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

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with χ(0) and C(0) being the static intrinsic response and stiffness, respectively. Since the constant k is entirely determined by quasi-static properties, it is no surprise that E is the internal energy at a given entropy S0 or the free energy at a given temperature T0. The structure <strong>of</strong> Eq.(B.2) reflects self—consistency between the treatment <strong>of</strong> collective and microscopic dynamics. It expresses the response <strong>of</strong> the system <strong>of</strong> interacting nucleons in terms <strong>of</strong> the response <strong>of</strong> the individual nucleons. In the local harmonic approximation [86], the inverse <strong>of</strong> the collective response function χ −1 (ω) is considered as the inverse <strong>of</strong> the damped oscillator response function χ−1 osc (ω) which coll is expressed as χ −1 osc (ω) =C F iγ − F − M ω F ω 2 (B.5) , where C F , γ F and M F are related to the derivative <strong>of</strong> the effective collective potential, calculated in linearized form, to a friction force and to an inertial one, respectively. The associated ”transport coefficients” have been marked by a superscript F to indicate that they are associated with the quantity δ< ˆ F >. The transport coefficients T¸= M,γ,C <strong>of</strong> the Q-mode are related to the transport coefficients T¸ F = M F ,γ F ,C F <strong>of</strong> the δ< ˆ F >-mode by the relation T¸ F k = 2 [86]. An expression like (B.5) may be obtained by expanding χ T¸ −1 (ω) (B.2) to second coll order in ω. In this way one gets C ≈ γ ≈ 1 1 k 2 χ coll (ω) k 2 M ≈ 1 2k 2 ∂χ −1 coll (ω) | ω=0, ∂ω ∂2χ −1 coll (ω) 117 ∂ω 2 |ω=0, (B.6) |ω=0 .
[1] S.G.Nilsson et al., Phys. Lett. B28 (1969) 458; Nucl. Phys. A 131 (1969) 1. [2] U.Mosel and W. Greiner, Z. Phys. 217 (1968) 256; 222 (1968) 261. [3] K.Rutz et al., Phys. Rev. C 56 (1997) 238. [4] P.Armbruster, Ann. Rev. Nucl. Part. Sci. 35 (1985) 135; IL Nuovo Cim. A110 (1997) 1111. [5] Yu.Ts.Oganessian et al., Nucl. Phys. A 239 (1975) 353. [6] R.K.Gupta, C.Parvulescu and A.Sandulescu, Z. Phys. A 283 (1977) 217; Z. Naturforsch. 32a (1977) 704. [7] S.H<strong>of</strong>mann et al., Z. Phys. A 350 (1995) 277; A 350 (1995) 281; A 354 (1996) 229; S.H<strong>of</strong>mann, Rep. Prog. Phys. 61(1998) 639. [8] G.Münzenberg, Rep. Prog. Phys. 51(1988) 57. [9] S.H<strong>of</strong>mann and G.Münzenberg, Rev. Mod. Phys. (to be published). [10] V.Ninov et al, Phys. Rev. Lett. 83 (1999) 1104. [11] M.G.Itkis et al, in Second Int. Conf. on Fission, St. Andrews, June 28-July 2, 1999. [12] Yu.Ts.Oganessian et al., Eur. Phys. J.A5(1999)63;Nature400(1999)242;A.V.Yeremin, V.K.Utyonkov and Yu.Ts.Oganessian, in Proc.Tours Symposium on Nuclear Physics III, Tours, 1997, eds. M. Arnould et al. (AIP,New York, 1998) p.16. [13] G.Münzenberg et al, in MAFF Collaboration-Meeting, München-November 27, 1998. 118
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Effects of
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1 Introduction 6 1.1 The DNS-concep
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Chapter 1 The elements existing in
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observed the rapid fall-of<
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Figure 1-1 illustrates the compound
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smaller than the extra-extra push e
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fusion and quasi-fission processes
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In the present chapter we have pres
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higher collective velocities to rep
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2.1 General considerations We want
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couplings. Diabatic basis states ψ
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Chapter 3 The synthesis of<
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is calculated within the TCSM using
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E adiab (MeV) n E diab (MeV) n 30 2
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E diab (MeV) n 60 55 50 45 40 100Mo
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3-5: Diabatic potentials for the sy
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3-7: The same as in Fig. 3-6 for th
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The estimated collective velocities
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3-10: Diabatic contributions as a f
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effects give a justification for th
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The similarity of
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4.1.3 Alternative microscopical met
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to the DNS concept [18, 34], cross
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U (MeV) 28 27 26 25 24 23 22 21 20
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U (MeV) 35 30 25 20 15 10 90Zr + 12
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4-1: Fusion barriers B Table TCSM
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U (MeV) 40 30 20 10 20 10 0 a) b) 9
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experimental separation energy allo
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means a neglect of
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the case of an ind
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single particle density matrix exte
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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: Appendix B The collective response
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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