Theoretical Analysis of Neutron Double-Differential Cross Section of n + 19 F at 14.2 MeV

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1 Commun. Theor. Phys. (Beijing, China) 47 (2007) pp c International Academic Publishers Vol. 47, No. 1, January 15, 2007 Theoretical Analysis of Neutron Double-Differential Cross Section of n + 19 F at 14.2 MeV DUAN Jun-Feng, 1 YAN Yu-Liang, 1 SUN Xiao-Jun, 1,2 ZHANG Yue, 1 and ZHANG Jing-Shang 1 1 China Institute of Atomic Energy, P.O. Box 275(41), Beijing , China 2 College of Physics and Information Technology, Guangxi Normal University, Guilin , China (Received March 1, 2006; Revised June 16, 2006) Abstract A new light nuclear reaction model has been developed and the double-differential measurements of 1p shell nuclei have been analyzed successfully. Now, the application of this model is expanded to 19 F of the 2s-1d shell nucleus. The double-differential cross section of total outgoing neutron for n + 19 F reactions at E n = 14.2 MeV has been calculated and analyzed, which agrees fairly well with the experimental measurements. In this paper, the contributions from different reaction channels to the double-differential cross sections have been analyzed in detail. The calculations indicate that this light nuclear reaction model is also able to be used for the 2s-1d shell nucleus so long as the related level scheme could be provided sufficiently. PACS numbers: s Key words: light nuclear reaction, double-differential cross section, pre-equilibrium emission, discrete level 1 Introduction The double-differential cross sections are important nuclear data applied to nuclear engineering. A new approach for description of neutron-induced light nucleus reaction was proposed in 1999 [1] based on the unified Hauser Feshbach and exciton model. In terms of this model all of the double-differential measurements of 1p shell nuclei have been analyzed successfully. Henceforth, the theoretical method to set up the file of doubledifferential cross section for neutron data libraries including the information of all outgoing particles for the light nuclei has been established. Since the unified Hauser Feshbach and exciton model [2] includes the description of the pre-equilibrium emission processes from a compound nucleus to the discrete levels of the residual nuclei with angular momentum and parity conservations. For light nuclei, the accurate kinematics has been obtained for various complex reaction processes including two-body separation and three-body breakup. [3,4] The theoretical calculations indicated that this method is very successful for the 1p shell nuclei. [5,6] Now, the application of this method is expanded to 19 F for 2s-1d shell in order to further verify the applicable range. 19 F is an important nucleus applied in nuclear engineering. The neutron data files have been established by using this new model including all kinds of cross sections and angular distributions, as well as double differential cross sections. The files of double-differential cross sections were obtained in American ENDF library calculated with TNG code, [7] but there are some defects could be improved. For instance the (n, nd) and (n, nt) reaction channels including the neutron emissions were absent in the ENDF library, which should be taken into account properly. In the new model, all of the residual states are the discrete levels below incident neutron energy of 20 MeV. All of the related discrete levels can be found from the Table of Isotopes 8-th. [8] So the continuous states are not needed in our model calculations, which is one of the main difference from TNG code calculation. Replacing the continuous states by the discrete levels, the information about the competitions between neutrons and charged particles, as well as the gamma decay can be given in more obvious and accurate physical pictures. In Sec. 2, the reaction channels opened below 20 MeV are listed in detail. The calculated results of doubledifferential cross section of total outgoing neutrons are given in Sec. 3, which agrees fairly well with the experimental data measured by Baba [9] in 1985 at incident neutron energy E n = 14.2 MeV. The contributions of neutron partial spectra from different partial reaction channels to the double-differential cross section of total outgoing neutron are analyzed in detail. The discussion and analysis are given in Sec Reaction Channels In view of the n + 19 F reaction with incident neutron energy E n < 20 MeV, the opened reaction channels and the corresponding reaction Q-values in unit of MeV are listed as follows: The project supported by National Natural Science Foundation of China under Grant No

2 No. 1 Theoretical Analysis of Neutron Double-Differential Cross Section of n + 19 F at 14.2 MeV 103 γ + 20 F, Q = 6.601, n + 19 F, Q = 0.000, p + 19 O, Q = 4.037, α + 16 N, Q = 1.522, d + 18 O, Q = 5.770, n + 19 t + 17 O, Q = 7.557, F = 5 He + 15 N, Q = 4.907, 2n + 18 F, Q = , np, pn + 18 O, Q = 7.994, nα, αn + 15 N, Q = 4.012, nd, dn + 17 O, Q = , nt, tn + 18 O, Q = For n + 19 F reactions, the sixteen opening channels are taken into account including (n, nd) and (n, nt) reaction channels, which are absent in American ENDF library. From the model calculations these two reaction channels should be considered because the cross sections of them are mb and mb, respectively, at E n = 20 MeV. The threshold energy of (n, 3 He) reaction channel is MeV and the cross sections are very small below 20 MeV, hence it can be ignored, as same as (1) in the TNG code calculation. Since the possibility of 5 He has been affirmed theoretically, [10] the 5 He emission from n + 19 F reaction is taken into account. As is well known, 5 He is unstable and separated into a neutron and an alpha particle spontaneously, therefore the (n, 5 He) channel belongs to the (n, nα) reaction channel. The reaction processes are always from the compound nucleus to the discrete levels for the first particle emissions and from levels to levels for the second particle emissions. There is no third particle emission in n + 19 F reactions. The numbers of the discrete levels in model calculation are listed in Tables 1 and 2, respectively at incident neutron energy E n = 14.2 MeV. Table 1 The reaction situation from compound nucleus 20 F to open k level of the residual nucleus for variety reactions at E n = 14.2 MeV. Channel k RN (n, n) 1-31, F (n, p) g.s-8 19 O (n, α) g.s-3 16 N (n, 5 He) g.s-3 15 N (n, d) g.s O (n, t) g.s-3 17 O Table 2 The reaction situation from compound nucleus 20 F to the open k 2-th level via the k 1-th level of the residual nucleus for variety reactions at E n = 14.2 MeV. Channel k 1 k 2 RN 104,106, g.s 125,126,128,129,131, ,136,138,139,140,143,144,147, , ,145,146,148 2 (n, 2n) 127, ,134,135,137,139,141,142,144, F 136, 138, 140, , , , , (n, np) 56,57,61,63-67,69,70,72,74-76, O 84-88,90-94,96,98,101,103,104,107,108 g.s (n, nα) 14,16,17,32-35,38-63,65,70,71 15 N 73,76-78,81-89,91-93,95-97,105 g.s 9-32,35,36 g.s (n, pn) O 33,34, , g.s 35-46,48 1 (n, αn) N 41-46, ,48 4 (n, tn) 4,5 g.s 16 O The symbols k, k 1, and k 2 refer to the order number of the excited levels of the corresponding residual nucleus in the reaction channel. Acronyms g.s and RN stand for the ground state and the residual nucleus, respectively. From Tables 1 and 2, one can see that the first thirteen excited levels of 19 F purely belong to the inelastic scattering reaction. Moreover, the 15-th excited level and the 18-th the 31-st, the 36-th, and the 37-th excited levels of 19 F still purely contribute to inelastic scattering reaction, while the excited 14-th, 16-th, 17-th, and 33-th 35-th excited levels of

3 104 DUAN Jun-Feng, YAN Yu-Liang, SUN Xiao-Jun, ZHANG Yue, and ZHANG Jing-Shang Vol F have the competitions between gamma decay and alpha particle emissions. The gamma decays belong to (n, n ) channel, while the alpha particle emissions belong to (n, nα) channel. The 32-th and the 38-th excited levels of 19 F purely contribute to (n, nα) channel. All of the discrete levels including level energy, spin, parity, level width, and gamma decay branch ratios are taken from the Table of Isotopes 8-th. [8] For some high energy levels, the spin and parity are undetermined, which could be judged by means of fitting measured data properly. 3 Calculated Results and Analysis The LUNF code for n + 19 F reactions has been developed and used for calculating the cross sections, the angular distributions, and the double-differential cross sections of all kinds of outgoing neutrons and charged particles from each partial reaction channel. The pre-equilibrium emission mechanism from compound nucleus to discrete levels of residual nucleus is the dominate reaction mechanism in light nucleus reaction. If the model codes do not include this reaction mechanism, then they would be unable to describe the reaction behavior of light nuclei. The comparisons of the calculated results with the double-differential measurements [9] are shown in Figs. 1 and 2 at E n = 14.2 MeV for outgoing angles of 25, 30, 45, 60, 75, 82.4, 105, 120, 135, and 150, respectively. As shown in Figs. 1 and 2, the calculated results agree well with the experimental measurements. Fig. 1 The energy-angular spectra of 25, 30, 45, 60, and 75 at E n = 14.2 MeV. The data for 30, 45, 60, and 75 are shifted downward by a factor of 10 2, 10 4, 10 6, and 10 8 respectively. Fig. 2 The energy-angular spectra of 82.4, 105, 120, 135, and 150 at E n = 14.2 MeV. The data for 105, 120, 135, and 150 are shifted downward by a factor of 10 2, 10 4, 10 6, and 10 8 respectively. Fig. 3 The partial energy-angular spectra of elastic peak and inelastic scattering neutrons of 60 at E n = 14.2 MeV. The solid line corresponds to the calculated total outgoing neutron energy-angle spectrum at outgoing angle θ L = 60 (the same as Figs. 4 and 5). The dashed line and the dotted lines correspond to the elastic peak and the partial energyangular spectra of inelastic scattering neutrons, respectively. Fig. 4 The partial energy-angular spectra of the first emitted neutron from secondary particles emissions of 60 at E n = 14.2 MeV. The dash-dot lines, the dashed lines and the dotted lines correspond to the first emitted neutrons from (n, nα), (n, np), (n, 2n) reaction channels, respectively.

4 No. 1 Theoretical Analysis of Neutron Double-Differential Cross Section of n + 19 F at 14.2 MeV 105 The contributions of the neutrons from elastic peak and the inelastic scattering channel to the doubledifferential cross section of total outgoing neutrons are shown in Fig. 3 at outgoing neutron angle θ L = 60 and E n = 14.2 MeV. The contributions of the first neutron and the second neutron emitted from secondary particles emission processes are shown in Figs. 4 and 5, respectively. The contributions, as shown in these figures, from the elastic scattering and the inelastic scattering are the dominant part at the outgoing energies ε n > 8 MeV in the doubledifferential cross sections. The first neutrons emitted from the (n, nα), (n, np), (n, 2n) reaction channels contribute to the outgoing energy region 2 MeV < ε n < 8 MeV. The contributions from the second neutrons emitted from (n, 2n) reaction channel in outgoing neutron energy below ε n < 2 MeV, meanwhile the neutrons from 5 He separation also contribute to this region. The cross section of (n, 2n) reaction channel in n + 19 F reactions is more larger than that of other light nuclei, such as 14 N [11] and 16 O, [12] so the secondary neutrons emitted from (n, 2n) channel is the dominate part in this low-energy region in the doubledifferential cross section. Fig. 5 The partial energy-angular spectra of the second emitted neutron from secondary particles emissions of 60 at E n = 14.2 MeV. The dash-dot lines, the dashed lines and the dotted lines correspond to the second emitted neutrons from (n, αn), (n, pn), (n, 2n) reaction channels, respectively. well as the gamma decays could be calculated by the optical model for each discrete level. Therefore, the much more accurate physical picture could be obtained than that from continuous states. Once the continuous states are used, then the corresponding level density parameters need to be given in the statistical model code. The general form of level density relate to angular momentum and parity reads [15] e 2 au ρ Jπ = P (π)r(j) 12 (2) 2σU(aU) 1/4 in Eq. (2) R(J) is the angular momentum factor and written by R(J) = 2J + 1 { 2 2πσ exp (J + } (1/2))2 3 2σ 2, (3) where σ is spin cut-off factor and U = E is the effective excitation energy, and is the pair correlation in the level density. This level density formula hints that there is always a level with angular momentum distribution given by Eq. (3) at each energy point. As the matter of fact, the discrete levels given by the level scheme have a definite parity and angular momentum, which is essentially different from the level scheme measured by experiment. In the level density formula P (π) = 1/2 means the numbers of positive parity and the negative parity in the continuous states are equal from each other. Actually, the measured parities of discrete levels have certain values. For instance, the parity and angular momentum distributions of 19 F are shown in Fig. 6, where the numbers of positive parities and the negative parities are not equal obviously. On the other hand, the maximum angular momentum is only 9.5 given by the level scheme, but in the statistical model codes they usually use about 20 as the maximum angular momentum in continuous states, where would have much spurious angular momenta states. Therefore, the angular momentum and parity distributions given by the level density formula Eq. (2) are an approximation. 4 Discussion and Summary The energies of discrete levels for light nuclei are generally given very high in the level scheme, so only the discrete levels are employed in the new light nuclear reaction model at the incident neutron energies below 20 MeV, while the continuous states are not needed, which is the main difference from the other available code (such as TNG, [7] GNASH, [13,14] UNF [2] ). The information on the competitions among neutrons and charged particles, as Fig. 6 The angular momentum and parity distributions of 19 F.

5 106 DUAN Jun-Feng, YAN Yu-Liang, SUN Xiao-Jun, ZHANG Yue, and ZHANG Jing-Shang Vol. 47 Fig. 7 Sketch map of levels. The solid lines and the shadow correspond to the discrete levels and the continuous level. In the theoretical calculation of American ENDF library, the continuous state was used above the 21-th level of 19 F. The levels exist everywhere in the continuous region according to the level density formula. This situation deviate from the level scheme, which is shown in Fig. 7. In this figure the left side shows the level scheme and the emission situation, while the right side is the continuous state, which is a competitive region including inelastic scattering and charged particles emissions, as well as the gamma decay. In this case the level density parameter needs to be adjusted in order to fit the measurements. Certainly, limited by the measurement condition the continuous states have to be employed in statistical model calculation for medium or heavy nuclei because the discrete levels at high excitation energy region could not be established. However, if there are more enough discrete levels for the light nuclei, then the model calculations ought to use discrete levels. The calculation results indicate that from the first excitation level to the 37-th excited level of 19 F are the main source of inelastic scattering as shown in Table 1. As shown in Table 2, following the first neutron emission, the second neutron emissions arise above the 104-th level of 19 F belonging to (n, 2n) channel and the proton emissions arise above the 56-th levels of 19 F belonging to (n, np) channel. In this paper, a new reaction model for light nuclei is expanded to be employed for neutron induced 19 F of the 2s-1d shell nucleus. According to the calculation results the application is also successful. The characteristic of this new model is that all particle emission processes are reached to the discrete levels of their residual nucleus, whereas the continuous states are not needed. Hence, the more obvious information about particle emission and competitions among all kinds decay modes could be obtained in the model calculations. The theoretical calculation indicates that the light nuclei even in 2s-1d shell nuclei could be calculated with this method so long as the related level scheme could be provided sufficiently. References [1] J.S. Zhang, et al., Nucl. Sci. Eng. 133 (1999) 218. [2] J.S. Zhang, Nucl. Sci. Eng. 142 (2002) 207. [3] J.S. Zhang and Y.L. Han, Commun. Theor. Phys. (Beijing, China) 36 (2001) 437. [4] J.S. Zhang and Y.L. Han, Commun. Theor. Phys. (Beijing, China) 37 (2001) 465. [5] J.S. Zhang, Commun. Theor. Phys. (Beijing, China) 39 (2003) 433. [6] J.S. Zhang, Commun. Theor. Phys. (Beijing, China) 39 (2003) 83. [7] C.Y. FU, Nucl. Sci. Eng. 61 (1998) 100. [8] R.B. Firestone and V.S. Shirley, Table of Isotopes 8th, John Wiley and Sons (1996). [9] M. Baba, et al., Conf. on Nucl. Data for Sci. and Tech., Santa, 1985, p [10] J.S. Zhang, Science in China Ser. G 47 (2004) 137. [11] Y.L. Yan, et al., Commun. Theor. Phys. (Beijing, China) 44 (2005) 128. [12] J.F. Duan, et al., Commun. Theor. Phys. (Beijing, China) 44 (2005) 701. [13] P.G. Young and E.D. Arthur, Los Alamos Scientific Laboratory LA-0974 (1977). [14] P.G. Young, et al., Los Alamos Scientific Laboratory LA- UR (1996). [15] D.Z. Ding, et al., Neutron Physics, Atomic Energy Press, Beijing (2002).

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