Many-body interactions and high-pressure equations of state in rare-gas solids

The T 0K equations of state (EOS) of rare-gas solids (RGS) (He, Ne, Ar, Kr, and Xe) are calculated in the experimentally studied ranges of pressures accounting for two- and three-body interatomic forces. Solid-state corrections to the pure two-body Aziz et al. potentials included the long-range Axilrod–Teller three-body interaction and short-range three-body exchange interaction. The energy-scale and length-scale parameters of the latter were taken as adjustable parameters of theory. The calculated T 0K EOS for all RGS are in excellent agreement with experiment in the whole range of pressures. The calculated EOS for Ar, Kr, and Xe exhibit inflection points where the isothermal bulk moduli have non-physical maxima indicating that account of only three-body forces becomes insufficient. These points lie at pressures 250, 200, and 175 GPa (volume compressions of approximately 4.8, 4.1, and 3.6) for Ar, Kr, and Xe, respectively. No such points were found in the calculated EOS of He and Ne. The relative magnitude of the three-body contribution to the ground-state energy with respect to the two-body one as a function of the volume compression was found to be non-monotonic in the sequence Ne–Ar–Kr–Xe. In a large range of compressions, Kr has the highest value of this ratio. This anomally high three-body exchange forces contributes to the EOS so large negative pressure that the EOS for Kr and Ar as a function of compression nearly coincide. At compressions higher approximately 3.5, the curves intersect and further on the EOS of Kr lies lower than that of Ar

Lattice distortion of quantum cryocrystals under pressure

The hcp lattice distortion parameter δ, the deviation of c/a ratio from the ideal hcp value √ 8/3 , have been calculated for solid He under pressure taking into account two- and three-body interatomic forces. The resulting lattice distortion parameter is small and negative, that is the lattice is slightly flattened compared with the ideal hcp lattice. It monotonically increases in absolute value with pressure and reaches 10⁻³ for molar volume of ~ 2.5 cm³/mol. Such small distrotions are most likely outside of possibilities of x-ray or neutron experiments but can be detected by optical methods based on measurements of the birefringence. The data on δ can be used as a probe of the many-body forces

Lattice distortion in hcp rare gas solids

The lattice distortion parameter δ≡c/a – √8/3 has been calculated as a function of molar volume for the hcp phases of He, Ar, Kr, and Xe. Results from both semi-empirical potentials and density functional theory are presented. Our study shows that δ is negative for helium in the entire pressure range. For Ar, Kr, and Xe, however, δ changes sign from negative to positive as the pressure increases, growing rapidly in magnitude at higher pressures

CP Violation in B and K Decays: 2003

These lectures give a brief description of CP violation in B and K meson decays with particular emphasize put on the determination of the CKM matrix. The following topics will be discussed: i) The CKM matrix, the unitarity triangle and general aspects of the theoretical framework, ii) Particle-antiparticle mixing and various types of CP violation, iii) Standard analysis of the unitarity triangle, iv) The ratio epsilon^prime/epsilon, v) The most important strategies for the determination of the angles $\alpha$, $\beta$ and $\gamma$ from B decays, vi) Rare decays $K^+\to\pi^+\nu\bar\nu$ and $K_L\to\pi^0\nu\bar\nu$ vii) Models with minimal flavour violation.Comment: Schladming lectures 2003, Main latex-file, 8 figures, 51 page

Molecular rotation in p-H₂ and o-D₂ in phase I under pressure

The orientational order parameter, rotational ground-state energy, and lattice distortion parameter (the deviation of the c/a ratio from the ideal hcp value 1.633) in hcp lattice of phase I of p-H₂ and o-D₂ are calculated using a semi-empirical approach. It is shown that the lattice distortion in these J-even species is small compared with that found in n-H₂, and n-D₂. The difference presumably is caused by the J-odd species

Poisson’s ratio in cryocrystals under pressure

We present results of lattice dynamics calculations of Poisson’s ratio (PR) for solid hydrogen and rare gas solids (He, Ne, Ar, Kr and Xe) under pressure. Using two complementary approaches — the semi-empirical many-body calculations and the first-principle density-functional theory calculations we found three different types of pressure dependencies of PR. While for solid helium PR monotonically decreases with rising pressure, for Ar, Kr, and Xe it monotonically increases with pressure. For solid hydrogen and Ne the pressure dependencies of PR are nonmonotonic displaying rather deep minimums. The role of the intermolecular potentials in this diversity of patterns is discussed

Sound velocities in solid hydrogen under pressure

We present results of semi-empirical lattice dynamics calculations of the sound velocities in solid hydrogen under pressure based on the many-body intermolecular potential and first-principle density-functional theory (DFT). Both the sound velocities and elastic moduli are in excellent agreement with data from Brillouin scattering measurements while Silvera–Goldman and Hemley–Silvera–Goldman potentials tend to overestimate the sound velocity. It is shown that the stiffer is the potential the greater is overestimated the sound velocity. As was the case for equation of state and Raman-active lattice phonon calculations, the employed many-body potential works well for phases I and II (up to ~ 140 GPa while for higher pressures the use of the DFT is preferable

What can we learn from neutrinoless double beta decay experiments?

We assess how well next generation neutrinoless double beta decay and normal neutrino beta decay experiments can answer four fundamental questions. 1) If neutrinoless double beta decay searches do not detect a signal, and if the spectrum is known to be inverted hierarchy, can we conclude that neutrinos are Dirac particles? 2) If neutrinoless double beta decay searches are negative and a next generation ordinary beta decay experiment detects the neutrino mass scale, can we conclude that neutrinos are Dirac particles? 3) If neutrinoless double beta decay is observed with a large neutrino mass element, what is the total mass in neutrinos? 4) If neutrinoless double beta decay is observed but next generation beta decay searches for a neutrino mass only set a mass upper limit, can we establish whether the mass hierarchy is normal or inverted? We base our answers on the expected performance of next generation neutrinoless double beta decay experiments and on simulations of the accuracy of calculations of nuclear matrix elements.Comment: Added reference

The possible test of the calculations of nuclear matrix elements of the (ββ)0ν(\beta \beta)_{0\nu}-decay

The existing calculations of the nuclear matrix elements of the neutrinoless double $\beta$-decay differ by about a factor three. This uncertainty prevents quantitative interpretation of the results of experiments searching for this process. We suggest here that the observation of the neutrinoless double $\beta$-decay of {\em several} nuclei could allow to test calculations of the nuclear matrix elements through the comparison of the ratios of the calculated lifetimes with experimental data. It is shown that the ratio of the lifetimes is very sensitive to different models

Recent advances in neutrinoless double beta decay search

Even after the discovery of neutrino flavour oscillations, based on data from atmospheric, solar, reactor, and accelerator experiments, many characteristics of the neutrino remain unknown. Only the neutrino square-mass differences and the mixing angle values have been estimated, while the value of each mass eigenstate still hasn't. Its nature (massive Majorana or Dirac particle) is still escaping. Neutrinoless double beta decay ($0\nu$-DBD) experimental discovery could be the ultimate answer to some delicate questions of elementary particle and nuclear physics. The Majorana description of neutrinos allows the $0\nu$-DBD process, and consequently either a mass value could be measured or the existence of physics beyond the standard should be confirmed without any doubt. As expected, the $0\nu$-DBD measurement is a very difficult field of application for experimentalists. In this paper, after a short summary of the latest results in neutrino physics, the experimental status, the R&D projects, and perspectives in $0\nu$-DBD sector are reviewed.Comment: 36 pages, 7 figures, To be publish in Czech Journal of Physic