Spectral flow of trimer states of two heavy impurities and one light condensed boson

The spectral flow of three-body (trimer) states consisting of two heavy (impurity) particles sitting in a condensate of light bosons is considered. Assuming that the condensate is weakly interaction and that an impurity and a boson have a zero-range two-body interaction, we use the Born-Oppenheimer approximation to determine the effective three-body potential. We solve the resulting Schr\"odinger equation numerically and determine the trimer binding energies as a function of the coherence length of the light bosonic condensate particles. The binding energy is found to be suppressed by the presence of the condensate when the energy scale corresponding to the coherence length becomes of order the trimer binding energy in the absence of the condensate. We find that the Efimov scaling property is reflected in the critical values of the condensate coherence length at which the trimers are pushed into the continuum.Comment: 10 pages including appendices, 4 figures, revised versio

Efimov States of Heavy Impurities in a Bose-Einstein Condensate

We consider the problem of two heavy impurity particles embedded in a gas of weakly-interacting light mass bosonic particles in the condensed state. Using the Bogoliubov approach to describe the bosonic gas and the Born-Oppenheimer approximation for the three-body dynamics, we calculate the modification to the heavy-heavy two-body potential due to the presence of the condensate. For the case of resonant interaction between the light bosons and the impurities, we present (semi)-analytical results for the potential in the limit of a large condensate coherence length. In particular, we find a formula for the modification of the Efimov scaling factor due to the presence of a degenerate bosonic gas background.Comment: 6 pages, 3 figures, final versio

Effective field theory of interactions on the lattice

We consider renormalization of effective field theory interactions by discretizing the continuum on a tight-binding lattice. After studying the one-dimensional problem, we address s-wave collisions in three dimensions and relate the bare lattice coupling constants to the continuum coupling constants. Our method constitutes a very simple avenue for the systematic renormalization in effective field theory, and is especially useful as the number of interaction parameters increases.Comment: 7 pages, 0 figure

Muon capture on nuclei: random phase approximation evaluation versus data for 6 ≤\le Z ≤\le 94 nuclei

We use the random phase approximation to systematically describe the total muon capture rates on all nuclei where they have been measured. We reproduce the experimental values on these nuclei to better than 15% accuracy using the free nucleon weak form factors and residual interactions with a mild $A$ dependency. The isospin dependence and the effects associated with shell closures are fairly well reproduced as well. However, the calculated rates for the same residual interactions would be significantly lower than the data if the in-medium quenching of the axial-vector coupling constant is employed to other than the true Gamow-Teller amplitudes. Our calculation thus suggests that no quenching is needed in the description of semileptonic weak processes involving higher multipole transitions and momentum transfer $\sim m_{\mu}$, with obvious importance to analogous weak processes.Comment: RevTeX4 10 pages, 2 figures. Revised according to referee report. Table 1 expanded. Accepted for publication in PR