Frank Laboratory of Neutron Physics, JINR, Dubna, Russia. Institute of Heavy Ion Physics, Peking University, Beijing, P.R. China. 1.

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1 SYSTEMATICS OF (,α) CROSS SECTIONS FOR 4-6 MeV NEUTRONS G.Khuukhekhuu 1, Yu.M.Gledeov, Guohui Zhag 3, M.V.Sedysheva, J.Mukhsaikha 1, M.Odsure 1 1) Nuclear Research Ceter, Natioal Uiversity of Mogolia, Ulaabaatar, Mogolia ) Frak Laboratory of Neutro Physics, JINR, Duba, Russia 3) Istitute of Heavy Io Physics, Pekig Uiversity, Beijig, P.R. Chia 1. Itroductio Neutro cross sectios are usually studied by three methods: experimetal measuremet, theoretical calculatio ad systematical aalysis. I the systematical aalysis both of the experimetal data ad theoretical models are used. From the systematical aalysis it is possible i practice to evaluate the eutro cross sectios of the uclides for which o experimetal data are available. Also, the systematical aalysis of the eutro cross sectios is useful to clarify uclear reactio mechaisms. For last years we have bee aalyzig kow experimetal (,α) cross sectios i the eergy rage of 6-0 MeV [1] ad aroud MeV [] ad observed some systematical regularity which i the literature is termed as the isotopic effect [3]. The statistical model, based o the Weisskopf-Ewig evaporatio model [4] ad costat uclear temperature approximatio [5], was suggested [1,6] to explai the isotopic effect. I additio, the experimetal study of the (,α) reactio i the MeV eutro eergy regio for broad mass of target uclei was carried out [7-17]. I this paper the results of the systematical aalysis of our experimetal (,α) cross sectios, usig the statistical model, for ew eergy rage of 46 MeV are described.. The (,α) Cross Sectio Formulae The direct ad pre-equilibrium mechaisms are eglected for several MeV eutros ad the compoud mechaism ca be cosidered, oly. The, accordig to Bohr s postulate, the (,α) cross sectio ca be writte as two stages process:, c( ) G. (1) Here: c ( ) ( R ) () is the compoud ucleus formatio cross sectio; where: is the target ucleus radius; - ; is the mass umber of the target uclei; cm / E( MeV ) is the wavelegth of the icidet eutros divided by ad is the icidet eutro eergy. The α-decay probability of the compoud ucleus is expressed as G( ), (3) where:, ad are the partial, alpha ad total level widths, respectively. α i i

2 I the framework of Weisskopf-Ewig [4], usig the costat temperature approximatio [5] ad the semi-classical formula for the iverse reactio cross sectio we ca get followig expressio for the α-width: B E S 1 V M R E 1 e de. (4) V E Here:,, ad are the spi, mass, eergy ad the Coulomb potetial for the outgoig α-particle, respectively; is the bidig eergy of α-particle for daughter ucleus; is the odd-eve effect parameter for the Weizsacker s formula [18]; is the thermodyamic temperature, where is the Boltzma costat. Similar formulae ca be writte for all partial level widths. The, eglectig the -emissio ad usig the approximatio for fast eutros, from (1), (), (3) ad (4) the fast eutro iduced (,α) reactio cross sectio is determied as follows (, ) max E Q R e Similar formula was obtaied by Cuzzocrea et al. [19]. The Coulomb potetial of α-particle ca be writte [0]: V Z.058 MeV. (6) 1/ 3 1/ ( A 3 ) 4 V 3 The (,α) reactio eergy ca be determied by the Weizsacker s formula for bidig eergy. The, if we eglect the odd-eve effect parameter from (5) ca write the (,α) cross sectio as followig K A R e. N Z 0.5 (, ) C, (7) where:, ad are the eutro, proto ad ucleo umbers, respectively, for the target ucleus; ad 1 exp 3 Z / 3 ( Z ) A ( A 3 ) / 3 V 1 / 3 1 / A ( A 3 ) C 3 (5) ; (8) K. (9) Here:,, ad are the Weizsacker's formula costats; ad MeV is the iteral bidig eergy of α-particle. Usig the Fermi gas model for level desity parameter [1] the uclear thermodyamic temperature [5] is expressed as follows max U 13.5( E Q ) (10) a A 3 The parameters ad i formula (7) ca be determied by two methods. First, they ca be foud by fittig of theoretical cross sectios to experimetal data as costat parameters at each eergy poit for all isotopes. Secod, ad parameters ca be directly obtaied from the formulae (8), (9) ad (10).

3 3. Aalysis of (,α) Cross Sectios 3.1. Systematics of the (,α) Cross Sectios The results of the systematics for experimetal (,α) cross sectios of the medium mass ad heavy uclei (40A149) at eutro eergies of 4, 5 ad 6 MeV [917] by usig the formula (7) are show i Figs.1, ad Ca 64 Z =4 MeV 40 Ca 64 Z =5 MeV Z 58 Ni 57 Fe 66 Z 67 Z /(R+ /) C=0.39 K=53. R² = Fe 95 Mo Fig.1. The depedece of the reduced (,α) cross sectios o the eutro excess parameter at 4 MeV. /(R+ /) 40 Ca 58 Ni C=0.66 K=53.9 R² = Z C=0.45 K=54.4 R² = 0.90 Fig.3. The same as i Fig.1 for 63 Cu 66 Z Z Cu Fig.. The same as i Fig.1 for 5 MeV. 95 Mo ,0 6 MeV. 95 Mo The values of fitted parameters ad are give i Figs.1, ad 3, also. It is see that the experimetal data of the eergy rage of 4 to 6 MeV is satisfactorily described by the theoretical lie drew by formula (7) with the fitted parameters ad. 57 Fe

4 3.. The (,α) Cross Sectios ad α-clusterizatio Factor The values of the theoretical ad experimetal (,α) cross sectios for eutro eergies of 4 to 6 MeV are show i Figs.4, 5 ad 6. The theoretical (,α) cross sectios were calculated by statistical model formulas (7), (8), (9) ad (10) =4 MeV =5 MeV (mb) experimet Fig.4. Theoretical ad experimetal (,α) cross sectios at =4 MeV experimet Fig.5. The same as i Fig.4 at 5 MeV. (mb) experimet 0,0 Fig.6. The same as i Fig.4 at 6 MeV. It is see that the statistical model formulae give overestimated values for the (,α) cross sectios at all eutro eergies. We assume that these results, perhaps, are caused by the α-particle clusterizatio effect [4]. The α-clusterizatio factor, which takes ito accout α-particle formatio probability o the surface of the compoud ucleus, was ot cosidered i formulae (7), (8) ad (9).

5 So, these formulas should be correct for eutro iduced ucleo emissio reactios [5]. As to (,α) reactio, the α-clusterizatio effect should be cosidered i the cross sectio formula. I order to evaluate the α-particle formatio factor or reduced α-width Bethe suggested [6] to use a reduced eutro width:. (11) Popov et al. ivestigated this hypothesis by usig the experimetal data of the (,α) reactio for resoace eutros [4] ad obtaied a followig relatio for the average reduced eutro-ad alpha-widths: W / I the case of fast eutro iduced (,α) reactio we suggest to obtai the α-clusterizatio factor by ormalizatio of theoretical cross sectio to experimetal data. This method meas that α-clusterizatio factor for (,α) reactio is determied i compariso with (,p) reactio assumig the eutro ad proto formatio factors are the same: 1. (13) W / p p The, from the ormalizatio of theoretical (,α) cross sectio to experimetal data the α- cluster formatio factor was foud to be: p Wp / 4.5. (14) (mb) experimet =4 MeV Fig.7. Experimetal ad theoretical (,α) cross sectios with α-cluster formatio factor 4.5 for 4 MeV. experimet =5 MeV Fig.8. The same as i Fig.7 for 5 MeV. experimet (1) 0,0 Fig.9. The same as i Fig.7 for 6 MeV. Figs.7, 8 ad 9 show that the theoretical (,α) cross sectios calculated by statistical model with the clusterizatio factor 4.5 are satisfactorily i agreemet with experimetal data for 4, 5 ad 6 MeV. So, takig ito accout the α-clusterizatio factor, the (,α) cross sectio formula (7) ca be rewritte i the followig form: NZ0.5 K 1 A e. (15) Wp /, C R

6 3.3. Aalysis of Existig (,α) Cross Sectios at 6 MeV The Fig.10 shows that our ad other existig (,α) cross sectio data at have the same regularity which is described by the statistical model lie. 40 Ca 64 Z 6 MeV Ni 63 Cu 66 Z 67 Z 0,0 Fig.10. The depedece of our ( ) ad other existig (ο) experimetal reduced (,α) cross sectios o the eutro excess parameter. 4. Coclusios 1. The systematical aalysis of (,α) cross sectios for 4-6 MeV eutros usig the statistical model was carried out. Some systematical regularity of the reduced (,α) cross sectios o the relative eutro excess parameter was observed. The tred of the (,α) cross sectios is satisfactorily described by the statistical model.. At the same time, statistical model formulas give overestimated values for the absolute (,α) cross sectios. We assume that these results, perhaps, are caused by the α-particle clusterizatio effect. The clusterizatio factor was foud to be 4.5 for 46 MeV eutros by ormalizatio of the theoretical (,α) cross sectios to experimetal oe. This value of the α-clusterig factor is i good agreemet with the result of Popov et al. for resoace eutros. 3. Both of our experimetal (,α) cross sectios ad other existig data at 6 MeV have the same systematical tred which is described by the statistical model, also. Refereces /(R+ /) C=0.8 K=51 R² = Fe 95 Mo G.Khuukhekhuu, Yu.M.Gledeov, M.V.Sedysheva, M.Odsure, J.Mukhsaikha ad T.Delgersaikha. I book: Neutro Spectroscopy, Nuclear Structure, Related Topics, JINR, Duba, 013, p G.Khuukhekhuu, M.Odsure, Yu.M.Gledeov ad M.V.Sedysheva. I book: Neutro Spectroscopy, Nuclear Structure, Related Topics, JINR, Duba, 01, p H.M.Hoag, U.Garuska, D.Kiela, A.Marcikowski ad B.Zwiegliski. Z.Phys.A, v.34, N3 (199), p V.F.Weisskopf ad D.H.Ewig, Phys. Rev., v.57, N6, 1940, p.47.

7 5. J.M.Blatt, V.F.Weisskopf, Theoretical Nuclear Physics, Joh Wiley & Sos, New York, G.Khuukhekhuu ad G.Uebat, Scietific Trasactios, Natioal Uiversity of Mogolia, N7(159), 000, Ulaabaatar, p Guohui Zhag, Jixiag Che, Cuoyou Tag, Yu.M.Gledeov, M.Sedysheva ad G.Khuukhekhuu. Nucl. Istr. Meth. Sectio A, v.566, N, 006, p Guohui Zhag, Rogtai Cao, Jixiag Che, Cuoyou Tag, Yu.M.Gledeov, M.Sedysheva, G.Khuukhekhuu, Nucl. Sci. Eg., v.153, 006, p Tag Guoyou, Bai Xihua, Shi Zhaomi, Che Jixiag, Yu.M.Gledeov, G.Khuukhekhuu, Yu.P.Popov, Chiese Joural of Nuclear Physics. v.17, N1, 1995, p Xuemei Zhag, Zemi Che, Yigtag Che, Jig Yua, Guoyou Tag, Guohui Zhag, Jixiag Che, Yu.M.Gledeov, G.Khuukhekhuu, M.V.Sedysheva. Phys. Rev. C, v.61, N5, 000, p Guohui Zhag, Rogtai Cao, Jixiag Che, Cuoyou Tag, Yu.M.Gledeov, M.Sedysheva, G.Khuukhekhuu, Nucl. Sci. Eg., v.156, N1, 007, p Guohui Zhag, Jiaguo Zhag, Rogtai Cao, Li-a Guo, Jixiag Che, Yu.M.Gledeov, M.V.Sedysheva, G.Khuukhekhuu, P.J.Szalaski. Nucl. Sci. Eg., v. 160, N1, 008, p Yu.M.Gledeov, M.V.Sedysheva, V.A.Stolupi, Guohui Zhag, Jiaguo Zhag, Hao Wu, Jiamig Liu, Jixiag Che, G.Khuukhekhuu, P.E.Koehler ad P.J.Szalaski. Phys. Rev. C, v.80, N4, 009, p Guohui Zhag, Hao Wu, Jiaguo Zhag, Jiamig Liu, Yuxiag Yi, Jixiag Che, Guoyou Tag, Yu.M.Gledeov, M.V.Sedysheva, G.Khuukhekhuu, P.E.Koehler ad P.J.Szalaski Appl. Rad. Isot., v.68, N1, 010, p Guohui Zhag, Yu.M.Gledeov, G.Khuukhekhuu, M.V.Sedysheva, P.J.Szalaski, Jiamig Liu, Hao Wu, Xiag Liu, Jixiag Che ad V.A.Stolupi. Phys. Rev. C, v.8, N1, 010, Guohui Zhag, Yu.M.Gledeov, G.Khuukhekhuu, M.V.Sedysheva, P.J.Szalaski, P.E.Koehler, Yu.N. Voroov, Jiamig Liu, Xiag Liu, Jihua Ha ad Jixiag Che. Phys. Rev. Lett., v.107, N5, 011, p Yu.M.Gledeov, M.V.Sedysheva, V.A.Stolupi, Guohui Zhag, Jihua Ha, Xiag Liu, Xiao Fa, Jixiag Che, G.Khuukhekhuu, P.J.Szalaski. Abstract of the XXI Iteratioal Semiar o Iteractio of Neutros with Nuclei, ISINN-1, JINR, Duba, p C.F.Vo.Weizsacker, Z. Phys. A, v.96, N7-8, 1935, p P.Cuzzocrea, E.Perillo ad S.Notarrigo, Nuovo Cimeto.A, v.4, N, 1971, p D.G.Garder ad Yu-We-Yu, Nucl. Phys., v.60, N1, 1964, p A.Bohr ad B.R.Mottelso, Nuclear Structure, v.1, W. A. Bejami, Ic. 1969, New York, Amsterdam.. Yu. P. Popov, M. Prztula, K. G. Rodioov, R. F. Rumi, M. Stempiski ad V. I. Furma, Yad. Fiz. v. 13, part 5 (1971), p Yu. P.Popov ad W.I.Furma, I book: III School o Neutro Physics, JINR, D , 1978, Duba, p N. P. Balabaov, V. A. Vtyuri, Yu. M. Gledeov, Yu. P. Popov. PEPAN, v. 1, part, (1990), p G.Khuukhekhuu, G.Uebat, M.Odsure, Yu.M.Gledeov, M.V.Sedysheva, B.Bayarbadrakh. JINR Comm., E , Duba, 007, p H.A.Bethe, Nuclear Physics B. Nuclear Dyamics, Theoretical, Rev. Mod. Phys., v.9, N, 1937, p EXFOR,