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

4.1.3 Alternative microscopical method
Since the isotopic composition <strong>of</strong> the nuclei forming the DNS is chosen with the condition <strong>of</strong>
the N/Z-equilibrium in the system, mass and charge evolutions (neutrons and protons transfer)
are related to each other. The charge number Z <strong>of</strong> the light fragment is used instead <strong>of</strong> the
charge asymmetry η Z. The potential is obtained by an iteration procedure [33, 73]
(Z +1)= Ũ (Z) +T · ln
Ũ
the microscopic transport coefficients ∆ where (±)
[74] Z
∆ (+)
= Z 1
∆t
α,β
| gαβ (R) | 2
∆ (−)
Z = 1 |
gαβ (R) |
∆t
α,β
2 n Z − n α(T )(1 Z
⎛
⎝∆(−) Z+1
∆ (+)
Z
n Z
(T )(1 − nZα
β (T )) sin2 [∆t(˜ɛ Z − ˜ɛ α Z
β (T)) sin2 [∆t(˜ɛ Z
⎞
, (4.2)
⎠
(˜ɛ Z − ˜ɛ α Z
β )2 /4
β )/2¯h]
− ˜ɛ α Z
β )/2¯h]
(˜ɛ Z − ˜ɛ α Z
β )2 /4
, (4.3)
characterise the rate <strong>of</strong> probability <strong>of</strong> the proton transfer from a heavy to a light nucleus
(∆ (+)
Z
or in the opposite direction (∆(−) Z ). The DNS temperature T is calculated using the
)
Fermi-gas expression T = E ∗ /a with the excitation energy E ∗ <strong>of</strong> the DNS and with level-
density parameter a = Atot/12 MeV −1 , where A tot is the total mass number <strong>of</strong> the system. In
the expression (4.3), ”α” and”β” are the quantum numbers characterising the single-particle
states in light and heavy nuclei respectively, n α(T) (n β(T )) are the temperature-dependent
occupation numbers <strong>of</strong> the single-particle states in a light (heavy) nucleus, g αβ are the matrix
elements for the nucleon transition from nucleus to nucleus because <strong>of</strong> the action <strong>of</strong> the mean
fields <strong>of</strong> the reaction partners [33, 73]. The time interval ∆t =1.5 × 10 −22 s must be larger
than the relaxation time <strong>of</strong> the mean field but considerably smaller than the characteristic
evolution time <strong>of</strong> the macroscopic quantities. The mutual influence <strong>of</strong> the mean fields <strong>of</strong> the
reaction partners leads to the renormalisation <strong>of</strong> the single-particle energies ˜ɛα(β) <strong>of</strong> the nuclei
[33, 73]. Peculiarities <strong>of</strong> the structure <strong>of</strong> interacting nuclei are explicitly taken into account in
the transport coefficients (4.3), which are calculated using realistic schemes <strong>of</strong> single particle
levels. For the single-particle spectrum, the spectrum for a spherically symmetric Woods-
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