  A systematic analysis of nuclear deformation is made for neutron-rich Ti, Cr,
and Fe isotopes to explore the nuclear structure in the island of inversion
near N = 40, where strong nuclear deformation is predicted. The nuclear ground
states are obtained by the Skyrme Hartree-Fock method in three-dimensional
coordinate space, which properly describes any nuclear shape. Three types of
Skyrme interactions are employed to generate various deformed states in its
isotopic chain. We find that in the island of inversion the occupation of
highly elongated intruder orbits induces not only large quadrupole deformation
but also large hexadecapole deformation. This appears as a sizable enhancement
of the nuclear matter radius, showing the characteristic shell effect of the
density profile near the nuclear surface. We show that the edge of the island
of inversion, where the intruder orbit starts being occupied, can be determined
by measuring the enhancement of the total reaction cross section at high
incident energy. The possibility of constraining the hexadecapole deformation
by a measurement of the total reaction cross sections is discussed.
