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

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As a result <strong>of</strong> Fig. 5-2, we find that the microscopical mass parameters keep the system near the entrance configuration for a sufficient long time comparable with the time <strong>of</strong> reaction even in an adiabatic potential. Therefore, this situation justifies the assumption <strong>of</strong> a fixed neck as we assume it in the DNS model [34]. When the DNS configuration exists a long time, then thermal fluctuations in the mass asymmetry coordinate play the essential role in the fusion process. Indeed, these fluctuations are responsible for the fusion in the DNS model. Thus, the dynamical restriction for the growth <strong>of</strong> the neck can be caused partly by a large microscopical mass parameter for the neck motion, partly by the potential energy surface intermediate between diabatic and adiabatic limits. In the adiabatic two-center shell model, the mass parameter M εε slightly increases with the deformation parameters β i <strong>of</strong> the two nuclei in the symmetric system 110 Pd+ 110 Pd as shown in Fig. 5-3. The small variation <strong>of</strong> Mεε is due to the shell structure. Therefore, the relatively large value <strong>of</strong> M εε is a general result for collisions <strong>of</strong> both spherical and deformed nuclei. Fig. 5-4 shows the mass parameter M εε at the touching configuration <strong>of</strong> symmetric systems η = 0 with βi = 1as a function <strong>of</strong> the mass number A = A1 + A2 =2A1. The mass Mεε increases with the mass <strong>of</strong> the system. It slightly decreases with increasing mass asymmetry <strong>of</strong> the DNS. 5.2.2 The diabatic two-center shell model Let us now consider the calculation <strong>of</strong> the mass parameters (5.32) with the diabatic single particle energies obtained with the method <strong>of</strong> maximum-symmetry in the diabatic two-center shell model [35, 57]. In the diabatic motion, the nucleons do not occupy the lowest single particle states as in the adiabatic case, but remain in their diabatic states. In comparison to the calculations with the adiabatic single particle levels, the numerical procedure with diabatic single particle levels is much easier because each level has a complete set <strong>of</strong> quantum numbers and the drawing <strong>of</strong> the levels as a function <strong>of</strong> a collective variable is simpler and unique. Due to the nonzero width <strong>of</strong> the single particle states, the distribution <strong>of</strong> single particle strength over more complicated states is a Lorentzian distribution ρk(ɛ) as introduced in (5.28) instead <strong>of</strong> the δ-function δ(ɛ − ɛk) [86]. The occupation number n(ɛ k)<strong>of</strong>astatek Eq. energy ɛk and the corresponding value <strong>of</strong> fk with 71 are obtained, respectively, from functions
5-4: Mass parameter Mεε as a function <strong>of</strong> the mass number A = A1 + A2 =2A1 for Figure systems (η = 0) calculated with adiabatic single-particle states for βi =1,λ =1.6, symmetric and ε =0.75. Units: mfm 2 with m = nucleon mass. 72
Page 1 and 2:
Effects of
Page 3 and 4:
1 Introduction 6 1.1 The DNS-concep
Page 5 and 6:
Chapter 1 The elements existing in
Page 7 and 8:
observed the rapid fall-of<
Page 9 and 10:
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
Page 15 and 16:
In the present chapter we have pres
Page 17 and 18:
higher collective velocities to rep
Page 19 and 20: 2.1 General considerations We want
Page 21 and 22: couplings. Diabatic basis states ψ
Page 23 and 24: Chapter 3 The synthesis of<
Page 25 and 26: is calculated within the TCSM using
Page 27 and 28: E adiab (MeV) n E diab (MeV) n 30 2
Page 29 and 30: E diab (MeV) n 60 55 50 45 40 100Mo
Page 31 and 32: 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: 5-3: 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 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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