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

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to the ones obtained in adiabatic calculations because we took the width Γ k <strong>of</strong> single-particle states into consideration. This is observed in Figs. 5-1and 5-6 comparing the values <strong>of</strong> M εε at the touching configuration <strong>of</strong> the nuclei for the reaction 110 Pd+ 110 Pd. Due to the effect <strong>of</strong> the width <strong>of</strong> the single-particle states, the occupation probabilities for single-particle levels with zero widths are distributed over more levels. This effect partially destroys the difference between the <strong>diabaticity</strong> and a<strong>diabaticity</strong> at crossings (or pseudo-crossings) <strong>of</strong> the single-particle levels. We want to stress that the differences between the diabatic and adiabatic single-particle levels appear only near the crossing points. Moreover, the distribution <strong>of</strong> the diabatic occupation numbers n(ɛ k) and the derivatives f k approaches the ones obtained in the adiabatic case for fixed values <strong>of</strong> ε, λ and excitation energy <strong>of</strong> the system (Fig. 5-8). Since we showed the similarity <strong>of</strong> the data obtained with adiabatic and diabatic levels using the same width, we can use diabatic single particle states in further calculations <strong>of</strong> mass parameters in order to simplify the numerical procedure. The obtained mass parameter for the neck degree <strong>of</strong> freedom is much larger than the one obtained in the hydrodynamical model with the Werner-Wheeler approximation. By applying the microscopical mass parameters we find a relatively stable neck during the time <strong>of</strong> reaction. In addition, a large energy threshold due to the diabatic (structural) forbiddenness effect [35, 36] hinders the motion to smaller internuclear distances. Therefore, the DNS configuration exists long enough, and thermal fluctuations in the mass asymmetry coordinate could develop and lead to fusion and quasifission, which are the essential reactions in the DNS concept. 77
(10 3 m fm 2) M εε M (10 λλ 4 m fm2) 12 96 Zr + 96 Zr 8 4 6 4 2 0,5 0,6 0,7 ε 0,8 0,9 1,0 1,3 1,4 1,5 1,6 λ 110 Pd + 110 Pd 136 Xe + 136 Xe 48 Ca + 172 Hf 5-6: Upper part: Mεε as a function <strong>of</strong> the neck coordinate ε at the touching configuration Figure the reactions: for 96 + Zr 96 (solid line), Zr 110Pd+ 110 (dashed line), Pd 136 + Xe 136 (dotted Xe and line) 48 + Ca 172 (dashed-dotted line). The excitation energy <strong>of</strong> the DNS in these Hf is 30MeV . Lower part: The same as in the upper part, but for Mλλ as a function reactions the elongation λ. Diabatic single-particle states are used. Units: mfm <strong>of</strong> 2 m = nucleon with mass. 78
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
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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
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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: (10 3 m fm 2) M , M λλ εε 25 20
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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Effects of diabaticity on fusion of heavy nuclei in the dinuclear model ...

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