In a neutrinoless double-beta decay ($0 ubetabeta$) experiment, energy resolution is important to distinguish between $0 ubetabeta$ and background events. CAlcium fluoride for studies of Neutrino and Dark matters by Low Energy Spectrometer (CANDLES) discerns the $0 ubetabeta$ of $^{48}$Ca using a CaF$_2$ scintillator as the detector and source. Photomultiplier tubes (PMTs) collect scintillation photons. At the Q-value of $^{48}$Ca, the current energy resolution (2.6%) exceeds the ideal statistical fluctuation of the number of photoelectrons (1.6%). Because of CaF$_2$s long decay constant of 1000 ns, a signal integration within 4000 ns is used to calculate the energy. The baseline fluctuation ($sigma_{baseline}$) is accumulated in the signal integration, thus degrading the energy resolution. This paper studies $sigma_{baseline}$ in the CANDLES detector, which severely degrades the resolution by 1% at the Q-value of $^{48}$Ca. To avoid $sigma_{rm baseline}$, photon counting can be used to obtain the number of photoelectrons in each PMT; however, a significant photoelectron signal overlapping probability in each PMT causes missing photoelectrons in counting and reduces the energy resolution. Partial photon counting reduces $sigma_{baseline}$ and minimizes photoelectron loss. We obtain improved energy resolutions of 4.5-4.0% at 1460.8 keV ($gamma$-ray of $^{40}$K), and 3.3-2.9% at 2614.5 keV ($gamma$-ray of $^{208}$Tl). The energy resolution at the Q-value is estimated to be improved from 2.6% to 2.2%, and the detector sensitivity for the $0 ubetabeta$ half-life of $^{48}$Ca can be improved by 1.09 times.
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