  A molecular dynamics simulation is performed to investigate spatial scale of
low energy excitation (LEE) in a single linear chain of united atoms. The self
part of the dynamic structure function, $S_\mathrm{S}(q,\omega)$, is obtained
in a wide range in frequency space ($\omega$) and reciprocal space ($q$). A
broad peak corresponding to the LEE is detected at $\omega/2\pi=2.5 \times
10^{11} \mathrm{s^{-1}}$ ($\equiv \omega_{\mathrm{LEE}}/2\pi$) on the contour
maps of $S_\mathrm{S}(q,\omega)$, near and below the glass transition
temperature ($T_{\mathrm{g}}$=230 K). The
$S_\mathrm{S}(q,\omega_{\mathrm{LEE}})$ is symmetric around a maximum along the
logarithm of $q$. The inverse of $q_{\mathrm{max}}$, giving the maximum
position of $S_\mathrm{S}(q,\omega_{\mathrm{LEE}})$, depends on temperature as
$2\pi/q_{\mathrm{max}}\sim T^{0.52}$ for $60 \mathrm{K}<T<T_{\mathrm{g}}$ and
$2\pi/q_{\mathrm{max}}\sim T^{0.97}$ for $T_{\mathrm{g}}<T<600 \mathrm{K}$,
which is the spatial scale of the motion corresponding to the LEE at low
temperatures. Based on a Gaussian approximation for the displacements of
monomer groups which give rise to the motion relevant to the LEE, it is found
that the number of monomers contained in a group is about 6.
