Research Journal of Recent Sciences _________________________________________________ ISSN 2277-2502 Vol. 3(ISC-2013), 20-22 (2014) Res. J. Recent. Sci. International Science Congress Association 20 Effect of Angular Momentum Transfer on Isomeric Cross-Section Ratio Najumunnisa T., Musthafa M.and Mohamed Aslam P.Department of Physics, University of Calicut, Kerala, INDIAAvailable online at: www.isca.in, www.isca.me Received 27th November 2013, revised 3rd January 2014, accepted 12th February 2014 AbstractThe isomeric cross-section ratios are calculated for the reactions 113In(a,n)116Sbm,g, 115In(,3n)116Sbm,g, 116Sn(p,n)116Sbm,g, 116Sn(d,2n)116Sbm,g, 117Sn(p,2n)116Sbm,g, 115In(,n)118Sbm,g, 116Sn(,pn)118Sbm,g, 118Sn(p,n)118Sbm,g 118Sn(d,2n)118Sbm,g, 119Sn(p,2n)118Sbm,g, 117Sn(n,p)117Inm,g, 118Sn(p,a)115Inm,g over the energy ranges from threshold up to 40 MeV using the nuclear reaction code EMPIRE 3.1. It is found that isomeric cross-section ratio depends on the spins of ground and isomeric states of residual nucleus as well as the incident energy. The isomeric cross-section ratio increases slowly for the cases where larger angular momentum (J) is carried away by the emitted particle and increases sharply when J is smaller.Key words: Nuclear reaction, isomeric cross-section ratio, angular momentum transfer, spin dependence, EMPIRE. Introduction In nuclear reaction, the relative population of isomeric state is generally expressed in terms of isomeric cross-section ratio (ICR) which is defined as the ratio of isomeric cross-section to the total cross-section (/ (m+g )). The study of ICR gives important information about the nuclear reaction mechanism, particularly the energy and angular momentum transfer during the reaction process as well as the progress of the nuclear reactions. ICR is expected to depend on several factors, such as spin of the target nucleus, type and energy of the projectile used, type of the emitted particle, and, more importantly, on the spins of the isomeric states concerned1-3. Satheesh et al4-5 reported that ICR found to depend on the magnitude of spins of the ground and isomeric states, energy difference between the levels, presence of intermediate states and some dependence on decay modes as well as on the onset of pre-equilibrium emission and also suggested that further study is needed to justify the exact dependence. In this background, we studied a set of nuclear reactions to investigate the dependence of ICR on various factors like relative spin of the isomeric and ground state, angular momentum carried away by the ejectiles, single particle or multiparticle emission. Statistical nuclear reaction code EMPIRE 3.1 is used for the analysis. The experimental data available from the literature7-12 are used for verifying the validity of theoretical predictions. Model Calculation: In the present study nuclear reaction code EMPIRE 3.1 which makes use of the Hauser-Feshbach and the Exciton model formalisms has been used. Hauser-Feshbach formalism helps in calculating the ground and isomeric cross-sections separately. The code accounts for the major nuclear reaction models, such as Spherical and deformed Optical Model including coupled-channels code ECIS06, Soft-rotator deformed Optical Model including coupled-channels code OPTMAN, Hauser-Feshbach statistical model including HRTW width fluctuation correction, and the optical model for fission with partial damping, Quantum-mechanical MSD TUL model (codes ORION and TRISTAN), and MSC NVWY model, Exciton model with Iwamoto-Harada cluster emission and Kalbach systematic angular distribution (code PCROSS), Hybrid Monte Carlo preequilibrium model (code DDHMS). A comprehensive library of input parameters based on the RIPL-3 covers nuclear masses, optical model parameters, ground state deformations, discrete levels and decay schemes, level densities, fission barriers and -ray strength functions. The experimental data is automatically retrieved from EXFOR/CSISRS library. The results can be converted into the ENDF-6 format using the accompanying EMPEND code. The package contains the full EXFOR library of experimental data in computational format C4 that are automatically retrieved during the calculations. In the present calculation Optical model parameters due to A. J. Koning13 have been used for both protons and neutrons that due to McFadden and Satchler14 for alpha. Discrete levels were taken from the RIPL-3 level file based on the 2007 version of ENSDF, width fluctuations are calculated within HRTW up to 3.00 MeV, Exciton model calculations are done with code PCROSS, cluster emission in terms of the Iwamoto-Harada model. Mean free path parameter in PCROSS set to 1.5. These theoretical calculations are compared with the available experimental data. Systems under study: The isomeric pairs 115Inm,g, 117Inm,g, 116Sbm,g and 118Sbm,g areproduced through the reactions 118Sn(p,a)115Inm,g, 117Sn(n,p)117Inm,g, 113In(a,n)116Sbm,g and 118Sn(p,n)118Sbm,g in the respective order. The nuclei 115Inm,g and 117Inm,g have isomeric state spin less than ground state spin while others two have isomeric spin greater than that of ground state spin. While studying the variation of isomeric cross-section ratio with incident energy, it is noticed that ICR also has some dependence on the angular momentum carried away by the Research Journal of Recent Sciences ______________________________________________________________ ISSN 2277-2502Vol. 3(ISC-2013), 20-22 (2014) Res. J. Recent. Sci. International Science Congress Association 21 emitted particles. Inorder to study this effect in detail the formation of isomeric pairs 116Sbm,g and 118Sbm,g through the reaction channels 113In(a,n)116Sbm,g, 115In(,3n)116Sbm,g, 116Sn(p,n)116Sbm,g, 116Sn(d,2n)116Sbm,g, 117Sn(p,2n)116Sbm,g, 115In(,n)118Sbm,g, 116Sn(,pn)118Sbm,g, 118Sn(p,n)118Sbm,g, 118Sn(d,2n)118Sbm,g and 119Sn(p,2n)118Sbm,g are considered.Results and DiscussionIn the present study many isotopes having isomeric pairs are formed in each case with various combinations of nuclear parameters like level spin, energy, life time, decay mode etc. The nuclei of interest in the present work are 115Inm,g, 117Inm,g, 116Sbm,g and 118Sbm,g. The cross-sections for the formation of these isomeric pairs are calculated for the incident energy ranges from reaction threshold up to 40 MeV using EMPIRE 3.1 and the isomeric cross-section ratios are plotted against incident energy in figure-1 along with available experimental data.The prediction of the present calculations agree well with the literature data. As can be seen that the isomeric cross-section ratio depends primarily on incident energy and relative spins of the isomeric pairs. In the case of 118Sbm,g and 116Sbm,g spin of isomeric state is greater than that of ground state while for 117Inm,g and 115Inm,g spin of isomeric state is less than that of ground state. The spin values of the ground and isomeric states of these nuclei are given in the table.1. From figure-1, it can be notice that ICR Figure-1 ICRs for the reactions 118Sn(p,n)118Sb, 113In(,n)116Sb, 17Sn(n,p)117Inand 118Sn(p,a)115Infor incident energy from threshold to 40 MeV Table-1 Spins of ground and isomeric states Nuclide Spin Ground state Isomeric state 118 Sb 1+ 8- 116 Sb 3+ 8- 117 In 9/2+ 1/2- 115 In 9/2+ 1/2- increases with incident energy for the case of 118Sb and 116Sb and latter it gets saturated whereas for 115In and 117In it decreases with incident energy and latter remains almost constant for further increase in energy. The EMPIRE calculation satisfactorily reproduces the available experimental data within the error limit for the reactions 118Sn(p,n)118Sb, 113In(,n)116Sb and 17Sn(n,p)117Inm,g and taking this as reference ICR is calculated for 118Sn(p,a)115Inm,g for which no experimental data is obtained. As indicated by Satheesh et al4-5, a nucleus with isomeric spin greater than the ground state spin, the isomeric cross-section ratio increases steadily upto certain energy and thereafter it gets saturated. This is due to the fact that as the energy of the incident particle increases, the state with lower spin gets populated initially and thereafter the higher spin state getting more and more populated and finally reaches an equilibration between the states. In the case of nuclei with isomeric spin less than that of ground state the isomeric cross-section ratio shows an initial increase with incident energy and thereafter it decreases up to certain energy and it remains almost constant on further increase of incident energy. Since at very low energy the ground state start populating irrespective of the spin state and after that sufficient energy is available for the population of the isomeric state the system prefer lower spin state first and then started populating the higher spin state accordingly and later get equilibrated as the previous case. In order to see the effect of angular momentum transfer in the reactions, the ICRs for 116Sbm,g and 118Sbm,g are calculated for various channels and are plotted in figure-2(a) and figure-2(b) respectively. It can be seen from figure-2(a) that ICR for the ,n) and (,3n) reactions increases sharply with the incident energy while that for other reactions increases slowly. In the case of reactions 113In(,n)116Sb and 115In(,3n)116Sb the angular Figure-2(a) ICR for the production of 116Sb Research Journal of Recent Sciences ______________________________________________________________ ISSN 2277-2502Vol. 3(ISC-2013), 20-22 (2014) Res. J. Recent. Sci. International Science Congress Association 22 Figure-2(b) ICR for the production of 118Sb Table-2 Possible values of angular momentum transferred by the emitted particles Reaction Possible 116 Sn(p,n) 116 Sb 7,8 117 Sn(p,2n) 116 Sb 6,7,8,9 113 In(a,n) 116 Sb 3,4 115 In(a,3n) 116 Sb 2,3,4,5 116 Sn(d,2n) 116 Sb 6,7,8,9 118 Sn(p,n) 118 Sb 7,8 119 Sn(p,2n) 118 Sb 6,7,8,9 115 In(a,n) 1 18 Sb 3,4 116 Sn(a,pn) 118 Sb 7,8,9 118 Sn(d,2n) 118 Sb 6,7,8,9 Momentum J, transfered by the emitted particle is smaller than that for other reactions. Similarly, in Figure- 2(b), the ICR for 115In(,n)118Sb reaction increases sharply but for other reactions it shows slow increase. Here J is smaller for 115In(,n)118Sb than that for other reactions. From this it can be say that for the cases where J is small, ICR increases sharply and vice versa. This indicates that when the emitted particle carries larger angular momentum, the higher spin isomer is slowly populated. ConclusionIt is found that the isomeric cross-section ratio critically depends on the spins of ground state and isomeric state as well as the incident energy. At extremely low energy, the ground state is preferentially populated irrespective of the spin state. As the energy increases, the higher spin state gets more populated. The ICR increases slowly for the cases in which angular momentum carried away by the emitted particle (J) is large and it increases sharply when J is smaller. References1.S.M. Qaim, A. Mushtaq and M. Uhl, Phys. Rev. C,38, 645 (1988) 2.F. Cserpak, S. Sudar, J. Csikai and S.M. Qaim, Phys. Rev. C,49, 1525 (1994)3.S. Sudar and S.M. Qaim, Phys. Rev. C,53, 2885 (1996)4.B. Satheesh and M.M. Musthafa, Int. J. Mod. Phys. E, 20, 2119-2131 (2011)5.B. Satheesh, M.M. Musthafa, B.P. Singh and R. Prasad, Int. J.Mod. Phys. E,21, 1250059 (2012)6.M. Herman, Empire 3.1 Rivoli, Modular system for nuclear reaction calculations and nuclear data evaluation, NEA Data Bank (2012)7.V.G. 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