Ternary fission of 250,252 Cf isotopes with 3 H and 6 He as light charged particle

Transcription

1 IOSR Journal of Appled Physcs (IOSR-JAP) e-issn: , PP Ternary fsson of 5,5 Cf sotopes wth H and 6 He as lght charged partcle Sreejth Krshnan 1, K. P. Santhosh 1 1 (School of Pure and Appled Physcs, Kannur Unversty, Swam Anandatheertha Campus, Payyanur 677, Kerala, Inda) Abstract: The spontaneous cold ternary fsson of 5,5 Cf sotope wth H and 6 He as lght charged partcle wth fragments n equatoral and collnear confguraton have been studed usng the Unfed ternary fsson model (UTFM). In both equatoral and collnear confguraton, the fragment combnatons wth the hghest relatve yeld are found to be the same. In the H accompaned ternary fsson of 5 Cf and 5 Cf sotope, the hghest relatve yeld s found for the ternary splttng 114 Pd+ H+ 1 Sb and 116 Pd+ H+ 1 Sb respectvely. Here the fragment combnatons possess the hghest Q value and ncludes the presence of near doubly magc nucleus 1 Sb (N=8, Z=51). In the case of 5 Cf and 5 Cf sotope wth 6 He as lght charged partcle, the hghest relatve yeld s found for the fragmentaton 1 Ru+ 6 He+ 14 Te and 114 Pd+ 6 He+ 1 Sn respectvely, whch s due to the presence of near doubly magc nucleus 14 Te (N=8, Z=5) and doubly magc nucleus 1 Sn (N=8, Z=5). Hence the presence of hgh Q value and doubly or near doubly magc nucleus plays a sgnfcant role n the ternary fsson of 5,5 Cf sotopes wth H and 6 He as lght charged partcle. Keywords: Spontaneous fsson, cold ternary fsson, relatve yeld, unfed ternary fsson model. I. Introducton The splttng of a radoactve nucleus nto three fragments s commonly referred to as ternary fsson and n most cases; one of the fragments s very lght compared to the man fsson fragments. Hence the process of ternary fsson s also referred to as lght charged partcle (LCP) accompaned ternary fsson. In 1947 Farewell et al., [1] reported the expermental observaton of ternary fsson process n the case of uranum sotope. The process of ternary fsson s found to occur for every once n 5 bnary fsson events wth alpha partcle as lght charged partcle and the observed alpha partcle s found to emt n a drecton perpendcular to the man fsson fragments. Dependng on the emsson of lght charged partcle, manly there are two dfferent confguratons n a ternary fsson process namely, equatoral and collnear confguraton. An equatoral confguraton s one n whch the lght charged partcle s emtted n a drecton perpendcular to the man fsson fragments. In the case of collnear confguraton, the lght charged partcle s emtted along the drecton of the man fsson fragments. A number of theoretcal and expermental works have been conducted n the feld of ternary fsson of varous sotopes. We have developed a model named as Unfed ternary fsson model (UTFM) [-7], n order to fnd the most favourable fragment combnatons n the ternary fsson process of varous sotopes and our model s brefly descrbed n the followng secton. II. Unfed ternary fsson model (UTFM) The lght charged partcle accompaned ternary fsson s energetcally possble only f Q value of the reacton s postve. e. m 1 Q M (1) Here M s the mass excess of the parent and m s the mass excess of the fragments. The nteractng potental barrer for a parent nucleus exhbtng cold ternary fsson conssts of Coulomb potental and nuclear proxmty potental of Block et al., [8, 9]. The nteractng potental barrer s gven by, wth V Cj V ( V Cj V Pj ) () 1 j ZZ je r j, the Coulomb nteracton between the fragments. Here Z and Z j are the atomc numbers of the fragments and r j s the dstance between fragment centres. The nuclear proxmty potental [8] between the fragments s, Natonal Conference on Current Advancements n Physcs rd &4 th February 17 1 Page Department of Physcs, St. John s College, Palayamkotta-67, Tamlnadu, Inda. DOI.979/

2 Ternary fsson of 5,5 Cf sotopes wth H and 6 He as lght charged partcle C C j z VPj( z) 4 b () ( C C j ) b Here Φ s the unversal proxmty potental and z s the dstance between the near surfaces of the fragments. The dstance between the near surfaces of the fragments for equatoral confguraton s consdered as z 1 = z = z 1 = z and for collnear confguraton the dstance of separaton are z 1 = z = z and z 1 = (C +z). The Süssmann central rad C of the fragments related to sharp rad R s, b C R (4) R For R we use sem emprcal formula n terms of mass number A as [8] 1/ 1/ R 1.8A.76.8A (5) The nuclear surface tenson coeffcent called Lysekl mass formula s gven as,.9517[ ( N Z) / A ] MeV/fm (6) where N, Z and A represents the neutron, proton and mass number of the parent, Ф, the unversal proxmty potental s gven as, /. 4.41e, for ε > (7) , for ε (8) wth z / b, where the wdth (dffuseness) of the nuclear surface b 1 ferm. Usng one-dmensonal WKB approxmaton, the barrer penetrablty P, probablty for whch the ternary fragments to cross the three body potental barrer s gven as, z exp ( V Q) dz (9) z1 The turnng ponts z 1 = represent touchng confguraton and z s determned from the equaton V(z )=Q, where Q s the decay energy. The potental V n eqn. 9, whch s the sum of Coulomb and proxmty potental gven by eqn., are computed by varyng the dstance between the near surfaces of the fragments. In eqn. 9 the mass parameter s replaced by reduced mass µ and s defned as, 1A m and A 1 () 1 A A where m s the nucleon mass and A 1, A and A are the mass numbers of the three fragments. The relatve yeld can be calculated as the rato between the penetraton probablty of a gven fragmentaton over the sum of penetraton probabltes of all possble fragmentaton as follows, P A, Z Y A, Z (11) P A, Z III. Results and dscusson The cold ternary fsson of 5,5 Cf sotope wth H and 6 He as lght charged partcle n both equatoral and collnear confguraton of fragments have been studed usng the concept of cold reacton valley, whch was ntroduced n relaton to the structure of mnma n the so called drvng potental. The drvng potental s defned as the dfference between the nteracton potental V and the decay energy Q of the reacton. Here the nteracton potental V s taken as the sum of Coulomb potental and nuclear proxmty potental. The Q values are calculated usng the recent mass tables of Wang et al., [] and for whch the expermental values are not avalable; we have taken the values from the mass tables of Koura et al., [11]. For a fxed lght charged partcle, the drvng potental can be calculated for all possble fragment combnatons as a functon of mass and charge asymmetres gven as A Z and 1 Z Z respectvely. A par of charges s sngled out for every A Z1 Z fxed mass par (A 1, A ) n whch the drvng potental s mnmzed. The schematc dagram for the equatoral and collnear emsson of three sphercal fragments at the touchng confguraton s shown n fgure 1. Natonal Conference on Current Advancements n Physcs rd &4 th February Page Department of Physcs, St. John s College, Palayamkotta-67, Tamlnadu, Inda. DOI.979/

3 Drvng potental (MeV) Ternary fsson of 5,5 Cf sotopes wth H and 6 He as lght charged partcle Fg.1. Schematc dagram for the touchng confguraton of the three sphercal fragments formed n the process of ternary fsson wth fragments n (a) equatoral and (b) collnear confguraton..1 H accompaned ternary fsson of 5,5 Cf sotopes wth fragments n equatoral confguraton. The spontaneous cold ternary fsson of 5 Cf and 5 Cf sotopes has been studed wth H as lght charged partcle usng the Unfed ternary fsson model (UTFM). In the H accompaned ternary fsson of 5 Cf sotope, the drvng potental s calculated for all possble fragment combnatons. Fgure (a) represents the plot of drvng potental versus fragment mass number A 1 found n the ternary fsson of 5 Cf sotope wth H as lght charged partcle. Here the mnmum s found for the fragment combnaton wth fragment mass number A 1 = 8 Be, 11 B, 1 B, 1 B, 14 C, C, 16 C, 17 N, 18 C, 19 N, O, 1 O, O, F, 4 Ne etc. The mnmum found for the fragment combnaton S+ H+ 7 Tl s due to the presence of near doubly magc nucleus 7 Tl (N=16, Z=81). The mnmum found around the fragment combnaton 8 Ge+ H+ 165 Tb s due to the presence of neutron magc number N=5 of 8 Ge. 5 (a) A = H 5 Cf Ge+ Tb 8 Be+ 9 Np S+ 7 Tl 114 Pd+ 1 Sb (b) A = H 5 Cf 5 8 Be+ 41 Np 8 Ge+ 167 Tb 4 S+ 7 Tl 116 Pd+ 1 Sb (c) A 5 Cf (d) A 5 Cf 8 Ge+ 16 Gd 6 S+ 8 Pb 1 Ru+ 14 Te 4 He+ Pu Ge+ 164 Gd 4 S+ 4 Hg 114 Pd+ 1 Sn 4 He+ 4 Pu 6 8 Fragment mass number A 1 Fg.. The drvng potental s plotted as a functon of fragment mass number A 1 n the case of H and 6 He accompaned ternary fsson of 5,5 Cf sotopes wth fragments n equatoral confguraton. The deepest mnmum found around the fragment combnaton 114 Pd+ H+ 1 Sb s due to the presence of near doubly magc nucleus 1 Sb (N=8, Z=51), whch may be the most sutable fragment combnaton n ths ternary fsson process. Ths can be verfed through the calculaton of barrer penetrablty and the relatve yeld of fragment combnatons obtaned n the cold reacton valley. The barrer penetrablty and hence the relatve yeld s calculated for each fragment combnaton found n the cold reacton valley plot. Fgure (a) represents the relatve yeld plotted as a functon of fragment mass numbers A 1 and A. From the plot, t s clear that the hghest relatve yeld s obtaned for the fragment combnaton 114 Pd+ H+ 1 Sb, whch ncludes the presence of near doubly magc nucleus 1 Sb. The second hghest relatve yeld s obtaned for the fragment combnaton 117 Ag+ H+ Sn, whch ncludes the presence of near doubly magc nucleus Sn (N=8, Z=5). The next hghest relatve yeld s obtaned for the fragment combnaton 119 Ag+ H+ 18 Sn whch ncludes the presence of proton shell closure Z=5 of 18 Sn. Natonal Conference on Current Advancements n Physcs rd &4 th February 17 Page Department of Physcs, St. John s College, Palayamkotta-67, Tamlnadu, Inda. DOI.979/

4 Relatve Yeld (%) Ternary fsson of 5,5 Cf sotopes wth H and 6 He as lght charged partcle In the H accompaned ternary fsson of 5 Cf sotope, the drvng potental s calculated and plotted as a functon of fragment mass number A 1 as shown n fgure (b). Here the deepest mnmum s found for the fragment combnaton 116 Pd+ H+ 1 Sb, whch ncludes the presence of near doubly magc nucleus 1 Sb (N=8, Z=51). The mnma found around the fragment combnatons 4 S+ H+ 7 Tl and 8 Ge+ H+ 167 Tb are due to the presence of near doubly magc nucleus 7 Tl (N=16, Z=81) and neutron shell closure N=5 of 8 Ge respectvely. The relatve yeld s calculated for all possble fragmentatons and plotted as a functon of fragment mass numbers A 1 and A as shown n fgure (b). From the plot, t s clear that the hghest relatve yeld s found for the fragment combnaton 116 Pd+ H+ 1 Sb, whch s the same fragment combnaton wth least drvng potental n the cold reacton valley plot. Also the fragment combnaton possess the presence of near doubly magc nucleus 1 Sb (N=8, Z=51). The next hghest relatve yeld found for the fragment combnaton 119 Ag+ H+ Sn s due to the presence of near doubly magc nucleus Sn (N=8, Z=5). The presence of doubly magc nucleus 1 Sn and hgh Q value makes the fragment splttng 117 Ag+ H+ 1 Sn a more probable one n ths ternary fsson process. (a) 114 Pd 1 Sb 5 Cf A = H (b) 116 Pd 1 Sb 5 Cf A = H (c) 1 Ru 14 Te 5 Cf A (d) 114 Pd 1 Sn 5 Cf A Fragment mass numbers A 1 and A Fg.. The relatve yeld s plotted as a functon of fragment mass numbers A 1 and A n the case of H and 6 He accompaned ternary fsson of 5,5 Cf sotopes wth fragments n equatoral confguraton.. 6 He accompaned ternary fsson of 5,5 Cf sotopes wth fragments n equatoral confguraton For the 5 Cf sotope wth 6 He as lght charged partcle, the drvng potental s calculated for all possble fragmentatons and potted as a functon of fragment mass number A 1 as shown n fgure (c). Here the deepest mnmum s found for the fragment combnaton 4 He+ 6 He+ Pu, whch possess doubly magc nucleus 4 He and a low Q value. The next mnmum s found around the fragment combnaton 1 Ru+ 6 He+ 14 Te, whch ncludes the presence of near doubly magc nucleus 14 Te (N=8, Z=5). The same fragment combnaton possesses the hghest Q value and hence may be the most sutable fragment splttng n ths ternary fsson process. The relatve yeld s calculated for all possble fragmentatons and plotted as a functon of fragment mass numbers A 1 and A as shown n fgure (c). In ths case, the hghest relatve yeld s found for the fragment combnaton 1 Ru+ 6 He+ 14 Te, whch ncludes the presence of near doubly magc nucleus 14 Te (N=8, Z=5). The next hgher relatve yelds are found for the fragment combnatons 114 Pd+ 6 He+ Sn and 116 Pd+ 6 He+ 18 Sn, whch nclude the presence of near doubly magc nucleus Sn (N=8, Z=5) and proton shell closure Z=5 of 18 Sn respectvely. In the 6 He accompaned ternary fsson of 5 Cf sotope, the drvng potental s calculated for all possble fragmentatons and plotted as a functon of fragment mass number A 1 as shown n fgure (d). Here the deepest mnmum s found for the fragment combnaton 4 He+ 6 He+ 4 Pu. The next mnmum found for the fragment combnaton around 114 Pd+ 6 He+ 1 Sn s due to the presence of doubly magc nucleus 1 Sn (N=8, Z=5). The relatve yeld s calculated and plotted as a functon of fragment mass numbers A 1 and A as shown n fgure (d). From the plot, the hghest relatve yeld s found for the fragment combnaton 114 Pd+ 6 He+ 1 Sn, whch s the same fragment combnaton wth hgh Q value and also possess the presence of doubly magc Natonal Conference on Current Advancements n Physcs rd &4 th February Page Department of Physcs, St. John s College, Palayamkotta-67, Tamlnadu, Inda. DOI.979/

5 Drvng potental (MeV) Ternary fsson of 5,5 Cf sotopes wth H and 6 He as lght charged partcle nucleus 1 Sn (N=8, Z=5). The next hgher relatve yelds are found for the ternary splttng 116 Pd+ 6 He+ Sn and 11 Ru+ 6 He+ 14 Te, of whch Sn (N=8, Z=5) and 14 Te (N=8, Z=5) are near doubly magc nucle.. H accompaned ternary fsson of 5,5 Cf sotopes wth fragments n collnear confguraton In the H accompaned ternary fsson of 5 Cf and 5 Cf sotopes wth fragments n collnear confguraton the drvng potental s plotted as a functon of fragment mass number A 1 as shown n fgure 4(a) and 4(b) respectvely. The fragment combnatons wth least drvng potental are also labeled. The relatve yeld n the case of 5 Cf and 5 Cf are calculated for all possble fragmentatons found n the cold reacton valley and plotted as shown n fgure 5(a) and 5(b) respectvely. In the case of 5 Cf sotope, the hghest relatve yeld s obtaned for the ternary splttng 114 Pd+ H+ 1 Sb, whch possess near doubly magc nucleus (N=8, Z=51). The next hgher relatve yelds found n the H accompaned ternary fsson of 5 Cf are for the fragment combnatons 117 Ag+ H+ Sn and 116 Pd+ H+ 11 Sb. In the case of 5 Cf sotope, the hghest relatve yeld s found for the fragment combnaton 116 Pd+ H+ 1 Sb, whch ncludes the presence of doubly magc nucleus 1 Sb. The fragment combnatons 119 Ag+ H+ Sn and 117 Ag+ H+ 1 Sn also possess a hgher relatve yelds n the ternary fsson of 5 Cf sotope wth H as lght charged partcle formed n collnear confguraton. (a) 5 Cf (b) 5 Cf A = H A = H 114 Pd+ 1 Sb 6 8 (c) 5 Cf A 1 Ru+ 14 Te Pd+ 1 Sb 6 8 (d) 5 Cf A 114 Pd+ 1 Sn 6 8 Fragment mass number A 1 Fg.4. The drvng potental s plotted as a functon of fragment mass number A 1 n the case of H and 6 He accompaned ternary fsson of 5,5 Cf sotopes wth fragments n collnear confguraton..4 6 He accompaned ternary fsson of 5,5 Cf sotopes wth fragments n collnear confguraton In the 6 He accompaned ternary fsson of 5 Cf and 5 Cf sotopes wth fragments n collnear confguraton the drvng potental s plotted as a functon of fragment mass number A 1 as shown n fgure 4(c) and 4(d) respectvely. The relatve yeld s calculated for all fragment combnatons found n the cold reacton valley plot. Fgure 5(c) and 5(d) represents the relatve yeld versus fragment mass numbers A 1 and A n the case of 5 Cf and 5 Cf sotopes respectvely. For 5 Cf sotope, the hghest relatve yeld s found for the splttng 1 Ru+ 6 He+ 14 Te, whch ncludes near doubly magc nucleus 14 Te. The next hgher relatve yelds are found for 114 Pd+ 6 He+ Sn, 116 Pd+ 6 He+ 18 Sn and 11 Pd+ 6 He+ 1 Sn. For the 5 Cf sotope, the fragment combnaton 114 Pd+ 6 He+ 1 Sn has the hghest relatve yeld, whch ncludes doubly magc nucleus 1 Sn. The next hgher relatve yelds are found for the splttng 116 Pd+ 6 He+ Sn, 11 Ru+ 6 He+ 14 Te, 118 Pd+ 6 He+ 18 Sn. Natonal Conference on Current Advancements n Physcs rd &4 th February Page Department of Physcs, St. John s College, Palayamkotta-67, Tamlnadu, Inda. DOI.979/

6 Ternary fsson of 5,5 Cf sotopes wth H and 6 He as lght charged partcle Fg.5. The relatve yeld s plotted as a functon of fragment mass numbers A 1 and A n the case of H and 6 He accompaned ternary fsson of 5,5 Cf sotopes wth fragments n collnear confguraton. IV. Concluson Usng Unfed ternary fsson model (UTFM), the spontaneous cold ternary fsson of 5,5 Cf sotopes wth H and 6 He as lght charged partcle wth fragments n equatoral and collnear confguraton has been studed. The fragment combnatons wth the hghest relatve yeld are found to be the same n both equatoral and collnear confguraton. In the H accompaned ternary fsson of 5 Cf and 5 Cf sotope, the most probable fragmentaton s found for 114 Pd+ H+ 1 Sb and 116 Pd+ H+ 1 Sb respectvely, n whch 1 Sb (N=8, Z=51) s a near doubly magc nucleus. In the ternary fsson of 5 Cf and 5 Cf sotope wth 6 He as lght charged partcle, the most probable fragmentaton s found for 1 Ru+ 6 He+ 14 Te and 114 Pd+ 6 He+ 1 Sn respectvely, whch s due to the presence of near doubly magc nucleus 14 Te (N=8, Z=5) and doubly magc nucleus 1 Sn (N=8, Z=5). Hence we can conclude that n the ternary fsson of 5,5 Cf sotopes wth H and 6 He as lght charged partcle, the presence of doubly or near doubly magc nucleus and hgh Q value plays an mportant role. Acknowledgements The author KPS would lke to thank the Unversty Grants Commsson, Govt. of Inda for the fnancal support under Major Research Project. No.4-76/1 (SR) dated --1. References [1]. G. Farewell, E. Segre and C. Wegand, Long range alpha-partcles emtted n connecton wth fsson. Prelmnary Report, Physcal Revew, 71(6), 1947, 7-. []. K. P. Santhosh, Sreejth Krshnan and B. Pryanka, Lght charged partcle accompaned ternary fsson of 4 Cm usng the Coulomb and proxmty potental, The European Physcal Journal A, 5(4), 14, 66. []. K. P. Santhosh, Sreejth Krshnan and B. Pryanka, The emsson probabltes of long range alpha partcles from even-even 44-5 Cm sotopes, Journal of Physcs G: Nuclear and Partcle Physcs, 41(), 14, 58. [4]. K. P. Santhosh, Sreejth Krshnan and B. Pryanka, 4 S accompaned ternary fsson of 4 Cm n equatoral and collnear confguraton, Internatonal Journal of Modern Physcs E, (11), 14, [5]. K. P. Santhosh, Sreejth Krshnan and B. Pryanka, Isotopc yeld n alpha accompaned ternary fsson of 5 Cf, Internatonal Journal of Modern Physcs E, 4(1),, 51. [6]. K. P. Santhosh, Sreejth Krshnan and B. Pryanka, α-accompaned cold ternary fsson of 8-44 Pu sotopes n equatoral and collnear confguraton, Physcal Revew C, 91(4),, 446. [7]. K. P. Santhosh and Sreejth Krshnan, Deformaton effects n the alpha accompaned cold ternary fsson of eveneven 44-6 Cf sotopes, The European Physcal Journal A, 5(4), 16, 8. [8]. J. Block, J. Randrup, W. J. Swateck, C. F. Tsang, Proxmty forces, Annals of Physcs, 5(), 1977, [9]. J. Block, W. J. Swateck, A generalzaton of the proxmty force theorem, Annals of Physcs, 1(1), 198, []. M. Wang, G. Aud, A. H. Wapstra, F. G. Kondev, M. MacCormck, X. Xu and B. Pfeffer, The AME 1 atomc mass evaluaton, Chnese Physcs C, 6(1), 1, [11]. H. Koura, T. Tachbana, M. Uno and M. Yamada, Nucldc mass formula on a sphercal bass wth an mproved even-odd term, Progress of Theoretcal Physcs, 11(), 5, 5-5. Natonal Conference on Current Advancements n Physcs rd &4 th February Page Department of Physcs, St. John s College, Palayamkotta-67, Tamlnadu, Inda. DOI.979/