Many-body aspects of positron annihilation in the electron gas

We investigate positron annihilation in electron liquid as a case study for many-body theory, in particular the optimized Fermi Hypernetted Chain (FHNC-EL) method. We examine several approximation schemes and show that one has to go up to the most sophisticated implementation of the theory available at the moment in order to get annihilation rates that agree reasonably well with experimental data. Even though there is basically just one number to look at, the electron-positron pair distribution function at zero distance, it is exactly this number that dictates how the full pair distribution behaves: In most cases, it falls off monotonously towards unity as the distance increases. Cases where the electron-positron pair distribution exhibits a dip are precursors to the formation of bound electron--positron pairs. The formation of electron-positron pairs is indicated by a divergence of the FHNC-EL equations, from this we can estimate the density regime where positrons must be localized. This occurs in our calculations in the range 9.4 <= r_s <=10, where r_s is the dimensionless density parameter of the electron liquid.Comment: To appear in Phys. Rev. B (2003

Transport and Phonon Damping in 4^{\bf 4}He

The dynamic structure function $S(k,\omega)$ informs about the dispersion and damping of excitations. We have recently (Phys. Rev. B {\bf 97}, 184520 (2018)) compared experimental results for $S(k,\omega)$ from high-precision neutron scattering experiment and theoretical results using the ``dynamic many-body theory'' (DMBT), showing excellent agreement over the whole experimentally accessible pressure regime. This paper focuses on the specific aspect of the propagation of low-energy phonons. We report calculations of the phonon mean-free path and phonon life time in liquid \he4 as a function of wave length and pressure. Historically, the question was of interest for experiments of quantum evaporation. More recently, there is interest in the potential use of $^4$He as a detector for low-energy dark matter (K. Schulz and Kathryn M. Zurek, Phys. Rev. Lett. {\bf 117}, 121302 (2016)). While the mean free path of long wave length phonons is large, phonons of intermediate energy can have a short mean free path of the order of $\mu$m. Comparison of different levels of theory indicate that reliable predictions of the phonon mean free path can be made only by using the most advanced many--body method available, namely, DMBT

The effective mass of two--dimensional 3He

We use structural information from diffusion Monte Carlo calculations for two--dimensional 3He to calculate the effective mass. Static effective interactions are constructed from the density-- and spin structure functions using sumrules. We find that both spin-- and density-- fluctuations contribute about equally to the effective mass. Our results show, in agreement with recent experiments, a flattening of the single--particle self--energy with increasing density, which eventually leads to a divergent effective mass.Comment: 4 pages, accepted in PR

Concentration Dependence of the Effective Mass of He-3 Atoms in He-3/He-4 Mixtures

Recent measurements by Yorozu et al. (S. Yorozu, H. Fukuyama, and H. Ishimoto, Phys. Rev. B 48, 9660 (1993)) as well as by Simons and Mueller (R. Simons and R. M. Mueller, Czhechoslowak Journal of Physics Suppl. 46, 201 (1976)) have determined the effective mass of He-3 atoms in a He-3/He-4 mixture with great accuracy. We here report theoretical calculations for the dependence of that effective mass on the He-3 concentration. Using correlated basis functions perturbation theory to infinite order to compute effective interactions in the appropriate channels, we obtain good agreement between theory and experiment.Comment: 4 pages, 1 figur

Pair Excitations and Vertex Corrections in Fermi Fluids

Based on an equations--of--motion approach for time--dependent pair correlations in strongly interacting Fermi liquids, we have developed a theory for describing the excitation spectrum of these systems. Compared to the known ``correlated'' random--phase approximation (CRPA), our approach has the following properties: i) The CRPA is reproduced when pair fluctuations are neglected. ii) The first two energy--weighted sumrules are fulfilled implying a correct static structure. iii) No ad--hoc assumptions for the effective mass are needed to reproduce the experimental dispersion of the roton in 3He. iv) The density response function displays a novel form, arising from vertex corrections in the proper polarisation. Our theory is presented here with special emphasis on this latter point. We have also extended the approach to the single particle self-energy and included pair fluctuations in the same way. The theory provides a diagrammatic superset of the familiar GW approximation. It aims at a consistent calculation of single particle excitations with an accuracy that has previously only been achieved for impurities in Bose liquids.Comment: to be published in: JLTP (2007) Proc. Int. Symp. QFS2006, 1-6 Aug. 2006, Kyoto, Japa