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

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Figure 1-2: Two ways <strong>of</strong> evolution <strong>of</strong> the DNS to quasi-fission and fusion. Within this model the evaporation residue cross-section can be written as Jmax = σER(Ec.m.) J=0 σc(Ec.m.,J) · PCN(Ec.m.,J) · Wsur(Ec.m.,J). (1.1) The capture cross-section σc describes the transition <strong>of</strong> the colliding nuclei over the Coulomb barrier and the formation <strong>of</strong> the DNS when the kinetic energy is transformed into the excitation energy <strong>of</strong> the DNS. This initial stage <strong>of</strong> a collision was recently studied with a dynamical model [38]. Calculations were performed for 48 Ca + 244 Pu and 74,76 Ge + 208 Pb reactions which could lead to the formation <strong>of</strong> the superheavy element Z=114. It was shown that for the considered reactions, there is an energy window for the bombarding energy Ec.m. at which the capture cross-section σc is large enough to have a physical interest. The value <strong>of</strong> J max corresponds to Ec.m. and is larger than the limit <strong>of</strong> the value <strong>of</strong> J for the compound nucleus formation. The probability <strong>of</strong> complete fusion PCN depends on the competition between the complete 13
fusion and quasi-fission processes after the capture stage in the DNS. In these reactions the quasi-fission channel dominates and leads to a strong reduction <strong>of</strong> the magnitude <strong>of</strong> the fusion cross-section. The surviving probability Wsur estimates the competition between fission and neutron evaporation in the excited compound nucleus and may be calculated according to the statistical model [39] on the basis <strong>of</strong> the Monte Carlo method. 1.2 Goals <strong>of</strong> the present work The basic microscopical model for the dinuclear system is the two-center shell model (TCSM) [40] (see Appendix). The usual parametrisation <strong>of</strong> the two-center potential consists <strong>of</strong> the relative distance between the centers (or elongation), the mass (charge) asymmetry η =(A1 − A2)/(A1 + A2), the deformations <strong>of</strong> the fragments β i and the neck coordinate ε. The elongation λ = l/(2R0) measures the length l <strong>of</strong> the system in units <strong>of</strong> the diameter 2R0 <strong>of</strong> the spherical compound nucleus. This variable can be used to describe the relative motion. The mass ratio between the fragments and the transition <strong>of</strong> the nucleons through the neck are described by the mass asymmetry η. The neck parameter ε = E0/E ′ is defined by the ratio <strong>of</strong> the actual barrier height E0 to the barrier height E ′ <strong>of</strong> the two-center oscillator. The deformations β i = a i/b i <strong>of</strong> axial symmetric fragments are defined by the ratio <strong>of</strong> their semiaxes. The neck grows with decreasing ε (Fig.1-3). The potential energy surface (PES) in these coordinates is generally calculated with the Strutinsky method [41]. This is an adiabatic approach since the nucleons occupy the single particle states up to the Fermi level in calculating the shell corrections. The adiabatic potential energy surfaces calculated as functions <strong>of</strong> the elongation <strong>of</strong> the DNS and <strong>of</strong> the neck parameter were used to study classical trajectories for various heavy ion reactions by using dissipative forces and mass parameters obtained with the Werner-Wheeler aproximation [42]. The fusion probabilities in the adiabatic TCSM are much larger than those obtained from experimental data and show an incorrect isotopic dependence. The reactions considered were for example the symmetric ones 90 Zr+ 90 Zr, 100 Mo+ 100 Mo, 110 Pd+ 110 Pd, 124 Sn+ 124 Sn and 136 Xe+ 136 Xe and asymmetric ones. Therefore, it is concluded that a hindrance exists which prohibits the fast growth <strong>of</strong> the neck and the motion to smaller elongations and allows the DNS to survive a time comparable with the reaction time. 14
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: smaller than the extra-extra push e
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 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
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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.
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[27] N.V.Antonenko et al., in 1 st
Page 121 and 122:
[63] Yu.F.Smirnov and Yu.M.Tchuvil
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[97] H. Hofmann et
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