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

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Figure 1-3: Shapes <strong>of</strong> the system 110 Pd+ 110 Pd as functions <strong>of</strong> ε and λ. Motivated by these results, we started to investigate possible factors which hinder the DNS to melt together in the elongation λ. We consider these factors to be diabatic effects in the potential energy surface [35] and a large mass parameter in the neck coordinate ε [43]. In- vestigating these factors, we try to find theoretical justifications for the basic assumptions <strong>of</strong> the model <strong>of</strong> fusion based on the DNS-concept. We would like to stress that the model <strong>of</strong> fusion, based on the DNS-concept, explains many experimental data concerning the production <strong>of</strong> superheavy elements and plays an important role for giving predictions for new experiments ([22],[27]). In the present work, using the TCSM, we want to study the following: • Diabatic potentials as a function <strong>of</strong> the relevant collective variables <strong>of</strong> the DNS for heavy- ion systems. • Microscopic mass parameters for the relevant coordinates <strong>of</strong> the DNS formed in collisions <strong>of</strong> heavy nuclei taking the width <strong>of</strong> single-particle states into account. • Whether the system has time for the growing <strong>of</strong> the neck. • Whether the system has time for destroying the ”memory” on the diabatic (structural) forbiddenness for the fusion in the elongation λ and to find the favorable fusion channel. • Within which model it is possible to describe the experimental quasi-fission products <strong>of</strong> fusion reactions. 15
In the present chapter we have presented an introduction <strong>of</strong> experimental and theoretical knowledge in the field <strong>of</strong> transuranium and superheavy elements. A brief review about the model <strong>of</strong> fusion based on the DNS-concept as well as a comparison <strong>of</strong> this model with other theoretical models <strong>of</strong> fusion have been presented. In chapter 2 we give a summary <strong>of</strong> the main ideas about <strong>diabaticity</strong> in heavy-ion collisions. Moreover, the methods <strong>of</strong> calculations <strong>of</strong> a diabatic basis in the TCSM are explained. The potential energy <strong>of</strong> the DNS as a function <strong>of</strong> the relevant collective variables <strong>of</strong> the diabatic TCSM is shown in chapters 3 and 4 for different heavy systems. In chapter 5 the calculation <strong>of</strong> microscopical mass parameters <strong>of</strong> the DNS formed in reactions with heavy nuclei is presented by using the adiabatic and diabatic TCSM and the width <strong>of</strong> the single-particle states. The competition between two possible fusion channels in elongation λ and in mass asymmetry η is studied for various heavy systems in chapter 6. In chapter 7 the quasi-fission process <strong>of</strong> the DNS is evaluated solving a transport master-equation for the exchange <strong>of</strong> nucleons between the parts <strong>of</strong> the DNS, which also takes the decay <strong>of</strong> the DNS in the elongation λ into account. A summary and the outlook <strong>of</strong> the work are given in chapter 8. 16
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: fusion and quasi-fission processes
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 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
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~ 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
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• The time-dependent transition b
Page 109 and 110:
Appendix A For describing nucleus-n
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where The volume is V0 = 1 2 m0ϖ 2
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ϕ nz(z) = ⎧ ⎪⎨ ⎪⎩ C−1
Page 115 and 116:
Appendix B The collective response
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[1] S.G.Nilsson et al., Phys. Lett.
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[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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