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

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are continuous with respect to z at z =0. Forz0, the oscillator frequencies ωz must be determined numerically from the assumption <strong>of</strong> volume-conservation. With the method suggested we can find the diabatic levels close to the adiabatic levels (Fig. 3-1). Differences take place only near the crossing points. In contrast to Ref. [57], we can consider the diabatic effects for any neck parameter ε. This yields a better shape parametrisation <strong>of</strong> the DNS. 3.2 Results and discussion In the calculations, we firstly consider symmetric collisions <strong>of</strong> spherical nuclei and then analyse asymmetric entrance channels, thermal and deformation effects. The diabatic contribution ∆V diab as a function <strong>of</strong> the elongation is presented for the reaction 100 Mo+ 100 Mo in Fig. 3-2. The nuclei are considered as spherical with ε =0.74, which supplies realistic shapes <strong>of</strong> the DNS for λ = 1.5 − 1.6. ∆V diab consists <strong>of</strong> contributions from neutrons and protons. The diabatic contribution increases with decreasing λ or R because many diabatic levels cross the Fermi level (Fig. 3-3). In general, the diabatic contribution increases with the mass number A <strong>of</strong> the system because <strong>of</strong> the larger number <strong>of</strong> level crossings. The diabatic contribution ∆V diab <strong>of</strong> many symmetric systems selected along the line <strong>of</strong> beta stability shows diabatic shell- structure effects [63, 64]. The role <strong>of</strong> these effects is demonstrated in Fig.3-4a by the diabatic contributions <strong>of</strong> neutrons and protons for the systems 90 Zr+ 90 Zr and 96 Zr+ 96 Zr. While the diabatic contributions <strong>of</strong> the protons are nearly the same in both the systems, the diabatic contributions <strong>of</strong> the neutrons are quite different. As a result, the total diabatic potential is more repulsive in the case <strong>of</strong> 90 Zr+ 90 Zr (Fig. 3-4b). Further diabatic potentials are presented in Figs.3-4c and 3-5 for the systems 130 Xe+ 130 Xe, 136 Xe+ 136 Xe, 100 Mo+ 100 Mo and 110 Pd+ 110 Pd. The neck parameter is fixed at ε =0.74 and the nuclei are considered as spherical. Excepting the potentials with the Xe isotopes (Fig. 3-4c), the diabatic potentials for all these systems have a pocket near to the touching configuration (λ =1.58) in which the DNS could stand some time and evolve in mass asymmetry. For smaller elongations, the diabatic potential is strongly repulsive in all symmetric systems. The diabatic potential is similar to the one calculated with the phenomenological double folding potential. In Fig. 3-5 we compare the diabatic potential <strong>of</strong> the system 110 Pd+ 110 Pd with the 27
E adiab (MeV) n E diab (MeV) n 30 25 20 15 10 5 30 25 20 15 10 5 λ 100Mo + 100Mo 1,1 1,2 1,3 1,4 1,5 1,6 1,1 1,2 1,3 1,4 1,5 1,6 3-1: Diagrams <strong>of</strong> adiabatic (upper part) and diabatic (lower part) neutron levels with Figure z =1/2 for j 100Mo+ 100 as a function <strong>of</strong> elongation λ. The nuclei are considered as spherical Mo ε =0.74. The adiabatic levels are calculated with the generalized TCSM Hamiltonian with and the diabatic levels with the diabatic Hamiltonian (3.4) using the maximum symmetry (A.14) method. 28 λ
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: is calculated within the TCSM using
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
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to the dependence of</stron
Page 85 and 86:
where the lifetime t 0 of</
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6-2: a) Time-dependent dynamical po
Page 89 and 90:
Table 6-1: Quasi-fission and inner
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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
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Y Z Y A 0,10 0,08 0,06 0,04 0,02 0,
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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
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
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[97] H. Hofmann et
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