Journal of Asian Scientific Research ENERGY SPECTRA AND ANGULAR DISTRIBUTION ANALYSIS OF 54 FE (N, D) REACTION. Mahdi H. Jasim. Zahida A.

Size: px

Start display at page:

Download "Journal of Asian Scientific Research ENERGY SPECTRA AND ANGULAR DISTRIBUTION ANALYSIS OF 54 FE (N, D) REACTION. Mahdi H. Jasim. Zahida A."

Matilda Walters
6 years ago
Views:

Journl of Asin Scientific Reserch journl homepge: http://essweb.com/journl-detil.php?id=5003 ENERGY SPECTRA AND ANGULAR DISTRIBUTION ANALYSIS OF 54 FE (N, D) REACTION Mhdi H.

Kdhum Deprtment of physics, college of science, University of Bghdd ABSTRACT The neutron induced chrged prticle emission in the pre-equilibrium nd equilibrium stges hve been considered in the present

1 Journl of Asin Scientific Reserch journl homepge: ENERGY SPECTRA AND ANGULAR DISTRIBUTION ANALYSIS OF 54 FE (N, D) REACTION Mhdi H. Jsim Deprtment of physics, college of science, University of Bghdd Zhid A. Dkhil Deprtment of physics, college of science, University of Bghdd Rsh J. Kdhum Deprtment of physics, college of science, University of Bghdd ABSTRACT The neutron induced chrged prticle emission in the pre-equilibrium nd equilibrium stges hve been considered in the present work using the Exciton model. An equidistnt spce model (ESM) includes different correction prmeters is considered in clculting the energy spectr nd double differentil cross-sections of deutron emissions, tht induced by neutron prticle t energy rnge MeV on 54 Fe isotope. An evlution of the present results with globl code Tlys indictes n cceptble greement in ddition to experimentl updte dt t interested region of study. Keywords: Cluster model, Sttisticl compound-nucleus rections, Angulr distribution, Emission spectr, Equidistnt spce model, Preequilibrium emission. JEL Clssifiction: C61, C67, C INTRODUCTION The prticle-hole excittions cused by the nucler rections, which proceed through number of nucleon-nucleon interctions, re described within the either semi clssicl models or the quntum-sttisticl theories of the preequilibrium emission (PE), by mens of the prticle hole stte densities. The exciton model of preequilibrium nucler rections provides simple wy to describe the continuum energy nd ngulr distributions of prticles emitted during the energy equilibrtion in light prticle induced rections for exmple (n,d) t incident energies of round 15 to 96 MeV. Becuse of its simplicity, its physicl trnsprency, its utility, nd its dptbility, the exciton model continues to be used in spite of the development of more microscopic nd quntum mechnicl models Fotin [1], [2]. 149

2 In this work the energy spectr nd ngulr distribution of emitted prticles re considered. Experimentl results concerning light chrged prticle production in neutron induced rections re vilble for iron t comprble incident neutron energies (28.5 MeV,62.7MeV nd 96MeV). Our dt together with those of experimentl work nd TALYS bsed evluted nucler dt librry Version 5 [3] provide complementry informtion on nucleon induced light chrged prticle emission t the prticulr mss region nd offer lrger bse for testing the nucler models of clustering in nuclei Bertrnd nd Peelle [4], Reymckers, et l. [5], Ivscu, et l. [6]. 2. THEORY In exciton model [7-9] the primry pre-equilibrium differentil cross section for the emission of prticle k with emission energy E k cn then be expressed in terms of lifetimes for vrious clsses of sttes, the composite nucleus formtion cross section σ CF, nd n emission rte W k, d de pe k K P CF mx mx p W ( p k 0 0 p p p p, p, E k ) ( p, p ) P( p where the fctor P represents the prt of the pre-equilibrium popultion tht hs survived emission. The bsic feeding term for pre-equilibrium emission is the compound formtion cross section σ cf, which is given by:, p ) CF rec direct where the rection cross section σ rec is directly obtined from the opticl model. The emission rte W k hs been derived by Cline nd Blnn [10] from the principle of micro reversibility, nd cn esily be generlized to two-component version Betk nd Dobes [11]. The emission rte for n ejectile k with reltive mss μ k nd spin s k is: 2sk 1 Wk ( p, p, Ek ) 3 k Ek k, ( p ) Z, p N, E tot k k ( 2 inv Ek tot ( p, p, E ) E where σ k;inv (E k ) is the inverse rection cross section, gin clculted with the opticl model, Z k (N k )is the chrge (neutron) number of the ejectile nd E tot is the totl energy of the composite system. For the prticle-hole stte density we use the expression of Betk nd Dobes [11]. Their formul is bsed on the ssumption of (ESM) nd is corrected for the effect of the Puli exclusion principle nd for the Finite depth of the potentil well. The two-component prticle-hole stte density is: k ) 150

3 ( p, p, E) p! h g n! p n g ( U A( p! h!( n 1)!, p )) n1 f ( p, U, V ) where g ᴫ nd g ᴫ re the single-prticle stte densities, A the Puli correction, U = Ex - P p;h with P p;h Fu's piring correction, Fu [12],for more detil bout corrections see Klbch [13], nd f is finite well function which given in following expression: f ( p, E x, V ) 1 h i1 i h Ex iv ( 1) i E X n1 ( E x iv ) 3. SPECTRA AND ANGULAR DISTRIBUTIONS Generlly, the pre-equilibrium models ignore the influence of ngulr momentum. This is esily shown to be rther smll for the nucleon emission, Betk [14],but is surely greter for clusters. Here, the effect rises from two fcts: (i) cluster emission is usully enhnced t higher ngulr moment, which mens incresed role of the nucler surfce nd consequently effective lowering of the Coulomb brrier, especilly in the cse of deformed nuclei (Blnn [15] nd Blnn nd Komoto [16]) nd (ii) mny of the quntities entering the pre-equilibrium rections re spin-(or both spin- nd energy-) dependent, nd their simple contrction to one vrible necessrily ffects the results. In nucleon-induced rections, the originl exciton (in fct, the incident neutron) is presumed to be the most energetic one for the most of the time nd s such it keeps the notion of its direction Betk [17], which is slowly smered out in the course of the rection. In the energy rnge of the pre equilibrium models, the nucleon-nucleon differentil cross section is nerly isotropic in the c.m. system, so tht in the lbortory system it is proportionl to cos. The emitted nucleon t the very erly stge of the rection is now just the leding prticle, nd the ngulr distribution is tht which corresponds to the degree of smering out the originlly shrp vlue during the time intervl from the cretion of the composite system to the prticle emission. The originl ngulr distribution formlism divides the cross section into two components, multistep direct nd multi-step compound, following the suggestion of Feshbc et l. [18]. The multistep direct (or MSD) prt is defined s lwys hving t lest one unbound prticle degree of freedom t ech stge of the rection, while in the multi-step compound (or MSC) prt the system psses through t lest one configurtion where ll of the prticles re bound so tht informtion bout the originl projectile's direction is lrgely lost. The MSD cross section is thus ssumed to exhibit forwrd-peked ngulr distributions, while the MSC cross section hs ngulr distributions which re symmetric bout 90 o in the center of mss Klbch [13]. 151

4 The bsic formul for the double differentil cross section for the included mechnisms in the rection A(, b)b cn be written in the three equivlent forms 2 d dd b d 4 d e 1 ex ex cos ex 1 (1 ) cos f msd e f msd e ex ex b e where ex is the slope prmeter ssocited with the exciton model nd its relted components.the quntity f msd (ε b ) is the frction of the cross section t the specified emission energy which is multi-step direct nd it is replced with the frction tht is preequilibrium. The ngle θ is mesured in the center-of-mss system. The generl form of the slope prmeter is: X X ex 1 3 ( e, e b 3 ) 5.2( X1) 4.0( X1) 1.9M M b ( X ebe1( e ) 130MeVe ebe3 ( e ) 35MeVe where e nd e b re given by the chnnel energies of the incoming nd outgoing prticles, ε nd ε b. The division of the cross section into the preequilibrium nd equilibrium prts in order to generte is quite stright forwrd, though there is seprte vlue for ech exit chnnel nd emission energy. The MSD or preequilibrium or forwrd-peked component includes the exciton model preequilibrium components (both primry nd secondry) s well s the cross sections from nucleon trnsfer, knockout nd inelstic scttering involving cluster degrees of freedom. Collective excittions nd elstic scttering re treted seprtely. Thus, for inelstic scttering: 3 ) 4 d d b msd d d b d d d d d d pre, 1 b pre,2 b NT b IN For other rection chnnels (knockout) it is: d d b msd d d b primry d d b sec ondry d d b NT d d b KO where the knockout contribution occurs only for (N,α), (C,N) nd (C,α) rections, where N is nucleon nd C is complex prticle (d, t, 3He or α-prticle). The corresponding equilibrium or symmetric component contins only the primry nd secondry evportion cross sections nd is given by: 152

5 d d b msc d d b d d primry eq. b sec ondry eq. 4. RESULTS & DISCUSSIONS The results could be divided into multi-chnnel when projectile energy chnged between 14 nd100mev. These results depend on the (ESM). Min results obtined from clcultion of energy spectr nd the double-differentil cross-sections using the Klbch systemtics. Fig.1 present energy spectr for deuteron t 14.8 MeV incident neutron energy when the cross point indicte dt from present work nd full dote show experimentl dt of Grimes nd Hight [19], with the tringles present dt from the theoreticl globl code TALYS by Koning, et l. [20]. As seen in fig1.n cceptble greement mong the present work compred with nd the experimentl results within error brs from of Grimes nd Hight [19]. Figure-1. energy spectr for deuteron t E(incident)=14.8MeV. The min obtin dt for double differentil cross-sections in fig2. pper in forwrd cse nd render shrp pek t certin vlues of emitted energy ( 7MeV ) but DDX hs pproximtely minor vlue in bckwrd cse. This cn help with design of prticle detector in lbortory systems nd present better prediction of fvorite ngle in experimentl work in ccelertions of prticles. Figure-2. DDX of E=20MeV 54 Fe (n, d) 53 Mn when the shrp pek locted t (7MeV). 153

The energy spectr of 54 Fe(n, d) in the rnge up to 25 MeV hs been exmined nd compred with well define Grimes nd Hight [19].Indistinguishble points hve been seen in fig.

6 The energy spectr of 54 Fe(n, d) in the rnge up to 25 MeV hs been exmined nd compred with well define Grimes nd Hight [19].Indistinguishble points hve been seen in fig.(3,4) from present results nd Tlys code dt,but we hve some restriction on Tlys code nd this come from the cluster emission threshold energy which is pproximtely vnish in Tlys dt. Figure-3. Energy spectr for deuteron t n incident energy of 28.5MeV. Figure-4. Energy spectr for deuteron t E(incident)=40MeV. The double-differentil cross-sections,fig.(5) show incresing in vlue with regrd to energy until rech one vlue of emission deuteron energy nd ngle pproximtely (30MeV,45 0 ). Figure-5. DDX of E inc =40MeV 54 Fe (n,d) 53 Mn 154

7 A comprison hs been done between present results nd experimentl dt of Slypen, et l. [21]. in 53.5,62.7MeV incident neutron energy nd fig.8 shows the divergence of energy spectr with respect of decrese the deuteron emission energy nd vice vers. Figure-6. energy spectr for deuteron t E(incident)=53.5MeV. Figure-7. energy spectr for deuteron t E(incident)=60MeV. Figure-8. Energy spectr for deuteron t E (incident) =62. 7MeV. In fig9. shows tht t the present incident energy the DDX increse with E but t nerly 10MeV it tkes stbly shpe nd this continues to nother ngle (less thn 90), wile in bckwrd the probbility is very less thn forwrd cse 155

8 Figure-9. DDX of E inc =60MeV 54 Fe (n, D). Figure-10. present DDX s function of cluster energy for 54 Fe (n, D) t scttering ngle=20(deg) nd E(incident)=96MeV compred with experimentl work Blidenu, et l. [22]. Figure-11. Present DDX s function of cluster energy for 54 Fe (n, D) t scttering ngle=160(deg) nd E(incident)=96MeV compred with experimentl work Blidenu, et l. [22]. Fig.10,11 show similr behvior in DDX vlue with regrd prcticl dt t ngle =20 0,160 0, the decresing vlue of DDX in bckwrd (160 deg) with n increse of E comes from the number of deuteron count in tht region of energy. 5. CONCLUSION A reltively nive nd surely oversimplified view on the cluster emission cn be found in the context of vrious pre-equilibrium model. The pre-equilibrium models my be completed by 156

9 presence of direct-type rections, like the pickup nd knockout, expressed for this purpose rther phenomenologiclly thn microscopiclly. All these pproches, lthough simple, re rther useful to yield relibly the overll trends nd lso correctly predict the mgnitude of cross-sections nd relted quntities. In this work theoreticl energy spectr nd double-differentil cross-sections for deuteron production in (15-96) MeV neutron-induced rections for iron-54 re reported bsed on the ESM model, which included ll vilble corrections such s surfce effect,volume, spin dependent, isospin, Puli blocking nd piring correction, bound-stte nd finite well depth, etc. This llows energy differentil cross-sections to be extrcted nd comprison with different model predictions to be performed. The comprison of the dt to the other theoreticl clcultions nd experimentl done with nucler-rection code shows clerly tht, despite the ccept greement obtined with the TALYS code improvements re still needed for deep understnding of rection mechnisms such s pickup nd knockout which is ply n importnt rule in cluster emission ( 2 D, 3 T,α). By using the results of DDX for certin isotope in (n, d) rection we cn improve the fcilities in lbs nd cn get right prediction of exct ngle detection of emitted prticle nd it give us relibly chnce to test the cluster structure of nuclei which support the ctul presence of clusters in nuclei. REFERENCES [1] O. V. Fotin, Phys. Atom. Nucl., vol. 73, pp , [2] M. Avrigenu nd V. Avrigenu, "Prtil level densities for nucler dt clcultions," Computer Physics Communictions, vol. 112, pp , [3] TALYS bsed evluted nucler dt librry Version 5, "Koning, A.J., Rochmn, D., vn der Mrck, S., Kopecky, J., Ch. Sublet, J., Pomp, S., Sjostrnd, H., Forrest, R. Buge, E. nd Henriksson, H. Relted pper: Koning, A.J. nd Rochmn,D. Modern nucler dt evlution with the TALYS code system," Nucler Dt Sheets, vol. 113, p. 2841, [4] F. E. Bertrnd nd R. W. Peelle, Phys. Rev., vol. C8, pp , [5] E. Reymckers, N. Nic, I. Slypen, S. Benck, J. P. Meulders nd V. Corclciuc, Light chrged prticle production induced by fst neutrons (EN = MEV) on 59Co nd ntfe. Louvin: Buchrest, Roumni,UCL, [6] M. Ivscu, M. Avrigenu, I. Ivscu nd V. Avrigenu, "Pre-equilibrium emission nd nucler level densities in neutron induced rections on Fe, Cr nd Ni isotopes," INDC(ROM)-020/LJ, [7] A. J. Koning nd M. C. Duijvestijn, Nucl. Phys., vol. A744, pp , [8] M. B. Chdwick, P. Oblozinsky, P. E. Hodgson nd G. Reffo, "Hndbook on photonucler dt for pplictions: Cross sections nd spectr, IAEA-TECDOC-1178(2000)," Phys. Rev., vol. C44, p. 814, [9] H. Gruppelr, P. Ngel nd P. E. Hodgson, Riv. Nuovo Cimento, vol. 9, pp , [10] C. K. Cline nd M. Blnn, Nucl. Phys., vol. A172, pp , [11] E. Betk nd J. Dobes, Zeit. Phys., vol. A279, pp , 1976; [12] C. Y. Fu, Nucl. Sci. Eng., vol. 86, pp ,

10 [13] C. Klbch Users mnul for PRECO Duke University, [14] E. Betk Act Phys. Slov., vol. 45, p. 625, [15] M. Blnn, Phys. Lett., vol. B 88, pp. 5-8, [16] M. Blnn nd T. T. Komoto, Phys. Rev., vol. C 24, pp , [17] E. Betk, Pre-equilibrium complex prticle emission, nucler theory, 21th ed. Sofi: Heron Press, [18] H. Feshbc A. Kermn, nd S. Koonin, Ann. Phys. (N.Y.), vol. 125, pp , [19] S. M. Grimes nd R. C. Hight, "Chrged prticle emission in rections of 15-MeV neutrons with isotopes of chromium, iron, nickel, nd copper," Phys. Rev., vol. C 19, pp , [20] A. J. Koning, S. Hilirey nd M. Duijvestijn, TALYS-1.0 A nucler rection progrm. User mnul December 21, [21] I. Slypen, N. Nic, A. Koning, E. Reymckers, S. Benck, J. P. Meulders nd V. Corclciuc, "Light chrged prticle emission induced by fst neutrons with energies between 25 nd 65 MeV on iron," J. Phys. G: Nucl. Prt. Phys., vol. 30, pp , [22] V. Blidenu, F. R. Lecolley, J. F. Lecolley nd T. Lefort, "Nucleon-induced rections t intermedite energies: New dt t 96 MeV nd theoreticl sttus," Phys. Rev., vol. C 70, p ,

Intro to Nuclear and Particle Physics (5110)

Intro to Nuclear and Particle Physics (5110) Intro to Nucler nd Prticle Physics (5110) Feb, 009 The Nucler Mss Spectrum The Liquid Drop Model //009 1 E(MeV) n n(n-1)/ E/[ n(n-1)/] (MeV/pir) 1 C 16 O 0 Ne 4 Mg 7.7 14.44 19.17 8.48 4 5 6 6 10 15.4.41