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

couplings. Diabatic basis states ψ dynamical diab ≡ φα are defined [57] by the condition that
α
the first-order dynamical coupling (2.9) vanishes. Introducing the decomposition W = n
wn(x, q), it is obtained [57]
−(∂/∂qn) | φα >= 1
2 [∆,wn] | φα >=
as the <strong>diabaticity</strong> criterion which is independent <strong>of</strong>
·∇+ (∇wn) 1
2 (∆wn)
·
q n
| φα > (2.12)
·
n and hence allows to define stationary
q
diabatic basis states. The relation (2.12) ascribes the change <strong>of</strong> any diabatic state with q n to a
collective displacement field ∇w n which scales all wave functions in the same way.
The <strong>diabaticity</strong> criterion (2.12) does not rigorously determine a diabatic representation
because the velocity field is not uniquely defined. Therefore, the following condition
0 (2.13)
is added. This condition is appropriate whenever the collective velocities are sufficiently smaller
than the Fermi velocity. The supplementary condition (2.13) then suggests to construct the di-
abatic basis states from adiabatic states by avoiding the dramatic changes <strong>of</strong> the wave functions
near pseudo-crossings.
2.2 Construction methods
In atomic physics, a large variety <strong>of</strong> construction methods for diabatic representations have
been considered [55, 61]. Within the TCSM, two methods for the construction <strong>of</strong> diabatic
states were developed [57] for central nucleus-nucleus collisions. The method <strong>of</strong> maximum
overlap is based on the construction <strong>of</strong> crossings <strong>of</strong> diabatic levels where pseudo-crossings occur
in the adiabatic TCSM. The construction <strong>of</strong> the diabatic states as a function <strong>of</strong> the relative
distance starts from the separated nuclei where adiabatic and diabatic states coincide. A
diabatic state at a smaller relative distance is obtained from a linear combination <strong>of</strong> a few
adiabatic states which maximizes the overlap with a diabatic state at somewhat larger relative
distance. Using the so constructed states, one is able to obtain step by step the diabatic states
for smaller relative distances. The method <strong>of</strong> maximum symmetry eliminates the symmetry-
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