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

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a behaviour correlates with the diabatic contributions to the potential energy [35]. The Such arise from the factor fluctuations ˜ k /Γ f 2 in Eq. (5.32) and are related to the increasing number k <strong>of</strong> crossings between the single particle levels near the Fermi level with decreasing λ [35]. The choice <strong>of</strong> the width <strong>of</strong> the single particle levels is crucial for the value <strong>of</strong> M diag in the diabatic and adiabatic cases within a reasonable variation. If instead <strong>of</strong> Γ both −1 0 =0.045 MeV−1 the value <strong>of</strong> Γ , −1 is taken as 0.03 MeV 0 −1 the lower limit , the value <strong>of</strong> Mεε becomes at times smaller, but remains larger than M 2.25 WW εε about one order <strong>of</strong> magnitude. For larger by the average width Γ increases and the function temperatures, ˜ k /Γ f 2 k becomes smoother. The mass parameter M εε depends on temperature T0 mainly due to the width Γ k <strong>of</strong> the single- levels ( Γk ∼ T particle 2 0 ). The value <strong>of</strong> M decreases with T εε −4 . One- and two-body inter- 0 actions [96] contribute to the nondiagonal and diagonal parts <strong>of</strong> the mass parameter, respec- tively. Whereas the one-body contribution to mass (nondiagonal part) is relatively insensitive to the temperature <strong>of</strong> the system, the two-body contribution to mass (diagonal part) increases strongly with decreasing temperature. The two-body interaction is considered in our calcu- lations using the width <strong>of</strong> the single-particle levels [86]. So, we can observe in Fig. 5-7 that M diag εε =1MeV )/M (T0 diag(T0 =1.5MeV) ∼ 5 on average for the values <strong>of</strong> ε =0.5− εε . We 1 that the contribution <strong>of</strong> the diagonal part M found diag to Mεε is the largest at quite a high εε excitation energy <strong>of</strong> 30MeV (T0 =1.3MeV ) <strong>of</strong> the DNS in fusion reactions. For comparison, the excitation energies <strong>of</strong> the initial DNS are smaller than 20MeV (T0 < 1.0MeV )inPb− and Bi− based cold fusion reactions. Hot fusion reactions <strong>of</strong> heavy nuclei have excitation energies <strong>of</strong> the initial DNS smaller than 40MeV (T0 =1.5MeV ) and a rapid decrease <strong>of</strong> the survival probability <strong>of</strong> the compound nucleus with increasing excitation energy. Finally, we should stress that the mass parameter M εε remains always much larger (e.g., 20−30 times for T0 =1.3MeV) in fusion reactions than the mass calculated with the hydrodynamical Werner-Wheeler approx- imation for T0 =1− 1.5MeV. The mass parameters at the touching configuration <strong>of</strong> the nuclei are the same in the adiabatic and diabatic descriptions because the single particle levels and occupation numbers are practically the same in these two limits. It is known that the mass parameters are smaller in the diabatic case for a zero width <strong>of</strong> single particle levels than in the adiabatic case [57]. We found values for the mass parameters M λλ and M εε within the diabatic TCSM which are closer 75
(10 3 m fm 2) M , M λλ εε 25 20 15 10 5 0 0,0 30 0,1 0,2 0,3 η 0,4 0,5 0,6 25 20 15 10 5 0 0,9 1,0 1,1 1,2 1,3 1,4 5-5: Upper part: Mass parameters Mλλ (solid line) and Mεε (dotted line) as functions Figure mass asymmetry η at the touching configuration for DNS which leads to the same compound <strong>of</strong> nucleus 220 The value <strong>of</strong> the neck coordinate is ε =0.75, and the excitation energy <strong>of</strong> the U. is 30MeV. The calculation is done with spherical nuclei. Lower part: The same as in the DNS part, but as a function <strong>of</strong> deformation β for the reaction upper 110Pd+ 110 (η = 0). Diabatic Pd states are used. Units: mfm single-particle 2 m = nucleon mass. with 76 β
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 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: the approximate expressions (Eqs. (
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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