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

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B Here, j i the height <strong>of</strong> the fusion barriers Bλ fus (t) andBη fus , and quasi-fission barrier denotes B λ . The values <strong>of</strong> Bη fus qf Bλ qf and are practically independent <strong>of</strong> time. The initial DNS <strong>of</strong> the reactions considered here are in or near the minimum <strong>of</strong> the total potential energy <strong>of</strong> the system as a function <strong>of</strong> λ and η. Moreover, they are in thermodynamic equilibrium because the diabatic and adiabatic potentials practically coincide. The temperature T (λ t) is calculated using the expression T (λ t)= E ∗ (λ t)/a where λ t is the elongation <strong>of</strong> the touching nuclei, i.e. <strong>of</strong> the initial DNS. In the calculations we assume that the excitation energy <strong>of</strong> the initial DNS is E ∗ (λ t)=30 MeV in all reactions considered. In (6.9), ω B j i is the frequency <strong>of</strong> the inverted harmonic oscillator approximating the potential in the variable j on the top <strong>of</strong> the fusion or barriers B quasifission j i ,andω is the frequency <strong>of</strong> the harmonic oscillator approximating the j j the variable j for the initial DNS. The frequencies ωB i and ωj are calculated using in potential the absolute values <strong>of</strong> the second derivative <strong>of</strong> the potential with respect to the variable j (on top <strong>of</strong> the barrier B the j i j Mjj (e.g, ωB i = mass parameter |∂2V/∂j2 i B | and for the initial DNS, respectively) as well as the corresponding j /Mjj ). The method <strong>of</strong> calculation <strong>of</strong> the mass parameters Mηη and M λλ is presented in chapter 5 [43]. The microscopical values <strong>of</strong> Mηη and Mλλ are close to the corresponding hydrodynamical values [84] at the touching configuration <strong>of</strong> the nuclei (see chapter 5). In our calculations <strong>of</strong> the fusion probabilities, the following values B λ η qf ≈ B 0.8—1.0 MeV, ¯hω fus ≈ 1.5—2.0 MeV, ¯hωλ ≈ 1.5—2.0 MeV and ¯hωη ≈ 0.8—1.0 ¯hω used are B λ reactions considered. The value <strong>of</strong> ¯hω fus at the inner fusion barrier in λ is about the for MeV 0.5—0.6 MeV and agrees with the one obtained in the calculations <strong>of</strong> fission [116] at the saddle point. The friction coefficients ((5.9) and (5.23)) in λ and in η obtained with Γ=2 MeV at the touching configuration λt have the same order <strong>of</strong> magnitude as the ones calculated within the one-body dissipation models [34]. The values obtained for P λ(η) fus rather weakly on depend Γ in (6.9)[34]. The possibility to apply the Kramers expression to relatively small barriers (B j /T > 0.5) was demonstrated in [117]. i 6.1 Results and discussion The time-dependent diabatic potentials for the reactions 110 Pd+ 110 Pd and 124 Sn+ 124 Sn are in Figs. 6-2a and 6-2b. The time-dependent inner fusion barrier B presented λ fus 87 in λ appears
6-2: a) Time-dependent dynamical potential V (λ, t) as a function <strong>of</strong> elongation λ for the Figure system 110 + Pd 110 The initial diabatic potential V (λ, t =0)=Vdiab(λ) and the adiabatic Pd. Vadiab(λ) are shown by solid and dotted curves, respectively. The diabatic potential potential (λ, t = t0) at the lifetime t0 <strong>of</strong> the DNS is presented by a dashed curve. The nuclei are V spherical with the neck parameter ε =0.74. The parameter Γ considered −1 0 =0.030MeV−1 is in the calculation <strong>of</strong> the single-particle widths. The fusion B used λ Bλ qf fus (t = t0) and quasi-fission in λ are indicated. These barriers are measured with respect to the minimum <strong>of</strong> barriers potential. b) The same as in a) but for the system the 124 + Sn 124 Sn. 88
Page 1 and 2:
Effects of
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1 Introduction 6 1.1 The DNS-concep
Page 5 and 6:
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
Page 33 and 34:
3-7: The same as in Fig. 3-6 for th
Page 35 and 36: The estimated collective velocities
Page 37 and 38: 3-10: Diabatic contributions as a f
Page 39 and 40: effects give a justification for th
Page 41 and 42: The similarity of
Page 43 and 44: 4.1.3 Alternative microscopical met
Page 45 and 46: to the DNS concept [18, 34], cross
Page 47 and 48: U (MeV) 28 27 26 25 24 23 22 21 20
Page 49 and 50: U (MeV) 35 30 25 20 15 10 90Zr + 12
Page 51 and 52: 4-1: Fusion barriers B Table TCSM
Page 53 and 54: U (MeV) 40 30 20 10 20 10 0 a) b) 9
Page 55 and 56: 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: where the lifetime t 0 of</
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 and 108: • The time-dependent transition b
Page 109 and 110: Appendix A For describing nucleus-n
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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