991, p. 612. [3] A.V. Daniel, et al., JINR Commun. E1-92-174, Dubna, 1992. [4] V. Yurevich, Radiat. Prot. Dosim. 116 (1–4) (2005) 636. [5] M.M. Meier, et al., Nucl. Sci. Eng. 102 (1989) 310. [6] M.M. Meier, et al., Nucl. Sci. Eng. 110 (1992) 289. [7] W.B. Amian, et al., Nucl. Sci. Eng. 112 (1992) 78. [8] W.B. Amian, et al., Nucl. Sci. Eng. 115 (1993) 1. [9] S. Stamer, et al., Phys. Rev. C 47 (1993) 1647. [10] B.E. Bonner, et al., Phys. Rev. C 18 (1978) 1418. [11] T. Nakamoto, et al., J. Nucl. Sci. Technol. 32 (1995) 827. [12] Yu. Bayukov, et al., Preprint ITEP-172, M., 1983. [13] Yu. Trebukhovsky, et al., Preprint ITEP 3-03, M., 2003. [14] N.S. Amelin, M.E. Komogorov, Phys. Particles and Nuclei Lett. 3 (100) (2000) 35; N.S. Amelin, M.E. Komogorov, JINR Commun. D11-2001-175, Dubna, 2001. [15] J. Cugnon, et al., Nucl. Phys. A 625 (1997) 729. [16] X. Ledoux, et al., Phys. Rev. Lett. 82 (1999) 4412. [17] S. Leray, et al., Phys. Rev. C 65 (2002) 044621. [18] R.G. Vassilkov, et al., At. Energ. 79 (1995) 257. [19] A. Letourneau, et al., Nucl. Instr. and Meth. B 170 (2000) 299. [20] D. Filges, et al., Eur. Phys. J. A 11 (2001) 467. [21] J.S. Fraser, et al., Phys. Canada 21 (2) (1965) 17. [22] J.S. Fraser, et al., Trans. Amer. Nucl. Soc. 28 (1978) 754.
Nuclear Instruments and Methods in Physics Research A 562 (2006) 747–749 www.elsevier.com/locate/nima
Production and multiplication of neutrons in lead targets induced by protons above 1 GeV Vladimir I. Yurevicha,, Robert M. Yakovlevb, Ratmir G. Vassilkovc, Vadim A. Nikolaevb, Vladimir G. Lyapinb, Igor O. Tsvetkovb a Joint Institute for Nuclear Research, Joliot Ccurie 6, Dubna 141980, Russia V.G. Khlopin Radium Institute, 2nd Murinsky Av. 28, St. Petersburg 194021, Russia c Moscow Radio-Engineering Institute of RAS, Warshavskoye chaussee 132, Moscow 113519, Russia b
Available online 2 March 2006
Abstract The results on neutron production in various lead targets obtained in measurements with 1–3.7 GeV proton beam by the TOF and threshold detector methods are given. It is shown that the modified Moving Source Model is a good tool for fitting of the neutron doubledifferential cross-section above 0.5 GeV with approximately constant temperature parameters. Analysis of available experimental data shows a saturation effect for the neutron multiplicity in the reaction Pbðp; nxÞ with the proton energy. For the extended lead target 20 diam: 60 cm secondary nuclear interactions in the target give a large and increasing with energy contribution to the neutron yield. For this target the mean neutron multiplicity per unit of proton energy has a broad maximum in a range 1–2 GeV. The same function but for the kinetic energy of neutrons continues to grow with the beam energy due to increasing of the average energy of neutrons. This phenomenon could be used for further multiplication of neutrons in a target-blanket system. r 2006 Elsevier B.V. All rights reserved. PACS: 25.40.Qa; 25.40.Sc; 28.20.v; 29.30.Hs Keywords: GeV protons; Lead targets; Neutron production; Moving source model; Neutron multiplicity
1. Introduction There are various important applications of neutron sources based on high-current accelerators with highenergy proton beam. Heavy metal targets are usually applied for the conversion of the proton kinetic energy to the neutron radiation, and Pb or Pb–Bi targets are often used for this purpose. A systematic experimental study of neutron production in various lead targets by 1–3.7 GeV protons was performed at the Dubna synchrophasotron for many years. The neutron double-differential cross-section and yields were measured by TOF method with thin ð10 10 0:6 cmÞ and two thick (8 8 8 and 20 diam: 20 cm) lead targets in a wide energy range from 0:3 to 500 MeV in angular interval 30 –150 . The spatial-energy distribuCorresponding author. Tel.: +7 096 216 3841; fax: +7 096 216 5894.
E-mail address: [email protected] (V.I. Yurevich). 0168-9002/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2006.02.038
tion of neutrons emitted from an extended lead target 20 diam: 60 cm was studied by the threshold detector method with a set of fission and fragmentation threshold detectors. Some results were earlier reported in Refs. [1–4]. In this paper, an analysis of experimental data on the neutron double-differential cross-section, neutron multiplicity, and neutron multiplication is presented. 2. Neutron double-differential cross-section Some available TOF results on the double-differential cross-section of neutron production in the reaction Pbðp; nxÞ for proton energies above 500 MeV were analyzed in the framework of modified Moving Source Model (MSM). The MSM includes four moving sources corresponding to main processes of the nuclear system decay with the neutron emission. These processes are (1) the collision of beam proton with one or a few nucleons mainly in the peripheral region of target nucleus, (2) the cascade in
ARTICLE IN PRESS V.I. Yurevich et al. / Nuclear Instruments and Methods in Physics Research A 562 (2006) 747–749
the central collision where many nucleons are involved in creation of an initial hot source, (3) the decay of this hot nuclear system by the fragmentation and (4) the deexcitation of the remnant by the neutron evaporation. Finally, an expression used in our analysis is !, ) ( 4 X d2 s E þ m pbi cos y ¼ pAi exp m Ti dEdO ð1 b2i Þ1=2 i¼1 (1)
100 T1
T2 10 T, MeV
748
T3 T4
where the neutron momentum is calculated as
1
p ¼ ðE 2 þ 2EmÞ1=2 ,
3. Mean neutron multiplicity in reaction The mean neutron multiplicity M was estimated by integration of Eq. (1) with found parameters over the
d2σ/dEdΩ, mb MeV-1 sr-1
7
10
30°(×104)
106
60°(×103)
105
90°(×102)
104
120°(×10)
103
150°
10
35 30 25 20 15 10 M20 5
0.5
1.0
1.5 2.0 Ep , GeV
2.5
3.0
3.5
Fig. 3. A dependence of the mean neutron multiplicities for all neutrons and neutrons with E420 MeV ðM 20 Þ on the proton energy for the reaction Pbðp; nxÞ: ’, our result; &, [5–10]; , [11]; , [13]; n, [16,17]; m, [18] (corrected on high-energy neutron leakage), , [19,20], the solid curve—our fit, the dashed curve—the Cugnon’s formula [15].
102 101 100
1
1 Ep , GeV
Fig. 2. The temperature parameters of the MSM sources found by the fitting of our ðÞ and the LANL ðÞ, KEK ðmÞ and ITEP ð’; .Þ results for the reaction Pbðp; nxÞ at different proton energies.
0 0.0
108
10-1
0.1 0.1
M, neutrons/interaction
E is the kinetic energy of neutron in lab. system (MeV), m – the neutron rest mass (MeV), y – the angle of emitted neutron in lab. frame. There are three parameters for each source: the amplitude Ai , the temperature T i and the velocity bi ¼ V i =c. A result of the fitting to our experimental data is shown in Fig. 1. The same fitting procedure was used for description of the neutron double-differential cross-section for the reaction Pbðp; nxÞ obtained by groups from LANL [5–10], KEK [11] and ITEP [12,13] at various proton energies. It is clearly seen in Fig. 2 that with increasing of the proton energy the temperatures of the sources become constant with values of T 1 ¼ 75 8, T 2 ¼ 21 2, T 3 ¼ 4:7 0:2, and T 4 ¼ 1:65 0:15 MeV. It is interesting to note that in recent studies of the intermediate-mass fragment (IMF) emission in central collisions of light-mass projectiles with heavy nuclei two components with different temperatures closed to the values found for T 2 and T 3 were observed. Probably, this fact means the same origin of the neutron and IMF sources.
10 E, MeV
100
1000
Fig. 1. A result of the neutron double-differential cross-section fitting for the reaction Pbðp; nxÞ at E p ¼ 2 GeV (measurement with 6-mm target).
neutron energy and the solid angle. The reaction crosssection of 1695 mb calculated with the code [14] was used. We obtained that M ¼ 21:8 3:4 neutrons per nuclear interaction of the 2-GeV proton with lead nucleus. The energy dependence of the mean neutron multiplicity was studied on a base of some available experimental results shown in Fig. 3. The fitting to these data gave an expression M ¼ 39ð1 expð0:22E p ÞÞ0:55 ,
(2)
ARTICLE IN PRESS V.I. Yurevich et al. / Nuclear Instruments and Methods in Physics Research A 562 (2006) 747–749
4. Mean neutron multiplicity for lead targets Values of the mean neutron multiplicity obtained for the studied lead targets are given in Table 1. A comparison of these data with the HERMES code prediction [19,20] made for some different lead targets shows a good agreement between our and the calculated results. The mean neutron multiplicity increases with the target dimension because of the neutron multiplication by secondary nuclear interactions inside a lead target. 5. Neutron multiplication in extended target The energy dependence of the neutron multiplication phenomenon for the extended lead target is shown in Fig. 4 where the mean neutron yield Y and the mean yield of neutrons produced in the primary p–Pb interactions Y 1 are presented. The energy dependence of Y 1 was calculated on a base of formula (2). The relative contribution of the primary interactions falls with the proton energy. But the contribution of the secondary interactions to the neutron production increases, and at 3 GeV it becomes about two times higher than in the first process. 6. Choice of beam energy for neutron production For the extended lead target the mean number of neutrons per unit of the proton energy has a maximum between 1 and 2 GeV and falls a bit at higher energies. At the same time the obtained experimental data show that a ratio of the mean kinetic energy of neutrons E kin to the proton energy slowly increases with the beam energy. The energy coming to the neutron production including the energy of neutron separation has the same tendency. A reason of this effect is a growing of the neutron average energy with the beam energy.
Table 1 The mean neutron multiplicities per beam proton interaction for the studied lead targets and two proton energies. For the target 20 diam: 60 cm the mean neutron yield per incident proton is given E p (GeV)
2.0 2.55
Target (cm) 10 10 0:6
888
21:8 3:4
25:6 3:8
20 diam: 20
20 diam: 60
41:4 6:2
44:2 5:3 63:5 7:6
100
80 Y, neutrons/incident proton
where E p is the proton energy in GeV. This dependence is closed to the Cugnon’s formula [15] as it shown in Fig. 3. Also the mean multiplicity of neutrons with energies above 20 MeV is presented in the same figure. Analysis of the experimental data shows that the mean kinetic energy of neutrons in the reaction Pbðp; nxÞ takes about 31% of the beam proton energy in GeV range.
749
60
40 Y1 20
0
0
1
2 Ep , GeV
3
4
Fig. 4. The neutron yield per incident proton Y and the primary interaction contribution Y 1 as functions of the proton energy for the lead target 20 diam: 60 cm: , our data; , [18] (corrected on high-energy neutron leakage), n, [21,22]; the solid curve—the HERMES code prediction [19].
It means that further multiplication of neutrons, for instance in a blanket placed around the extended lead target, probably could shift the maximum of the value Y =E p to a higher energy range. Thus, the question about the optimal proton energy for the neutron production has to be considered for a target-blanket system because of the neutron multiplication effect out of a target. References [1] R.G. Vassilkov, V.I. Yurevich, in: Proceedings of ICANS-XI, KEK, Tsukuba, 22–26 October 1990; KEK Report 90-25, 1991, p. 340. [2] V.A. Nikolaev, et al., in: Proceedings of ICANS-XI, KEK, Tsukuba, 22–26 October 1990; KEK Report 90-25, 1991, p. 612. [3] A.V. Daniel, et al., JINR Commun. E1-92-174, Dubna, 1992. [4] V. Yurevich, Radiat. Prot. Dosim. 116 (1–4) (2005) 636. [5] M.M. Meier, et al., Nucl. Sci. Eng. 102 (1989) 310. [6] M.M. Meier, et al., Nucl. Sci. Eng. 110 (1992) 289. [7] W.B. Amian, et al., Nucl. Sci. Eng. 112 (1992) 78. [8] W.B. Amian, et al., Nucl. Sci. Eng. 115 (1993) 1. [9] S. Stamer, et al., Phys. Rev. C 47 (1993) 1647. [10] B.E. Bonner, et al., Phys. Rev. C 18 (1978) 1418. [11] T. Nakamoto, et al., J. Nucl. Sci. Technol. 32 (1995) 827. [12] Yu. Bayukov, et al., Preprint ITEP-172, M., 1983. [13] Yu. Trebukhovsky, et al., Preprint ITEP 3-03, M., 2003. [14] N.S. Amelin, M.E. Komogorov, Phys. Particles and Nuclei Lett. 3 (100) (2000) 35; N.S. Amelin, M.E. Komogorov, JINR Commun. D11-2001-175, Dubna, 2001. [15] J. Cugnon, et al., Nucl. Phys. A 625 (1997) 729. [16] X. Ledoux, et al., Phys. Rev. Lett. 82 (1999) 4412. [17] S. Leray, et al., Phys. Rev. C 65 (2002) 044621. [18] R.G. Vassilkov, et al., At. Energ. 79 (1995) 257. [19] A. Letourneau, et al., Nucl. Instr. and Meth. B 170 (2000) 299. [20] D. Filges, et al., Eur. Phys. J. A 11 (2001) 467. [21] J.S. Fraser, et al., Phys. Canada 21 (2) (1965) 17. [22] J.S. Fraser, et al., Trans. Amer. Nucl. Soc. 28 (1978) 754.