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

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explicitly assumed in the DNS model [34], which describes the experimental fusion data quite well. The nuclei in the DNS could be hindered to melt together in R due to diabatic effects or due to a specific behaviour <strong>of</strong> the mass parameters. In this chapter we study the diabatic potentials for heavy nuclear systems as a function <strong>of</strong> the elongation λ, the neck coordinate ε and the mass asymmetric η using the method <strong>of</strong> maximum symmetry within the generalized TCSM [35]. In the previous calculations [57] a simplified version <strong>of</strong> the TCSM was used and the role <strong>of</strong> the neck coordinate was not taken into account. We will compare our results with nucleus-nucleus potentials obtained by using a double folding procedure for the nuclear interaction. The calculations are performed for the symmetric systems 90 Zr+ 90 Zr, 96 Zr+ 96 Zr, 100 Mo+ 100 Mo, 110 Pd+ 110 Pd, 130 Xe+ 130 Xe and 136 Xe+ 136 Xe. The asymmetric systems 110 Pd+ 136 Xe, 86 Kr + 160 Gd and 48 Ca+ 198 Hg are also studied. The applicability <strong>of</strong> the diabatic method will be discussed for collisions near the Coulomb barrier. 3.1 The diabatic potential In a diabatic description the nucleons do not occupy the lowest free single-particle levels as in the adiabatic case, but remain in the diabatic levels during the collective motion <strong>of</strong> the nuclear system. As a result, the diabatic potential energy surface is raised with respect to the adiabatic potential energy surface and new potential barriers for collective variables may appear. The values <strong>of</strong> these barriers can be also estimated by calculations <strong>of</strong> the structural forbiddenness <strong>of</strong> fusion [36]. The concept <strong>of</strong> structural forbiddenness is based on the difference created by action <strong>of</strong> the Pauli principle between the state <strong>of</strong> the compound nucleus and the state <strong>of</strong> the separated heavy nuclei [63]. The total diabatic potential is defined as V diab(q) =V adiab(q)+∆V diab(q), (3.1) where the set <strong>of</strong> collective coordinates <strong>of</strong> the system is denoted by q. The adiabatic potential energy =ELDM + VN + δEshell + δEpair − E Vadiab(q) CN LDM 25 (3.2)
is calculated within the TCSM using the liquid drop energy ELDM, the Strutinsky prescription for the shell correction δE shell, pairing correction δEpair and the proximity nuclear potential VN to improve the adiabatic energy for large elongations [42]. The adiabatic potential energy normalised to the liquid drop energy E is CN LDM The diabatic contribution ∆V diab is expressed as ∆V diab(q) = α = α ≈ α ɛ diab (q)n α diab − α α ɛ diab α (q)(ndiab α <strong>of</strong> the spherical compound nucleus. ɛ adiab α (q)n adiab α n − adiab(q)) + α α (q) n adiab α (q)(ɛ diab α α (q) − ɛadiab (q)) ɛ diab α (q)(ndiab − n α adiab(q)), (3.3) α where the contribution from the second term with (ɛ diab (q)−ɛ α adiab α (q)) is assumed to be negligible because the adiabatic and diabatic single-particle levels differ only in the area <strong>of</strong> the pseudo- <strong>of</strong> adiabatic states [57]. The diabatic occupation probabilities n crossings diab α are determined the configuration <strong>of</strong> the separated nuclei. The adiabatic occupation probabilities n by adiab α with q according to the ground-state configuration where only the lowest levels are occupied. diabatic levels ɛ The diab are classified by the quantum numbers α = jz,lz,sz,nρ,nz <strong>of</strong> the α eigenstates <strong>of</strong> the diabatic Hamiltonian. We only used the diagonal elements <strong>of</strong> the symmetry- violating parts <strong>of</strong> the generalized TCSM Hamiltonian. Non-diagonal elements arise only from the spin-orbit potential V LS (A.3), the centrifugal potential V L 2 (A.4) and the neck potential H1 (A.16). The first two potentials contain l x, l y, s x and s y. The diabatic Hamiltonian is expressed as vary d = H0 + Vlz sz H + Vl 2 + H, (3.4) z where H0 is the Hamiltonian <strong>of</strong> a two-center oscillator (A.15). The influence <strong>of</strong> the neck parameter ε is taken into account by means <strong>of</strong> the diagonal contribution <strong>of</strong> the difference H ≡ H1(ε) − H1(ε =1)= (ε − 1) 2 2 z m0ω z ′2 cz (1+ ′ dz + ′2 (3.5) ), where the coefficients c and d are determined by requiring that the potential and its derivative 26
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: Chapter 3 The synthesis of<
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
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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