ЯДЕРНАЯ ФИЗИКА, 2014, том 77, № 3, с. 345-348
ЯДРА
CALCULATIONS OF DOUBLE-DIFFERENTIAL TRITON EMISSION CROSS SECTIONS AT 62-MeV PROTON-INDUCED REACTIONS
© 2014 A. Aydin1)*, I. H. Sarpun2), A. Kaplan3)
Received June 26, 2013
Double-differential cross sections (d?a/dQde) have been calculated and analyzed for triton production in proton-induced reactions on 27Al, 54'56Fe, 197Au, and 208Pb target nuclei at incident energy of 62 MeV. Calculations of double-differential cross sections have been performed using nuclear models implemented in the TALYS 1.2 code. The calculated results of the double-differential cross sections for triton emission have been compared with the existing experimental data.
DOI: 10.7868/S0044002714020032
1. INTRODUCTION
The study of light charged particles (p, d, t, 3He, a) emitted in proton-induced reactions is interesting due to several reasons. New accelerator-driven technology that utilizes spallations, such as the production of tritium and the transmutation of radioactive waste, is of a growing interest in such type of reactions due especially to the emerging new ideas concerning the hybrid systems [1, 2]. Such systems are supposed to use intense high-energy proton beams (1 GeV or more), which induce spallation reactions on heavy targets. A large number of high-energetic neutrons along with light charged particles are produced. The accelerator-driven system (ADS) requires the nuclear reaction data of common cross sections and especially the data of neutron- and proton-induced energy—angle correlated spectra of secondary light particles (neutron, proton, deuteron, triton, helium, and alpha-particle) as well as doubledifferential cross sections to model the performance of the target/blanket assembly. Knowledge of involved reaction cross sections is required in order to benchmark the nuclear reaction codes in the region of incident energies up to 200 MeV where many reaction mechanisms compete. Due to specific experimental difficulties, experimental results concerning light charged particle production in proton-induced reactions are rather scarce [3]. Therefore, new nuclear cross-section data are needed to improve the theoretical predictions of neutron and charged-particle
'-'Faculty of Arts and Sciences, Kirikkale University, Turkey.
2)Faculty of Arts and Sciences, Afyon Kocatepe University, Turkey.
3)Faculty of Arts and Sciences, Suleyman Demirel University, Isparta, Turkey.
E-mail: a.aydin63@gmail.com
production, shielding requirements, activation, radiation heating, and material damage. Besides, the nuclear cross-section data are needed for refinement of the nuclear theories. Nuclear reaction models are frequently needed to provide estimate of the particle-induced reaction cross sections, especially if experimental data are not available or are unlikely to be produced due to the experimental difficulty. Obtaining the reaction systematic is an important part of the work concerned with the prediction and calculation of nuclear reaction cross sections [4—7]. The reaction systematic is widely used for the reaction cross-section evaluation supplementing result of measurements and calculations by theoretical models [8—14].
In our previous works, we investigated nucleon mean-free-path dependence in triton, deuteron, and helium production and calculated double-differential deuteron emission cross sections at the incident proton energy of 62 MeV [9—11, 15]. In this study, we have calculated double-differential triton emission cross sections for 27Al, 54>56Fe, 197Au, and 208Pb target nuclei at the incident proton energy of 62 MeV. The calculated results of double-differential cross sections for triton emission have been also compared with the experimental data [16].
2. CALCULATION METHODS
In this study, calculations of double-differential cross sections were performed using nuclear models implemented in the TALYS 1.2 code [13]. The use of TALYS involved calculations by the pre-equilibrium exciton model and the Hauser—Feshbach model. The pre-compound model implements new expressions for internal transition rates and new parameterization of the average squared matrix element for the residual
4 ЯДЕРНАЯ ФИЗИКА том 77 № 3 2014
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Fig. 1. The comparison of calculated double-differential cross section of (p,xt) reaction on 27Al with the experimental data. Experimental values were taken from EXFOR (#00292001) [16, 18].
Fig. 2. The same as in Fig. 1, but for the case 54Fe(p,xt) reaction. Experimental values were taken from EXFOR (#00291001) [16, 19].
interaction obtained using the optical model potential from [12].
The TALYS 1.2 code was developed to analyze and predict nuclear reactions involving neutrons, photons, and light charged particles (A ^ 4) in the 1-keV—200-MeV energy range for target nuclei heavier than the carbon [13]. Several state-of-the-art models are included in TaLyS. The default model to describe the pre-equilibrium process in TALYS is the two-component exciton model (EM); in this model the time evolution of the nuclear state is described by the total energy of the system and the total number of particles (protons and neutrons) above the Fermi surface and corresponding holes below it. Paper [14]
Fig. 3. The same as in Fig. 1, but for the case 56 Fe(p,xt) reaction. Experimental values were taken from EXFOR (#00294023) [16, 20].
offers a detailed description of the model. This model provides a good predictive power for nucleon-induced reactions. TALYS includes the phenomenological model proposed by Kalbach [17] to take in account the nucleon transfer (NT) and the knock-out (KO) reactions not covered by the exciton model. The total pre-equilibrium (PE) cross section is given as a sum of three contributions:
da^_da^ da^ daK0 dE ~ dE + dE + dE '
Three parameters in TALYS can be used to control how the NT and the KO contributions are added. The preeqcomplex flag allows to switch on or off the use of the Kalbach model for NT (pickup, stripping) and KO reactions, in addition to the exciton model, in the pre-equilibrium region. "Cstrip" and "Cknock" are two adjustable parameters, respectively for the NT and the KO processes, to scale the complex-particle pre-equilibrium cross section per outgoing particle. The scaling factor can vary between 0 and 10.
3. RESULTS AND CONCLUSIONS
Double-differential cross sections are consistently calculated using nuclear theoretical models for 27Al, 54,56 Fe,197 Au, and 208 Pb target nuclei at the incident proton energy of 62 MeV. The calculated results of double-differential cross sections of triton emission have been compared with the experimental data [16, 18—22] as shown in Figs. 1—5. The theoretical models provide the good description of the shape and magnitude of the double-differential cross section of tritons emission for some emission angles and energies.
ROEPHAfl OH3HKA tom 77 № 3 2014
CALCULATIONS OF DOUBLE-DIFFERENTIAL TRITON EMISSION CROSS SECTIONS 347
d2a/dQde 107
105 103 101 10-1
10
1-3
0
mb/(sr MeV) 19?Au(P,xt)
Ep = 61.5 MeV • Bertrand et al. [21]
'-rr^Z -TALYS 1.2
124°, X108 ^^ -
•••*••*«»«.
99°, x106
75°, X104 50°, x102
J_i_I_i_I_i_I_LVJ_I
10 20 30 40 50 60
Triton energy, MeV
Fig. 4. The same as in Fig. 1, but forthe case 197 Au(p,xt) reaction. Experimental values were taken from EXFOR (#O0295020)[16, 21].
d 2a/dQde, mb/(sr MeV) 107
105
103
101
10-1
l8Pb( p, xt) = 62.9 MeV
Bertrand et al. [22] -TALYS 1.2
10-
40 50 60 Triton energy, MeV
Fig. 5. The same as in Fig. 1, but for the case 208Pb(p, xt) reaction. Experimental values were taken from EXFOR (#O1146004) [16, 22].
In Fig. 1, the calculated results are lower than the experimental values at 30°. In addition, the experi-
Total cross sections for triton production at 62-MeV incident protons
Reaction <rth, mb (TALYS 1.2) crexp, mb (^th - ^expV /^exp, %
27 Al (p,xt) 4.5 8.8 ± 0.1 [18] -48.8
54 F e(p,xt) 5.1 6.9 ± 0.07 [19] -27.7
56 F e(p,xt) 7.6 12.7 ±0.1 [20] -40.5
197Au(p, xt) 19.2 21.3 ± 0.2 [21] -10.1
208 Pb (p,xt) 19.4 27.0 [22] -28.1
mental and calculated data are in good agreement at the triton emission energy range 7—30 MeV for other angles. There is a discrepancy between experimental and calculated data above 30 MeV. In Fig. 2, the calculated results are in harmony with the experimental data for the triton emission energy region 7—35 MeV except 160°. In Fig. 3, the theoretical calculations are in good agreement with the experimental data at emission energies of 10 < E < 40 MeV. Also there is a discrepancy above 40 MeV. In Fig. 4, for the angles of 30°, 50°, 75° model calculations are in agreement with the experimental value up to the emission energy of 50 MeV. In Fig. 5, the shape of the theoretical results has similar structure within the experimental data and discrepancy appears below 20 MeV and above 50 MeV.
Additional, the triton production cross sections were determined by integrating the energy differential cross sections. They are reported in the table. The first column indicates the theoretical triton production cross sections (ath), whereas the second column presents the experimental triton production cross sections (aexp), and last column indicates the relative differences (in %) between theoretical values and experimental data, calculated as (ath — aexp)/aexp. As can be seen from the table, TALYS 1.2 code underestimates the triton production cross sections at 62 MeV proton energy.
TALYS 1.2 code calculations have been made in the framework of the pre-equilibrium exciton model and the Hauser—Feshbach model. The calculation results have been compared with the available experimental data and the conclusions can be summarized as follows:
1. The calculated results of the double-differential cross sections for triton emission are compared with the experimental data [16, 18—22] at incident proton energy 62 MeV as shown in Figs. 1—5. Generally, the magnitude and shape of the calculated results are in go
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