We study the extension of our translationally invariant treatment of few-body nuclear systems to heavier nuclei. At the same time we also introduce state-dependent correlation operators. Our techniques are tailored to those nuclei that can be dealt with in LS coupling, which includes all nuclei up to the shell closure at A = 40. We study mainly p-shell nuclei in this paper. A detailed comparison with other microscopic many-body approaches is made, using a variety of schematic nuclear interactions. It is shown that our methodology produces very good energies, and presumably also wave functions, for medium mass nuclei.

Abstract. The elementary dipole excitations of the ionized clusters Na~-, Na~ and Na~ are investigated by solving the equations of the Random-Phase Approximation. The ground and excited states are described using the jellium model for the ionic background and a non-local energy density functional for the valence electrons. Non-local effects are specifically analyzed. The excitation energies thus obtained approach better than those of the Local Density Approximation both the full Hartree-Fock and the experimental results.

We apply the time-dependent local-spin-density approximation to describe ground states and spindensity oscillations in the linear response regime of two-dimensional nanostructures of arbitrary shape. For this purpose, a frequency analysis of the simulated real-time evolution is performed. It is shown that the recently proposed spin-density waves in the ground state of certain parabolic quantum dots lead to the prediction of a novel class of excitations, soft spin-twist modes with energies well below that of the spin dipole oscillation. PACS numbers: 73.20.Dx, 72.15.Rn Recent advances in semiconductor technology nowadays allow the fabrication of nanostructures with many different shapes. In these systems the electrons, which are laterally confined at the semiconductor boundary, form a two-dimensional quantum dot with a shape which, to a certain extent, follows that of the nanostructure. This opens up the exciting possibility to produce and study an enormous variety of quantum dots, or artificial atoms as they are often called. For instance, it has been shown that the electronic structure in the small vertical quantum dots of Ref.[1] is given by the successive filling of shells obeying Hund's rules as in atoms. Very relevant information about electronic excitations in quantum dots is also presently obtained from sophisticated far-infrared absorption [2] and light scattering experiments [3].Up to now, the great majority of experimental and theoretical efforts were focused on quantum dots with circular symmetry. Many of the properties of circular dots are well reproduced by considering the electrons as confined by a parabolic potential, or by a simple jellium disk. To treat the electronic interactions, besides exact diagonalization for very small dots [4], the most successful approaches have been mean field theories like Hartree-Fock (HF) [5] and density functional in the local-spin-density approximation [6,7] (LSDA).The latter ones have been extended using the randomphase approximation (RPA) to analyze collective excitations [5,8]. To our knowledge, all theoretical approaches addressing collective excitations in 2D quantum dots are limited from the start by the circular symmetry assumption. In this Letter we show how LSDA can describe both ground state and linear response of 2D quantum dots of arbitrary shape by using, respectively, energy minimization and real-time simulation of the spin-density oscillations as basic principles. We will show how from the response frequencies in the different channels (density, spin, and free responses) it is possible to gain information about the system deformation in a quantitative way. Besides, we will also analyze the effect on the response of the recently proposed spin-density waves (SDW's) in the ground state of particular parabolic quantum dots. They could generate soft spin-twist modes, at energies well below that of dipole spin oscillation.Several authors have recently addressed the problem of describing quantum dot ground states within LSDA. In particular, in Ref.[6] th...

The possibility of a novel type of semiconductor quantum dots obtained by spatially modulating the spin-orbit coupling intensity in III-V heterostructures is discussed. Using the effective mass model we predict confined one-electron states having peculiar spin properties. Furthermore, from mean field calculations (local-spin-density and Hartree-Fock) we find that even two electrons could form a bound state in these dots.Comment: 9 pages, 3 figures. Accepted in PRB (Brief Report) (2004

Cooper pairing in two dimensions is analyzed with a set of renormalized equations to determine its binding energy for any fermion number density and all coupling assuming a generic pairwise residual interfermion interaction. Also considered are Cooper pairs ͑CP's͒ with nonzero center-of-mass momentum ͑CMM͒ and their binding energy is expanded analytically in powers of the CMM up to quadratic terms. A Fermi-sea-dependent linear term in the CMM dominates the pair excitation energy in weak coupling ͑also called the BCS regime͒ while the more familiar quadratic term prevails in strong coupling ͑the Bose regime͒. The crossover, though strictly unrelated to BCS theory per se, is studied numerically as it is expected to play a central role in a model of superconductivity as a Bose-Einstein condensation of CPs where the transition temperature vanishes for all dimensionality dр2 for quadratic dispersion, but is nonzero for all dу1 for linear dispersion.The original Cooper pair ͑CP͒ problem 1 in two ͑2D͒ and three ͑3D͒ dimensions possesses ultraviolet divergences in momentum space that are usually removed via interactions regularized with large-momentum cutoffs.2 One such regularized potential is the BCS model interaction which is of great practical use in studying Cooper pairing 1 and superconductivity.3 Although there are controversies over the precise pairing mechanism, and thus over the microscopic Hamiltonian appropriate for high-T c superconductors, some of the properties of these materials have been explained satisfactorily within a BCS-Bose crossover picture 4-7 via a renormalized BCS theory for a short-range interaction. In the weak-coupling limit of the BCS-Bose crossover description one recovers the pure mean-field BCS theory of weakly bound, severely overlapping CPs. For strong coupling ͑and/or low density͒ well separated, nonoverlapping ͑so-called ''local''͒ pairs appear 4 in what is known as the Bose regime. It is of interest to detail how renormalized Cooper pairing itself evolves independently of the BCS-Bose crossover picture in order to then discuss the possible BoseEinstein ͑BE͒ condensation ͑BEC͒ of such pairs. We address this here in a single-CP picture, while considering also the important case ͑generally neglected in BCS theory͒ of nonzero center-of-mass-momentum ͑CMM͒ CPs that are expected to play a significant role in BE condensates at higher temperatures.In this report we derive a renormalized Cooper equation for a pair of fermions interacting via either a zero-or a finiterange interaction. We find an analytic expression for the CP excitation energy up to terms quadratic in the CMM which is valid for any coupling. For weak coupling only the linear term dominates, as it also does for the BCS model interaction. 8 The linear term was mentioned for 3D as far back as 1964 ͑Ref. 9, p. 33͒. For strong coupling we now find that the quadratic term dominates and is just the kinetic energy of the strongly bound composite pair moving in vacuum.The CP dispersion relation enters into each summand in the BE dis...

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We provide a quantitative determination of the crystallization onset for two electrons in a parabolic two-dimensional confinement. This system is shown to be well described by a roto-vibrational model, Wigner crystallization occurring when the rotational motion gets decoupled from the vibrational one. The Wigner molecule thus formed is characterized by its moment of inertia and by the corresponding sequence of rotational excited states. The role of a vertical magnetic field is also considered. Additional support to the analysis is given by the Hartree-Fock phase diagram for the ground state and by the random-phase approximation for the moment of inertia and vibron excitations.

The electronic spin precession in semiconductor dots is strongly affected by the spin-orbit coupling. We present a theory of the electronic spin resonance at low magnetic fields that predicts a strong dependence on the dot occupation, the magnetic field and the spin-orbit coupling strength. Coulomb interaction effects are also taken into account in a numerical approach.PACS 73.21. La, χ nℓ+ (r, η) ≡ ϕ nℓ+ (r)