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

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the mass (5.26) as M cr = ¯h2 Γ 2 4π 2 α=β,k1,k2 |Fk1k2 |2 [ɛ 2 αk1 +(Γ/2)2 ][ɛ 2 βk2 +(Γ/2)2 ] n(ɛk1 − n(ɛk2 ) ) (5.30) . ɛk2 − ɛk1 The energy spreading <strong>of</strong> the single particle states is taken into account in Eq.(5.30). A line broadening happens if collisions <strong>of</strong> particles and holes with the background result in single particle and single hole strength functions that are concentrated around the original single particle energies. The quantity Dρk determines the average strength function for a particle in state k [101]. In the limit ɛk1 = ɛk2 = ɛk, for ɛα ≈ ɛk and ɛβ ≈ ɛα, i.e. when two neighboring levels near the level k are considered, and 8/π 2 ≈ 1, Eq.(5.30) leads to Eq.(5.15). Thus, diagonal terms in the mass parameters appear because <strong>of</strong> the finite width <strong>of</strong> the single particle levels due to the residual interaction. 5.2 Results <strong>of</strong> the calculations 5.2.1 The adiabatic two-center shell model Since collisions above the Coulomb barrier are discussed, we firstly consider spherical nuclei with βi = 1and then analyse the deformation effects. In order to calculate the width <strong>of</strong> the single particle states, we use the expression [86, 102] = Γk 1 Γ0 (ɛk − ɛ F ) 2 +(πT0) 2 1+[(ɛ k − ɛ F ) 2 +(πT0) 2 ]/c 2 . (5.31) Here, ɛ F is the Fermi energy. Both parameters Γ0 and c are known from experience with the optical model potential and the effective masses [86]. Their values are in the following ranges: 0.030 MeV −1 ≤ Γ0 −1 ≤ 0.061MeV −1 , 15 MeV≤ c ≤ 30 MeV. The quadratic dependence <strong>of</strong> the numerator can be obtained from the collision term in the Landau theory <strong>of</strong> Fermi liquid [103] and has been also verified within a microscopic approach based on an effective interaction <strong>of</strong> Skyrme type [104]. Since each single particle state has its own width, Eq. (5.15) is generalised as (Q i = λ, η, η Z,ε,β1,β2): M diag ij =¯h2 k 65 k f Γ2 ∂ɛ k ∂Qi k ∂ɛ k ∂Q j . (5.32)
5-1: Dependence <strong>of</strong> the mass parameter Mεε (lower part) and <strong>of</strong> the shell correction Figure (upper part) on ε for the system δU 110 + Pd 110 at λ =1.6. In the calculation <strong>of</strong> Mεε, an Pd energy <strong>of</strong> 30MeV <strong>of</strong> the DNS and adiabatic single-particle states are used. The mass excitation in the Werner-Wheeler approximation is presented by a dashed calculated M parameter WW εε line in the lower part. Units: mfm 2 with m = nucleon mass. 66
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: following ratio in the limit <stron
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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