Numerical Evaluation of Sn Isotope Cross Sections by Photoneutron Activation Method

Transcription

1 Nuerical Evaluation of Sn Isotope Cross Sections by Photoneutron Activation Method C. Oprea ), A. Oprea ), A. Mihul ) ) Joint Institute for Nuclear Research, Frank Laboratory of Neutron Physics, 98 Dubna, Moscow Region, RF ) Departent for Nuclear Physics, Faculty of Physics, University of Bucharest, RO-775 Magurele, Roania Abstract. Photoneutron cross section reactions on natural Sn were evaluated using Talys code for incident neutron energy up to soe ten s of MeV s. For each Sn isotope the contribution of copound, direct and preequilibriu echanis were extracted. The isoer cross sections and isoer ratios were calculated. The results are copared with existing experiental data obtained by bresstrahlung source and activation ethods. INTRODUCTION Nuclear reactions induced by gaa quanta with eission of neutrons are efficient in fundaental and applied researches. In fundaental researches with the help of the photoneutron reactions new data on atoic nuclei structure and states as well as on nuclear reaction echanis are obtained. In applied researches these reactions are used in nuclear safeguard, nucleosynthesis, radiation transport, isotopes productions and any others [,]. In the present report the photoneutron reactions on Sn nucleus will be analyzed. This nucleus has ten natural isotopes with the following atoic ass abundances, respectively: -.96% -.66 %, 5-.5 %, 6-. %, %, 8-. %, %, -.85 %, -.7 %, -5.9 % [-5]. For all isotopes the (,xn) cross section (x=,,,) and the isoeric ratio in the (,n) reaction for incident photon energy fro the neutron threshold (89 MeV) up to 6 MeV were evaluated. Also analyses of the contribution of copound, direct and preequlibriu processes to the cross section as well as of discrete and continuu states were perfoed. With the help of Talys the cross sections were evaluated. Talys is a freeware software working under Linux operating syste and is dedicated to nuclear reactions calculations [6,7]. Isoer states are of a great interest fro a long tie in nuclear physics and they can be considered excited states of atoic nuclei with high spins value and consequently very large tie of life copared with other excited nuclear states. For soe isotopes of Sn the isoeric ratios in (,n) reactions were not easured in the Great Dipole Resonance (GDR) region. Because the related cross sections are known as calculated by using Talys then it is possible to estiate the isoeric ratio starting fro the threshold up to soe axial energy of the Brehsstrahlung X-ray source. THEORETICAL BACKGROUND Isoer ratio R, is defined as the ratio between the cross sections of etastable () and ground state (g) isotope production: R (), g g cross sections of isotope production in etastable and ground states, respectively.

2 In Talys the isoer ratio is defined slightly different [7]: R () g Relations (,) are theoretically because in the experient the isoeric ratios are easured using other expression. Experiental isoeric ration in the case of Brehsstrahlung source of incident gaas is [8,9]: R exp E E th E N E E de N E g E de () Eth where E th = neutron threshold energy of incident gaas, E = axiu energy of gaas, N = concentration of investigated isotope, = incident gaa flux. The analysis of isoeric ratios is starting fro neutron threshold ( 8MeV) up to 6 MeV. In this large energy interval, including the GDR region, it is possible to act the known copound, direct and preequilibriu [] nuclear reaction echaniss. As it will be deonstrated below in the analyzed cases the copound processes are doinant so the Hauser-Feshbach foralis can be applied. In this case the cross section has the for []: T T Tc W () c where T = penetrability coefficients, W = width fluctuation correction factor, = reduced wavelength of incident particle, c = incident, eergent and possible outgoing channels respectively. Su is taken over all possible open channels c. Our case xn, x =,,, The ain eleents in the Hauser-Feshbach cross section forula () are the penetrability coefficients. The penetrability coefficient represents the probability of a particle to pass a potential barrier. The transission coefficients are increasing with energy but their values are always lower than one. The width fluctuation correction factor W represents a correlation between incident channel () and outgoing channels (c). At low incident energies this factor is equal with one indicating no correlation between ingoing and outgoing channels (Bohr hypothesis) and it is decreasing slow with the energy showing soe dependencies between ingoing and outgoing channels. There are a few ways for the calculation of the correction factor W and they are described very detailed in [7]. The cross sections and isoer ratios are evaluated using Talys codes. Talys provides very precise nuclear reaction evaluations starting with kev up to MeV, that is very useful for describing of experiental data or nuclear data generation. By free contributions of any authors the nuclear reactions echaniss (copound, direct, pre-equilibriu), nuclear data like energy levels, nuclear data density, nuclear odels and any others in a unitary friendly easy to use interface were ipleented [6,7].

3 In the next paragraph soe of definitions ipleented in Talys like exclusive and inclusive cross sections will be used. The cross section is defined exclusive when the outgoing channel is exactly specified by the nuber of eergent particles (plus any nuber of photons). For exaple (,n) exclusive cross section is considered as in the outgoing channel exists two neutrons and only two neutrons (plus any nuber of photons). By coparison inclusive cross sections can be understood when in outgoing channel the eergent particle is coing fro other type of reaction. We have a (,n) inclusive cross section when the registered neutrons coe fro other photonuclear reactions involving neutrons like (,xn), (,np), (,np), (,np), (,n) etc [7]. RESULTS AND DISCUSSION The photoneutron cross sections for all natural isotopes of Sn nucleus were calculated For each nucleus the inclusive (,n) cross sections have been obtained and later they were decoposed in the corresponding exclusive (,xn) (x =,,,). The contribution of copound, direct and pre-equilibriu processes were obtained. Also a separation into discrete and continuu processes was effectuated. For isotopes where it was possible we have extracted the isoer and ground state production cross sections (, g ) in the exclusive (,n) reactions. In ultiple eission processes of type (,np), (,np), (,np), (,np), (,np) and others with the participation of charged particles a lot of isoer states are produced but they were not considered as their cross section usually are very low since they are partially suppressed by the presence of nuclear Coulob field. Further only the results on (,n) reaction on Sn and Sn are presented (Figures and ). In the Figures and the photoneutron cross sections for the Sn(,n) Sn and Sn(,n) 9 Sn have been represented. In the Figures.a and.a the (,n) inclusive reactions are shown. The inclusive (,n) reactions is a superposition of (,n), (,n), (,n) exclusive processes. The experiental data are described very well by (,n) exclusive reactions []. In the Figures.b and.b the inclusive (,n) cross section is separated in copound and direct processes. The pre-equilibriu processes were neglected as resulted fro the evaluations. In the Figures.c and.c the exclusive (,n) cross section is represented as su between discrete and continuu processes. At low energies the processes on discrete levels are predoinant but with the increasing of energy the role of continuu processes becoe ore iportant. In the Figures.d and.d the cross sections of Sn(,n),g Sn and Sn(,n),g9 Sn reactions are represented. Soe odels of Brehsstrahlung sources were used together with the cross sections of isoer and ground state production for the isoer ratios evaluations. The isoer ratios can be easy calculated by using relation () and cross sections fro Figures.d and.d. In order to be closer to the experient it is necessary to use the expression (). The evaluation of the incident X-ray flux is a quite coplex question for which any papers in the literature are dedicated. In the present evaluation of isoer ratios the siplest two cases have been used. In the first case the incident flux is considered unity with gaa energy fro neutron threshold up to 6 Mev. In the second case a continuous X-ray source with a flux based on Kraers forula was considered []. E ~ Ic ibz E E E (5) I c = intensity of gaa quanta; i b = electron bea current; E = energy of accelerated electrons; Z = charge of stopping eleent.

4 n [b] 5 5 a 5 - (,n) inclusive - (,n) exclusive - (,n) enclusive - (,n) enclusive 5 - (,n) exp. data 5 5 b - Copound processes - Direct processes n [b] 8 6 c - Sn(,n) g Sn - Sn(,n) Sn 5 5 d - Total (,n) - Continuu processes - Discrete processes - (,n) processes E E Figure. Cross section of Sn(,n) Sn reaction. a) Inclusive (,n) cross section and contribution of (,xn) (x=,,) processes. Results are copared with experiental data. b) Decoposition into direct and copound processes (pre-equilibriu states are neglected) c) Decoposition into discrete and continuu processes d) Isotopes production,g Sn of isoer and ground states, respectively. The incident gaa flux (5) is decreasing with energy and therefore the axiu energy E fro () ust be taken up to 5 MeV in order to have enough statistics in the experient. The incident flux can be calculated using other ore coplicated odels like Schiff odel [] or by Monte Carlo siulation. In the Table are shown the ain properties of isotopes considered in the calculation of isoeric ratios [5]. Table. Main properties of isoer () and ground (g) states of Sn isotopes used for isoer ratios calculation Isotope Isoer () Ground (g) J J Sn (7/) +. (/) + 5.9d 7 Sn (/) -.6 d (/) + stable 9 Sn (/) - 9. d (/) + stable Sn (/) y (/) h 5 Sn (/) +.6 (/) - 9. d

5 In Table are represented the isoer ratios for the Sn isotopes () if the flux of incident gaas is equal with one and () if the flux is calculated by Kraers forula (5) with different axi energy E. 5 a - (,n) inclusive - (,n) exclusive - (,n) enclusive - (,n) enclusive 5 - (,n) exp. data 5 b - Copound processes - Direct processes n [b] n [b] 5 5 c - Total (,n) - Continuu processes - Discrete processes - (,n) processes 5 5 d - Sn(,n) 9g Sn - Sn(,n) 9 Sn E E Figure. Cross section of Sn(,n) 9 Sn reaction. a) Inclusive (,n) cross and contribution of (,xn) (x=,,) processes. Results are copared with experiental data. b) Decoposition into direct and copound processes (pre-equilibriu states are neglected) c) Decoposition into discrete and continuu processes d) Isotopes production: 9,g Sn of isoer and ground states respectively. Table. Isoer ratios calculated for Sn isotopes obtained in (,n) reaction. ) = ;E = 5 MeV; = ;E = 5 MeV; ~(E -E )/E (6); E = 5 MeV; E = MeV Reaction R R R Sn(,n),g Sn.±..±.7.995±.59 8 Sn(,n) 7,g Sn.8±.5.768±..66±. Sn(,n) 9,g Sn.±.5.6±..±.8 Sn(,n),g Sn.58±.5.±.5.7±. 5 Sn(,n),g Sn.75±.5.87± ±.95 The results in Table were evaluated nuerically based on relations (-5) ipleented in Talys, starting fro neutron threshold up to 5 and 5 MeV, respectively, with step. MeV (which is the source of showed errors). In the first and second case of Table (R, R ) the incident flux was taken unity just for siplicity. The axiu gaa energy first was considered 5 MeV because the axiu energy in the Figures and is also up to 5 MeV. Fro relation (5) it results that an experient is liited by the energy of stopped electrons E. If electron energy (E ) is taken

6 MeV than the axiu energy of gaa quanta (E ) should be up to 5 MeV for a suitable incident intensity and statistics of events. This is the situation of the second and third cases of Table where for useful coparisons the intensity was taken unity (R ) and after in accordance with (5) (R ). The R case is ore close to reality and therefore these evaluations are needed in new easureents on isoer ratios of Sn isotopes. Fro Table it is shown that if the spin of isoer states is greater than the spin of the ground state then the isoer ratio is less then unity and greater than one if vice versa. This has the following explanation: due to the selection rules, the levels with high spin values are less populated than those with lower spin values. Exception sees to be the first case of Sn(,n),g Sn reaction but in this case a) the isoer state has a not so great value and b) the difference between spins values of isoer and ground states is not so high too. CONCLUSIONS The cross sections and isoer ratios of photoneutron reactions on Sn isotopes in the region of GDR were evaluated. The cross sections were obtained with Talys and for isoer ratios soe odels of incident gaa were used. The Talys code allowed to extract the contributions of different processes to the cross section (copound - direct - preequilibriu or discrete - continuu). A very good agreeent between theoretical cross section evaluations and experiental data fro literature has been obtained. The agreeent between theoretical and experiental cross sections evaluations has given a serious base for isoer ratios calculations. Then the isoer ratios were calculated using Talys cross sections, different incident gaa flux and axiu values of gaa incident energies. One of future tasks is to easure experientally the isoer ratios fro Table which is possible to the basic installations of JINR Dubna. Acknowledgeents. The work is partially supported by the Cooperation Progra of Roanian Plenipotentiary Representative to JINR Dubna for year. REFERENCES [] B.S. Ishkhanov, V.V. Varlaov, Physics of Atoic Nuclei () [] B.S. Ishkhanov, S.Yu. Troschiev, Moscow University Physics Bulletin () [] [] G. Audi, A.H. Wapstra, Nucl. Phys A, 565, -65 (99) [] G. Audi, A.H. Wapstra, Nucl. Phys. A 595, 8-9 (99) [5] K.J.R. Rosan, P.D.P. Taylor, Pure Appl. Che. 7, (999) [6] The Talys Codes [7] A.J. Koning, S. Hilaire, M. Duijvestij, Talys-. A nuclear reaction progra, User anual. Peten NRG (9) [8] D.T. Tran, T.A. Truong, T.K. Nguyen, T.V. Nguyen, V.C. Phan, A.G. Belov, O.D. Maslov, Physics of Particles and Nuclei Letters (9) [9] D.T. Tran, T.A. Truong, T.V. Nguyen, V.C. Phan, A.G. Belov, O.D. Maslov, T.T.M. Trinh, Physics of Particles and Nuclei Letters -8 (6) [] E. Gadioli, P.E. Hodgson, Pre-equilibriu Nuclear Reactions, Oxford University Press (99) [] W. Hauser, H. Feshbach, Phys. Rev. 87 (95) [] V.V. Varlaov, B.S. Ishkhnov, V.N. Orlin, V.A. Chetvertkova, Bulletin of Russian Acadey of Sciences: Physics Allerton Press Inc. () [] H.A. Kraers, Philos. Mag (9) [] L.I. Schiff, Phys. Rev (95) [5] R.B. Firestone, V.S. Shirley, S.Y.F. Chu, C.M. Baglin, J. Zipkin, Tables of Isotopes. CD ROM Edition, Wiley-Interscience (996)