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

imation). In the second order term the ”nucleonic” part appears only as an average <strong>of</strong> the
corresponding operator. Consistently with the harmonic approximation, this average is to be
built with that density operator for the nucleons ρ qs(Q0) which in the quasi-static picture is to
be calculated with the Hamiltonian at Q0, namely, ˆ H(x i,p i,Q0). The operator ρ qs(Q0) isthe
canonical distribution for the temperature T0. The coupling term between the collective and
intrinsic motion is proportional to the first order in δQ = Q − Q0 with an operator ˆ F given by
the derivative <strong>of</strong> the mean field with respect to Q in the neighborhood <strong>of</strong> Q0.
The local motion in the Q variable can be described in terms <strong>of</strong> the so-called collective
response function χ coll(ω) [86] (see Appendix). In the linear response theory [86], the mass
coefficient for a slow collective motion can be expressed as [86, 87, 92, 93]
where
= M(Q) 1
2k2 ∂2 coll(ω)) (χ −1
∂ω2 =(1+ |ω=0 C(0)
χ(0) )2 [M cr + γ2 (0)
M cr = 1
2
∂2χ(ω) ∂ω2 |ω=0 = 1
2
∂2χ ′
(ω)
∂ω 2
|ω=0
], (5.2)
χ(0)
is the inertia in the zero-frequency limit <strong>of</strong> the second derivative <strong>of</strong> the intrinsic response
function. M cr can be shown to be similar to the one <strong>of</strong> the cranking model [86]. Here a
response function χ(ω) for ”intrinsic” motion appears and measures how, at some given Q0
temperature T0, the nucleonic degrees <strong>of</strong> freedom react to the coupling term ˆ FδQ. The
and
response function χ(ω) =χ intrinsic ′(ω) +iχ ′′
(5.3)
(ω) is written in terms <strong>of</strong> the reactive χ ′(ω)
dissipative χ and ′′
parts [86]. χ(0) and C(0) are the zero-frequency limit <strong>of</strong> the intrinsic
(ω)
response function and stiffness, respectively (see Appendix). For many applications, the value
<strong>of</strong> C(0)/χ(0) ≪ 1. The additional term γ 2 (0)/χ(0) in Eq. (5.2) gives a positive contribution to
M where γ(0) is the friction coefficient defined as [86]
= −i γ(0) ∂χ(ω)
∂ω |ω=0 = ∂χ′′ (ω)
∂ω |ω=0 = 1
2T0 ψ′′
(5.4)
(0).
dissipative part <strong>of</strong> the intrinsic response function χ The ′′
is connected with the dissipative
(ω)
<strong>of</strong> the correlation function ψ part ′′
through the fluctuation-dissipation theorem [86]
(ω)
χ ′′
= (ω) 1
¯h
¯hω
tanh(
2T0 )ψ′′
(5.5)
(ω).
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