ρ$_{i}$ ( ⃗ r$_{i}$, Ω$_{i}$ , α$_{iλ}$ ) ≡ ρ$_{i}$ ( r$_{i}$, θ ′ $_{i}$, α$_{iλ}$ ) = ρ 0 i 1 + exp [( r$_{i}$ − R$_{i}$ ( θ ′ $_{i}$, α$_{iλ}$ )) /a$_{i}$ ] , (6) R$_{i}$ ( θ ′ $_{i}$, α$_{iλ}$ ) = R 0 i ( 1 + ∑ λ α$_{iλ}$Y$_{λ}$ 0 ( θ ′ $_{i}$) ) = R 0 i ( 1 + ∑ λ α$_{iλ}$ √ 2 λ + 1 π P$_{λ}$ (cos θ ′ $_{i}$) ) . (7) cos θ ′ 1 = cos Ω 1 cos θ 1 − sin Ω 1 sin θ 1 sin φ 1 , (8) cos θ ′ 2 = cos Ω 2 (cos Ω 3 cos θ 2 − sin Ω 3 sin θ 2 cos φ 2 ) − sin Ω 2 sin θ 2 sin φ 2 . (9) ∫ ρ$_{i}$ ( ⃗ r$_{i}$, Ω$_{i}$ , α$_{iλ}$ ) d $^{3}$r$_{i}$ = A$_{i}$, (10) V$_{NN}$ ( ⃗ r ) = V 0 δ ( ⃗ r ) , (11) V$_{N}$ ( R, Ω , α$_{iλ}$ ) = V 0 ∫ ρ 1 ( r 1 , θ ′ $_{1}$, α 1 $_{λ}$) ρ 2 ( r 2 , θ ′ $_{2}$, α 2 $_{λ}$) r 2 $_{1}$dr 1 d (cos θ 1 ) dφ 1 , (12) cos θ 2 = ( r 1 cos θ 1 − R ) /r 2 , (13) r 2 = √ r 2 1 + R 2 − 2 r 1 R cos θ 1 , (14) φ 2 = φ 1 . (15) ρ$_{i}$ ( ⃗ r$_{i}$, Ω$_{i}$ , α$_{iλ}$ ) ≈ ρ$_{i}$ ( ⃗ r$_{i}$, Ω$_{i}$ , 0) + ∑ λ α$_{iλ}$ [ ∂ ∂α$_{iλ}$ ρ$_{i}$ ( ⃗ r$_{i}$, Ω$_{i}$ , α$_{iλ}$ ) | ∀ α =0 ] , (16) V$_{N}$ ( R, Ω , α$_{iλ}$ ) ≈ V$_{N}$ ( R, Ω , 0) + ∑ i,λ α$_{iλ}$ [ ∂ ∂α$_{iλ}$ V$_{N}$ ( R, Ω , α$_{iλ}$ ) | ∀ α =0 ] , (17) and in order to cover all possible orientation configura- tions, one more angle Ω 3 , is needed to rotate the oscilla- tion axis of one of the nuclei about the corresponding y or z axis to account for the off-plane orientations. For con- venience, a rotation about the y axis is considered. The Ω 3 rotation is not indicated in the figure. We approxi- mate the nuclear density distributions by two-parameter Fermi functions, which can be conveniently expressed in terms of the angles θ ′ 1 and θ ′ 2 as where ρ 0 i is a normalization constant, a$_{i}$ is the diffuseness parameter and R$_{i}$ ( θ ′ $_{i}$, α$_{iλ}$ ) denotes the deformed nuclear radius of each nucleus. For small amplitude vibrations, this quantity is expanded in terms of spherical harmonics, The normalization constants ρ 0 i in Eq. (6) are obtained from the equation, where A$_{i}$ is the mass number of the i th nucleus. For the equivalent sharp radii of the spherical nuclei, we take the values given by R 0 i = 1 . 31 A 1 / 3 i − 0 . 84 fm. A global description of the nucleus-nucleus potential can be achieved via the folding potential Eq. (5) by con- sidering a zero-range nucleon-nucleon interaction, which is equivalent to a finite-range nucleon-nucleon in- teraction [25–28]. Then, the nuclear potential Eq. (5) becomes where θ ′ 1 and θ ′ 2 are given by Eq. (8) and Eq. (9), re- spectively with to as the ZZ configuration. The other orientation cor- responds to the case when vibrations are perpendicular to the direction of the relative motion indicated by red FIG. 2: (color online) The s-wave potential barriers of $^{64}$Ni + $^{64}$Ni system are plotted versus center to center distance for different quadrupole deformations and orientations. The blue curves represent the oblate (upper curve) and prolate (lower curve) deformations along the relative motion. The red curves stand for the prolate (upper curve) and oblate (lower curve) deformations that are perpendicular to the rel- ative motion direction. The bare potential with no defor- mation is indicated by the black color. The potentials are computed by summing the Coulomb V$_{C}$ and nuclear V$_{N}$ con- tributions with deformation variables equal to their variances, | α 12 | = | α 22 | = β 2 = 0 . 215. The zero-range potential strength in Eq. (11) is taken as V 0 = − 456 MeVfm 3 [25]. respectively. Fig. 2 shows examples of potential energies in head-on collisions of two $^{64}$Ni nuclei for different orientations and deformations as a function of the relative distance. In this figure, for simplicity, only the quadrupole vibrations of both nuclei in two different orientations are shown. One of them corresponds to the case when vibrations are along the direction of the relative motion indicated by blue curves. In the following, this orientation is referred From the geometry displayed in Fig. 1, it is possible to deduce the following relations between angles, In order to simplify the numerical simulations, a further approximation is introduced. For small amplitude vibra- tions, Taylor expansions of the nuclear densities and the nuclear potential are introduced to the first order around α$_{iλ}$ = 0 to give, 3  70  80  90  100  110  120  130  9  10  11  12  13  14 Potential (MeV) R (fm)