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Double core-hole (DCH) spectroscopy is investigated systematically for neonatomic system in the interaction with ultraintense x-ray pulses with photonenergy from 937 eV to 2000 eV. A time-dependent rate equation, implemented inthe detailed level accounting approximation, is utilized to study the dynamicalevolution of the level population and emission properties of the highlytransient plasmas. For x-ray pulses with photon energy in the range of 937-1030eV, where $1s\rightarrow 2p$ resonance absorption from single core-hole (SCH)states of neon charge states exist, inner-shell resonant absorption (IRA)effects play important roles in the time evolution of population and DCHspectroscopy. Such IRA physical effects are illustrated in detail byinvestigating the interaction of x-ray pulses at a photon energy of 944 eV,which corresponds to the $1s\rightarrow 2p$ resonant absorption from the SCHstates ($1s2s^22p^4$, $1s2s2p^5$ and $1s2p^6$) of Ne$^{3+}$. After averagingover the space and time distribution of the x-ray pulses, DCH spectroscopy atphoton energies of 937, 944, 955, 968, 980, and 990 eV (corresponding to the$1s\rightarrow 2p$ resonance energies of Ne$^{2+}$-Ne$^{7+}$, respectively) arestudied in detail. The complex mechanisms of producing the DCH states arediscussed, taking the DCH spectroscopy at 937 and 980 eV as examples. Forphoton energy larger than 1362 eV, there are no resonance absorption in theinteraction, resulting in a similar physical picture of DCH spectroscopy. Thedominant DCH states are due to higher ionization stages of Ne$^{7+}$-Ne$^{9+}$,while the DCH spectroscopy from lower charge states Ne$^{2+}$-Ne$^{6+}$ aremuch weaker. With the increase of x-ray photon energy, the contributions fromthe lower charge states become larger.

Double core-hole spectroscopy of transient plasmas produced in the interaction of ultraintense x-ray pulses with neon