Commun. Theor. Phys. (Beijing, China) 36 (2001) pp. 437 442 c Internationa Academic Pubishers Vo. 36, No. 4, October 15, 2001 Mode Cacuation of n + 6 Li Reactions Beow 20 MeV ZHANG Jing-Shang and HAN Yin-Lu China Nucear Data Center, China Institute of Atomic Energy, Beijing 102413, China (Received Apri 30, 2001) Abstract Based on the unified Hauser Feshbach and exciton mode for ight nucei, the cacuations of reaction cross sections and the doube-differentia cross sections for n + 6 Li are performed. Since a of the first-partice emissions are from the compound nuceus to the discrete eves, the anguar momentum couping effect in pre-equiibrium mechanism must be taken into account. The fitting of the measured data indicates that the three-body break-up process needs to be invoved, and the pre-equiibrium reaction mechanism dominates the reaction processes. In ight nuceus reactions the recoi effect must be taken into account. PACS numbers: 25.10.+s Key words: pre-equiibrium emission, discrete eves, three-body break-up process 1 Introduction The neutron interaction with 6 Li is important from the appication point of view, since ithium is the major tritium breeding materia in thermonucear fusion reactor system. On the other hand the three-body breakup process is a subject to be studied in nucear physics. The neutron spectra from direct three-body breakup through 7 Li n + d + α and the three-body breakup through 6 He n + n + α of the residua nuceus of the (n,p) reaction channe, as we as from other neutron production channes strongy differ from each other. The doube differentia cross sections coud provide the information for anayzing the components from the differentia reaction mechanism. The neutron energy-anguar spectra have been measured by Chiba at E n = 4.2,5.4,6.0 and 14.2 MeV in 1985. [1] Afterwards, Baba and Xia measured the data at E n = 14.1 MeV in 1990 [2] and at E n = 14.2 MeV in 1993, [3] respectivey. Recenty, Ibaraki and Baba performed the neutron doube-differentia measurements at 18 MeV in 1997. [4] To anayze the experimenta data a new approach for ight nuceus of the 1P she has been deveoped and the cacuations for n + 12 C [5] and n + 16 O [6] are successfuy made. The first-partice emissions can be described through pre-equiibrium and equiibrium mechanism. To conserve the anguar momentum from compound nuceus to the discrete eves of the residua nuceus, the anguar momentum couping effect in pre-equiibrium emission process is proposed. [6] The representations of doubedifferentia cross sections of sequentia partice emissions and the three-body breakup process have been given in Refs [5] [8]. In Sec. 2, the reaction channes opened beow 20 MeV are isted in detai. The representations of the doube differentia cross sections of the three-body breakup processes are presented in Sec. 3. The comparison of the cacuated resuts and the experimenta data are given in Sec. 4. 6 Li nuceus is known to have a dominant custer structure, the direct three-body breakup of n + d + α and the two-body breakup reaction processes from the excited eves of 6 Li have been cacuated, and the cacuated resuts are discussed. To anayze the reaction mechanism, the components in the incusive spectrum of neutrons are aso discussed in this section. A summary is given in Sec. 5. 2 Reaction Channes of the n + 6 Li Reaction In view of the n+ 6 Li reactions for E n 20 MeV, the reaction channes are isted as foows: γ + 7 Li, Q = 7.249 MeV, p + 6 He, β,t 1/2 = 806.7 ms, Q = 2.725 MeV, d + 5 He(n + α), Q = 1.475 MeV, n + 6 Li = t + α, Q = 4.782 MeV, 2n + 5 Li(p + α), Q = 3.700 MeV, n,p + 5 He(n + α), Q = 4.594 MeV, n,d + α, Q = 1.475 MeV. The discrete eve schemes used for every reaction channe at E n 20 MeV are taken from Ref. [9], and given in Tabe 1 for the energy, spin, parity and eve width.
438 ZHANG Jing-Shang and HAN Yin-Lu Vo. 36 Tabe 1 The eve schemes of 5 He, 6 He, 5 Li, 6 Li and 7 Li. E k (I π )Γ (MeV) 5 He 6 He 5 Li 6 Li 7 Li 0.000(0.5 + )0.602 0.000(0 + ) 0.000(1.5 )1.50 0.000(1 + ) 0.000(1.5 ) 4.000(0.5 + )4.1 1.797(2 + )0.133 7.500(0.5 ) 2.186(3 + ) 0.478(0.5 ) 16.76(1.5 + )0.076 13.60(1 ) 16.66(1.5 + )0.3 3.563(0 + )8.2 10 6 4.630(3.5 )0.093 4.310(2 + )1.72 6.680(2.5 )0.88 5.366(2 + )0.540 7.460(2.5 )0.089 5.650(1 + )1.5 9.670(3.5 )0.40 15.80(3 + )17.8 9.850(1.5 + )1.20 11.240(1.5 )0.260 The reaction situation from the compound nuceus 7 Li to the discrete eves of the residua nucei up to 20 MeV is presented in Tabe 2. Tabe 2 The reaction situation from the compound nuceus 7 Li to the discrete eves of the residua nucei up to E n = 20 MeV. E a th (MeV) k 1 k 2 Channe (n, n) 4.160 2 (n, n) 6 Li (n, p) 3.182 gs b (n, p) 6 He(gs) (n, p) 4.979 1 2 (n, 2np)α (n, d) 2.767 gs 1 (n, nd)α (n, t) 0 gs (n, t)α (n, nd) 2.533 1 gs (n, nd)α (n, nd) 4.160 3 gs (n, nd)α (n, nd) 6.266 4 gs (n, nd)α (n, nd) 6.598 5 gs (n, nd)α (n, nd) 18.45 6 gs (n, nd)α (n, np) 6.266 4 gs (n, 2np)α (n, np) 6.598 5 gs (n, 2np)α (n, np) 18.45 6 gs (n, 2np)α (n, 2n) 18.45 6 gs (n, 2np)α a The term E th refers to the threshod energy needed to open the k 2 eve of the residua nuceus via the k 1 eve. b The acronym gs refers to the ground state. The main reaction channe of n+ 6 Li is (n,tα) with the Q-vaue of 4.782 MeV. Beow 20 MeV the excited eves are ony up to the seventh eve (15.80(3 + )) of 6 Li. A of the excited eves of 6 Li can emit the secondary partice ike neutron, proton and deuteron, except the second excited eve (3.563(0 + )), which aows the two-custer separation of d + α energeticay, but it is ony decayed through gamma emission to the ground state of 6 Li, due to anguar momentum forbidden ( 6 Li d + α are a in positive parities with the spin 0 + 1 + + 0 + ), so the ineastic scattering reaction channe mainy comes from the second excited state. The residua nuceus 6 He is yieded from proton emission. The ground state of 6 He is unstabe through beta decay and contributes to the (n,p) reaction with the threshod energy of 3.182 MeV, whie the first excited state of 6 He has the energy of 1.797 MeV, which is beow the neutron binding energy, so it ony decays through three-body break-up process ( 6 He n + n + α) and contributes to (n, 2np)α channe with the threshod energy of 4.979 MeV. Meanwhie the reaction channes (n,2n) 5 Li and (n,np) 5 He aso beong to (n,2np)α channe, since 5 Li and 5 He are unstabe and spontaneousy separated into p+α and n+α, respectivey. Through the first deuteron emission (n,d) 5 He with the threshod energy of 2.767 MeV, 5 He spontaneousy becomes n and α partices, so it beongs to the reaction channe (n,nd)α. The reaction situation from the compound nuceus 7 Li to the discrete eves of the residua nucei up to E n = 20 MeV is presented in Tabe 2. Therefore, the reaction mechanism in the n + 6 Li system eading to decay into n + d + α may proceed via three different reaction channes. The reaction channes to 6 Li(n,nd)α channe invoved in the cacuation are as foows: (a) n + 6 Li n + 6 Li, (b) n + 6 Li d + 5 He, (c) n + 6 Li 7 Li n + d + α, 6 Li d + α ; 5 He n + α ; (direct three-body breakup process). 3 The Representation of Doube Differentia Cross Sections The formuation of the sequentia partice emission, the two-body separation and the three-body breakup processes have been obtained. The energy baance is stricty taken into account, which is necessary for the reaction of the ight nucei. The representations of doube differentia cross section of the second-partice emission have been presented. [5,6] The spectra of the outgoing partices with mass m i from the three-body breakup process of the residua nuceus with mass M in the residua recoi nuceus system (RNS) [5] are obtained by [8] 8 S(ǫ i ) = ǫ i (ǫ i(max) ǫ i ), i = 1,2,3, (1) πǫ 2 i(max) where the maximum energies of the three-body breakup process are ǫ i(max) = (M m i /M)E, i = 1,2,3, (2)
No. 4 Mode Cacuation of n + 6 Li Reactions Beow 20 MeV 439 where E refers to the tota kinetic energy reeased from the three-body breakup process. In center-of-mass system (CMS) the doube differentia cross section of the emitted partice from the three-body breakup process is presented by d 2 σ dǫ c i dωc i = σ 4π (2+1)f mi (ǫ c i)p (cos θi), c i = 1,2,3,(3) where the Legendre coefficient reads f mi (ǫ c i) = ( 1) where β = 4β fm1 (c) b a S(ǫ) ( ǫ c P i + β 2 ǫ ǫ 2β ǫ c i ) dǫ, (4) m i E c M 1 /M 1 and M 1 is the mass of residua nuceus, EM c 1 stands for the energy of residua nuceus in CMS, respectivey. f m1 (c) is the Legendre expansion coefficient of the first emitted partice m 1. The integration imits in Eq. (4) are given by we with the measurements. Fig. 1 The 6 Li(n, t) 4 He cross section. The data are taken from EXFOR fie. a = ( ǫ c i β) 2, b = min{ǫ r i(max), ( ǫ c i + β)2 }. (5) The superscripts c and r stand for the energies in CMS and RNS, respectivey. The energy region of ǫ c i is given by ǫ c i(max) = ( ) β + ǫ r 2 i(max), (6) { ( ) β ǫ r 2 ǫ c i(min) = i(max), if ǫ r i(max) < β, 0, if β (7) ǫ r i(max). The formua is used for the three-body breakup process of 6 He as the residua nuceus of the (n,p) reaction channe. 4 Resuts and Discussions The LUNF code for n + 6 Li is deveoped for cacuating the cross sections and the energy-anguar spectra of a kinds of outgoing partices in n + 6 Li reactions. The potting of the (n,t)α cross sections are shown in Fig. 1. The fittings agree fairy we with the measurements. The cacuations of the doube-differentia cross sections of outgoing neutron from different reaction channes and the comparisons with the experimenta data have been performed. The eve width broadening and the energy resoution must be taken into account for fitting the experimenta data. [5] The comparisons between the cacuated resuts and experimenta data are shown in Figs 2 and 3 for an incident neutron energy E n = 5.4 MeV and outgoing anges of 30 45, 60, 75, 90, 110, 125 and 135. Meanwhie, the comparisons of the outgoing neutrons at an incident neutron energy E n = 14.1 MeV for outgoing anges of 20, 30, 37.5, 45, 52.5, 60, 75, 90, 105, 120, 135 and 150 are shown in Figs 4 and 5. The comparisons of the outgoing neutrons at an incident neutron energy E n = 18 MeV for outgoing anges of 20, 30, 37.5, 45, 52.5, 60, 70, 80, 90, 105, 120, 135 and 150 are shown in Figs 6 8. A of the fittings agree Fig. 2 The energy-anguar spectra of 30, 45, 60 and 75 at E n = 5.4 MeV. The data are taken from Ref. [1]. Fig. 3 The energy-anguar spectra of 90, 110, 125 and 135 at E n = 5.4 MeV. The data are taken from Ref. [1].
440 ZHANG Jing-Shang and HAN Yin-Lu Vo. 36 In this mode the sequentia partice emission and the two-body breakup process, as we as the three-body processes are incuded, from which the different respective neutron energy-anguar distributions are obtained as the components of the tota energy-anguar spectrum of outgoing neutron. The partia spectra of the outgoing neutron, as an exampe, are shown in Fig. 9 at E n = 14.1 MeV for outgoing ange of 90 ; the first peak on the right-hand side in the tota energy-anguar distribution mainy comes from the emission from 7 Li to the first excited eve. The detaied notations are given in the figure caption. Fig. 4 The energy-anguar spectra of 20, 30, 37.5, 45, 52.5 and 60 at E n = 14.1 MeV. The data are taken from Ref. [2]. Fig. 5 The energy-anguar spectra of 75, 90, 105, 120, 135 and 150 at E n = 14.1 MeV. The data are taken from Ref. [2]. Fig. 6 The energy-anguar spectra of 20, 30, 37.5, 45 and 52.5 at E n = 18 MeV. The data are taken from Ref. [4]. The pre-equiibrium mechanism dominates reaction processes of n + 6 Li beow 20 MeV. The cacuations indicate that ony the equiibrium mechanism coud not give the reasonabe resuts even at ow neutron incident energies. At E n = 14.1 MeV, as an exampe, the preequiibrium state occupies the percentage of P pre-eq = 86.5%, whie equiibrium state ony has P eq = 13.5%. The Kabach parameter in the exciton mode K = 100 MeV 3 is used in the cacuations. Since ight mass of the target, the energies of the secondary partice emissions have very wide energy range due to recoi effect. The energy range of the ring-type spectra of the second emitted partices coud be about a few MeV. For this reason in the cacuation it must be treated as a continuum spectra. [5] If the residua nucei were treated as static in CMS, then the spectra of the outgoing partices woud have a wrong shape and the energy baance coud not be hed. Since this approach can cacuate the doube differentia cross sections of a kinds of outgoing partices, the energy-anguar distributions of neutron and deuteron as we as apha partice can be obtained with fu energy baance. As is we known the deuterium-production cross sections are aso important in the fusion reactor system, but there is not any information from the wordwide neutron data ibraries, in which the neutron information from channe (n, nd)α is represented in the ineastic channe with the pseudo eves. Meanwhie, the neutron spectra from the channe (n, 2np)α are cacuated by four-body phase space method, which are isotropic in CMS.
No. 4 Mode Cacuation of n + 6 Li Reactions Beow 20 MeV 441 Fig. 7 The energy-anguar spectra of 60, 70, 80, 90 and 105 at E n = 18 MeV. The data are taken from Ref. [4]. Fig. 8 The energy-anguar spectra of 120, 135 and 150 at E n = 18 MeV. The data are taken from Ref. [4]. Fig. 9 The partia spectra of the secondary neutrons of 90 at E n = 14.1 MeV. Designations K = 1 5 correspond to the first emitted neutron from the compound nuceus 7 Li to the Kth excited eves of 6 Li, respectivey; designations i and j correspond to the second emitted neutrons from the fourth and fifth excited eves of 6 Li to the ground state of 5 Li; designation k corresponds to the neutrons from the three-body breakup of the residua nuceus 6 He of the (n, p) channe; designations and m correspond to the neutrons from the ground state and the first excited state, respectivey, of 5 He residua nuceus of the (n, d) channe; designation d corresponds to the neutron from the direct three-body breakup of the compound nuceus 7 Li. The fu ine is the cacuated energy-anguar spectrum. 5 Summary The statistica reaction mode is often used in evauation of nucear data for medium to heavy nucei, from the mode cacuation of n + 6 Li one can see that it sti can be appied to the ight nucei. However the preequiibrium reaction mechanism dominates the reaction processes. The key point is the anguar momentum couping effect in pre-equiibrium mechanism of the partice emissions from the compound nuceus to the discrete eves to be taken into account. [6] The cacuations indicate that the equiibrium statistic reaction mode does not work to describe the reaction behaviors for ight nucei. Recenty, Chiba et a. [10] cacuated neutron spectra by DWBA and the fina-state interaction theory, the comparison with the measured data gives a good agreement ony at high energy region. Instead of the fina-state interaction, the particehoe excitation is used in this approach. The resuts can give a good agreement with the experimenta data in the whoe energy region. In view of the eve widths of the residua nucei, they are amost in the order of magnitude of severa hundred kev or severa MeV, which corresponds to the direct and pre-equiibrium reaction processes. In this case it is hard to distinguish between the direct and the pre-equiibrium mechanism. This is the characteristic
442 ZHANG Jing-Shang and HAN Yin-Lu Vo. 36 of ight nucear reactions. Because of a strong recoi effect in the ight nuceus reaction, the energy baance is stricty taken into account. Therefore, the fie-6 for the doube-differentia cross sections can be set up for the reaction channes of (n,2np)α and (n,nd)α in neutron data ibrary. Since the cross sections of a reaction channes and the doube differentia cross sections of a kinds of the outgoing partices can be cacuated beow 20 MeV in this way we do not need the pseudo-eves in the ineastic scattering channe to make up the information for the outgoing neutrons. Acknowedgment The authors woud ike to thank M. Chiba for providing us the experimenta data for theoretica anayses. References [1] S. Chiba, et a., J. Nuc. Sci. Tech. 22 (1985) 771. [2] M. Baba, et a., JAERI-M-90-025 (1990) p. 383. [3] H.H. XIA, et a., China J. Nuc. Phys. 15 (1993) 367. [4] M. Ibaraki and M. Baba, 6 Li, 7 Li and 9 Be Neutron Emission Cross Sections at 18 MeV Neutron Energy (private communication). [5] J.S. ZHANG, Y.L. HAN and L.G. CAO, Nuc. Sci. Eng. 133 (1999) 218. [6] J.S. ZHANG, Y.L. HAN and X.L. FAN, Commun. Theor. Phys. (Beijing China) 35 (2001) 579. [7] J.S. ZHANG, CNIC-01430, CNDC-0025, INDC(CRP)- 049/L, Commu. Nuc. Data Progress 22 (1999) 1. [8] J.S. ZHANG, CNIC-01475, CNDC-0027, INDC(CRP)- 050/L, Commu. Nuc. Data Progress 23 (2000) 14. [9] R.B. Firestone and V.S. Shirey, Tabe of Isotopes 8th, John Wiey & Sons (1996). [10] S. Chiba, et a., Phys. Rev. C58 (1998) 2205.