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The triaxial deformation in $^{10}$Be is investigated using a microscopic $\alpha+\alpha+n+n$ model. The states of two valence neutrons are classified based on the molecular-orbit (MO) model, and the $\pi$-orbit is introduced about the axis connecting the two $\alpha$-clusters for the description of the rotational bands. There appear two rotational bands comprised mainly of $K^\pi = 0^+$ and $K^\pi = 2^+$, respectively, at low excitation energy, where the two valence neutrons occupy $K^\pi = 3/2^-$ or $K^\pi = 1/2^-$ orbits. The triaxiality and the $K$-mixing are discussed in connection to the molecular structure, particularly, to the spin-orbit splitting. The extent of the triaxial deformation is evaluated in terms of the electro-magnetic transition matrix elements (Davydov-Filippov model, Q-invariant model), and density distribution in the intrinsic frame. The obtained values turned out to be $\gamma = 15^o \sim 20^o$., Comment: 15 pages, latex, 3 figures

The molecule-like structure of the C isotopes (A=12, 14, 16) is investigated using a microscopic $\alpha+\alpha+\alpha+n+n+\cdot \cdot \cdot$ model. The valence neutrons are classified based on the molecular-orbit (MO) model, and both $\pi$-orbit and $\sigma$-orbit are introduced around three $\alpha$-clusters. The valence neutrons which occupy the $\pi$-orbit increase the binding energy and stabilize the linear-chain of 3$\alpha$ against the breathing-like break-up. However, $^{14}$C with the $\pi$-orbit does not show clear energy minimum against the bending-like path. The combination of the valence neutrons in the $\pi$- and the $\sigma$-orbit is promising to stabilize the linear-chain state against the breathing- and bending- modes, and it is found that the excited states of $^{16}$C with the $(3/2^-_\pi)^2(1/2^-_\sigma)^2$ configuration for the four valence neutrons is one of the most promising candidates for such structure., Comment: 9 pages, latex, 4 figures

The structure of the second 0^+ state of ^{10}Be is investigated using a microscopic $\alpha+\alpha+n+n$ model based on the molecular-orbit (MO) model. The second 0^+ state, which has dominantly the (1/2^+)^2 configuration, is shown to have a particularly enlarged $\alpha-\alpha$ structure. The kinetic energy of the two valence neutrons occupying along the $\alpha-\alpha$ axis is reduced remarkably due to the strong $\alpha$ clustering and, simultaneously, the spin-orbit interaction unexpectedly plays important role to make the energy of this state much lower. The mixing of states with different spin structure is shown to be important in negative-parity states. The experimentally observed small-level spacing between 1^- and 2^- (~ 300 keV) is found to be an evidence of this spin-mixing effect. ^{12}{Be} is also investigated using $\alpha+\alpha+4n$ model, in which four valence neutrons are considered to occupy the (3/2^-)^2(1/2^+)^2 configuration. The energy surface of ^{12}Be is shown to exhibit similar characteristics, that the remarkable $\alpha$ clustering and the contribution of the spin-orbit interaction make the binding of the state with (3/2^-)^2(1/2^+)^2 configuration properly stronger in comparison with the closed p-shell (3/2^-)^2(1/2^-)^2 configuration., Comment: 14 pages, 4 figures