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

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is chosen with the condition <strong>of</strong> the N/Z-equilibrium in the system, mass and charge evolutions are described analogously. A diffusion process leads to the exchange <strong>of</strong> nucleons between the two touching fragments, thus generating a time-dependent distribution in the Z(A) variables <strong>of</strong> the DNS. This process can be described by a master-equation [33, 44, 73, 119] for the probability PZ(t) <strong>of</strong> finding the system at the time t in the configuration with the charge number <strong>of</strong> the light fragment Z. The asymmetric DNS evolves to a compound nucleus or to a symmetric DNS. The melting <strong>of</strong> the DNS nuclei in variable R is strongly hindered [35, 36, 42, 66]. The decay in R affects the motion <strong>of</strong> the system in Z. In order to take the effect <strong>of</strong> the DNS decay into consideration, we can rewrite the known master-equation for PZ(t) [33, 44, 73, 119] as follows ∂PZ(t) ∂t =∆(−) (Z+1) P (Z+1)(t)+∆ (+) (Z−1) P − (∆ (Z−1)(t) (+) Z +∆(−) Z +Λqf Z ) P (7.1) Z(t), where the microscopically calculated transport coefficients ∆ (±) Λ and qf Z Z given by the expression (4.3) are is the rate <strong>of</strong> decay probability in R. In the right side <strong>of</strong> Eq. (7.1), only the transitions Z ⇀↽ Z + 1and Z ⇀↽ Z − 1are taken into account in the spirit <strong>of</strong> the independent-particle model. For decay, the DNS should overcome the potential barrier B qf, which coincides with the depth <strong>of</strong> the pocket in the double-folding nucleus-nucleus potential as a function <strong>of</strong> R. The bottom <strong>of</strong> this pocket corresponds to the distance Rm = R1+R2+0.5fm (Ri is the radius <strong>of</strong> the nuclei). The values <strong>of</strong> the quasifission barriers B qf which depend on Z are mainly responsible the lifetime t0 <strong>of</strong> the DNS. During this time, the DNS evolves in the variables Z. The decay for the DNS in R is treated using the one-dimensional Kramers rate <strong>of</strong> probability Λ <strong>of</strong> qf Z (6.9). In our calculations, the values ¯hω Bqf =1.0 MeV and ¯hω =2.0 MeV are used for the reactions considered. The measurable quasi-fission charge (mass) yield is expressed through the formation prob- PZ(t) <strong>of</strong> the DNS configuration with charge (mass) asymmetry Z and the decay probaability in R described by the Kramers rate Λ bility qf Z Z(t0) =Λ Y qf Z 95 t0 0 PZ(t)dt. (7.2)
The value <strong>of</strong> t0 is determined in the solution <strong>of</strong> the Eq. (7.1). The decay <strong>of</strong> the DNS with Z > ZBG (ZBG corresponds to the barrier <strong>of</strong> the DNS potential energy as a function <strong>of</strong> the asymmetry) mainly contributes to the quasi-fission yield, and the lifetime t0 is calculated charge the condition from Λ Z>ZBG qf Z t0 PZ(t)dt ≈ 1. It is assumed that the DNS with Z
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
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 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: Chapter 7 In the quasi-fission proc
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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