  With the development of radioactive beam facilities, studies concerning the
shell evolution of unstable nuclei have recently gained prominence. Intruder
components, particularly s-wave intrusion, in the low-lying states of light
neutron-rich nuclei near N=8 are of importance in the study of shell evolution.
The use of single-nucleon transfer reactions in inverse kinematics has been a
sensitive tool that can be used to quantitatively investigate the
single-particle orbital component of selectively populated states. The
spin-parity, spectroscopic factor (or single-particle strength), and effective
single-particle energy can all be extracted from such reactions. These
observables are often useful to explain the nature of shell evolution, and to
constrain, check, and test the parameters used in nuclear structure models. In
this article, the experimental studies of the intruder components in low-lying
states of neutron-rich nuclei of He, Li, Be, B, and C isotopes using various
single-nucleon transfer reactions are reviewed. The focus is laid on the
precise determination of the intruder s-wave strength in low-lying states.
