Three-body correlations for the ground-state decay of the lightest two-proton emitter 6 Be are studied both theoretically and experimentally. Theoretical studies are performed in a three-body hyperspherical-harmonics cluster model. In the experimental studies, the ground state of 6 Be was formed following the α decay of a 10 C beam inelastically excited through interactions with Be and C targets. Excellent agreement between theory and experiment is obtained demonstrating the existence of complicated correlation patterns which can elucidate the structure of 6 Be and, possibly, of the A=6 isobar.

Resonance-decay spectroscopy is used to study particle-unbound excited states produced in interactions of E/A = 10.7 MeV 10 C on Be and C targets. After inelastic scattering, structures associated with excited states in 10 C were observed at 5. 22, 5.29, 6.55, 6.56, 6.57, and 8.4 MeV which decay into the 2p + 2α final state. This final state is created via a number of different decay paths, which include prompt and sequential two-proton decay to the ground state of 8 Be, α decay to 6 Be g.s. , and proton decay to the 2.345-MeV state of 9 B. For the sequential two-proton decay states (5.22 and 6.55 MeV), angular correlations between the first two decay axes indicate that the spin of these states are nonzero. For the prompt two-proton decay of the 5.29-MeV state, the three-body correlations between the two protons and the core are intermediate between those measured for ground-state 6 Be and 45 Fe decays. The 6.55-and 6.57-MeV structures are most probably associated with the same level, which has a 14% two-proton decay branch with a strong "diproton" character and a 86% sequential two-proton decay branch. Correlations between the fragments following the three-body decay of the 2.345-MeV state of 9 B can be approximately described by sequential α decay to the 5 Li intermediate state. The 8.06-and 9.61-MeV 10 B states that decay into the d + 6 Li 2.186 channel are confirmed. Evidence for cluster structure in 13 N is obtained from a number of excited states that decay into the p + 3α exit channel.

The complete three-body correlation pictures are experimentally reconstructed for the two-proton decays of the 6 Be and 45 Fe ground states. We are able to see qualitative similarities and differences between these decays. They demonstrate very good agreement with the predictions of a theoretical three-body cluster model. Validity of the theoretical methods for treatment of the three-body Coulombic decays of this class is thus established by the broad range of lifetimes and nuclear masses spanned by these cases. Implementations for decay dynamics and nuclear structure of 2p emitters are discussed.

There are very few direct experimental tests of the inverse square law of gravity at distances comparable to the scale of the Solar System and beyond. Here we describe a possible space mission optimized to test the inverse square law at a scale of up to 100 AU. For example, sensitivity to a Yukawa correction with a strength of 10 −7 times gravity and length scale of 100 AU is within reach, improving the current state of the art by over two orders of magnitude. This experiment would extend our understanding of gravity to the largest scale that can be reached with a direct probe using known technology. This would provide a powerful test of long-distance modifications of gravity including many theories motivated by dark matter or dark energy.

Generalized PT symmetry provides crucial insight into the sign problem for two classes of models. In the case of quantum statistical models at non-zero chemical potential, the free energy density is directly related to the ground state energy of a non-Hermitian, but generalized PT -symmetric Hamiltonian. There is a corresponding class of PT -symmetric classical statistical mechanics models with non-Hermitian transfer matrices. We discuss a class of Z(N) spin models with explicit PT symmetry and also the ANNNI model, which has a hidden PT symmetry. For both quantum and classical models, the class of models with generalized PT symmetry is precisely the class where the complex weight problem can be reduced to real weights, i.e., a sign problem. The spatial two-point functions of such models can exhibit three different behaviors: exponential decay, oscillatory decay, and periodic behavior. The latter two regions are associated with PT symmetry breaking, where a Hamiltonian or transfer matrix has complex conjugate pairs of eigenvalues. The transition to a spatially modulated phase is associated with PT symmetry breaking of the ground state, and is generically a first-order transition. In the region where PT symmetry is unbroken, the sign problem can always be solved in principle using the equivalence to a Hermitian theory in this region. The ANNNI model provides an example of a model with PT symmetry which can be simulated for all parameter values, including cases where PT symmetry is broken.