  We have studied the explosion dynamics of methane clusters irradiated by
intense, femtosecond, 38 nm (32.6 eV) XUV laser pulses. The ion time-of-flight
spectrum measured with a Wiley-McLaren-type time-of-flight spectrometer reveals
undissociated molecular $\textrm{CH}_4^+$ ions, fragments which are missing
hydrogen atoms due to the breakage of one or more C-H bonds $(\textrm{CH}_3^+,
\textrm{CH}_2^+ \ \textrm{and}\ \textrm{CH}^+)$ and the recombination product
$\textrm{CH}_5^+$. Also visible on the time-of-flight traces are atomic and
molecular hydrogen ions $(\textrm{H}^+ \textrm{and}\ \textrm{H}_2^+)$, carbon
ions, and larger hydrocarbons such as $\textrm{C}_2 \textrm{H}_2^+$ and
$\textrm{C}_2\textrm{H}_3^+$. No doubly-charged parent ions
$(\textrm{CH}_4^{2+})$ were detected. The time-of-flight results show that
total and relative ion yields depend strongly on cluster size. The absolute
yields of $\textrm{CH}^+_5$ and $\textrm{H}^+$ scale linearly with the yields
of the other generated fragments up to a cluster size of
$\langle\textrm{N}\rangle=70,000 \ \textrm{molecules}$, then begin to decrease,
whereas the yields of the $\textrm{CH}_n^+(n=1-4) $ fragments plateau at this
cluster size. The behavior of $\textrm{H}^+$ may be understood through the
electron recombination rate, which depends on the electron temperature and the
cluster average charge. Moreover, the $\textrm{CH}_5^+$ behavior is explained
by the depletion of both $\textrm{CH}_4^+$ and $\textrm{H}^+$ via electron-ion
recombination in the expanding nanoplasma.
