Effects of diabaticity on fusion of heavy nuclei in the dinuclear model ...

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nucleus grows, gaining nucleons from its partner nucleus till the dinuclear system dissociates. Preliminary estimations show that the heights <strong>of</strong> the barriers for the asymmetric and symmetric fissions as well as the competition between asymmetric and symmetric fission channels and the properties <strong>of</strong> charge, mass, energetic distributions <strong>of</strong> the fission products are reproduced in this approach. The spontaneous fission process could be considered as a tunneling process in the mass asymmetry degree <strong>of</strong> freedom η. The role <strong>of</strong> diffusion and friction in the tunneling in η for the dinuclear system could be considered using the Lindblad axiomatic approach for open quantum systems [123, 124]. Changes in the deformation <strong>of</strong> the nuclei during the tunneling process could also be taken into account. The nuclei Fm and Cf are especially attractive for this study. Using the structural forbiddenness concept [63], we could study the hindrances for the fragmentation process in λ and η degrees <strong>of</strong> freedom. The comparison <strong>of</strong> the calculated energy thresholds (fission barriers) for the fission in λ and η variables could provide the answer about the favorable fission path. 109
Appendix A For describing nucleus-nucleus collisions, we use the TCSM [40] as a single-particle model. The Hamiltonian <strong>of</strong> the model is H = − ¯h2 ∇ 2 2m0 + V (ρ,z)+V LS(r, p, s)+V L 2(r, l), (A.1) in cylinder coordinates z, ρ and ϕ. The momentum-independent part <strong>of</strong> the potential may be expressed as V (ρ, z) = f0 2 m0ω 2 z ′2 (1+ cz ′ The momentum-dependent parts are with the abbreviation z ′ V LS = − ¯hκ L2 = − V 1 ¯hκµ 2 m0ω 3 0 , l dz + ′2 )+ 1 2 m0α 2 gz (1+ ′2 )ρ 2 (A.2) . m0ω0 , (∇V × p) · s , (A.3) N (N +3) δif , (A.4) +¯hκµω0 = z − zi . The positions <strong>of</strong> the centers are denoted by z1 and z2, z1 ≤ 0 ≤ z2. The behaviour <strong>of</strong> V (ρ, z) along the z-axis can be seen from Fig. A-1, where the potential is plotted below the associated nuclear surface. To the left <strong>of</strong> z1 and to the right <strong>of</strong> z2 the potential (A.2) is simply that <strong>of</strong> a deformed oscillator. Between the centers, however, there are considerable deviations caused by a variable barrier and by the need <strong>of</strong> joining the 110 2
Page 1 and 2:
Effects of
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1 Introduction 6 1.1 The DNS-concep
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Chapter 1 The elements existing in
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observed the rapid fall-of<
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Figure 1-1 illustrates the compound
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smaller than the extra-extra push e
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fusion and quasi-fission processes
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In the present chapter we have pres
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higher collective velocities to rep
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2.1 General considerations We want
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couplings. Diabatic basis states ψ
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Chapter 3 The synthesis of<
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is calculated within the TCSM using
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E adiab (MeV) n E diab (MeV) n 30 2
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E diab (MeV) n 60 55 50 45 40 100Mo
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3-5: Diabatic potentials for the sy
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3-7: The same as in Fig. 3-6 for th
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The estimated collective velocities
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3-10: Diabatic contributions as a f
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effects give a justification for th
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The similarity of
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4.1.3 Alternative microscopical met
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to the DNS concept [18, 34], cross
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U (MeV) 28 27 26 25 24 23 22 21 20
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U (MeV) 35 30 25 20 15 10 90Zr + 12
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4-1: Fusion barriers B Table TCSM
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U (MeV) 40 30 20 10 20 10 0 a) b) 9
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experimental separation energy allo
Page 57 and 58: means a neglect of
Page 59 and 60: the case of an ind
Page 61 and 62: single particle density matrix exte
Page 63 and 64: following ratio in the limit <stron
Page 65 and 66: 5-1: Dependence of
Page 67 and 68: the microscopical mass parameter <s
Page 69 and 70: 5-3: Mass parameter Mεε as a func
Page 71 and 72: 5-4: Mass parameter Mεε as a func
Page 73 and 74: the approximate expressions (Eqs. (
Page 75 and 76: (10 3 m fm 2) M , M λλ εε 25 20
Page 77 and 78: (10 3 m fm 2) M εε M (10 λλ 4 m
Page 79 and 80: ~ f k (MeV -1) 0,20 0,15 0,10 0,05
Page 81 and 82: V (MeV) 30 25 20 15 10 5 0 -5 -10 1
Page 83 and 84: to the dependence of</stron
Page 85 and 86: where the lifetime t 0 of</
Page 87 and 88: 6-2: a) Time-dependent dynamical po
Page 89 and 90: Table 6-1: Quasi-fission and inner
Page 91 and 92: 6-3: Time-dependent average width <
Page 93 and 94: Chapter 7 In the quasi-fission proc
Page 95 and 96: The value of t0 is
Page 97 and 98: Y Z Y A 0,10 0,08 0,06 0,04 0,02 0,
Page 99 and 100: estimated from the difference betwe
Page 101 and 102: elements from Z=104 to Z=112 in the
Page 103 and 104: fission process is an important fac
Page 105 and 106: the neck coordinate ε and
Page 107: • The time-dependent transition b
Page 111 and 112: where The volume is V0 = 1 2 m0ϖ 2
Page 113 and 114: ϕ nz(z) = ⎧ ⎪⎨ ⎪⎩ C−1
Page 115 and 116: Appendix B The collective response
Page 117 and 118: [1] S.G.Nilsson et al., Phys. Lett.
Page 119 and 120: [27] N.V.Antonenko et al., in 1 st
Page 121 and 122: [63] Yu.F.Smirnov and Yu.M.Tchuvil
Page 123 and 124: [97] H. Hofmann et
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