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A Study of Binary Fission and Ternary Fission in 232-238U

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A Study of Binary Fission and Ternary Fission in 232-238U Bulg. J. Phys. 46 (2019) 16–27 A Study of Binary Fission and Ternary Fission in 232-238U N. Sowmya, H.C. Manjunatha Department of Physics, Government College for Women, Kolar-563101, Karnataka, India Received: December 04, 2018 Abstract. We studied the binary fission and ternary fission of uranium isotopes 232−238U. The total potential for binary and ternary fission of different fission fragments of uranium are calculated using recent proximity potential. The bi- nary and ternary fission half-life of uranium isotopes for the different fission fragment combinations are calculated. The variation of logarithmic half-life of binary and ternary fission as a function of mass number is graphically repre- sented. Branching ratios correspond to ternary and binary fission is also calcu- lated. A detail study of branching ratio of binary fission with respect to ternary fission is also helps us to predict the dominant mode of fission in the uranium. The calculated parameters are compared with the experiments and it agrees well with the calculations. PACS codes: 25.85.-w 1 Introduction Spontaneous fission was discovered by two Russians [1]. Ternary fission was discovered by Chinese scientists in cooperation with French researchers [2]. Cluster decay was predicted in 1980 [3] and was experimentally confirmed in 1984 [4]. Alpha decay was discovered in France by Henri Becquerel [5] and it was identified as 4He emission by the UK professor Ernest Rutherford [6]. Wahl [7] measured the neutron induced fission of 235U, 238U and 239Pu. Pellereau et al. [8] used SOFIA (Studies On Fission with Aladin) program to study fission yields of 238U. Khan [9] studied the fission of 238U induced by the proton and bremsstrahlung photon. Clarke [10] measured neutron multiplicity distribution from photo fission of 235U by induced high energy gamma rays. Duke et al. [11] studied correlations between fragment mass and kinetic energy in neutron in- duced fission of 238U. Tsien et al. [12] experimentally proved the existence of tri-partition and quadri-partition of 235U. Makarenko et al. [13] studied sponta- neous fission half lives of uranium. 16 1310–0157 c 2019 Heron Press Ltd. A Study of Binary Fission and Ternary Fission in 232−238U Muga et al. [14] studied ternary fission of 236U and 234U using triple coinci- dence technique. Todorovic´ and Antanasijevic´ [15] studied cross sections of binary and ternary fission fragments of U and Th. Bonetti et al. [16] measured the spontaneous fission half-life and decay constant of 232U. Frank Asaro and Perlman [17] studied decay properties of 232U by using alpha particle spectro- graph and counters. Kikunaga et al. [18] studied the half life of 229Th from the activity ratio of 232U and 233U. Nethaway and Mendoza [19] measured the mass yield distributions in fission of 234U and 236U. Tischler et al. [20] measured time spectra of fission fragments of 236U and 238U. Maslov [21] observed the excita- tion of two quasi particle states at saddle deformations of fissioning nuclei such as 238U. McNally et al. [22] measured neutron induced fission cross section of 237U. Blocki et al. [23] formalized a theorem for interaction potential between two curved surfaces. Blocki and Switecki [24] improved the nuclear proximity po- tentials for the surfaces having large curvature. Using various proximity poten- tials Raj kumar [25] studied effects of iso-spin on nuclear fusion cross sections. Yao et al. [26,27] theoretically studied cluster and alpha decay half-lives of even- even nuclei using fourteen different proximity potentials and compared with that of experimental values. Dutt and Puri [28] using twelve different proximity po- tentials, studied fusion barrier heights and fusion cross sections for 60 known reactions. Within the preformed cluster decay model, Kumar and Sharma [29] studied cluster radioactivity in 208Pb using different proximity potentials. Ma- junatha and Sowmya [30] theoretically studied ternary fission in fermium using different proximity potentials. Previous workers [31–33] studied different decay modes in superheavy element. Aim of the present work is to predict the dominant fission mode of uranium isotopes 232−238U. In the present work, we have studied the binary fission and ternary fission of uranium isotopes 232−238U. The total potential for binary and ternary fission of different fission fragments of uranium are calculated using re- cent proximity potential. The binary and ternary fission half-life of uranium isotopes for the different fission fragment combinations are calculated. Branch- ing ratios correspond to ternary and binary fission is also calculated. A detail study of branching ratio of binary fission with respect to ternary fission is also helps us to predict the dominant mode of fission in the uranium. The calcu- lated parameters are compared with the experiments and it agrees well with the calculations. 2 Theory The total interacting potential between two nuclei of fission fragments is taken as the sum of the coulomb potential and proximity potential is given as [30] V = VNij(R) + VCij(R) (1) 17 N. Sowmya, H.C. Manjunatha The Coulomb interaction energy VCij describes the force of repulsion between the two interacting charges and we consider the pairwise interaction of the three fragments. The Coulomb energy expression [34] is defined as 2 8ZiZje > Rij ≥ Ri + Rj; > Rij < 2 V = ZiZje Cij ∆ R − R ≤ R ≤ R + R (2) > i j ij i j > Rij :> 2 ZiZje λ R ≤ Rij ≤ Ri − Rj with [34] " 4 # (Ri + Rj − Rij) ∆1 ∆ = 1 − 3 3 160Ri Rj ∆ = R2 + 4R (R + R ) + 20R R − 5R2 − 5R2 1 ij ij i j i j i j 2 2 2 15Ri − 3Rj − 5Rij λ = 3 10Ri where Rij is the centre-to-centre distance between the fragments i and j. For the nuclear part of the potential VNij, we have used the proximity potential VPij or the short-range Yukawa plus exponential nuclear attractive potential VPij amongst the three fragments. The proximity potential VPij is defined as z V (Z) = 4πγR¯ Φ (3) P ij ij b In the above equation, γ is the specific nuclear surface tension and it is given by " 2# N − Z 2 γ = γ0 1 − KS MeV/fm ; A (4) γ0 = 1:460734 and Ks = 4:0: In the above equation (3), Φ is the universal proximity potential and z is the distance between the near surfaces of the fragments. b = 0:99 is the nuclear surface thickness. Φ in above equation is the universal function, independent of the shapes of nuclei or the geometry of the nuclear system, but depends on the minimum separation distance ξ = z=b. In the present work, we have used the following universal function '(ξ) 8 −" <−4:41 exp for 0 ≤ " ≤ 1:9475 Φ(") = 0:7176 :−1:7817+0:9270"+0:0169"2 −0:05148"3 for 0 ≤ " ≤ 1:9475 (5) 18 [58]J.H.Roberts, R.Gold, R.J.Armani, Phys. Rev. 174, 1482 (1968). [59]A.Spadavecchia, B.Hahn, Helv. Phys. Acta 40, 1063 (1967). [60]H.R.von Gunten, Actinides Rev. 1, 275 (1969). [61]D.Galliker, E.Hugentobler, B.Hahn, Helv. Phys. Acta 43, 593 (1970) [62]D.Storzer, Thesis Universitat Heidelberg (1970). [63]J.D.Kleeman, J.F.Lovering, Geochim. Cosmochim. Acta 35, 637 (1971). [64]W.M.Thury, Acta Phys. Aus. 33, 375 (1971). [65]M.P.T.Leme, C.Renner, M.Cattani, Nucl. Inst. Meth. 91, 577 (1971). [66]H.A.Khan, S.A.Durrani, Rad. Effects 17, 133 (1973). [67]K.N.Ivanov, K.A.Petrzhak, Sov. Atom. Energy 36, 514 (1975). [68]V.Emma, S.LoNigro, Nucl. I n s t . Meth. 128, 355 (1975). [69]G.A.Wagner, B.S.Reimer, H.Fau1, R.van der Linden, R.Gijbels, Geochim. Cosmochim. Acta 39, 1279 (1975). [70]K.Thie1, W.Herr, Earth Planet . Sci. Letters 30, 50 (1976). [71]M.Kase, J.Kikuchi, T.Doke, Nucl. Inst. Meth. 154, 335 (1978). [72]A.G.Popeko, G.M.Ter-Akopian, Nucl. Inst. Meth. 178, 163 (1980). [73]E.R.V.Spaggiari, An. Acad. Brasil. Cienc., 52, 213 (1980). [74]Z.N.R.Baptista, M.S.M.Mantovani, F.B.Ribeiro, An. Acad. Brasil. Cienc., [75]J.C.Hadler, C.M.G.Lattes, A.Marques, M.D.D.Marques, D.A.B.Serra, G.Bigazzi, Nucl. Tracks 5,46 [76]H.G.deCarvalho , J B.Martins , E.L.Medeiros. O.A.P.Tavares, Nucl. Inst . Meth. 197, 417 (1982) [77]R.Vartanian, Helv. Phys. Acta 57, 416 (1984). [78]M.P.lvanov, G.M.Ter-Akopian, B.V.Fefilov, A.S.Voronin, Nucl. Instr . Meth. A234,15 2 (1985). [79] S.N.Belenky, M.D.Skorokhvatov, A.V.Etenko, Sov. Atom. Energy 55, 528 (1983). 232−238 FigureA Study1. Schematic of Binary configurations Fission and of Ternarythree nuclei Fission in U Figure 1. Schematic configurations of three nuclei. where R¯ is the mean radius of curvature. The arrangement of fission fragments considered in the present work is as shown in Figure1. The distance between the centers of the interacting fragments Rij can be denoted as R32 = R3 + R2, R31 = R1 + R3 and R12 = R32 + R31. The radius of each fragment is defined as 1=3 −1=3 Ri = 1:28A1 − 0:76 + 0:8A2 (6) (“i” taking the values of 1, 2 and 3 corresponding to fragments A1, A2 and A3). For process such as binary fission and alpha ternary fission the barrier penetra- bility P is given as [35] 8 b 9 < 2 Z p = P = exp − 2µ(V − Q)dz : (7) } : a ; Here µ = mA1A2=A, where m is the nucleon mass and A1, A2 are the mass numbers of fragments respectively and A = A1 + A2. For fission process, first turning point is determined from the equation V (a) = Q and second turning point b = 0.
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