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

ϕ nz(z) =
⎧
⎪⎨
⎪⎩
C−1 z1 U (−nz1 − 1
2 ,− (z − z1 )) if z< 0
2kz1
C−1 z2 U (−n − z2 1
2 , z2 2k (z − z2)) z>0 if
⎫
⎪⎬
⎪⎭ , (A.11)
with normalization factors Cz1 and Cz2 . The quantum number nz assumes different values on
both sides <strong>of</strong> the origin, too. As the energy
=¯hω(nz + E 1
2 )+¯hωρ(2nρ+ lz | +1) (A.12)
|
should not depend on z, the values nz1 and nz2 are related by
+ ωz1(nz1 1
2 )=ωz2(nz2 + 1
). (A.13)
2
U(a, x) denotes a parabolic cylinder function [40]. The values <strong>of</strong> nz must be determined
numerically from assuring the continuity <strong>of</strong> the logarithmic derivative <strong>of</strong> (A.11) in z =0.
The Hamiltonian (A.1) can be split into several parts which are treated separately
H0 is the Hamiltonian <strong>of</strong> a two-center oscillator
and H1 is given by
H1 = f0
H = H0 + H1 + V LS + V L 2 . (A.14)
H0 = − ¯h2 ∇ 2
2m0
2 m0ω 2 z ′2 (cz ′
dz + ′2 )+ (f0 1) −
2
+ 1
2 m0ω 2 z ′2 + 1
m0ω 2 z ′2 + 1
m0ω
2
ρ
2 ρ2 (A.15)
,
2 m0
α 2 gz (1+ ′2 − ω ) 2
ρ 2 (A.16)
,
ωρ is an optimal value between ωρ = min(ωρ1,ωρ2) andωρ = where 1
2 (ωρ1 ωρ2). +
During the calculation <strong>of</strong> matrix elements it turns out to be advantageous to introduce
another quantum number
Nρ =2nρ+ | lz | (A.17)
114
ρ