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

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experiment have to be developed to describe the extremely small fraction <strong>of</strong> the total cross section leading to fusion. Predictions based on these models are useful in the preparation <strong>of</strong> the next generation <strong>of</strong> experiments. The macroscopic models ([14], [15], [16]) do not reproduce the excitation function <strong>of</strong> the reactions used for the synthesis <strong>of</strong> superheavy elements. Compensat- ing the dissipative losses in the relative motion, the macroscopical dynamical model (MDM) <strong>of</strong> Swiatecki [16] and the surface friction model by Fröbrich [15] have to take an extra-extra-push energy into account leading to an excitation energy <strong>of</strong> the compound nucleus which results too large compared to the experimental data for superheavy elements [17]. In addition, the MDM concept yields too large evaporation residue cross sections as demonstrated for example for the 100 Mo + 100 Mo and 110 Pd + 110 Pd reactions [18] since the MDM does not take into account the competition between complete fusion and quasi-fission processes. In the MDM, the following qualitative picture was considered: i) after the capture, the neck between the nuclei grows quite quickly and a deformed united system is formed; (ii) the united system either overcomes the saddle point and moves to the equilibrium state <strong>of</strong> the compound nucleus or goes to the quasi-fission channel. The choice <strong>of</strong> the channel <strong>of</strong> complete fusion or quasi-fission depends on the initial kinetic energy <strong>of</strong> the projectile. Another method to calculate fusion cross sections is based on the dinuclear system (DNS) concept [19]. Within this concept, calculations <strong>of</strong> the complete fusion probability and optimal excitation energy for the production <strong>of</strong> compound nuclei between Z=102 and Z=114 are in agreement with the experimental data ([20], [21] and [22]). The model based on the DNS- concept gives an explanation <strong>of</strong> the reduction <strong>of</strong> the fusion cross sections by quasi-fission and can be used for the prediction <strong>of</strong> evaporation residue cross sections in the production <strong>of</strong> heavy and superheavy elements by cold and hot fusion reactions [22]. The main idea <strong>of</strong> the DNS- concept is the assumption that complete fusion and deep inelastic transfer reactions are similar nuclear processes. Both <strong>of</strong> them are realized according to similar scenarios. The scenario <strong>of</strong> the complete fusion process is as follows. At the capture stage, after full dissipation <strong>of</strong> the collision kinetic energy, the DNS is formed. The complete fusion process is the DNS evolution that proceeds via nucleon transfer, shell by shell from one nucleus to the other. The DNS nuclei retain their individuality throughout their way to the compound nucleus. This peculiarity <strong>of</strong> the DNS evolution is the consequence <strong>of</strong> the shell structure <strong>of</strong> the nuclei. 9
Figure 1-1 illustrates the compound nucleus formation process in the framework <strong>of</strong> the MDM and the DNS-concept. Reviews on the theoretical basis <strong>of</strong> the DNS-concept and on the model treating the competition between fusion and quasi-fission are given in Refs. [17], [21] and [23]. Newer calculations based on the MDM model are the following: In Japan an approach is being developed on the basis <strong>of</strong> the MDM model with the fluctuation-dissipation effects [24], for the description <strong>of</strong> hot fusion <strong>of</strong> heavy symmetric systems leading to the formation <strong>of</strong> superheavy elements. Estimation <strong>of</strong> the formation cross sections <strong>of</strong> superheavy elements in the standard statistical model taking into account the limitations on fusion from empirical systematics were made in Ref. [25]. In [26], a simple model for description <strong>of</strong> cold fusion reactions based on the doubly magic lead target nucleus was proposed. This model assumes that the compound nucleus is formed by quantal tunneling through the fusion barrier. The model predicts that the most promising reaction for the production <strong>of</strong> superheavy nuclei is 208 Pb( 86 Kr,1n) 293 118, but the predicted cross section for this reaction is considerably larger (670 pb) than the production cross section obtained in Berkeley [10]. The model <strong>of</strong> fusion based on the DNS-concept predicts a production cross section <strong>of</strong> the order <strong>of</strong> 10 −2 pb [27] for this reaction. 1-1: Illustration <strong>of</strong> the compound nucleus formation in the framework <strong>of</strong> the MDM and Figure DNS-concept. 10
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: observed the rapid fall-of<
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 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 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.
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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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