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

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
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