The linear chain structure of α clusters has been a long dream of
nuclear structure physics. The stabilization is essentially difficult, and some extra
mechanisms are needed to be introduced. One of the candidates is the increase
of the isospin, which means adding valence neutrons. Even if the linear-chain
configurations are difficult to be stabilized in the N = Z nuclei, it is considered
that higher stability may be possible if we move on to the neutron rich side.
It has been discussed mainly in the two α cluster cases that when the neutrons
occupy the so-called σ orbit, which is parallel to the symmetry axis, an elongated
shape is favored for the lowering of the energy of the valence neutron. This effect
is further examined in the C isotopes, where three α clusters are located with a
linear shape, and valence neutrons are added to these three α clusters. Another
possible mechanism is the increase of the angular momentum by rotating the
nucleus rapidly: the linear chain configuration with large moment of inertia is
favored when the centrifugal force strongly acts. This effect is examined in 16O
(four α linear chain) and 24Mg (six α linear chain). Finally, the appearance of
rod shape in C isotopes is investigated in the framework of the cranking covariant
density functional theory, and coherent effect of these two mechanisms, adding
neutron (high isospin) and rotating the system (high spin) is discussed.
Keywords: neutron-rich nuclei, cluster structure