Intranuclear cascade with emission of light fragment code implemented in the transport code system PHITS

Nuclear Instruments and Methods in Physics Research B 291 (2012) 38–44

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Intranuclear cascade with emission of light fragment code implemented in the transport code system PHITS Y. Sawada a, Y. Uozumi a,⇑, S. Nogamine a, T. Yamada a, Y. Iwamoto b, T. Sato b, K. Niita c a

Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, Fukuoka 819-0395, Japan Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195, Japan c Research Organization for Information Science and Technology (RIST), Tokai, Ibaraki 319-1106, Japan b

a r t i c l e

i n f o

Article history: Received 5 April 2012 Received in revised form 10 July 2012 Available online 21 September 2012 Keywords: Nuclear spallation reaction Light fragment Intermediate energy Nucleon correlation Particle and Heavy Ion Transport code System (PHITS) Intranuclear cascade model Light fragment emission

a b s t r a c t The Intranuclear Cascade with Emission of Light Fragment (INC–ELF) code has been developed and implemented in the Particle and Heavy Ion Transport code System (PHITS). The INC–ELF code explicitly includes nucleon correlations within the framework of the INC model to describe light fragment emissions from nuclear spallation reactions by using the model in Phys. Rev. C 84, (2011) 064617. In addition to the degrees of freedom of nucleons, the developed code also accounts for pions, Ds, and N⁄s, and can cover energy ranges up to 3 GeV. The predictive capabilities of the ELF/PHITS system have been verified through comparison with a diverse set of experimental observations. In particular, the verification was conducted with abundant double-differential cross-section data covering a wide range of reactions (e.g., (p, p’x), (p, nx), (p, dx), (p, 3Hex), (p, ax) and (p, px) reactions) over a wide energy range (between 400 MeV and 1.5 GeV). As a result, our ELF/PHITS code has demonstrated strong predictive capability for all of these data, although areas requiring future study remain due to the lack of experimental data on high-energy cluster production. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction The general-purpose Particle and Heavy Ion Transport code System (PHITS) [1] is a useful tool in various applications such as radiotherapy, radiation protection, isotope production, space technology, and radiation shielding, as well as in the design of accelerators and radiation detectors. Since PHITS can estimate the probability density of energy deposited by charged particles into materials or the human body on a nanometer scale [2], its usefulness covers practical applications and basic research, in addition to macroscopic particle transport simulation. For instance, PHITS provides specific information about physical and biological doses delivered to human body cells or advanced microelectronic devices. This is one of the greatest advantages of PHITS with respect to fundamental research on cancer therapy, space research, and material science. Since highly energetic particles travel a sufficiently long distance in materials, they undergo nuclear reactions with high probability. The nuclear reaction model, which plays an essential role in PHITS, assumes a two-step model composed of dynamic and static phases, where the latter is computed by the Generalized Evaporation Model (GEM) code [3]. For the former phase, PHITS uses any of three codes.

⇑ Corresponding author. E-mail address: [email protected] (Y. Uozumi). 0168-583X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nimb.2012.08.025

One is the JQMD code [4], which is based on Quantum Molecular Dynamics (QMD). The others are the Bertini [5,6] and JAM [7] codes of the intranuclear cascade (INC) model. These three codes describe nuclear reactions at incident nucleon energies between 0.1 and 3 GeV, where a large number of particles and clusters of fragments are emitted as a result of nuclear spallation reactions. Secondary ions emitted from reactions have higher atomic number as compared with the primary protons, and therefore the ability of secondary ions to deposit charge is greater due to their large Linear Energy Transfer (LET). From a quantitative point of view, the importance of secondary light clusters is higher for the biological dose than for the physical dose. Since the biological effectiveness of secondary light clusters (e.g., a particles) is high, they are associated with large biological doses. Recent data indicate that secondary light clusters contribute more to the biological dose than do primary protons with energy of 500 MeV [8]. Another relevant issue related to light clusters is Single-Event Upset (SEU) in logic and memory circuits. Recent studies have revealed that secondary ions are responsible for a considerable portion of SEUs in integrated circuits [9,10]. Although such nuclear events are rare, they can deposit large amounts of energy and become a significant factor in SEU rate calculations. High-energy light clusters are produced in the dynamical phase. Although they are less numerous than low-energy clusters, which are reasonably well explained by the evaporation model GEM, the influence of high-energy clusters on applications is expected to be

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Y. Sawada et al. / Nuclear Instruments and Methods in Physics Research B 291 (2012) 38–44 12

C(p,xp’) Ep = 392 MeV

DDX [ mb/sr MeV ]

1

10 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

t and 3He

a

1.2 2000

1.5 2250

1.7 2500

90°(×10−4)

INC INC+cluster °

105 (×10 )

100

181

INC-ELF Exp.

200 300 Proton Energy [MeV]

400

Ta(p,xp’) Ep = 392 MeV

101 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

20° 45°(×10−2)

90°(×10−4)

INC INC+cluster

105°(×10−6)

0 Fig. 2. Diagram of disintegration of a preformed deuteron by the impact of an incident proton.

−6

Fig. 3. Double-differential cross sections for the 12C (p, p’x) reaction at 392 MeV. Results are multiplied by the indicated factor for display. Closed circles are experimental data from [19].

DDX [ mb/sr MeV ]

ki (fm) kf (fm MeV/c)

d

40°(×10−2)

0

Fig. 1. Diagram of preformed deuteron knockout via (a) direct and (b) exchange processes.

Table 1 Parameters for knockout and indirect-pickup processes for three types of clusters.

20°

100

200 300 Proton Energy [MeV]

INC-ELF Exp.

400

Fig. 4. Same as Fig. 3, but on the 181Ta (p, p’x) reaction at 392 MeV. Closed circles are experimental data from [15].

significant due to their much higher energies relative to those of evaporated particles. It is of urgent importance for PHITS to include a reliable reaction model that can produce accurate predictions of cluster emissions from the dynamical phase. Although the INC model describes the fast dynamic phase of nuclear spallation reactions, it cannot predict cluster production cross sections. Recently, intensive efforts have been devoted [11–14] to solving this problem. The surface-coalescence model was proposed in [11,12]. In [13], the exciton model was used for cluster emission in addition to the coalescence model in the cascade process. In [14], nucleon correlations were introduced into INC as initial-state and final-state interactions, which are responsible for cluster knockout and indirect pickup (or coalescence) processes, respectively. Uozumi et al. examined their model by comparing its predictions with experimental double-differential cross sections (DDXs) of reactions with energies between 160 and 400 MeV, demonstrating that calculations agree well with experimental data on emission of light clusters (d, t, 3He, and 4He). In the present work, the INC model with Emission of Light Fragment (ELF) code is developed on the basis of the model in [14] and

implemented in PHITS. Although the model in [14] is valid for energy ranges below the pion-production threshold (about 400 MeV), the INC–ELF code enables predictions of nucleon-induced reactions in up to a beam energy of 3 GeV which produce nucleons, light clusters (d, t, 3He and 4He), and pions. In addition, INC–ELF includes the disintegration process of a preformed deuteron. The predictive abilities of ELF/PHITS are discussed by comparing the results with experimental data for various types of reactions at energies up to a few GeV. In particular, we focus on DDX spectra for reactions with energies above 500 MeV. In our next paper, we will discuss the results for other quantities, including the space distribution of particle flux and the mass distribution of residual products.

2. Overview of the INC–ELF code The basic assumption in the INC model is that nuclear reactions can be described as a succession of quasi-free nucleon–nucleon collisions. Our approach incorporates several important aspects

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Y. Sawada et al. / Nuclear Instruments and Methods in Physics Research B 291 (2012) 38–44 56

56

Fe(p,xn) Ep = 800 MeV

10 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

INC-ELF Exp.

30° 60°(×10−2)

DDX [ mb/sr MeV ]

DDX [ mb/sr MeV]

1

120°(×10−4)

0

200 400 600 Neutron Energy [MeV]

Fig. 5. Same as Fig. 3, but on the experimental data from [20].

56

102 101 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

15°

60°(×10−4)

90°(×10−6)

0

208

30

°

DDX [ mb/sr MeV ]

DDX [ mb/sr MeV ]

INC-ELF Exp.

°

−3

60 (×10 )

120°(×10−6)

0

200 400 600 Neutron Energy [MeV]

102 101 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

800

0

1500

56

Fe (p, n) reaction at 1.5 GeV. Closed circles are

208

Pb(p,xn) Ep = 800 MeV

10 101 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

500 1000 Neutron Energy [MeV]

Fig. 7. Same as Fig. 3, but on the experimental data from [21].

2

INC-ELF Exp.

30°(×10−2)

800

Fe (p, n) reaction at 800 MeV. Closed circles are

Fe(p,xn) Ep = 1.5 GeV

Pb(p,xn) Ep = 1.5 GeV

15°

INC-ELF Exp.

30°(×10−2)

60°(×10−4)

90°(×10−6)

500 1000 Neutron Energy [MeV]

1500

Fig. 6. Same as Fig. 3, but on the 208Pb (p, n) reaction at 800 MeV. Closed circles are experimental data from [20].

Fig. 8. Same as Fig. 3, but on the experimental data from [21].

in addition to the basic INC framework. The present model is essentially the same as that in [14,15], and a thorough description of the model can be found there. Therefore, its main features are only briefly presented here. For the target nucleus, initial nucleon positions are randomly distributed inside a sphere, in which nucleon density follows the Woods–Saxon distribution with a nuclear radius r0 of (0.976 + 0.0206A1/3)1/3A1/3 fm, where A is the nuclear mass number, and with a diffuseness of 0.54 fm. All the nucleons are inside a binding potential V0 with a depth of 45 MeV. The initial nucleon momenta are uniformly distributed inside the Fermi sphere. Next, a projectile is sent to the target nucleus with an impact parameter chosen at random. Intranuclear NN collisions are described by the cross section rNN. When an energetic particle approaches another target nucleon to within pffiffiffiffiffiffiffiffiffi a distance of rNN =p, they undergo a collision. The Pauli blocking operator Q is introduced as

where pi and pj are the momenta of the scattered particles and H denotes the Heaviside function. The parameters of the NN cross sections and angular distributions are taken from a treatment presented in [16]. To broaden the applicable energy range, in addition to nucleons, Ds, N⁄s, and pions are also considered with their respective isospin degrees of freedom. All channels handled for a two-body collision are

Q ¼ 1  f1  Hðpi  pF Þgf1  Hðpj  pF Þg;

208

Pb (p, n) reaction at 1.5 GeV. Closed circles are

N þ N ! N þ D ðor N Þ; N þ D ðor N Þ ! N þ N; N þ p ! N þ D ðor N Þ; D þ p ! N ; in addition to baryon–baryon elastic scattering. The following three decay channels are also considered:

D ! N  þ p; N  ! N þ p; N  ! D þ p:

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Y. Sawada et al. / Nuclear Instruments and Methods in Physics Research B 291 (2012) 38–44 27

74

Al(p,xd) Ep = 558 MeV

10 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

INC-ELF Exp. 20° 30°(×10−2)

40°(×10−4) 50°(×10−6) 60°(×10−7)

0

200 400 Deuteron Energy [MeV]

Fig. 9. Same as Fig. 3, but on the experimental data from [22].

27

10 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

600

Al (p, d) reaction at 558 MeV. Closed circles are

INC-ELF Exp. 20°

30°(×10−3)

40°(×10−6)

0

200 400 Deuteron Energy [MeV]

197

INC-ELF Exp. 20°

DDX [ mb/sr MeV ]

DDX [ mb/sr MeV ]

Fe(p,xd) Ep = 558 MeV

30°(×10−2)

40°(×10−4)

50°(×10−6) 60°(×10−7)

0

200 400 Deuteron Energy [MeV]

600

Fig. 10. Same as Fig. 3, but on the 56Fe (p, d) reaction at 558 MeV. Closed circles are experimental data from [22].

All of these channels are described in essentially the same way as in JQMD [4]. The details of light cluster production are presented in [14]. Clusters are produced in two ways, namely, through initial-state and final-state interactions, which are responsible for the knockout and indirect-pickup processes, respectively. For the knockout calculation, the existence of a cluster state is assumed under the initial-state interaction in the target nucleus. The direct and exchange processes in the deuteron knockout are depicted in Fig. 1(a) and (b), respectively. The criterion for cluster knockout is defined as a parameter ki as

r nm 6 ki ; where rnm is the distance in space between two nucleons of n and m. In the case of indirect pickup, the criterion for cluster formation at the final state is the distance in phase space between the escaping nucleon and other nucleons. The clustering criterion is written as a parameter kf in the form

r nm pnm 6 kf ;

600

Fig. 11. Same as Fig. 3, but on the 74Ge (p, d) reaction at 558 MeV. Closed circles are experimental data from [22].

56

101 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

Ge(p,xd) Ep = 558 MeV

1

DDX [ mb/sr MeV ]

DDX [ mb/sr MeV ]

1

101 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

Au(p,xd) Ep = 1.2 GeV

15°

20°(×10−3)

65°(×10−5)

100°(×10−7)

0

200

INC-ELF Exp.

400 600 800 1000 1200 Deuteron Energy [MeV]

Fig. 12. Same as Fig. 3, but on the 197Au (p, d) reaction at 1.2 GeV. Closed circles are experimental data from [23].

where rnm and pnm are distances between nucleons n and m in the space and the momentum space phase, respectively. We determined these parameters for three clusters d, t, 3He, and a. The parameter values of these criteria are listed in Table 1, which were determined in [14] to best reproduce experimental DDXs for (p, dx) reaction data [14] on targets of 12C to 197Au at 300 and 392 MeV, and (p, 3Hex) and (p, ax) reaction data [17,18] on 59Co and 197Au at 160 and 200 MeV. Note that inclusion of the cluster knockout process has a negligible influence on the (p, p’x) DDX spectra, as demonstrated in the next section. In the present work, we added a cluster disintegration process for the case of deuteron. The diagram of this process is shown in Fig. 2. The underlying physical principle is that the sign of nuclear force can alternate with the change of relative angular momentum between two nucleons. We assumed the criterion to be the distance in space between the target nucleon and the neighboring nucleon, which was determined to give the best accounts of spectral DDXs of (p, p’x) reactions at 300 and 392 MeV on many target nuclei from 12C to 209Bi. Finally the proton–neutron distance

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Y. Sawada et al. / Nuclear Instruments and Methods in Physics Research B 291 (2012) 38–44

Ni(p,xα) Ep = 1.2 GeV

Ni(p,x 3He) Ep = 1.2 GeV

58

1

101 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

15°

DDX [ mb/sr MeV ]

DDX [ mb/sr MeV ]

58

20°(×10−3)

65°(×10−5) INC-ELF Exp. 100°(×10−7)

0

200

400

600

800

10 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

15°

20°(×10−3)

65°(×10−5) INC-ELF Exp. 100°(×10−7)

0

1000 1200

200

400 600 800 α Energy [MeV]

3

He Energy [MeV]

Fig. 13. Same as Fig. 3, but on the 58Ni (p, 3He) reaction at 1.2 GeV. Closed circles are experimental data from [24].

58

Fig. 15. Same as Fig. 3, but on the experimental data from [24].

197

101 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

Au(p,x 3He) Ep = 1.2 GeV

15°

DDX [ mb/sr MeV ]

DDX [ mb/sr MeV ]

197

20°(×10−3)

65°(×10−5) INC-ELF Exp. 100°(×10−7)

0

200

400

600

800

1000 1200

3

He Energy [MeV]

Fig. 14. Same as Fig. 3, but on the are experimental data from [23].

197

Au (p, 3He) reaction at 1.2 GeV. Closed circles

1.2 < d < 1.8 fm was fixed as the deuteron disintegration condition, while deuteron knockout occurs under d 6 1.2 fm. At the end of each INC–ELF calculation, information about residual nuclei is transferred to the evaporation stage of GEM. The input configuration of the residue for GEM is characterized by the number of protons and neutrons, the nuclear excitation energy, and the momentum. 3. Verification of the model We tested the performance of the ELF cascade model in the PHITS implementation for proton-induced reactions for a wide range of beam energies. A detailed comparison with experimental data was also performed in the energy range between 160 MeV and 1.5 GeV for a variety of emitted particles (p, n, d, 3He, a, and pions). The DDXs for 12C (p, p’x) at 392 MeV are shown in Fig. 3, where three different calculations are compared with experimental data

101 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11

1000 1200

Ni (p, a) reaction at 1.2 GeV. Closed circles are

Au(p,xα) Ep = 1.2 GeV

15°

20°(×10−3)

65°(×10−5)

°

−7

100 (×10 )

0

200

400 600 800 α Energy [MeV]

INC-ELF Exp.

1000 1200

Fig. 16. Same as Fig. 3, but on the 197Au (p, a) reaction at 1.2 GeV. Closed circles are experimental data from [23].

[19], indicated by dots. Solid lines represent the results obtained with the INC–ELF, which include both the cluster production and the preformed deuteron disintegration. Broken lines indicate the results of the INC model in [14] with the cluster production but without the deuteron disintegration. Dash-dotted lines show the results obtained with the standard INC including neither cluster production nor disintegration. In general, rather large discrepancies tend to appear between standard INC calculations and data on light targets and forward angles; the resultant quasi-free peaks are narrower and higher than in the experimental observations. The inclusion of the cluster production has almost no influence. However, inclusion of the disintegration process appears to reduce the extent of this negative effect. A similar comparison is presented in Fig. 4 for 181Ta (p, p’x) at 392 MeV, where experimental data are taken from [15]. In this case, the contribution from the disintegration process is negligible, and calculations both with and without deuteron disintegration provide a satisfactory account of the experimental data. In Figs. 5–8, the DDXs for neutron production

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Y. Sawada et al. / Nuclear Instruments and Methods in Physics Research B 291 (2012) 38–44 12

C(p,xπ +) Ep = 730 MeV

12

10−1

100

DDX [ mb/sr MeV ]

10−2

10 10

−3 −4

60°(×10−2)

−5

10−6 10−7

10

10−3 10−4 10−5

−9

10−6 10−7

10 0

200

400 π + Energy [MeV]

60°(×10−2)

90°(×10−4)

10−8

90°(×10−4)

10−8

15°

10−2

INC-ELF Exp.

DDX [ mb/sr MeV ]

15°

10−1

10

−9

0

600

Fig. 17. Same as Fig. 3, but on the 12C (p, p+) reaction at 730 MeV. Closed circles are experimental data from [25].

63

Cu(p,xπ +) Ep = 730 MeV 15

10−1

°

INC-ELF Exp.

10−2 −3

60°(×10−2)

−4

10−5 10−6

90°(×10−4)

10−7

10 DDX [ mb/sr MeV ]

DDX [ mb/sr MeV ]

400 π - Energy [MeV]

10−3 10−4

10−6 10−7

10−9

10−9

Fig. 18. Same as Fig. 3, but on the are experimental data from [25].

400 π + Energy [MeV]

600

63

Cu (p, p+) reaction at 730 MeV. Closed circles

are presented for (p, nx) reactions for Fe and Pb targets at beam energies of 0.8 and 1.5 GeV, respectively. Calculations with the present model are in close agreement with experimental observations [20,21] over the entire energy range in all spectra. The predictive power of the proposed model with respect to light cluster emissions was also examined. Figs. 9–11 show the results of verification of deuteron production reactions at 558 MeV for Al, Fe, and Ge targets, respectively. In these experiments [22], parts of the energy spectra (between 100 and 370 MeV) were observed at angles between 20° and 60°, and close agreement was observed for these data sets. Our calculations predicted a bump above 400 MeV at 20° attributed to quasi-free deuteron knockout, which has been observed experimentally [14] for (p, dx) reactions at 392 MeV. The inclusion of the cluster knockout process allows for production of high-energy deuterons with energies close to those of incident protons. Deuteron spectra for higher incident energies are displayed in Fig. 12 for the reaction of a 1.2 GeV proton bombardment of an Au target. Experimental observations [23] are reproduced reasonably well by our calculations. Although experimental DDXs exist only

60°(×10−2)

10−5

10−8

200

15°

−2

10−8

0

600

Cu(p,xπ -) Ep = 730 MeV

10−1

100

10

200

INC-ELF Exp.

Fig. 19. Same as Fig. 3, but on the 12C (p, p) reaction at 730 MeV. Closed circles are experimental data from [25].

63

10

C(p,xπ -) Ep = 730 MeV

90°(×10−4) INC-ELF Exp.

0

200

Fig. 20. Same as Fig. 3, but on the are experimental data from [25].

400 π - Energy [MeV]

63

600

Cu (p, p) reaction at 730 MeV. Closed circles

for energies below 200 MeV, the calculations also predict the existence of deuterons of higher energies (around 1 GeV). We stress again that parameters for cluster production criteria in these calculations were determined for reactions induced by protons of energies between 160 and 400 MeV. In Figs. 13–16, spectral DDXs of (p, 3He) and (p, a) reactions are examined for Ni and Au targets at a beam energy of 1.2 GeV. The calculation results are in reasonably close agreement with experimentally obtained data [23,24], which were observed only for lower-energy parts of the spectra (below 200 MeV). As in the case of deuterons, high-energy spectra (around 1 GeV) are predicted by the calculations. These results of high-energy ranges may indicate large differences between our model and other INC models [11–13] including only the coalescence or the pre-equilibrium (exciton) process but disregarding the knockout. We tested the capability of the INC–ELF code to describe pion emission from proton-induced reactions. Spectral DDXs are shown in Figs. 17–20 for (p, p+) and (p, p) reactions for C and Cu targets at 730 MeV, respectively. Overall, our calculations are in close

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agreement with experimental results [25], indicating that the INC– ELF model provides an accurate description of the physics of pion production. 4. Conclusion The INC–ELF code was developed and implemented as part of PHITS. Its predictive power was examined by comparing calculation results with a variety of experimental observations; the results obtained from the code were in close agreement with the DDXs of proton-induced reactions emitting nucleons, light clusters, and pions at proton-incident energies up to a few GeV. High energy regions of the cluster spectra must be experimentally verified in the future. References [1] K. Niita, N. Matsuda, Y. Iwamoto, H. Iwase, T. Sato, H. Nakashima, Y. Sakamoto, L. Sihver, PHITS: Particle and Heavy Ion Transport code System (2010). Version 2.23, JAEA-Data/Code 2010-022. [2] T. Sato, Y. Kase, R. Watanabe, K. Niita, L. Sihver, Radat. Res. 171 (2009) 107. [3] S. Furihata, Nucl. Instrum. Methods B 171 (2000) 251. [4] K. Niita, S. Chiba, T. Maruyama, H. Takada, T. Fukahori, Y. Nakahara, A. Iwamoto, Phys. Rev. C 52 (1995) 2620. [5] H.W. Bertini, Phys. Rev. C 131 (1963) 1801. [6] H.W. Bertini, Phys. Rev. C 188 (1969) 1711. [7] Y. Nara, N. Otuka, A. Ohnishi, K. Niita, S. Chiba, Phys. Rev. C 61 (2000) 024901. [8] F. Ballarini, M. Biaggi, A. Ferrari, A. Ottolenghi, M. Pelliccioni, D. Scannicchio, J. Radiat. Res. 43 (2002) 99. [9] P.E. Dodd, J.R. Schwank, M.R. Shaneyfelt, J.A. Felix, P. Paillet, V. Ferlet-Cavrois, J. Baggio, R.A. Reed, K.M. Warren, R.A. Weller, R.D. Schrimpf, G.L. Hash, S.M. Dalton, K. Hirose, H. Saito, IEEE Trans. Nucl. Sci. 54 (6) (2007) 2303.

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