We report on an improved measurement of the $2\nu \beta \beta$ half-life of ${}^{136}$Xe performed by EXO-200. The use of a large and homogeneous time-projection chamber allows for the precise estimate of the fiducial mass used for the measurement, resulting in a small systematic uncertainty. We also discuss in detail the data-analysis methods used for double-$\beta$ decay searches with EXO-200, while emphasizing those directly related to the present measurement. The ${}^{136}$Xe $2\nu \beta \beta$ half-life is found to be $T_{1/2}^{2\nu \beta \beta }$ = $2.165\pm 0.016\left(\mathrm{stat}\right)\pm 0.059\left(\mathrm{sys}\right)\times {10}^{21}$ yr. This is the most precisely measured half-life of any $2\nu \beta \beta$ decay to date.

Quantum Monte Carlo calculations of electromagnetic moments and transitions are reported for $A\le 9$ nuclei. The realistic Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon potentials are used to generate the nuclear wave functions. Contributions of two-body meson-exchange current (MEC) operators are included for magnetic moments and $M1$ transitions. The MEC operators have been derived in both a standard nuclear physics approach and a chiral effective field theory formulation with pions and nucleons including up to one-loop corrections. The two-body MEC contributions provide significant corrections and lead to very good agreement with experiment. Their effect is particularly pronounced in the $A=9$, $T=3/2$ systems, in which they provide up to $\sim 20\%$ ($\sim 40\%$) of the total predicted value for the ${}^9$Li (${}^9$C) magnetic moment.

This paper details the solar neutrino analysis of the 385.17-day phase-III data set acquired by the Sudbury Neutrino Observatory (SNO). An array of ${}^3$He proportional counters was installed in the heavy-water target to measure precisely the rate of neutrino-deuteron neutral-current interactions. This technique to determine the total active ${}^8$B solar neutrino flux was largely independent of the methods employed in previous phases. The total flux of active neutrinos was measured to be $5.{54}_{-0.31}^{+0.33}{\text{(stat.)}}_{-0.34}^{+0.36}\text{(syst.)}\times {10}^6$ cm${}^{-2}$ s${}^{-1}$, consistent with previous measurements and standard solar models. A global analysis of solar and reactor neutrino mixing parameters yielded the best-fit values of $\Delta m^2=7.{59}_{-0.21}^{+0.19}\times {10}^{-5}{\text{eV}}^2$ and $\theta =34.4_{-1.2}^{+1.3}\text{degrees}$.

Background: The $\beta$ decays of ${}^3$H and ${}^6$He can play an important role in testing nuclear wave-function calculations and fixing low-energy constants in effective-field theory approaches. However, there exists a large discrepancy between previous measurements of the ${}^6$He half-life.

Purpose: Our measurement aims at resolving this long-standing discrepancy in the ${}^6$He half-life and providing a reliable $ft$ value and Gamow-Teller matrix element for comparison with theoretical ab initio calculations.

Method: We measured the ${}^6$He half-life by counting the $\beta$-decay electrons with two scintillator detectors operating in coincidence.

Results: The measured ${}^6$He half-life is $806.89\pm 0.{11}_{\mathrm{stat}}{}_{-0.19}^{+0.23}{}_{\mathrm{syst}}$ ms corresponding to a relative precision of $3\times {10}^{-4}$. Calculating the statistical rate function we determined the $ft$ value to be $803.{04}_{-0.23}^{+0.26}$ s.

Conclusions: Our result resolves the previous discrepancy by providing a higher-precision result with careful analysis of potential systematic uncertainties. The result provides a reliable basis for future precision comparisons with ab initio calculations.

Background: Time-reversal-invariance violation, or equivalently $CP$ violation, may explain the observed cosmological baryon asymmetry as well as indicate physics beyond the Standard Model. In the decay of polarized neutrons, the triple correlation $D\langle {\vec{J}}_n\rangle /J_n·({\vec{\beta }}_e\times {\widehat{p}}_{\nu })$ is a parity-even, time-reversal-odd observable that is uniquely sensitive to the relative phase of the axial-vector amplitude with respect to the vector amplitude. The triple correlation is also sensitive to possible contributions from scalar and tensor amplitudes. Final-state effects contribute to $D$ at the level of 10${}^{-5}$ and can be calculated with a precision of 1$\%$ or better.

Purpose: We have improved the sensitivity to $T$-odd, $P$-even interactions in nuclear $\beta$ decay.

Methods: We measured proton-electron coincidences from decays of longitudinally polarized neutrons with a highly symmetric detector array designed to cancel the time-reversal-even, parity-odd Standard-Model contributions to polarized neutron decay. Over 300 million proton-electron coincidence events were used to extract $D$ and study systematic effects in a blind analysis.

Results: We find $D=[-0.94\pm 1.89\left(\mathrm{stat}\right)\pm 0.97\left(\mathrm{sys}\right)]\times {10}^{-4}$. This differs from the result of our recent paper [Phys. Rev. Lett. 107, 102301 (2011)] due to refinement of corrections for background and backscattering.

Conclusions: This is the most sensitive measurement of $D$ in nuclear $\beta$ decay. Our result can be interpreted as a measurement of the phase of the ratio of the axial-vector and vector coupling constants ($C_A/C_V=\left|\lambda \right|e^{i{\phi }_{AV}}$) with ${\phi }_{AV}=180.{012}^{\circ }\pm 0.{028}^{\circ }$ (68$\%$ confidence level). This result can also be used to constrain time-reversal-violating scalar and tensor interactions that arise in certain extensions to the Standard Model such as leptoquarks.

Background: Neutrino-nucleus quasi-elastic scattering is crucial to interpret the neutrino oscillation results in long baseline neutrino experiments. There are rather large uncertainties in the cross section, due to insufficient knowledge on the role of two-body weak currents.

Purpose: Determine the role of two-body weak currents in neutrino-deuteron quasi-elastic scattering up to GeV energies.

Methods: Calculate cross sections for inclusive neutrino scattering off deuteron induced by neutral and charge-changing weak currents, from threshold up to GeV energies, using the Argonne $v_{18}$ potential and consistent nuclear electroweak currents with one- and two-body terms.

Results: Two-body contributions are found to be small, and increase the cross sections obtained with one-body currents by less than 10$\%$ over the whole range of energies. Total cross sections obtained by describing the final two-nucleon states with plane waves differ negligibly, for neutrino energies $\gtrsim$ MeV, from those in which interaction effects in these states are fully accounted for. The sensitivity of the calculated cross sections to different models for the two-nucleon potential and/or two-body terms in the weak current is found to be weak. Comparing cross sections to those obtained in a naive model in which the deuteron is taken to consist of a free proton and neutron at rest, nuclear structure effects are illustrated to be non-negligible.

Conclusion: Contributions of two-body currents in neutrino-deuteron quasi-elastic scattering up to GeV are found to be smaller than 10$\%$. Finally, it should be stressed that the results reported in this work do not include pion production channels.