Table of contents

We review recent progress in the laser and microwave spectroscopy of antiprotonic helium atoms carried out at CERN's Antiproton Decelerator facility (AD). Laser transitions were here induced between Rydberg states (n, ℓ) and (n ± 1, ℓ − 1) of (n ∼ 40 and ℓ ≲ n − 1 being the principal and orbital angular momentum quantum numbers of the antiproton orbit). Successive refinements in the experimental techniques improved the fractional precision on the frequencies from 3 parts in 10⁶ to ∼1 part in 10⁸. These included a radiofrequency quadrupole decelerator, which reduced the energy of the antiprotons from 5.3 MeV (the energy of the beam emerging from AD) to ∼100 keV. This enabled the production of in ultra-low density targets, where collisional effects with other helium atoms are negligible. A continuous wave pulse-amplified dye laser, stabilized against a femtosecond optical frequency comb, was then used to measure the frequencies with ppb-scale precision. This progress in the experimental field was matched by similar advances in computing methods for evaluating the expected transition frequencies in three-body QED calculations. The comparison of experimental (ν_exp) and theoretical (ν_th) frequencies for seven transitions in and five in yielded an antiproton-to-electron mass ratio of . This agrees with the known proton-to-electron mass ratio at the level of ∼2 × 10⁻⁹. The experiment also set a limit on any CPT-violating difference between the antiproton and proton charges and masses, to a 90% confidence level. If on the other hand we assume the validity of the CPT invariance, the result can be taken to be equal to m_p/m_e. This can be used as an input to future adjustments of fundamental constants. The hyperfine structure of a state in has also been measured by microwave spectroscopy to a precision of 3 × 10⁻⁵. This corresponds to the accuracy of the most precise three-body QED calculations. Further increases in the experimental precision may soon yield an improvement in the value of the antiproton magnetic moment.

Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semiconductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a two-step method of symmetry breaking at the unrestricted Hartree–Fock level and of subsequent symmetry restoration via post Hartree–Fock projection techniques. Quantitative and qualitative aspects of the two-step method are treated and validated by exact diagonalization calculations.

Strongly-correlated phenomena emerging from symmetry breaking include the following.

1. Chemical bonding, dissociation and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot, with potential technological applications to solid-state quantum-computing devices.

2. Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. Such electron molecules exhibit ro-vibrational excitation spectra, in analogy with natural molecules.

3. At high magnetic fields, the REMs are described by parameter-free analytic wave functions, which are an alternative to the Laughlin and composite-fermion approaches, offering a new point of view of the fractional quantum Hall regime in quantum dots (with possible implications for the thermodynamic limit).

4. Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs). For a small number of bosons, the RBMs are energetically favored compared with the Gross–Pitaevskii solutions describing vortex formation.

We discuss the present status concerning experimental signatures of such strongly correlated states, in view of the promising outlook created by the latest experimental improvements that are achieving unprecedented control over the range and strength of interparticle interactions.

The subject of clustering has a lineage which runs throughout the history of nuclear physics. Its attraction is the simplification of the often uncorrelated behaviour of independent particles to organized and coherent quasi-crystalline structures. In this review the ideas behind the development of clustering in light nuclei are investigated, mostly from the stand-point of the harmonic oscillator framework. This allows a unifying description of alpha-conjugate and neutron-rich nuclei, alike. More sophisticated models of clusters are explored, such as antisymmetrized molecular dynamics. A number of contemporary topics in clustering are touched upon; the 3α-cluster state in ¹²C, nuclear molecules and clustering at the drip-line. Finally, an understanding of the ¹²C+¹²C resonances in ²⁴Mg, within the framework of the theoretical ideas developed in the review, is presented.

Our safety, comfort and peace of mind are heavily dependent upon our capability to prevent, predict or postpone the failure of components and structures on the basis of sound physical principles. While the external loadings acting on a material or component are clearly important, There are other contributory factors including unfavourable materials microstructure, pre-existing defects and residual stresses. Residual stresses can add to, or subtract from, the applied stresses and so when unexpected failure occurs it is often because residual stresses have combined critically with the applied stresses, or because together with the presence of undetected defects they have dangerously lowered the applied stress at which failure will occur. Consequently it is important that the origins of residual stress are understood, opportunities for removing harmful or introducing beneficial residual stresses recognized, their evolution in-service predicted, their influence on failure processes understood and safe structural integrity assessments made, so as to either remove the part prior to failure, or to take corrective action to extend life. This paper reviews the progress in these aspects in the light of the basic failure mechanisms.