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Register a new userGeneralized Second-Order Thomas-Fermi Method for Superfluid Fermi Systems
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Using the $hbar$-expansion of the Greens function of the Hartree-Fock-Bogoliubov equation, we extend the second-order Thomas-Fermi approximation to generalized superfluid Fermi systems by including the density-dependent effective mass and the spin-orbit potential. We first implement and examine the full correction terms over different energy intervals of the quasiparticle spectra in calculations of finite nuclei. Final applications of this generalized Thomas-Fermi method are intended for various inhomogeneous superfluid Fermi systems.
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We determine the energy density $xi (3/5) n epsilon_F$ and the gradient correction $lambda hbar^2( abla n)^2/(8m n)$ of the extended Thomas-Fermi (ETF) density functional, where $n$ is number density and $epsilon_F$ is Fermi energy, for a trapped two-components Fermi gas with infinite scattering length (unitary Fermi gas) on the basis of recent diffusion Monte Carlo (DMC) calculations [Phys. Rev. Lett. {bf 99}, 233201 (2007)]. In particular we find that $xi=0.455$ and $lambda=0.13$ give the best fit of the DMC data with an even number $N$ of particles. We also study the odd-even splitting $gamma N^{1/9} hbar omega$ of the ground-state energy for the unitary gas in a harmonic trap of frequency $omega$ determining the constant $gamma$. Finally we investigate the effect of the gradient term in the time-dependent ETF model by introducing generalized Galilei-invariant hydrodynamics equations.
We show that the contributions of three-quasiparticle interactions to normal Fermi systems at low energies and temperatures are suppressed by n_q/n compared to two-body interactions, where n_q is the density of excited or added quasiparticles and n is the ground-state density. For finite Fermi systems, three-quasiparticle contributions are suppressed by the corresponding ratio of particle numbers N_q/N. This is illustrated for polarons in strongly interacting spin-polarized Fermi gases and for valence neutrons in neutron-rich calcium isotopes.
Using effective field theory methods, we calculate for the first time the complete fourth-order term in the Fermi-momentum or $k_{rm F} a_s$ expansion for the ground-state energy of a dilute Fermi gas. The convergence behavior of the expansion is examined for the case of spin one-half fermions and compared against quantum Monte-Carlo results, showing that the Fermi-momentum expansion is well-converged at this order for $| k_{rm F} a_s | lesssim 0.5$.
I discuss the advantages and disadvantages of several procedures, some known and some new, for constructing stationary states within the mean field approximation for a system with pairing correlations and unequal numbers spin-up and spin-down fermions, using the two chemical potentials framework. One procedure in particular appears to have significant physics advantages over previously suggested in the literature computational frameworks. Moreover, this framework is applicable to study strongly polarized superfluid fermion systems with arbitrarily large polarizations and with arbitrary total particle numbers. These methods are equally applicable to normal systems.
The atomic nucleus is composed of two different kinds of fermions, protons and neutrons. If the protons and neutrons did not interact, the Pauli exclusion principle would force the majority fermions (usually neutrons) to have a higher average momentum. Our high-energy electron scattering measurements using 12C, 27Al, 56Fe and 208Pb targets show that, even in heavy neutron-rich nuclei, short-range interactions between the fermions form correlated high-momentum neutron-proton pairs. Thus, in neutron-rich nuclei, protons have a greater probability than neutrons to have momentum greater than the Fermi momentum. This finding has implications ranging from nuclear few body systems to neutron stars and may also be observable experimentally in two-spin state, ultra-cold atomic gas systems.
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