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

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considered, the diabatic potential has a minimum as a function <strong>of</strong> ε around ε =0.65 − 0.85. Since the mass parameter in ε has been shown to be large [43], it strongly hinders the growth <strong>of</strong> the neck even for a small energy gain from the diabatic contributions during a variation <strong>of</strong> the neck coordinate. Fig. 3-9 shows diabatic potentials as a function <strong>of</strong> λ for the asymmetric systems 110 Pd+ 136 Xe, 86 Kr + 160 Gd and 48 Ca+ 198 Hg, which lead to the same compound nucleus 246 Fm. These diabatic potentials are also strongly repulsive for smaller elongations and the quasi-fission bar- rier <strong>of</strong> the pocket becomes larger with the increase <strong>of</strong> the mass asymmetry η. In the upper part <strong>of</strong> Fig. 3-10, the diabatic contributions for the system 220 U( 110 Pd+ 110 Pd) are shown for η =0and0.5 atε =0.74. For an asymmetric clusterization <strong>of</strong> 220 U, the diabatic hindrance for the motion to smaller values <strong>of</strong> λ is smaller than for the symmetric configuration. This means that the evolution <strong>of</strong> the asymmetric DNS to the compound nucleus is more favored, which is supported by the experimental data. Since the diabatic effects are small near the touching <strong>of</strong> the nuclei, they are not important for the potential <strong>of</strong> the DNS as a function <strong>of</strong> the mass asymmetry at the touching configuration <strong>of</strong> the nuclei. The difussion process in the mass asymmetry η at the touching configuration <strong>of</strong> the nuclei starts after the formation <strong>of</strong> the initial DNS at the pocket <strong>of</strong> the potential in λ for a large fixed value <strong>of</strong> ε, e.g., ε =0.74. This slow difussion process is studied using an adiabatic potential which will be presented in chapter 4. The dependence <strong>of</strong> the diabatic contribution on the temperature is presented in the lower part <strong>of</strong> Fig. 3-10 for the system 220 U( 110 Pd+ 110 Pd). For this calculation, we take the occupa- probabilities n tion diab α given by the Fermi-distribution at finite temperature for the touching configuration <strong>of</strong> the nuclei. This temperature could be related to the excitation <strong>of</strong> the nuclei in the approaching phase <strong>of</strong> the collision. The initial excitation energy <strong>of</strong> the system decreases the repulsive character <strong>of</strong> the diabatic contribution due to smaller occupation numbers <strong>of</strong> the diabatic states under the Fermi-level. If these states are occupied and cross the Fermi-level from below, they increase the repulsive contributions <strong>of</strong> the potential, while occupied states above the Fermi-level, crossing it from above with decreasing λ, diminish the diabatic contributions. The diabatic contributions increase with prolate deformations and decrease for oblate deformations (Fig. 3-11). However, in order to conclude about an advantageous fusion with oblate nuclei, the corresponding mass parameters should first be analysed. 33
3-7: The same as in Fig. 3-6 for the systems Figure 90 + Zr 90 and Zr 96 + Zr 96 for λ =1.54, Zr is near to the minimum <strong>of</strong> the pocket in λ (upper part). The diabatic contributions for which these systems are presented as a function <strong>of</strong> ε in the lower part. 34
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: 3-5: Diabatic potentials for the sy
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.
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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