content_image/388842.jpg content_image/388843.jpg content_image/388844.jpg content_image/388845.jpg content_image/388848.jpg content_image/388849.jpg content_image/388846.jpg content_image/388847.jpg content_image/388850.jpg content_image/388851.jpg content_image/388852.jpg content_image/388853.jpg content_image/388868.jpg
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 

<img src='content_image/388842.jpg'>

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, 

<img src='content_image/388843.jpg'>

From the geometry displayed in Fig. 1, it is possible to deduce the following relations between angles, 

<img src='content_image/388844.jpg'>

<img src='content_image/388845.jpg'>

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 

<img src='content_image/388848.jpg'>

where θ 1 and θ 2 are given by Eq. (8) and Eq. (9), re- spectively with 

<img src='content_image/388849.jpg'>

<img src='content_image/388846.jpg'>

<img src='content_image/388847.jpg'>

<img src='content_image/388850.jpg'>

<img src='content_image/388851.jpg'>

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, 

<img src='content_image/388852.jpg'>

<img src='content_image/388853.jpg'>

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 

<img src='content_image/388868.jpg'>

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 

