Finite Range Density Research Articles

Above-barrier heavy-ion fusion cross-sections using the relativistic mean-field approach: Case of spherical colliding nuclei

In the present work, the influence of the nuclear matter density on the DF potential and on the Coulomb barrier parameters is studied systematically for collisions of spherical nuclei. The value of the parameter BZ=ZPZT/(AP1/3+AT1/3) (estimating the Coulomb barrier height) varies in these calculations from 10 MeV up to 150 MeV. We have introduced self-consistent relativistic mean field (RMF) density in the present analysis. For the nucleon-nucleon effective interaction, the M3Y forces with the finite range exchange term and density dependence are employed. The above barrier fusion cross sections are calculated within the framework of the trajectory model with surface friction. Results are compared with the previous study in which the nuclear density came from the Skyrme Hartree-Fock (HF) calculations and with the high precision experimental data. This comparison demonstrates that i) agreement between the theoretical and experimental cross sections obtained with RMF and HF densities is of the same quality and ii) the values of the only adjustable parameter (friction strength) obtained with RMF and HF densities strongly correlate with each other.

Many-body dynamics of holes in a driven, dissipative spin chain of Rydberg superatoms

Strong, long-range interactions between atoms in high-lying Rydberg states can suppress multiple Rydberg excitations within a micron-sized trapping volume and yield sizable Rydberg level shifts at larger distances. Ensembles of atoms in optical microtraps then form Rydberg superatoms with collectively enhanced transition rates to the singly excited state. These superatoms can represent mesoscopic, strongly interacting spins. We study a regular array of such effective spins driven by a laser field tuned to compensate the interaction-induced level shifts between neighboring superatoms. During the initial transient, a few excited superatoms seed a cascade of resonantly facilitated excitation of large clusters of superatoms. Due to spontaneous decay, the system then relaxes to the steady state having nearly universal Rydberg excitation density . This state is characterized by highly non-trivial equilibrium dynamics of quasi-particles—excitation holes in the lattice of Rydberg excited superatoms. We derive an effective many-body model that accounts for hole mobility as well as continuous creation and annihilation of holes upon collisions with each other. We find that holes exhibit a nearly incompressible liquid phase with highly sub-Poissonian number statistics and finite-range density–density correlations.

Helium and Hydrogen Adsorbed on Spheres and Cylinders

We examine the metastable and unstable regimes of condensation of superfluid helium and parahydrogen on spheres and cylinders at finite temperatures, employing finite range density functionals. The goal is to compare calculations of sizes and spreads of films at the onset of metastability and of instability with the predictions of a simple phenomenological model that contemplates the curvature of the substrate. We have focused on two cases, helium on nanospheres and nanocylinders of different materials, and hydrogen on fullerenes. We are able to locate the onset of metastability and of spinodal instability in the adsorption isotherms of every sample and to extract the width of the condensed fluid. It is shown that the predictions of the so-called simple model agree surprisingly well with the more elaborate calculations.

Shape and Pairing Fluctuation Effects on Neutrinoless Double Beta Decay Nuclear Matrix Elements

Nuclear matrix elements (NME) for the most promising candidates to detect neutrinoless double beta decay have been computed with energy density functional methods including deformation and pairing fluctuations explicitly on the same footing. The method preserves particle number and angular momentum symmetries and can be applied to any decay without additional fine tunings. The finite range density dependent Gogny force is used in the calculations. An increase of 10%-40% in the NME with respect to the ones found without the inclusion of pairing fluctuations is obtained, reducing the predicted half-lives of these isotopes.

On the impact of large amplitude pairing fluctuations on nuclear spectra

The influence of large amplitude pairing fluctuations is investigated in the framework of beyond mean field symmetry conserving configuration mixing calculations. In the numerical application the finite range density dependent Gogny force is used. We investigate the nucleus 54Cr with particle number and angular momentum projected wave functions considering the axial quadrupole deformation and the pairing gap degree of freedom as generator coordinates. We find that the effects of the pairing fluctuations increase with the excitation energy and the angular momentum. The self-consistency in the determination of the basis states plays an important role.

Fluid Helium in a Narrow Pore at Zero Temperature

The zero temperature adsorption isotherm of 4He in a rigid cylindrical pore with alkali metal walls is computed within finite-range density functional theory, with the radius of the tube as a parameter. It is shown that starting from narrow pores and increasing the radius, the adsorbed helium first becomes bound in a quasi-onedimensional phase, and finally condenses into a quasi-twodimensional configuration by going through an almost filling situation. The results are in agreement with recent calculations for carbon nanotubes based on thermodynamical approaches.

Absorption Spectrum of Na Atoms Attached to Helium Nanodroplets

We present an analysis of the electronic 3p←3s excitation of Na atoms attached to 3He and 4He droplets. Once the ground state structure of the doped drops has been obtained within finite-range density functional theory, we determine the time-correlation function of the Na atom evolving in the full three-dimensional 2Π1/2, 2Π3/2 and 2Σ1/2 potentials generated by its pairwise interaction with the helium atoms. The Fourier analysis of the time-correlation function determines the absorption spectrum of Na, which is compared with the experimental spectrum. We show that the existence of a redshifted shoulder in the absorption line of Na@4HeN, absent in Na@3HeN, is due to the wider vibrational motion of the dopant atom in the dimple it causes on the surface of the droplet.

Helium in polygonal nanopores at zero temperature: Density functional theory calculations

We investigate adsorption of helium in nanoscopic polygonal pores at zero temperature using a finite-range density functional theory. The adsorption potential is computed by means of a technique denoted as the elementary source method. We analyze a rhombic pore with Cs walls, where we show the existence of multiple interfacial configurations at some linear densities, which correspond to metastable states. Shape transitions and hysterectic loops appear in patterns which are richer and more complex than in a cylindrical tube with the same transverse area.

Excitation energy dependence of the symmetry energy of finite nuclei

A finite-range density and momentum-dependent effective interaction is used to calculate the density and temperature dependence of the symmetry energy coefficient ${C}_{\mathrm{sym}}(\ensuremath{\rho},T)$ of infinite nuclear matter. This symmetry energy is then used in the local density approximation to evaluate the excitation energy dependence of the symmetry energy coefficient of finite nuclei in a microcanonical formulation that accounts for thermal and expansion effects. The results are in good harmony with the recently reported experimental data from energetic nucleus-nucleus collisions.

New Beyond-Mean-Field Theories: Examination of the Potential Shell Closures atN=32or 34

A beyond-mean-field theory of new generation has been developed and applied for the first time to discuss the controversial N=32 and/or N=34 shell closures and the puzzling behavior of the transition probabilities from the ground to the first 2(+) state in the titanium isotopes. In the numerical applications, the finite range density dependent Gogny interaction has been used. As compared with the experimental data for several calcium, titanium, and chromium isotopes, we obtain a good agreement for the excitation energies and a reasonable one for the transition probabilities. Our calculations support a shell closure for N=32 but not for N=34.

Condensation of helium in nanoscopic alkali wedges at zero temperature

We present a complete calculation of the structure of liquid $^4$He confined to a concave nanoscopic wedge, as a function of the opening angle of the walls. This is achieved within a finite-range density functional formalism. The results here presented, restricted to alkali metal substrates, illustrate the change in meniscus shape from rather broad to narrow wedges on weak and strong alkali adsorbers, and relate this change to the wetting behavior of helium on the corresponding planar substrate. As the wedge angle is varied, we find a sequence of stable states that, in the case of cesium, undergo one filling and one emptying transition at large and small openings, respectively. A computationally unambiguous criterion to determine the contact angle of $^4$He on cesium is also proposed.

Growth of Helium Shells inside Spherical Adsorbers

The adsorption of helium on spherical cavities is investigated employing finite range density functional theory. It is known that for films outside spherical walls, a growth instability occurs above a critical film thickness. This instability may be overcome by stable capillary condensation inside the gap between an inner sphere and an outer spherical cavity bounded by spherical graphene, metallic sheets and voids in bulk metals. When a C60 fullerene is placed at the center of the spherical well, one can observe the competition between the formation of helium shells on the walls and the attraction of the opposite adsorbing field.

Adsorption of Helium on Au Nanowires

The growth of helium films on Au nanowires is investigated within finite range density functional theory. It is shown that as in previous studies of helium adsorption on spherical surfaces, submonolayer condensation and stable layering transitions take place, and that a growth instability appears above a finite film thickness. The competition between unstable film growth on a single tube and stable capillary condensation in an array of nanowires is examined in a simplified mean field-like model. Results are displayed to illustrate adsorption and its stable and unstable patterns outside solid nanowires, cavities in bulk gold and in the gap between a cavity and an inner concentric cylinder.

Finite Size Effects in Adsorption of Helium Mixtures by Alkali Substrates

We investigate the behavior of mixed 3He-4He droplets on alkali surfaces at zero temperature, within the frame of Finite Range Density Functional theory. The properties of one single 3He atom on 4He_N4 droplets on different alkali surfaces are addressed, and the energetics and structure of 4He_N4+3He_N3 systems on Cs surfaces, for nanoscopic 4He drops, are analyzed through the solutions of the mean field equations for varying number N3 of 3He atoms. We discuss the size effects on the single particle spectrum of 3He atoms and on the shapes of both helium distributions.

Wetting of Spherical Surfaces by Quantum Fluids

We study adsorption of atoms and fluids on spherical surfaces and present resugts for helium on weak to moderately strong adsorbers such as Cs, Li and Mg. We investigate the growth of a helium film as a function of the number of atoms, by means of a finite range density functional theory. We identify a crossover between nonadsorption and weak adsorption as the sphere radius increases. Path Integral Monte Carlo simulations provide semiquantitative support to these predictions.

Adsorption of atoms and fluids on spherical surfaces

The adsorption of helium on buckyballs at zero temperature is studied using finite range density functional and path integral Monte Carlo methods. The results include strong binding for ${\mathrm{C}}_{n}$ fullerenes $(n>~20)$ with a maximum number of adsorbed helium atoms at saturated vapor pressure, and a transition to no adsorption for weakly attractive potentials, exemplified by the case of a small Mg sphere. We show that a simple model describing the film as a continuum characterized by bulk parameters yields predictions in qualitative agreement with the more accurate computations.

Mean-field based approaches to pairing correlations in atomic nuclei

The evolution of the pairing correlations from closed shell to midshell nuclei is analyzed in the Sn isotopes with the Finite Range Density Dependent Gogny force. As theoretical approaches we use the Hartree–Fock–Bogoliubov, the Lipkin–Nogami, their particle number projected counterparts and the full variation after particle number projection method. We find that whereas all approaches succeed rather well in the description of the total energy they differ significantly in the pairing correlation content of the wave functions. The description of the evolution from the weak to the strong pairing regime is also approach dependent, specially at shell closure.

NUCLEAR MATTER PROPERTIES USING DIFFERENT SETS OF PARAMETERS IN THE GOGNY INTERACTION

In the present work we use the finite range density dependent effective Gogny interaction to study the equation of state of polarized nuclear matter. Six sets of the interaction parameters are used and a comparison is made with the calculations of Friedman and Pandharipande using a realistic interaction. One of the parameter sets (D1) gives similar results for the properties of polarized nuclear matter while the other parameter sets (D1S, D250, D260, D280 and D300) yield results which are reasonably comparable with the realistic interaction calculation of Friedman and Pandharipande

Multipole response of doped He3 drops

The multipole response of HeN3 drops doped with very attractive impurities, such as a Xe atom or an SF6 molecule, has been investigated in the framework of the Finite-Range Density Functional Theory and the Random Phase Approximation. We show that volume (L=0) and surface (L=1, 2) modes become more fragmented, as compared with the results obtained for pure HeN3 drops. In addition, the dipole mean energy goes smoothly to zero when N increases, indicating that for large N values these impurities are delocalized in the bulk of the drop.

Behavior of shell effects with the excitation energy in atomic nuclei

We study the behavior of shell effects, like pairing correlations and shape deformations, with the excitation energy in atomic nuclei. The analysis is carried out with the finite temperature Hartree-Fock-Bogoliubov method and a finite range density dependent force. For the first time, properties associated with the octupole and hexadecupole deformation and with the superdeformation as a function of the excitation energy are studied. Calculations for the well quadrupole deformed 164Er and 162Dy, superdeformed 152Dy, octupole deformed 224Ra, and spherical 118Sn nuclei are shown. We find, in particular, the level density of superdeformed states to be 4 orders of magnitude smaller than for normal deformed ones.