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

n(ɛ) anddn(ɛ)/dɛ calculated with zero width <strong>of</strong> the levels
n(ɛ k)=
n(ɛ)ρk(ɛ)dɛ, (5.34)
k = − f dn(ɛ)
ρk(ɛ)dɛ. (5.35)
dɛ
The Lorentzian distribution increases the diffuseness <strong>of</strong> the Fermi-distribution. The Fermi
distribution which is given at the touching configuration <strong>of</strong> the nuclei in the DNS is destroyed
if the further motion <strong>of</strong> the system runs diabatically. To treat the diabatic case, we use the
following function n(ɛ) for an arbitrary configuration <strong>of</strong> the system
n(ɛ) =
N
l=0
a l (ϑ(ɛ − ɛ l) − ϑ(ɛ − ɛ l+1)) , (5.36)
where ϑ(x) is the Heavyside’s function and ɛ l the energy <strong>of</strong> single particle state l with the
occupation number a l. Here, the numbers l =0,...,N count the single particle states in the
region <strong>of</strong> the Fermi level. The values ɛ0 and ɛ N+1 are the low and high limits <strong>of</strong> the single
particle energies. For lower and higher energies, the occupation numbers are one and zero,
respectively. Therefore, we assume a0 = 1and a N = 0 in (5.36). The derivative dn(ɛ)/dɛ is
expressed as
− dn(ɛ)
dɛ =(1−a1)δ(ɛ ɛ1)+ −
N−1
then obtain
fk with (5.35) as follows
We
k =(1−a1)ρk(ɛ1)+ f N−1
(al−1 − al)δ(ɛ − ɛl)+aN−1δ(ɛ − ɛN ). (5.37)
l=2
l=2
(a l−1 − a l)ρ k(ɛ l)+a N −1ρ k(ɛ N ). (5.38)
In the calculations we assume the same average width for each Lorentzian ρ k(ɛ). The diabatic
occupation numbers a l are fixed at the touching configuration <strong>of</strong> the system using a Fermi
for a smaller temperature T distribution ∗
0 < T0. value <strong>of</strong> T The ∗
0
is chosen in such a way
that the occupation numbers n(ɛ k) (5.34) and the values <strong>of</strong> f k (5.35) obtained at the touching
configuration <strong>of</strong> the nuclei, using either the exact expresions (Fermi distribution and (5.33)) or
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