We place unprecedented constraints on recoil corrections in the $\beta$ decay of ${}^8\mathrm{Li}$, by identifying a strong correlation between them and the ${}^8\mathrm{Li}$ ground state quadrupole moment in large-scale ab initio calculations. The results are essential for improving the sensitivity of high-precision experiments that probe the weak interaction theory and test physics beyond the standard model. In addition, our calculations predict a $2^{+}$ state of the $\alpha +\alpha$ system that is energetically accessible to $\beta$ decay but has not been observed in the experimental ${}^8\mathrm{Be}$ energy spectrum, and has an important effect on the recoil corrections and $\beta$ decay for the $A=8$ systems. This state and an associated $0^{+}$ state are notoriously difficult to model due to their cluster structure and collective correlations, but become feasible for calculations in the ab initio symmetry-adapted no-core shell-model framework.

An unexplained $>4\sigma$ discrepancy persists between “beam” and “bottle” measurements of the neutron lifetime. A new model proposed that conversions of neutrons $n$ into mirror neutrons $n^{\prime }$, part of a dark mirror sector, can increase the apparent neutron lifetime by 1% via a small mass splitting $\mathrm{\Delta }m$ between $n$ and $n^{\prime }$ inside the 4.6 T magnetic field of the National Institute of Standards and Technology Beam Lifetime experiment. A search for neutron conversions in a 6.6 T magnetic field was performed at the Spallation Neutron Source which excludes this explanation for the neutron lifetime discrepancy.

A nuclear mass survey of rare-earth isotopes has been conducted with the Canadian Penning Trap mass spectrometer using the most neutron-rich nuclei thus far extracted from the CARIBU facility. We present a collection of 12 nuclear masses determined with a precision of $\le 10$ keV/$c{}^2$ for $Z=58–63$ nuclei near $N=100$. Independently, a detailed study exploring the role of nuclear masses in the formation of the $r$-process rare-earth abundance peak has been performed. Employing a Markov chain Monte Carlo (MCMC) technique, mass predictions of lanthanide isotopes have been made which uniquely reproduce the observed solar abundances near $A=164$ under three distinct astrophysical outflow conditions. We demonstrate that the mass surface trends thus far mapped out by our measurements are most consistent with MCMC mass predictions given an $r$ process that forms the rare-earth peak during an extended $(n,\gamma )\rightleftarrows (\gamma ,n)$ equilibrium.

We discuss the possibility of the transition magnetic moments (TMM) between the neutron n and its hypothetical sterile twin “mirror neutron” $n^{\prime }$ from a parallel particle “mirror” sector. The neutron can be spontaneously converted into mirror neutron via the TMM (in addition to the more conventional transformation channel due to $n-n^{\prime }$ mass mixing) interacting with the magnetic field $\mathbf{B}$ as well as with mirror magnetic field ${\mathbf{B}}^{\prime }$. We derive analytic formulae for the average probability of $n-n^{\prime }$ conversion and consider possible experimental manifestations of neutron TMM effects. In particular, we discuss the potential role of these effects in the neutron lifetime measurement experiments leading to new, testable predictions.

The LEGEND Collaboration is searching for neutrinoless double-beta ( 0 ν β β ) decay by operating high-purity germanium detectors enriched in Ge 76 in a low-background liquid argon environment. Building on key technological innovations from the GERmanium Detector Array (GERDA) experiment and the MAJORANA DEMONSTRATOR experiment, LEGEND-200 has performed a first 0 ν β β decay search based on 61.0 kg yr of data. Over half of this exposure comes from our highest performing detectors, including newly developed inverted-coaxial detectors, and is characterized by an estimated background level of 0.5 − 0.2 + 0.3 cts / ( keV ton yr ) in the 0 ν β β decay signal region. A combined analysis of data from GERDA, the MAJORANA DEMONSTRATOR, and LEGEND-200, characterized by a 90% confidence level exclusion sensitivity of 2.8 × 10 26 yr on the half-life of 0 ν β β decay, reveals no evidence for a signal and sets a new observed lower limit at T 1 / 2 0 ν > 1.9 × 10 26 yr (90% confidence level). Assuming the decay is mediated by Majorana neutrinos, this corresponds to an upper limit on the effective Majorana mass in the range m β β < 75 – 200 meV , depending on the adopted nuclear matrix element.

The possibility that a neutron can be transformed to a hidden sector particle remains intriguingly open. Proposed theoretical models conjecture that the hidden sector can be represented by a mirror sector, and the neutron n can oscillate into its sterile mirror twin $n^{\prime }$, exactly or nearly degenerate in mass with n. Oscillations $n-n^{\prime }$ can take place in vacuum or in an environment containing regular matter and a magnetic field, in which only the neutron will be subject to interactions with the environment. We describe the propagation of the oscillating $n-n^{\prime }$ system in a cold neutron beam passing through dense absorbing materials in connection to the possible regeneration type of experiments, where the effect of $n\to n^{\prime }\to n$ transformation can be observed.