Arab Journal of Nuclear Science and Applications, (), (319-33) 017 Yields of Possible Ternary Fission Channels of 60 No in Configuration M. M. Botros and A. S. Hashe Departent of Physics, Faculty of Science, Cairo University, Giza, Egypt Received: /1/015 Accepted: 30/1/016 ABSTRACT The yields of the collinear ternary fission channels of 60 No were studied in the fraework of the three cluster odel for all possible accopanied light particles of even ass nubers in the range 4 A. The folding nuclear interaction potential is calculated in ters of the M3Y-Reid nucleon-nucleon force. The deforation of the participating fragents and their relative orientations with respect to each other are considered. The suggested ost probable channels are indicated as the ones characterized with a axiu relative yield and showing a peak in the Q-value and iniized with respect to energy. Aong the indicated favored channels, a collinear ternary fission of the 60 No isotope is indicated to be 1 14 96 ost probable through the fragentation channels of 58Ce + 6C + 38 Sr 1, 58Ce + 16 6 C + 38 96 Sr, 140 54 Xe + 8O + 40 98 Zr, 1 58 Ce 10 + 4Be+ 100 40Zr, 1 60 Nd 1 + 4Be + 38 96 Sr, Sn 84 + 18Ar + 34 Se 84, Sn+ 18Ar + 34 Se 40 88, Sn + 16S+ 36 Kr 136 and Te + 3 1 Mg+ 9. Keywords: Ternary fission / Double folding odel/fission Yield/Three cluster ode INTRODUCTION Talking about fission, one thinks alost autoatically about a nucleus that splits into two heavy fragents (binary fission) (1) and the ternary fission, which is defined theatrically as the three fragents are of coparable asses (). The ternary fission process has been extensively studied, both for spontaneous fission decay and neutron induced fission reactions. Several experients (3) have clearly shown that the fission of a nucleus into three coparable fragents could be detected and that the probability of such events could reach 0.03 relative to binary fission events. The two heavy fragents in ternary fission are accopanied by a light charged particle, such as H, He, Be, C, N, or O isotopes as well as heavier nuclei up to ass nuber 36 (4,5). Although it is not one of the usual nuclei predicted in the cluster decay process, the 10 Be particles are observed as eitted light particles once per ~ 10 5 spontaneous fission events (6). Also, ternary fission events have been observed fro 56 Ni (7) and 60 Zn (8) nuclei at high angular oenta through defored shapes where the lighter ass consists of two or three α-particles. In ternary fission, as the ass nuber of the accopanied light particle increases, the probability of the ternary fission process decreases sharply (9). Due to the strong effect of the Coulob field and the barrier properties on the eission probability, we have effects of other paraeters, such as the fissibility paraeter (Z /A), deforations, the isospin asyetry of the parent nucleus, and the cluster preforation probability of light particles inside the parent as well as shell effects (10). It is found that the shell effects ay reduce the ternary fission barriers significantly (11). Although the ternary fission probability is relatively sall; its data are of interest for nuclear physics. An overall study of the ternary fission proble and the related question about the possibility of a three-body clusterization inside heavy nuclei is still an open issue that needs further theoretical and experiental detailed studies (9). In the present paper, a detailed analysis and discussion is conducted on the yield of light charged particles accopanying the fission of 60 No, which has a very high spontaneous fission probability; in the fraework of the three clusters odel (TCM). 319
Arab Journal of Nuclear Science and Applications, (), (319-33) 017 Nobeliu (No) is an artificial heavy eleent of atoic nuber Z = 10, (1). Nobeliu has 17 radioisotopes. The first isotope to be synthesized (and correctly identified) was 54 No in 1966. There are 1 known radioisotopes with known half-lives whose ass nubers range fro - 6, and 3 isoers, 51 No, 53 No, and 54 No. The present work focuses on the isotope 60 No, the doinant decay ode of this isotope is the spontaneous fission (SF). (13) The three cluster odel is proposed to explain the particle accopanying binary fission of radioactive nuclei. The three cluster odel is developed as an extension of the prefored cluster odel of Gupta and Collaborators (14-18). The advantage of this odel is that, for a fixed third fragents, we can calculate the fragentation potential iniized in charge coordinate (19,0). Fro the theoretical investigations of the ternary fission of 60 No, it is seen that the closed shell effect of any one of the two heavier fragents ay also play an iportant role in ternary fission. However, in these theoretical studies, the probable ternary configuration is generally chosen by soe intelligent guess or fro the Q-value systeatic. The role of the spherical closed shell alone is not enough, and perhaps, the role of the defored closed shell should be taken into account in our study, we will include the deforation and orientation effects of the fragents in detail. The obvious difficulty involved in the theoretical studies of ternary fission is the coplete iniization of the potential energy for the ass asyetry involved in this process. In the case of binary fission of a nucleus having ass nuber (A), the ass asyetry involved has only (A/) cobinations, which further can be iniized with respect to the charge asyetry. THEORTETICAL OUTLINE The three cluster odel (TCM) (0-) is worked out in ters of the collective coordinate of the ass and charge asyetry A1 A Z 1 Z A, Z (1) A1 A Z1 Z Where 1 and stand for heavy and light fragents respectively and the third fragent (light charged particle) in TCM is denoted by 3 and is fixed and hence only the ass asyetry between 1 and is considered. Relative separation distance R, which in TCM characterizes, respectively the nucleon division between the outgoing fragents and the Sharing of the available Q-value to the kinetic energies E i of the fragents (i.e. Q=E 1 +E +E 3 ), with the Q-value for the three decay. Touching configuration of the fragents eans R R R, R R R & R R R. () Where R i (i = 1,, 3) is the radius of the nucleus i. 1 1 13 1 3 3 3 The ternary fragentation potential or the driving potential between the three nuclei is defined as 3 V d ( R,, ) Bii V ij ( R,, ) (3) i 1 j i Here B ii are the binding energies of the three fragents in energy units (3), and β are the deforation paraeters of the two heavy fragents A 1 and A (4). V ( R,, ) =V ( R,, ) +V ( R,, ) (4) ij Cij Nij Where V Cij and V Nij are the Coulob and nuclear interaction potentials between the fragents i and j. Here θ is the angle of orientation, i.e. the angle between the syetry axis and the fission axis, with its rotation easured in anti-clockwise direction, β is the deforation paraeters of the fragents and R the relative separation between the two nuclei i and j. To obtain the Coulob potential for two non-overlapping defored nuclei in a uch sipler closed for, several recent studies were ade to describe the interaction between spherical defored 30
Arab Journal of Nuclear Science and Applications, (), (319-33) 017 (5) or two defored nuclei (6, 7). (5), which presented analytical expressions of the Coulob interaction between a spherical projectile and a defored target which are valid for any separation distance between the. (8-30) In the present work, denoting the charge densities of the two interacting nuclei (1, ) by ρ 1 and ρ respectively, the Coulob interaction between the is given by: 1 V ˆ ˆ C R, 1, dr1 dr 1 r1 r, R r r (5) 1 For axial syetry of the defored nucleus, R ' R rˆ. ˆ R 1 Y rˆ. ˆ Y rˆ. ˆ... (6) 0 0 3 30 i i i i i i Fig. (1): Scheatic configuration of two axially syetric defored nuclei, whose syetry axes are oriented and lying in the sae plane (φ = 0 ). The nuclear part of the HI real potential for defored defored pair using the double folding odel derived fro M3Y NN force. (30) is given by: V R, ˆ, ˆ dr dr r V ( s) r, (7) where ˆ R N 1 1 1 1 NN is the separation vector joining the two center of asses of the interacting nuclei, are the directions of the syetry axes of nucleus 1 and nucleus respectively and V NN ( s R r1 r) is the finite range NN interaction. We will assue V NN to be the well-known M3Y-Reid force (31).We proceed in siplifying exactly as in the Coulob potential. The only difference is to replace the Fourier transfor of Coulob potential by the sae quantity for NN - interaction. Moreover, the charge densities are replaced by atter densities. The light charged particle accopanying the ternary fission. In collinear configuration the second fragent is considered to lie in between the first and the third fragent. Following Ref (19, 3), the surface separation distances s ij for the collinear configuration are considered as s s s & s R s. (8) 13 3 1 3 with s = 0 corresponding to the touching configuration of the three fragents, the fragent is considered spherical and the quadrupole (β ) deforations of the fragents A 1 and A are considered for two different orientations, naely 90 90, 0 0, 0 90 and 90 0 as shown scheatically in figures (.6.a), (.6.b), (.6.c) and (.6.d) respectively. ˆ 1 and 31
Arab Journal of Nuclear Science and Applications, (), (319-33) 017 (a) R r A A ij 0 i j (b) β (90 90 ) orientation R r A 1 Y / r A 1 Y 3 / 1 / 1 3 / 1 0 1 1 0 0 0 R r A Y r A 13 0 1 1 0 0 3 R r A Y r A 3 0 0 0 3 (c) β (0 0 ) orientation R r A 1 Y 0 r A 1 Y 1 0 1 1 0 1 1 0 0 0 R r A Y r A 13 0 1 1 0 0 3 R r A Y r A 3 0 0 0 3 (d) β (0 90 ) orientation R r A 1 Y 0 r A 1 Y 3 / 1 0 1 3 / 1 0 1 1 0 0 0 R r A Y r A 13 0 1 1 0 0 3 R r A Y r A 3 0 0 0 3 Fig. (), (a): Scheatic diagra of three spherical nuclei at the touching collinear configuration. The touching configuration is defined by the surface separation s 1 = s 3 = 0 & s 13 = R. Touching configurations of the defored heavy A 1 and light A fragents with the spherical third particle in the (b) 90 90 (c) 0 0 (d) 0 90 orientations. A seiclassical forulation of the proble of the penetration of an α - particle through the barrier, based on the Wentzel Kraers - Brillouin (WKB) approxiation (33, 34), was found as a suitable approxiation. The decay width in general was defined as a product of the assault frequency and the penetration probability (35, 36). For penetrability calculations of all the three fragents are fixed and the otion is with respect to the separation distance of the three fragents. The penetrability is the WKB integral, s 1/ P exp V ( s ) Q ds, s t (9) with s t = 0, the touching configuration, as the first turning point, s as the second turning point and s 1 is an interediate point (see Figure (3)) satisfying 1. V s V s t V s Q, (10) 3
Arab Journal of Nuclear Science and Applications, (), (319-33) 017 340 V B 60 No Sn+ Ar+ 84 Se 300 V(s) (MeV) 60 0 1 Sharp surface A 1 + +A fragents V(s) V 0 Q-value = 77.36 MeV 140 s t s B s 1 s 100 0 4 6 8 10 1 14 16 18 0 Surface separation s (f) Fig. (3): The interaction potential as a function of the surface separation s of all the three spherical fragents eitted collinearly during the ternary fission of 60 No, Ar is the third nucleus. The decay path, the Q value and the turning points are also labeled. Figure (3) shows that for the inner and outer turning points, respectively, at s = s t and s, the transission (penetration) probability P consists of three contributions: the penetrability P 1 fro s t to s 1, the de-excitation probability W 1 at s 1, and then the penetrability P fro s 1 to s. Thus, P P W P (11) 1 1 M. Greiner et al. (37) suggested to scale the de-excitation probability W 1 exponentially with the excitation energy E 1 is W1 exp( b E1) (1) For heavy cluster eission the paraeter b is very sall and assued to be 0, this eans that W 1 = 1. So we deduce that s 1 1/ P1 exp V ( s ) V ( st ) ds, s t s 1/ (13) P exp V ( s ) Q ds, s 1 P P1P. The potential V (s) is the su of the Coulob and attractive potentials, as a function of the surface separation s. The reduced ass of the three fragents is defined as, 1 Z 3 p N 3 n 13, (14) 1 Z 3 p N 3 n Where p = 938.70 u is the proton ass, n = 939.5653 u is the neutron ass and µ 1 is given by Z 1 p N 1 n Z p N n 1. (15) Z N Z N 1 p 1 n p n The relative yield (19, 3) for all the charge iniized fragentation channels is calculated as the ratio between the penetration probability of a given fragentation channel over the su of penetration probabilities of all possible fragentation channels as 33
Arab Journal of Nuclear Science and Applications, (), (319-33) 017 P ( A i, Z i) Y ( A i, Z i). P ( A i, Z i) (16) where P (A i, Z i ) is the sae as the penetration probability corresponding to a given fragentation; here A i denotes A 1 + A + and Z i denote Z 1 + Z + Z 3. The ost probable ternary fission channel is the one which have the axiu yield. RESULTS AND DISCUSSION The interaction potential (Coulob + nuclear) between the fragents is calculated by increasing the value of surface separation s for collinear eission. The surface separations between fragents 1 and 3 as well as between and 3 are varied uniforly and hence the inter fragent distance between fragents 1 and varies autoatically. Figure (4) presents the penetration probability calculated in collinear configuration of the fragents as a function of fragent ass nubers A 1 and A. In other words, as a function of ass asyetry η A between the fragents A 1 and A (the third fragent ass nuber is ), η A = 0 corresponding to A 1 = A is also shown. The ass nuber in the horizontal axis toward the left side of η A = 0 corresponds to the light fragent ass nuber A and that toward the right side of η A = 0 corresponds to the heavy fragent ass nuber A 1. For every fixed ass pair (A 1, A ) a pair of charges is singled out for which the penetration probability is axiized. The fragent cobination 84 Sn Ar Se has the axiu penetration probability. 18 30 34 Ar 18 30 Penetration probability 10 10-8 60 No A 1 + + A = Ar 10-9 10-10 10-11 10-1 10-13 84 Se Sn 10-14 10-15 60 70 90 100 110 10 140 1 160 170 Fragent ass nubers A & A 1 Fig. (4): The penetration probability calculated for collinear eission of the fragents in ternary fission 60 of nucleus for fixed third fragent = Ar. No 10 Figure (5) shows the relative yield percent for all possible charge iniized (ost favored) third fragents of even ass nubers ranging fro = 4 to = plotted as a function of fragent ass nubers A 1 and A. The calculations are perfored over the full range of the allowed ass asyetry (η A ), of the two heavier nuclei, A 1 and A which are considered to be spherical. For every fixed ass pair (A 1, A ) a pair of charges is singled out for which the relative yield is axiized. 18 34
Arab Journal of Nuclear Science and Applications, (), (319-33) 017 0.8 0.7 0.6 0.5 0.4 60 No A 1 + + A 118 Cd 14 Ag 17 Te 19 Cd I 138 Te = 4 He 1.75 1. 1.5 1.00 0.75 60 No 116 Pd 118 Pd Sn Sn = 14 C 114 Pd Sn A 1 + + A 11 Ru Te 0.3 0. 0. 0.1 0.5 0.0 0.00 40 60 100 10 140 160 1 00 0 60 70 90 100 110 10 140 1 160 170 1 190 00 Fragent ass nubers A & A 1 (a) Fragent ass nubers A & A 1 (b) 3..8.4.0 1.6 60 No A 1 + + A 108 Ru 106 Mo 110 Ru Sn Sn Te = 0 O 4.0 3.6 3..8.4.0 60 No A 1 + + A 100 Zr 10 Mo 104 Mo Sn Te Sn = 6 Ne 1. 1.6 0.8 1. 0.8 0.4 0.4 0.0 0.0 40 60 100 10 140 160 1 00 40 60 70 90 100 110 10 140 1 160 170 1 190 00 Fragent ass nubers A & A 1 (c) Fragent ass nubers A & A 1 (d) 7. 6.4 60 No 94 Sr Te = 3 Mg 9 8 60 No Ge = Ca 5.6 A 1 + + A 7 A 1 + + A Sn 4.8 4.0 3. 6 5 4 74 Zn Ge Ge 16 Sn Sn Te.4 1.6 0.8 0.0 3 1 0 55 65 75 85 95 105 115 15 135 145 155 40 60 70 90 100 110 10 140 1 160 170 1 190 Fragent ass nubers A & A 1 Fragent ass nubers A & A 1 (f) (e) 60 Fig. (5): The % relative yields of 10No for different charge iniized third fragents are plotted as a function of the fragent ass nubers (A 1 and A ). The ost probable fragent cobinations are labeled In Figure (5b), the third fragent is 14 6C 8 and the two heavier nuclei A 1 and A are considered to be spherical. The highest relative yield percent is obtained for the fragent cobination 14 114 Sn C Pd. This is due to the effect of the doubly agic nucleus Sn (Z =, N 6 8 68 = ) and the neutron agic nucleus 14 6C 8(N = 8) in this fragent cobination. Another three axia 14 116 14 11 corresponding to the channels Sn C Pd, Te C Ru and 14 118 6 8 7 6 8 70 6 8 68 Sn C Pd are also labeled. This is due to the effect of the near doubly agic nuclei 35
Arab Journal of Nuclear Science and Applications, (), (319-33) 017 Sn (Z =, N = ), Te (Z =, N = ) and Sn (Z =, N = ) and the neutron agic nucleus 14 6C (N = 8) in these cobinations. 8 Figure (5a), (5c), (5d), (5e) and (5f) are the sae as fig. (5b) but for the fragents are 4 He, 0 O, 6 Ne, 3 Mg and Ca respectively. Fro figure (5), it is seen that the closed shell effect of any one of the two heavier spherical fragents or both plays an iportant role in ternary fission. The fragent cobinations, which have the highest relative yield percentage for even ass nubers ranging fro 4, the neutron and proton nubers of the heavy, light and third fragents A 1, A and respectively. The corresponding decay energy (Q), relative yield percent, potential barrier height (V B ) and barrier position (s B ) are listed in table 1. The neutron and proton agic nubers are written as bold face nubers. We have used only even ass nubers of the third nucleus because the potential and the Q-value systeatics favor the even-ass third fragent in the ternary fission of odd ones. 60 10No than the Table (1): The fragent cobinations which have the highest % relative yield and, iniized with respect to energy, for 4, in the ternary fission of for collinear configuration A3 Fragent cobination Z1 N1 Z N Z3 N3 Q SB % yield VB (MeV) (MeV) (f) 4 138 4 118 Te + He + Cd 86 70 45.58 0.65% 47.45 0.18 4 14 53I + He + 47Ag 53 79 47 77 45.09 0.66%.88 0.18 4 16 Sn + He + Sn 76 59.33 0.61% 47.71 0.18 19 4 17 Cd + He + Te 81 75.98 0.6% 47.34 0.18 4 Sn + He + Sn 59.91 0.19% 47.70 0.18 140 6 114 54Xe + He + Pd 54 86 68 34. 0.75% 36.7 0.37 137 6 117 55Cs + He + 45Rh 55 45 7 33. 0.7% 35.39 0.37 6 10 Sn + He + Sn 84 70 35.55 0.71% 37.55 0.37 6 6 13 53I + He + 47Ag 53 47 76 4 35.01 0.77% 36.71 0.37 6 14 Sn + He + Sn 74.39 0.73% 37. 0.37 6 16 Sn + He + Sn 76 47.39 0.74% 37.49 0.36 6 16 Cd + He + Te 74 35.33 0.74% 37.14 0.37 8 10 1 14 16 131 8 11 Sn + He + Sn 8 14 Te + He + Cd 8 14 Sn + He + Sn 16 8 16 Sn + He + Sn 10 116 Te + 4Be + Pd 10 118 Sn + 4Be + Cd 10 10 Sn + 4Be + Cd 10 1 Sn + 4Be + Cd 1 114 Te + 4Be + Pd 1 118 Sn + 4Be + Cd 1 10 Sn + 4Be + Cd 14 11 Te + 6C + 14 114 Sn + 6C + Pd 14 116 Sn + 6C + Pd 14 118 Sn + 6C + Pd 16 110 Te + 6C + 16 11 Sn + 6C + Pd 16 114 Sn + 6C + Pd 16 116 Sn + 6C + Pd 81 76 76 71 76 74 76 70 70 7 74 68 70 7 68 68 70 7 66 66 68 70 6 4 6 4 8 6 8 6 10 30.47 9.70 35.60 36.03 45..10.94. 36.56 37.37 37.85.76.63.56 51.34.. 45.54 45.11 1.57% 1.% 1.38% 0.99% 1.90%.04%.59%.53% 1.% 1.58% 1.95% 1.% 1.59% 1.58% 1.4% 1.66% 1.56% 1.7% 1.63% 60 No 10 158 30.54 30.17 30.51 30.51 47...45.43 43.06 43.66 43.63 59.89 60.87 60.83 60.81 56.15 57.11 57.07 57.03 0. 0. 0. 0. 0.47 0.47 0.47 0.47 0. 0. 0. 0.51 0.51 0.51 0.51 0.55 0.54 0.54 0.54 36
Arab Journal of Nuclear Science and Applications, (), (319-33) 017 18 0 4 6 Te + 6C + Sn + 6C + Sn + 6C + Te + 8O + Sn + 8O + Sn + 8O + Te + 8O + Sn + 8O + Sn + 8O + Te + 8O + Te + 8O + Sn + 8O + 16 Sn + 8O + Te + 10Ne + Sn + 10Ne + Sn + 10Ne + Sn + 10Ne + 18 108 18 11 Pd 18 114 Pd 0 106 4Mo 0 108 0 110 104 4Mo 108 110 4 10 4Mo 4 104 4Mo 4 108 4 110 6 100 40Zr 6 10 4Mo 6 104 4Mo 6 106 4Mo 8 Te + 10Ne + 30 Te + 1Mg + Sn + 1Mg+ 8 40Zr 30 96 30 98 40Zr 3 Te + 1Mg + 3 76 4 4 4 4 40 4 4 4 64 66 68 64 64 66 6 64 66 60 6 64 66 60 60 6 64 6 1 8 1 8 14 8 16 10 16 36.89 37.14 37.54.49.0.0 49..1 49.76 43. 4.65.13 43.0 54.05 55.4 55.6 54.63.0% 1.% 1.98%.57%.%.83%.1%.15%.00%.3% 1.94%.16% 1.70% 3.% 3.03% 3.41%.54%.87 53.76 53.7 68.79 70.06 70.01 65.98 67.18 67.14 63. 63.38 64.57 64.53. 79.79 79.7 79.67 0.57 0.57 0.57 0.56 0.56 0.56 0.58 0.58 0.58 0.60 0.60 0.60 0.60 0.59 0.59 0.59 0.59 98 40 58 10 18.15 4.64% 75.95 0.60 38 40 58 58 1 18 59.96 6.33 4.66% 5.9% 89. 91.38 0.59 0.59 94 38 56 1 0 57. 6.53% 87. 0.61 34 94 34 Sn + S + Kr 36 58 16 18 63.43 4.0% 315.38 0.57 16 36 36 90 14 36Kr 36 9 14 36 94 14 38 14 36Kr 40 86 16 34Se 40 88 16 36Kr 40 90 16 36Kr 4 84 16 34Se 4 86 16 36Kr 4 88 16 36Kr 4 90 16 36Kr 84 16 34Se 86 16 36Kr 88 16 36Kr 18 3Ge 84 18 34Se 86 18 34Se 18 34Se 76 0 30Zn 0 3Ge 0 3Ge 0 3Ge 74 0 30Zn 0 3Ge 0 3Ge 0 3Ge Te + Si + 36 54 65. 6.% 97.90 0.61 36 Sn + Si + 38 54 14 67.41 6.33% 300.11 0.60 Sn + Si + 38 56 66.98 5.35% 300.03 0.60 88 38 Te + Si + 36 14 4 6.01 7.1% 96.16 0.6 Te + S + 34 71.49 6.36% 307.31 0.61 40 Sn + S + 36 16 4 74.68 9.33% 309.85 0.60 Sn + S + 36 54 73.54 5.74% 309.76 0.60 Te + S + 34 71.73 8.15% 305.7 0.6 4 Sn + S + 36 73.06 5.% 308.5 0.61 16 6 Sn + S + 36 73.07 5.% 308.15 0.61 Sn + S + 36 54 71.57.87% 308.06 0.61 Te + S + 34 65.95 6.9% 304.1 0.6 Sn + S + 36 16 8 68.1 6.30% 306.63 0.6 Sn + S + 36 67.87 5.34% 306.54 0.6 Te + Ar + 3 77.41 5.% 314.0 0.61 Sn + Ar + 34 18 8 81.4 10.0% 316.96 0.61 Sn + Ar + 34 79.1 3.79% 316.88 0.61 Sn + 84 Ar + 34 18 30 77.36 9.88% 315. 0.6 Te + Ca + 30.04 4.06% 31.59 0.6 Sn + Ca + 3 83.61 5.54% 34.81 0.61 0 30 Sn + Ca + 3 84.87 9.88% 34.71 0.61 Sn + Ca + 3 83.98 6.38% 34.63 0.61 Te + Ca + 30.16 3.76% 30.3 0.6 Sn + Ca + 3 81.86 5.41% 33.41 0.6 0 3 Sn + Ca + 3.77 8.18% 33.3 0.6 16 Sn + Ca + 76 3 81.30 3.93% 33.5 0.6 37
Arab Journal of Nuclear Science and Applications, (), (319-33) 017 Fro Table (1) it is clear that the barrier positions corresponding to the fragent cobinations for each are nearly the sae and they increase in the range fro = 4 to 4 and they are nearly constant in the range fro = 6 to. Figure (6) presents the highest % relative yields as well as the corresponding Q-values of the fragent cobinations listed in table (1) as a function of the fragent ass nuber. The third nuclei having the axiu in the relative yield and the axiu in the Q-values are labeled. The third nuclei like 10 Be, 0 O, 6 Ne, 30 Mg, 34 S, 40 S, 4 6 8 1 10 16 1 18 16 4 16 18 Ar 18 6 relative yield and the axiu in the Q-value. The fragent cobination has the highest relative yield percent. and Ca have the axiu in the 0 30 Sn S Kr 34 94 16 18 36 58 Q (MeV) 90 70 60 60 No 10 Be Q 0 O 6 Ne 30 Mg 34 S 40 S Ar Ca 40 30 8 % Relative Yield 4 0 16 1 8 4 0 6 10 14 18 6 30 34 38 4 54 Third fragent ass nuber Fig. (6): The highest % relative yields and their corresponding Q-values plotted as a function of the third fragent ass nuber 4 Figure (7) presents the lowest driving potentials corresponding to the ost probable fragent cobinations of the spherical case, the β case and the β +4 case plotted as a function of the fragent ass nuber 4. 10 - +4 - +4 A 1 + + A 60 No Fragentation potential (MeV) 110 100 90 70 60 6 10 14 18 6 30 34 38 4 54 Fragent ass nuber Fig. (7): The lowest driving potentials corresponding to the ost probable fragent cobinations of the spherical case Fro figure (7) it is clear that that the inclusion of quadrupole deforation (β ) of the two heavy fragents A 1 and A reduces the driving potential copared to the spherical case and the inclusion of quadrupole deforation (β ) and hexadecapole deforation (β 4 ) of A 1 and A reduces the driving potential than the spherical and β cases. Figure (8) presents the relative yield percent calculated in collinear configuration of the fragents as a function of fragent ass nubers A 1 and A with the inclusion of quadrupole 38
Arab Journal of Nuclear Science and Applications, (), (319-33) 017 deforation (β )and hexadecapole deforation (β 4 ) of the two heavy nuclei A 1 and A for = 3 (figures (8a) and (8b)). 16 14 60 No 9 Sr - 136 Te = 3 Mg 18 16 60 No 9 Sr +4 - +4 136 Te = 3 Mg 1 A 1 + + A 14 A 1 + + A 10 1 8 6 10 8 4 0 84 Se 94 Zr Sn 1 Ba 40 60 70 90 100 110 10 140 1 160 170 1 190 Fragent ass nubers A & A 1 6 4 0 84 Se 94 Zr Sn 1 Ba 40 60 70 90 100 110 10 140 1 160 170 1 190 Fragent ass nubers A & A 1 (a) (b) Fig. (8): the calculated % relative yields of 60 No for A 10 158 3 = 3 with the inclusion of quadrupole and hexadecapole deforations plotted as a function of the fragent ass nubers (A 1 and A ). The ost probable fragent cobinations are labeled By coparing figure (7) with the corresponding plot in the spherical case shown in figure (5e), it can be seen that the fragent cobination with highest yield is found to be changed. In the spherical 3 94 case the fragent cobination with highest yield is Te 1Mg 0 with relative yield 56 percent of 6.53 % but when quadrupole deforation is included the fragent cobination with 136 3 9 highest yield is found to be Te84 1Mg 0 54 with higher % relative yield of 13.0 %. The fragent cobination with highest yield obtained when hexadecapole deforation is included is also 136 3 9 Te84 1Mg 0 54 but the corresponding relative yield percent increases to 15.10 %. The increase in the relative yield percent is due to the reduction in the potential barrier height when quadrupole and hexadecapole deforations are included. Table (): The ost probable fragent cobinations and their corresponding values of penetration probabilities and % relative yields for = 6, 0 and 3 accopanied ternary fission of 60 10 No 158 for the spherical case and defored cases Penetration A3 Shape of A1 & A Fragent cobination % yield probability 5.14 x 10-1 0.77% 5.04 x 10-1 0.75% 4.98 x 10-1 0.74% 4. x 10-1 0.7% 4.7 x 10-1 0.71% 6 β - β β +4 - β +4 131 53 I 6 13 + He + 47 Ag 140 54 Xe 6 114 + He + Pd Cd 6 16 + He + Te 137 55 Cs 6 117 + He + 45Rh Sn 6 10 + He + Sn 19 49 In 6 15 + He + 51Sb 53 I 6 1 + He + 47 Ag Sn 6 10 + He + Sn 1 56 Ba 6 108 + He + Ru 19 49 In 6 15 + He + 51Sb 135 51 Sb 6 119 + He + 49 In 53 I 6 1 + He + 47Ag 1 56 Ba 6 108 + He + Ru 140 6 114 + He + Pd 54 Xe 6.67 x 10-1 5.76 x 10-1 4.7 x 10-1 1.63 x 10-1 5.7 x 10-1 4.86 x 10-1 3.91 x 10-1 1.67 x 10-1 1.1 x 10-1.74%.36% 1.94% 0.67%.74%.33% 1.88% 0.% 0.58% 39
Arab Journal of Nuclear Science and Applications, (), (319-33) 017 0 3 β - β β +4 - β +4 β - β β +4 - β +4 + 8O + + 8O + + 8O + + O + Sn Sn Te Sn Sn Te Cd 0 110 0 108 0 106 4Mo 0 11 8 0 108 8 0 106 8 4Mo 0 10 8 Pd + O + + O + 10 + O + Sn Te 0 108 Ru 0 106 Mo + 8O + + O + Te Sn Sn 8 + 1Mg + + 1Mg + + Mg + Te 56 Ba Sn 4 3 94 3 96 40Zr 3 98 1 40Zr 3 9 1 3 84 1 34Se 3 94 1 40Zr 3 9 1 3 94 1 40Zr 3 84 1 34Se 136 + Mg + 1 + Mg + + Mg + 136 + Mg + + Mg + 1 + Mg + Te Sn 56 Ba 1.36 x 10-3 1.36 x 10-3 1.3 x 10-3 1.03 x 10-3.8 x 10-4 1. x 10-4 1.09 x 10-4.33 x 10-4 1.51 x 10-4 5.36 x 10-6 3.60 x 10-6.93 x 10-6 3.71 x 10-7 5.51 x 10-8 7.0 x 10-8 3.58 x 10-7 6.36 x 10-8 5.07 x 10-8.83%.%.57%.15% 11.3% 7.55% 5.% 14.0% 9.07% 6.53% 4.39% 3.56% 13.% 3.04%.51% 15.1%.67%.13% Table( ) shows the ost probable fragent cobinations and their corresponding values of penetration probabilities and % relative yields for = 6, 0 and 3 accopanied ternary fission of No for the spherical case and defored cases. 60 10 158 Table (3) shows the favored fragentation channels for the investigated collinear ternary fission of 60 No. The favored cobinations listed in Table 3 are obtained by iniizing the energy and axiizing the relative yield for all possible fragentation channels with light fragents of even. The heavy fragents appearing in the illustrated favored channels of iniu energy are often prolate nuclei with relative high deforations. However, the ternary fission of 60 No prefers highly defored prolate fragents when the three fragents are arranged collinearly. Three of the predicted favored fragentation channels show equal heavy fragents (A 1 =A ), naely 1 Cd + 16 6 C + 1 Cd, 106 4 Mo 106 + 18Ar + 4 Mo 104 104, and 41Nb + 0Ca + 41 Nb. The heavy fragents involved in the last two channels are highly defored prolate nuclei, β = 0.361 0.391. The Q-values and Yield (%) for the presented fragentation channels in Table 3 are tabulated, respectively, in coluns 3 and 4. The axia of the relative yield (Y > 15 %) are obtained for the fragent cobinations 18 Ar + 84 84 40 88 136 3 9 34Se, Sn + 18Ar + 34Se, Sn + 16S + 36Kr and Te + 1Mg +. Sn + Table( 3): The corresponding favored channels (colun ) in the collinear ternary fission of 60 No as estiated fro the calculations for the even 4 (colun 1). The last two coluns present, respectively, the corresponding decay energy Q (MeV) and the relative yield Y(%) for each indicated favored channel iniized with respect to energy. The deforations of the heavy fragents A 1 and A are considered. A3 4 Favored Fragent cobinations 135 4 11 Sn + He + Sn 4 14 54Xe + He + Pd 137 4 119 51Sb + He + 49In 154 4 10 60Nd + He + 40Zr 1 4 106 58Ce + He + 4Mo Q (MeV) 43.01 41.01 40.9 30. 34.17 Relative Yield, Y (% ) 1.06 1.04 1.03 0.18 0.18 330
Arab Journal of Nuclear Science and Applications, (), (319-33) 017 10 1 14 16 3 40 16 Sn + Be + 19 Sn + Be + 1 60Nd + 4Be + 154 60Nd + 4Be + 1 58Ce + 4Be + 10 14 Cd 10 11 Cd 10 98 10 96 10 100 40Zr Sn + Be + 16 Sn + Be + 1 60Nd + 4Be + 14 Cd + 6C + 1 58Ce + 6C + 1 Cd + 6C + 1 58Ce + 6C + Sn + 8O + Te + 8O + Sn + 8O + 140 54Xe + 8O + 136 Te + 1Mg + Sn + 1Mg + 1 56Ba + 1Mg + 1 60Nd + 1Mg + 13 Cd + 1Mg + Sn + 16S + 136 Te + 16S + 158 6S + 16S + 1 Cd + 16S + Sn + 18Ar + Te + 18Ar + 1 60Nd + 18Ar + Sn + 18Ar + 106 4Mo + 18Ar + 16 Sn + 0Ca + 14 Cd + 0Ca + Sn + 0Ca + 104 41Nb + 0Ca + 1 10 Cd 1 1 Cd 1 96 14 1 Cd 14 96 16 1 Cd 16 96 108 104 4Mo 106 98 40Zr 3 9 3 94 40Zr 3 84 34Se 3 76 3Zn 3 105 4Mo 40 88 36Kr 40 84 34Se 40 6 4Cr 40 98 84 34Se 3Ge 6 4Cr 84 34Se 106 4Mo 3Ge 84 34Se 3Ge 104 41Nb CONCLUSIONS 45.57.53 19.43 1. 4.08 37.85 37.16 13.61 49.90 30.37 43.14 5.4.1 49. 49.0 40.61 53.73.14.15 8.89 51.0 74.68 68. 4.59 65.49 81.4 77.41 36.38 77.36 70.33 81.30..77 73. 5.83 5.05 0.0 0.01 0.01 8.77 7.11 0.01 7.15 0.0 7.47 0.03 8. 7.33 5.71 0.17 15.10.67.13 < 10 4 0. 15.10 4.89 < 10 4 0.0 15.60.30 < 10 4 16. < 10 4 9.91 6.57 5. < 10 4 In this paper we studied the collinear ternary fission of 60 No of the three cluster odel for all possible accopanied light particles of even ass nubers 4. The folding nuclear and Coulob interaction potentials are calculated based on the M3Y-Reid nucleon-nucleon force for the nuclear part. The relative yields are calculated as functions of ass and charge asyetries at a touching configuration. We indicated the ost probable ternary fragent cobinations which have iniu energy and axiu relative yield in spherical case and in the presence of the deforation of the fragents and their relative orientations. The ost probable fragent cobinations which have the highest relative yields with the inclusion of β only and with the inclusion of β 4 are found to be changed and the values of their relative yields are increased copared to the spherical case. 331
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