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

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Chapter 5 The present fusion models can be distinguished by the choice <strong>of</strong> the relevant collective variables along which fusion mainly occurs. While many models study the fusion in R at a practically fixed value <strong>of</strong> η, the DNS model [34] considers the DNS evolution in mass asymmetry by nucleon or cluster transfers as the main path to the compound nucleus. The DNS model assumes basically that the neck degree <strong>of</strong> freedom is fixed in the evolution in η and the nuclei are hindered from melting together by a variation in the relative distance R. In this chapter, we study dynamical restrictions for the growth <strong>of</strong> the neck in the DNS and suggest proper methods <strong>of</strong> the calculation <strong>of</strong> the DNS inertia tensor. There are various macroscopical and microscopical approaches to calculating the inertia tensor [82]. The macroscopical approaches (see, for example, [16, 83]) are based on the hydro- dynamical model <strong>of</strong> the nucleus. A calculation <strong>of</strong> the inertia tensor with a theory for quantum fluid dynamics is suggested in Ref. [84]. By using a random-matrix model to describe the coupling between a collective nuclear variable and intrinsic degrees <strong>of</strong> freedom, and with the help <strong>of</strong> the functional integral approach, mass parameters are derived in Ref. [85]. In the linear response theory [86, 87] the inertia tensor is found for fissioning nuclei. The microscopical approaches mainly use the cranking type expression and perform calculations in different single particle bases applying adiabatic [40, 88] or diabatic [57] two-center shell models. Difficulties in the cranking type calculations arise for collective motions with large amplitudes, for example, in fusion or fission, due to pseudo—crossings or crossings <strong>of</strong> levels in the single particle spectrum. Some publications disregard the contributions from the crossings (pseudo—crossings), which 57
means a neglect <strong>of</strong> effects <strong>of</strong> configuration changes on the mass parameters during the evolution <strong>of</strong> the nuclear shape in spite <strong>of</strong> the fact that the collective inertia is strongly influenced by level crossings (pseudo—crossings) [89, 90]. In order to overcome this problem, two—body collisions should be regarded which lead to a width <strong>of</strong> the single particle levels and an effective reduction <strong>of</strong> the level crossing effects. For example, calculations <strong>of</strong> the nuclear inertia in a generalized cranking model with pairing correlations yielded masses <strong>of</strong> about one order <strong>of</strong> magnitude larger than the ones without pairing [91]. One <strong>of</strong> the aims <strong>of</strong> this chapter is to obtain analytical expressions for mass parameters using models and methods which include residual interaction effects. In sect. 5.1, the mass parameters are obtained within the linear response theory, taking the fluctuation-dissipation theorem and the width <strong>of</strong> single particle states into account. The same mass parameters are also derived by Fermi’s golden rule and by smoothing the single particle spectrum in the mean—field cranking formula. In sect. 5.2, the mass parameters for the relevant collective variables (mass asymmetry, elongation, neck and deformation parameters) <strong>of</strong> the DNS and strongly deformed nuclear systems are evaluated in the two-center shell model with adiabatic and diabatic bases. 5.1 Microscopical inertia 5.1.1 Derivation from collective response function Let us consider a nuclear system described by a single collective coordinate Q and intrinsic single particle coordinates x i (with the conjugated momentum p i) and assume the following effective Hamiltonian [86] ˆH(xi,pi,Q)= ˆ H(xi,pi,Q0) +(Q − Q0) ˆ F (xi,pi,Q0) + 1 2 (Q − Q0) 2 < ∂2H(xi,pi,Q) ˆ ∂Q2 . (5.1) >Q0,T0 The shape <strong>of</strong> the nuclear mean field is changed with the collective coordinate Q that intro- duces the coupling between Q and the nucleonic degrees <strong>of</strong> freedom x i. Eq. (5.1) is obtained by expanding the Hamiltonian to second order in the vicinity <strong>of</strong> Q0 (local harmonic approx- 58
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
Page 11 and 12: smaller than the extra-extra push e
Page 13 and 14: 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: experimental separation energy allo
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 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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