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The Meson Bond Barrier to Nuclear Fission

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The Meson Bond Barrier to Nuclear Fission AU0524285 The Meson Bond Barrier to Nuclear Fission PETER NORMAN Moaash University, Victoria pnormanraj surf. net. au SUMMARY. The Coulomb barrier to nuclear fusion is sometimes described as a barrier to nuclear fission. In tliis paper it will be shown that it is more meaningfiil to describe the repulsive Coulomb force between the daughters of fission as the cause of fission rather than a barrier. In fact it is this force which breaks the meson bonds between the daughters and imparts kinetic energy to them. This process may therefore be described as a quantum jump ratheT than a 'tunneling'. The Bemal liquid drop layered alpha particle model of a heavy nucleus shows that the sixth layer of alpha particles is not closed and is inherently unstable. This nucleus therefore either gradually decays by radiating alpha and beta particles until most of the sixth layer has been shed or it undergoes spontaneous fission to form a heavy daughter rarely containing less than four closed layers and a lighter daughter never containing less than three closed layers. It will be shown how each alpha decay involves the breaking of five or six meson bonds and each spontaneous fission breaks about thirty bonds. 1. Introduction way. Because of isospin it is assume that 6 equal The underlying nuclear structure of heavy elements meson bonds strongly bind the 2 protons and 2 may be visualized as 6 concentric layers of alpha neutrons of a 4He nucleus (alpha particle) into a particles. This structure is based on Bemal's [1] model tetrahedral structure. The total meson bond energy, of a drop of a monatomic liquid in which hard spheres E.,,. of the 4He nucleus is defined as the empirically representing atoms are densely packed. This model determined binding energy, Eu, of this nucleus successfully explained many properties of such liquids corrected for the Coulomb repulsive energy, Ec, so as well as those of metallic glasses. Norman [2].[7] that: E,n = 6 MB == Eh + Er where Eh = 28.3*MeV and showed how Bemal's model may be used to account Er = 0.8 MeV, Therefore 1 MB = 4.84 MeV. The for the size, density, quadrupole moment and binding total number of meson bonds in any nucleus is equal to energy levels of many nuclei if the hard spheres are the value of Em tor that nucleus divided by 4.84 MeV. alpha particles. Accordingly an oxygen 16 nucleus is A table of the values of Eb Et, Em and the number of modeled as a single tetrahedral layer of 4 alpha MB for the decay products of U235 is provided in particles. A second layer of 4 alpha particles models Appendix 1. The data that is provided in Table 3 sulfur 32, a third layer of 6 alphas models nickel 56, a indicates the manner in which the number of meson fourth closed layer of 12 alphas forms the core of all bonds between successive layers increases in order to nuclei containing at least 52 protons, and a fifth layer balance the increasing Coulomb repulsion. of 12 additional alphas forms a basis for those nuclei with 76 or more protons. Norman [3],[4] has also 3. Alpha Decay shown that this latter structure of 38 alphas constitutes The net energy balance of an alpha decay may be the stable end point of the radioactive decay of heavy written as follows: nuclei such as uranium. Furthermore, when a uranium A E, = E, (I) nucleus undergoes fission induced by thermal neutrons it forms a light fragment with a core of no less than 3 where A Eb is the difference between the sum of the alpha layers and a heavier daughter with a core of binding energies of the two daughter nuclei and the rarely less than 4 alpha layers. bOinding energy of the mother nucleus. Ek is the kinetic energy of the alpha particle. This is exemplified by the alpha decay of 23SU where 2. Meson Bonds If the inter-nucleon bond between two adjacent A Eb = 4(MeV) and Ek = 4(MeV). nucleons in a nucleus is mediated by the exchange of However, equation U) takes no account of the virtual mesons then the tune averaged meson bond difference AE. between the powerful repulsive (MB) energy. Em may be calculated in the following Coulomb energv of the mother nucleus and the sum of 179 AJpha Decay the Coulomb energies of the daughter nuclei. Adding AEt j AEm + Ek (MeV) A E to both sides of (1) gives: Released I Absorbed c al AE r AE =AE + E (2) ^U-> Th + a 33 29 + 4 = 33 b t c k -31Pa -> "7Ac - a 33 28 + 5 = 33 Subtracting A Eb from both sides of C2) gives: 227Ac -> n?Fr + a 32 28 + 5=33 227 7 AEC = AEc-AEb + E, (3) Th-> "'Ra + a 33 2"'+6 = 33 In all alpha decays A Ec - A Eb = A Em " Ra ->" Rn-ra 32 27 + 6 = 33 il9 :L 32 25-6= 3i where AEm is the meson bond barrier being the Rn-> Po-a 21 difference between the meson energy of the mother Po -»-"Pb + a 31 24 + 7 = 31 nucleus and the sum of the meson energies of Hie two "'At-» ""Bi + a iZ 24 + 8 = 32 :l'Bi-> "Tl + tt 31 25 + 6 = 31 daughters. It can be seen in Table 1 that this 2 "Po -> -^Pb + a 32 24 + 8 = 32 difference is approximately equivalent to 6 meson Table 1 Energy balances for U alpha decay chain bonds (namely 29. lMeV). Equation (3) may be rewritten as: A£, = AEj, + E (4) v 4. Fission Energy Balance This equation was previously used in reference [4] to 23 23S The fission of a "U nucleus into 2 daughters each describe alpha decay in U as Coulomb breaking of larger than an alpha particle has previously been the 6 meson bonds between the two daughter nuclei. discussed by Norman [3],[5] in terms of the layered In this way an alpha particle "tunnels' through the so- alpha particle models of nuclear structure. In those called Coulomb barrier. The total energy balance (in papers it was shown that the lighter daughter never has MeV) is indicated in Figs, land 2 for the initial decay 233 a core of less than 14 alpha particles whereas the of U and in Table 1 for all 10 alpha decays in the heavier daughter rarely has a core of less than 26 decay chain of '""'U. alphas. Th + alpha An example of the energy balance (in MeV) involved = 909 in the fission of 235U is illustrated in Figures 3 and 4. 235 Ti 141r M92 iAEc = -33 Ec = 876 ^^ ! 1—* !~^n + Ba + Kr E = 909 o o o h iAEc =- 325 c = 534 0 0 0 I Et, = -1784 4-AEb=-4 = -1788 E,, = -1784 E =-2664 iAEb =-173 Eb = -1957 = -2o93 i— T E, = 4 E~=-2541 J3 Fig.l Schematic energy balance of "U alpha decaj EIU =-2693 tA Em = 152 tEk = 173 Fig.3 Schematic energy balance of a 'JU fission. A Ec = ; 33 MeV=Coulomb barrier. j325 MeV = Coulomb barrier ". Meson bond barrier = 6MB • Meson bond barrier = 30 MB = T A Em = 29 MeV • = t AEm= 152 MeV 4MeV.=iAEh = -4MeV tEk= viAEh=-173MeV , A Er - A Em + Ek •R (Note: E-o is included in Em) Ec= AEm+Ek (Note: Eb is included m Em ) Fig. 2 The meson bond barrier. AEm, to the alpha decav of ii5U. Fig.4 The meson bond barrier, ?A Em, to the fission of a B5U nucleus 180 It will now be shown that in each of these fission The mechanism for fission consistent with the layered processes the separation of the 2 initial unstable alpha particle model is based on the bond structures of daughters involves the breaking of approximately 30 closed layer nuclei as first outlined in reference [6] and meson bonds. This will be indicated in Table 2 by a as listed below in Table 3. Noting that there is a total number of examples of fission ranging across the bi- of 60 meson bonds between layers 4 and 5 it appears modal fission spectrum of 2iiU. In tliis Table the that in the fission process about 30 of these bonds are numbers refer to the meson bonds associated with the broken after the uranium nucleus is destabilized either terms of the equations. The derivation of the bonds in by deformation or the absorption of a thermal neutron. each nucleus is to be found in Appendix 2. [Layer jl| 2 235 U: Neutrons: 2 Daughters: Broken Bonds Alphas/1 4 i 4 12 12 16 between daughters: Layer | 157 77 ' n + Sm + Zn 6x6 12x6 j 12x6 16x6 556 363 164 29 Layer , =24 t =24 =36 = 96 • 2n + :"Ba + MB ex 4x3/2 4;c3 6x4 12x4 12x5 16x6 556 327 198 31 Layer =6 1=12 =24 = 48 I =60 =96 92K:: MB 24+6124+12 36+241 72+48 I 72+60 96+96 556 325 201 30 in + ex =30 =36 =60 =120 =132 =192 140Xe | Closed 28^28 76OSn6 556 316 210 30 [Nucleus 1?2 24x2 40x2 2n + Sn + ]Mo MB 49x1 N-Z =48 =80 =49 55b 294 230 32 235 MB 30 |30+36 (66+60 126+120J246+132 378+192 U -* n + 128Sn -- 10fMo Core =66 =126 =378 =570_ 556 290 236 30 =246 MB 30 66 126 48+246 80+3^8 49+570 ~'J\J —> 3n + ;i0Pd H- "°Pd Total =294 =458 =619 556 261 261 34 (Model) Table 2 Meson bonds involved in the creation of the MB 29 67 127 296 456 646 initial products of "U fission.
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