Understanding the puzzle of angular momentum conservation in beta decay and related processes.

We ask the question of how angular momentum is conserved in electroweak interaction processes. To introduce the problem with a minimum of mathematics, we first raise the same issue in elastic scattering of a circularly polarized photon by an atom, where the scattered photon has a different spin direction than the original photon, and note its presence in scattering of a fully relativistic spin-1/2 particle by a central potential. We then consider inverse beta decay in which an electron is emitted following the capture of a neutrino on a nucleus.

Neutron Star Matter as a Dilute Solution of Protons in Neutrons.

Neutron stars contain neutron-rich matter with around 5% protons at nuclear saturation density. In this Letter, we consider equilibrium between bulk phases of matter based on asymmetric nuclear matter calculations using chiral effective field theory interactions rather than, as has been done in the past, by interpolation between the properties of symmetric nuclear matter and pure neutron matter. Neutron drip (coexistence of nuclear matter with pure neutrons) is well established, but from earlier work it is unclear whether proton drip (equilibrium between two phases, both of which contain protons and neutrons) is possible.

Superfluid Density of Neutrons in the Inner Crust of Neutron Stars: New Life for Pulsar Glitch Models.

Calculations of the effects of band structure on the neutron superfluid density in the crust of neutron stars made under the assumption that the effects of pairing are small [N. Chamel, Phys. Rev.

Supernova matter at subnuclear densities as a resonant Fermi gas: enhancement of neutrino rates.

At low energies nucleon-nucleon interactions are resonant and therefore supernova matter at subnuclear densities has many similarities to atomic gases with interactions dominated by a Feshbach resonance. We calculate the rates of neutrino processes involving nucleon-nucleon collisions and show that these are enhanced in mixtures of neutrons and protons at subnuclear densities due to the large scattering lengths. As a result, the rate for neutrino pair bremsstrahlung and absorption is significantly larger below 10(13) g cm(-3) compared to rates used in supernova simulations.

Towards a metallurgy of neutron star crusts.

In the standard picture of the crust of a neutron star, matter there is simple: a body-centered-cubic lattice of nuclei immersed in an essentially uniform electron gas. We show that, at densities above that for neutron drip (∼ 4 × 1 0(11)  g cm(-3) or roughly one-thousandth of nuclear matter density), the interstitial neutrons give rise to an attractive interaction between nuclei that renders the lattice unstable. We argue that the likely equilibrium structure is similar to that in displacive ferroelectric materials such as BaTiO3.

Spin diffusion in trapped clouds of cold atoms with resonant interactions.

We show that puzzling recent experimental results on spin diffusion in a strongly interacting atomic gas may be understood in terms of the predicted spin diffusion coefficient for a generic strongly interacting system. Three important features play a central role: (a) Fick's law for diffusion must be modified to allow for the trapping potential; (b) the diffusion coefficient is inhomogeneous, due to the density variations in the cloud; and (c) the diffusion approximation fails in the outer parts of the cloud, where the mean free path is long.

Bosonic and fermionic dipoles on a ring.

We show that dipolar bosons and fermions confined in a quasi-one-dimensional ring trap exhibit a rich variety of states because their interaction is inhomogeneous. For purely repulsive interactions, with increasing strength of the dipolar coupling there is a crossover from a gaslike state to an inhomogeneous crystal-like one. For small enough angles between the dipoles and the plane of the ring, there are regions with attractive interactions, and clustered states can form.

Constraints on neutron star radii based on chiral effective field theory interactions.

We show that microscopic calculations based on chiral effective field theory interactions constrain the properties of neutron-rich matter below nuclear densities to a much higher degree than is reflected in commonly used equations of state. Combined with observed neutron star masses, our results lead to a radius R=9.7-13.

Clock shifts of optical transitions in ultracold atomic gases.

We calculate the shift, due to interatomic interactions, of an optical transition in an atomic Fermi gas trapped in an optical lattice, as in recent experiments of Campbell et al. [Science 324, 360 (2009)]. Using a pseudospin formalism to describe the density matrix of atoms, we derive a Bloch equation which incorporates both spatial inhomogeneity of the probe laser field and interatomic interactions.

Induced interactions and the superfluid transition temperature in a three-component Fermi gas.

We study many-body contributions to the effective interaction between fermions in a three-component Fermi mixture. We find that effective interactions induced by the third component can lead to a phase diagram different from that predicted if interactions with the third component are neglected. As a result, in a confining potential a superfluid shell structure can arise even for equal populations of the components.

Collisional properties of a polarized Fermi gas with resonant interactions.

Highly polarized mixtures of atomic Fermi gases constitute a novel Fermi liquid. We demonstrate how information on thermodynamic properties may be used to calculate quasiparticle scattering amplitudes even when the interaction is resonant and apply the results to evaluate the damping of the spin dipole mode. We estimate that under current experimental conditions the mode would be intermediate between the hydrodynamic and collisionless limits.

Coherence and clock shifts in ultracold fermi gases with resonant interactions.

Using arguments based on sum rules, we derive a general result for the average shifts of rf lines in Fermi gases in terms of interatomic interaction strengths and two-particle correlation functions. We show that near an interaction resonance shifts vary inversely with the atomic scattering length, rather than linearly as in dilute gases, thus accounting for the experimental observation that clock shifts remain finite at Feshbach resonances.

Velocity of vortices in inhomogeneous Bose-Einstein condensates.

We derive, from the Gross-Pitaevskii equation, an exact expression for the velocity of any vortex in a Bose-Einstein condensate, in equilibrium or not, in terms of the condensate wave function at the center of the vortex. In general, the vortex velocity is a sum of the local superfluid velocity, plus a correction related to the density gradient near the vortex. A consequence is that in rapidly rotating, harmonically trapped Bose-Einstein condensates, unlike in the usual situation in slowly rotating condensates and in hydrodynamics, vortices do not move with the local fluid velocity.

Resonant fermi gases with a large effective range.

We calculate the equation of state of a Fermi gas with resonant interactions when the effective range is appreciable. Using an effective field theory for a large scattering length and large effective range, we show how calculations in this regime become tractable. Our results are model independent, and as an application, we study the neutron matter equation of state at low densities of astrophysical interest 0.

Landau levels and the Thomas-fermi structure of rapidly rotating bose-einstein condensates.

We show that, within mean-field theory, the density profile of a rapidly rotating harmonically trapped Bose-Einstein condensate is of the Thomas-Fermi form as long as the number of vortices is much larger than unity. Two forms of the condensate wave function are explored: (i) the lowest Landau level (LLL) wave function with a regular lattice of vortices multiplied by a slowly varying envelope function, which gives rise to components in higher Landau levels; (ii) the LLL wave function with a nonuniform vortex lattice. From variational calculations, we find it most favorable energetically to retain the LLL form of the wave function but to allow the vortices to deviate slightly from a regular lattice.

Effective theory of Feshbach resonances and many-body properties of Fermi gases.

For calculating low-energy properties of a dilute gas of atoms interacting via a Feshbach resonance, we develop an effective theory in which the parameters that enter are an atom-molecule coupling strength and the magnetic moment of the molecular resonance. We demonstrate that, for resonances in the fermionic systems 6Li and 40K that are under experimental investigation, the coupling is so strong that many-body effects are appreciable even when the resonance lies at an energy large compared with the Fermi energy. We calculate a number of many-body effects, including the effective mass and the lifetime of atomic quasiparticles in the gas.

Universal behavior of the energy of trapped few-boson systems with large scattering length.

We calculate energy levels of two and three bosons trapped in a harmonic oscillator potential with oscillator length a(osc). The atoms are assumed to interact through a short-range potential with a scattering length a, and the short-distance behavior of the three-body wave function is characterized by a parameter theta. For large positive a/a(osc), the energies of states that, in the absence of the trap, correspond to three free atoms approach values independent of a and theta.

Cold bose gases with large scattering lengths.

We calculate the energy and condensate fraction for a dense system of bosons interacting through an attractive short range interaction with positive s-wave scattering length a. At high densities n>>a(-3), the energy per particle, chemical potential, and square of the sound speed are independent of the scattering length and proportional to n(2/3), as in Fermi systems. The condensate is quenched at densities na(3) approximately 1.

Influence of induced interactions on the superfluid transition in dilute fermi gases.

We calculate the effects of induced interactions on the transition temperature to the BCS state in dilute Fermi gases. For a pure Fermi system with two species having equal densities, the transition temperature is suppressed by a factor (4e)(1/3) approximately 2.2, and for nu fermion species, the transition temperature is increased by a factor (4e)(nu/3-1) approximately 2.