The MONUMENT experiment measures ordinary muon capture (OMC) on isotopes relevant for neutrinoless double-beta (0$\nu\beta\beta$) decay and nuclear astrophysics. OMC is a particularly attractive tool for improving the theoretical description of 0$\nu\beta\beta$ decay. It involves similar momentum transfers and allows testing the virtual transitions involved in 0$\nu\beta\beta$ decay against experimental data. During the 2021 campaign, MONUMENT measured OMC on $^{76}$Se and $^{136}$Ba, the isotopes relevant for next-generation 0$\nu\beta\beta$ decay searches, like LEGEND and nEXO. The experimental setup has been designed to accurately extract the total and partial muon capture rates, which requires precise reconstruction of energies and time-dependent intensities of the OMC-related $\gamma$ rays. The setup also includes a veto counter system to allow selecting a clean sample of OMC events. This work provides a detailed description of the MONUMENT setup operated during the 2021 campaign, its two DAQ systems, calibration and analysis approaches, and summarises the achieved detector performance. Future improvements are also discussed.

In this work, we have studied the $2\nu\beta\beta$ decay of $^{76}$Ge and $^{96}$Zr isotopes utilizing large-scale shell-model calculations. The GWBXG effective interaction has been employed in the calculation of $2\nu\beta\beta$-decay nuclear matrix elements (NMEs). We have tested the effective interaction by comparing the predicted spectroscopic properties, such as energy spectra and transition probabilities, with the available experimental data. The variation of cumulative NMEs with respect to the $1^+$ state energies of the intermediate nucleus is also studied, corresponding to $0^+_{\rm g.s}\rightarrow0^+_{\rm g.s}$, $0^+_{\rm g.s}\rightarrow0^+_{2}$, and $0^+_{\rm g.s}\rightarrow2^+_{1}$ transitions between the parent and granddaughter nuclei. The extracted half-lives using the shell-model predicted NMEs show good agreement with the recent experimental data. The comparison of the shell-model predicted NMEs with previous NMEs available in the literature is discussed. Also, the computed branching ratios for the $2\nu\beta\beta$ decay of $^{76}$Ge and both the $2\nu\beta\beta$ and single-$\beta$ decay of $^{96}$Zr are reported.

LiSrAlF$_6$ crystals doped with $^{229}$Th are used in a laser-based search for the nuclear isomeric transition. Two spectroscopic features near the nuclear transition energy are observed. The first is a broad excitation feature that produces red-shifted fluorescence that decays with a timescale of a few seconds. The second is a narrow, laser-linewidth-limited spectral feature at $148.38219(4)_{\textrm{stat}}(20)_{\textrm{sys}}$ nm ($2020407.3(5)_{\textrm{stat}}(30)_{\textrm{sys}}$ GHz) that decays with a lifetime of $568(13)_{\textrm{stat}}(20)_{\textrm{sys}}$ s. This feature is assigned to the excitation of the $^{229}$Th nuclear isomeric state, whose energy is found to be $8.355733(2)_{\textrm{stat}}(10)_{\textrm{sys}}$ eV in $^{229}$Th:\thor:LiSrAlF$_6$.

We study bottom quark energy loss via the nuclear modification factor ($R_\mathrm{AA}$) and elliptic flow ($v_2$) of non-prompt $D^0$ and $J/\psi$ in relativistic heavy-ion collisions at the LHC. The space-time profile of quark-gluon plasma is obtained from the CLVisc hydrodynamics simulation, the dynamical evolution of heavy quarks inside the color deconfined QCD medium is simulated using a linear Boltzmann transport model that combines Yukawa and string potentials of heavy-quark-medium interactions, the hadronization of heavy quarks is performed using a hybrid coalescence-fragmentation model, and the decay of $B$ mesons is simulated via PYTHIA. Using this numerical framework, we calculate the transverse momentum ($p_\mathrm{T}$) dependent $R_\mathrm{AA}$ and $v_2$ of direct $D$ mesons, $B$ mesons, and non-prompt $D^0$ and $J/\psi$ from $B$ meson decay in Pb+Pb collisions at $\sqrt{s_\mathrm{NN}}=5.02$ TeV. We find the mass hierarchy of the nuclear modification of prompt $D$ and $B$ mesons depends on their $p_\mathrm{T}$. Both $R_\mathrm{AA}$ and $v_2$ of heavy flavor particles show strong $p_\mathrm{T}$ and centrality dependences due to the interplay between parton energy loss, medium geometry and flow, and hadronization of heavy quarks. Non-prompt $D^0$ and $J/\psi$ share similar patterns of $R_\mathrm{AA}$ and $v_2$ to $B$ mesons except for a $p_\mathrm{T}$ shift during the decay processes. Therefore, future more precise measurements on non-prompt $D^0$ and $J/\psi$ can help further pin down the bottom quark dynamics inside the quark-gluon plasma.

The extended kernel ridge regression (EKRR) method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models. These are: (i) the isospin dependent $A^{1/3}$ formula, (ii) relativistic continuum Hartree-Bogoliubov (RCHB) theory, (iii) Hartree-Fock-Bogoliubov (HFB) model HFB25, (iv) the Weizs\"acker-Skyrme (WS) model WS$^\ast$, and (v) HFB25$^\ast$ model. In the last two models, the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models, respectively. For each model, the resultant root-mean-square deviation for the 1014 nuclei with proton number $Z \geq 8$ can be significantly reduced to 0.009-0.013~fm after considering the modification with the EKRR method. The best among them was the RCHB model, with a root-mean-square deviation of 0.0092~fm. The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined and it was found that after considering the odd-even effects, the extrapolation power was improved compared with that of the original KRR method. The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron $N=126$ and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.

We study to what extent the unique observation of $\Lambda\Lambda$ hypernuclei by their weak decay into known $\Lambda$ hypernuclei, with lifetimes of order 10$^{-10}$ s, rules out the existence of a deeply bound doubly-strange (${\cal S}$=$-$2) $H$ dibaryon. Treating ${_{\Lambda\Lambda}^{~~6}}{\rm He}$ (the Nagara emulsion event) in a realistic $\Lambda-\Lambda-{^4}$He three-body model, we find that the ${_{\Lambda\Lambda}^{~~6}}{\rm He}\to H + {^4{\rm He}}$ strong-interaction lifetime increases beyond 10$^{-10}$ s for $m_H < m_{\Lambda}+m_n$, about 176 MeV below the $\Lambda\Lambda$ threshold, so that such a deeply bound $H$ is not in conflict with hypernuclear data. Constrained by $\Lambda$ hypernuclear $\Delta{\cal S}$=1 nonmesonic weak-interaction decay rates, we evaluate the $\Delta{\cal S}$=2 $H\to nn$ weak-decay lifetime of $H$ in the mass range $2m_n \lesssim m_H < m_{\Lambda}+m_n$. The resulting $H$ lifetime is of order 10$^4$ s, many orders of magnitude shorter than required to qualify for a dark-matter candidate. A lower-mass absolutely stable $H$, $m_H\lesssim 2m_n$, is likely to be ruled out by established limits of nuclear stability such as for $^{16}$O.