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A. Fabrocini

Publications and source records attributed to A. Fabrocini.

At least 19 recordsLinked to original sources
arXiv2007

Renormalized Fermi hypernetted chain approach in medium-heavy nuclei

The application of the Correlated basis function theory and of the Fermi hypernetted chain technique, to the description of the ground state of medium-heavy nuclei is reviewed. We discuss how the formalism, originally developed for symmetric nuclear matter, should be changed in order to describe finite nuclear systems, with different number of protons and neutrons. This approach allows us to describe doubly closed shell nuclei by using microscopic nucleon-nucleon interactions. We presents results of numerical calculations done with two-nucleon interactions of Argonne type,implemented with three-body forces of Urbana type. Our results regard ground-state energies, matter, charge and momentum distributions, natural orbits, occupation numbers, quasi-hole wave functions and spectroscopic factors of 12C, 16O, 40Ca, 48Ca and 208Pb nuclei.

nucl-th↗
arXiv2006

Ground state of medium-heavy doubly-closed shell nuclei in correlated basis function theory

The correlated basis function theory is applied to the study of medium-heavy doubly closed shell nuclei with different wave functions for protons and neutrons and in the jj coupling scheme. State dependent correlations including tensor correlations are used. Realistic two-body interactions of Argonne and Urbana type, together with three-body interactions have been used to calculate ground state energies and density distributions of the 12C, 16O, 40Ca, 48Ca and 208Pb nuclei.

nucl-th↗
arXiv2005

Spin-orbit and tensor interactions in homogeneous matter of nucleons: accuracy of modern many-body theories

We study the energy per particle of symmetric nuclear matter and pure neutron matter using realistic nucleon--nucleon potentials having non central tensor and spin--orbit components, up to three times the empirical nuclear matter saturation density, $ρ_0=0.16$ fm$^{-3}$. The calculations are carried out within the frameworks of the Brueckner--Bethe--Goldstone (BBG) and Correlated Basis Functions (CBF) formalisms, in order to ascertain the accuracy of the methods. The two hole--line approximation, with the continuous choice for the single particle auxiliary potential, is adopted for the BBG approach, whereas the variational Fermi Hypernetted Chain/Single Operator Chain theory, corrected at the second order perturbative expansion level, is used in the CBF one. The energies are then compared with the available Quantum and Variational Monte Carlo results in neutron matter and with the BBG, up to the three hole--line diagrams. For neutron matter and potentials without spin--orbit components all methods, but perturbative CBF, are in reasonable agreement up to $ρ\sim$ 3 $ρ_0$. After the inclusion of the LS interactions, we still find agreement around $ρ_0$, whereas it is spoiled at larger densities. The spin--orbit potential lowers the energy of neutron matter at $ρ_0$ by $\sim$ 3--4 MeV per nucleon. In symmetric nuclear matter, the BBG and the variational results are in agreement up to $\sim$ 1.5 $ρ_0$. Beyond this density, and in contrast with neutron matter, we find good agreement only for the potential having spin--orbit components.

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arXiv2004

Recent results in CBF theory for medium-heavy nuclei

We extend the correlated basis functions theory (CBF) for nuclei with different number of protons and neutrons and in j-j coupling scheme. By means of the Fermi hypernetted chain integral equations, in conjunction with the single operator chain approximation (FHNC/SOC), we evaluate the ground state and the one-body densities for 40Ca, 48Ca and 208Pb nuclei. The realistic Argonne V8' two-nucleon potentials has been used. We compare the ground-state properties of these nuclei calculated by using correlation functions with and without tensor components.

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arXiv2004

Ground state properties of a dilute homogeneous Bose gas of hard disks in two dimensions

The energy and structure of a dilute hard-disks Bose gas are studied in the framework of a variational many-body approach based on a Jastrow correlated ground state wave function. The asymptotic behaviors of the radial distribution function and the one-body density matrix are analyzed after solving the Euler equation obtained by a free minimization of the hypernetted chain energy functional. Our results show important deviations from those of the available low density expansions, already at gas parameter values $x\sim 0.001$. The condensate fraction in 2D is also computed and found generally lower than the 3D one at the same $x$.

cond-mat.stat-mech↗
arXiv2004

Energy and Structure of Hard-Sphere Bose Gases in three and two dimensions

The energy and structure of dilute gases of hard spheres in three dimensions is discussed, together with some aspects of the corresponding 2D systems. A variational approach in the framework of the Hypernetted Chain Equations (HNC) is used starting from a Jastrow wavefunction that is optimized to produce the best two--body correlation factor with the appropriate long range. Relevant quantities describing static properties of the system are studied as a function of the gas parameter $x=ρa^d$ where $ρ$, $a$ and $d$ are the density, $s$--wave scattering length of the potential and dimensionality of the space, respectively. The occurrence of a maximum in the radial distribution function and in the momentum distribution is a natural effect of the correlations when $x$ increases. Some aspects of the asymptotic behavior of the functions characterizing the structure of the systems are also investigated.

cond-mat.stat-mech↗
arXiv2003

Microscopic study of the He2-SF6 trimers

The He2-SF6 trimers, in their different He isotopic combinations, are studied both in the framework of the correlated Jastrow approach and of the Correlated Hyperspherical Harmonics expansion method. The energetics and structure of the He-SF6 dimers are analyzed, and the existence of a characteristic rotational band in the excitation spectrum is discussed, as well as the isotopic differences. The binding energies and the spatial properties of the trimers, in their ground and lowest lying excited states, obtained by the Jastrow ansatz are in excellent agreement with the results of the converged CHH expansion. The introduction of the He-He correlation makes all trimers bound by largely suppressing the short range He-He repulsion. The structural properties of the trimers are qualitatively explained in terms of the shape of the interactions, Pauli principle and masses of the constituents.

physics.atm-clus↗
arXiv2003

Energy and structure of dilute hard- and soft-sphere gases

The energy and structure of dilute hard- and soft-sphere Bose gases are systematically studied in the framework of several many-body approaches, as the variational correlated theory, the Bogoliubov model and the uniform limit approximation, valid in the weak interaction regime. When possible, the results are compared with the exact diffusion Monte Carlo ones. A Jastrow type correlation provides a good description of the systems, both hard- and soft-spheres, if the hypernetted chain energy functional is freely minimized and the resulting Euler equation is solved. The study of the soft-spheres potentials confirms the appearance of a dependence of the energy on the shape of the potential at gas paremeter values of $x \sim 0.001$. For quantities other than the energy, such as the radial distribution functions and the momentum distributions, the dependence appears at any value of $x$. The occurrence of a maximum in the radial distribution function, in the momentum distribution and in the excitation spectrum is a natural effect of the correlations when $x$ increases. The asymptotic behaviors of the functions characterizing the structure of the systems are also investigated. The uniform limit approach results very easy to implement and provides a good description of the soft-sphere gas. Its reliability improves when the interaction weakens.

cond-mat.soft↗
arXiv2003

Deuteron distribution in nuclei and the Levinger's factor

We compute the distribution of quasideuterons in doubly closed shell nuclei. The ground states of $^{16}$O and $^{40}$Ca are described in $ls$ coupling using a realistic hamiltonian including the Argonne $v_{8}^\prime$ and the Urbana IX models of two-- and three--nucleon potentials, respectively. The nuclear wave function contains central and tensor correlations, and correlated basis functions theory is used to evaluate the distribution of neutron-proton pairs, having the deuteron quantum numbers, as a function of their total momentum. By computing the number of deuteron--like pairs we are able to extract the Levinger's factor and compare to both the available experimental data and the predictions of the local density approximation, based on nuclear matter estimates. The agreement with the experiments is excellent, whereas the local density approximation is shown to sizably overestimate the Levinger's factor in the region of the medium nuclei.

nucl-th↗
arXiv2002

Final-state interactions in the response of nuclear matter

Final-state interactions in the response of a many-body system to an external probe delivering large momentum are normally described using the eikonal approximation, for the trajectory of the struck particle, and the frozen approximation, for the positions of the spectators. We propose a generalization of this scheme, in which the initial momentum of the struck particle is explicitly taken into account. Numerical calculations of the nuclear matter response at 1 $< |{\bf q}| <$ 2 GeV/c show that the inclusion of this momentum dependence leads to a sizable effect in the low energy tail. Possible implications for the analysis of existing electron-nucleus scattering data are discussed.

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arXiv2001

Single particle properties of 16O and 40Ca

We discuss some single particle properties of $^{16}$O and $^{40}$Ca using correlated basis function theory and Fermi hypernetted chain equations with central and tensor correlations. In particular, we concentrate on one body density matrix, momentum distribution, natural orbits and quasi hole states. The correlations are variationally generated by a realistic hamiltonian containing the Argonne $v'_{8}$ two-nucleon and Urbana IX three-nucleon interactions. The correlated momentum distributions show the well known enhancement at large momenta, with a relative importance of the different correlations (Jastrow and tensor) similar to that in nuclear matter. The natural orbits and their occupation numbers are obtained by diagonalization of the density matrix. The correlated first natural orbits occupations are depleted by more than 10%, whereas the first following ones are occupied by a few percent. The spectroscopic factors of the valence states are lowered by $\sim 8-12%$ with respect to unity by central and tensor correlations, confirming that short range correlations alone are not able to explain the values extracted from $(e,e'p)$ experiments.

nucl-th↗
arXiv2001

Deuteron distribution in nuclear matter

We analyze the properties of deuteron-like structures in infinite, correlated nuclear matter, described by a realistic hamiltonian containing the Urbana $v_{14}$ two-nucleon and the Urbana TNI many-body potentials. The distribution of neutron-proton pairs, carrying the deuteron quantum numbers, is obtained as a function of the total momentum by computing the overlap between the nuclear matter in its ground state and the deuteron wave functions in correlated basis functions theory. We study the differences between the S- and D-wave components of the deuteron and those of the deuteron-like pair in the nuclear medium. The total number of deuteron type pairs is computed and compared with the predictions of Levinger's quasideuteron model. The resulting Levinger's factor in nuclear matter at equilibrium densityis 11.63. We use the local density approximation to estimate the Levinger's factor for heavy nuclei, obtaining results which are consistent with the available experimental data from photoreactions.

nucl-th↗
arXiv2001

Ambiguities in the implementation of the impulse approximation for the response of many-fermion systems

Within the impulse approximation the response of a many body system at large momentum tranfer can be written in a simple and transparent form, allowing to directly relate the inclusive scattering cross section to the properties of the target ground state. Although the physics assumptions underlying impulse approximation are well defined, their implementation involves ambiguities that may cause significant differences in the calculated responses. We show that, while minimal use of the impulse approximation assumptions naturally leads to write the response in terms of the target spectral function, the widely used alternative definition in terms of the momentum distribution involves a more extended use of the same assumtpions. The difference between the responses resulting from the two procedures is illustrated by two examples.

nucl-th↗
arXiv2001

A correlated model for lambda-hypernuclei

We study the properties of hypernuclei containing one lambda hyperon in the framework of the correlated basis function theory with Jastrow correlations. Fermi hypernetted chain integral equations are derived and used to evaluate energies and one-body densities of lambda hypernuclei having a doubly closed shell nucleonic core in the jj coupling scheme, from Carbon to Lead. We also study hypernuclei having the least bound neutron substituted by the lambda particle. The semi-realistic Afnan and Tang nucleon-nucleon potential and Bodmer and Usmani lambda-nucleon potential are adopted. The effect of many-body forces are considered by means either of a three body lambda-nucleon-nucleon potential of the Argonne type or of a density dependent modification of the lambda-nucleon interaction, fitted to reproduce the lambda binding energy in nuclear matter. While Jastrow correlations underestimate the attractive contribution of the three body $\la$ interaction, the density dependent potential provides a good description of the lambda binding energies over all the nuclear masses range, in spite of the relative simplicity of the model.

nucl-th↗
arXiv2001

Bose-Einstein Condensates in the Large Gas Parameter Regime

Bose-Einstein condensates of 10$^4$ $^{85}$Rb atoms in a cylindrical trap are studied using a recently proposed modified Gross-Pitaevskii equation. The existence of a Feshbach resonance allows for widely tuning the scattering length of the atoms, and values of the peak gas parameter, $x_{pk}$, of the order of 10$^{-2}$ can be attained. We find large differences between the results of the modified Gross-Pitaevskii and of the standard Thomas-Fermi, and Gross-Pitaevskii equations in this region. The column densities at $z=0$ may differ by as much as $\sim 30%$ and the half maximum radius by $\sim 20%$. The scattering lengths estimated by fitting the half maximum radius within different approaches can differ by $\sim 40%$.

cond-mat.soft↗
arXiv2000

One Body Density Matrix, Natural Orbits and Quasi Hole States in 16O and 40Ca

The one body density matrix, momentum distribution, natural orbits and quasi hole states of 16O and 40Ca are analyzed in the framework of the correlated basis function theory using state dependent correlations with central and tensor components. Fermi hypernetted chain integral equations and single operator chain approximation are employed to sum cluster diagrams at all orders. The optimal trial wave function is determined by means of the variational principle and the realistic Argonne v8' two-nucleon and Urbana IX three-nucleon interactions. The correlated momentum distributions are in good agreement with the available variational Monte Carlo results and show the well known enhancement at large momentum values with respect to the independent particle model. Diagonalization of the density matrix provides the natural orbits and their occupation numbers. Correlations deplete the occupation number of the first natural orbitals by more than 10%. The first following ones result instead occupied by a few percent. Jastrow correlations lower the spectroscopic factors of the valence states by a few percent (~1-3%) and an additional ~8-12% depletion is provided by tensor correlations. It is confirmed that short range correlations do not explain the spectroscopic factors extracted from (e,e'p) experiments. 2h-1p perturbative corrections in the correlated basis are expected to provide most of the remaining strength, as in nuclear matter.

nucl-th↗
arXiv2000

Ground State Correlations in 16O and 40Ca

We study the ground state properties of doubly closed shell nuclei $^{16}$O and $^{40}$Ca in the framework of Correlated Basis Function theory using state dependent correlations, with central and tensor components. The realistic Argonne $v_{14}$ and $v'_{8}$ two-nucleon potentials and three-nucleon potentials of the Urbana class have been adopted. By means of the Fermi Hypernetted Chain integral equations, in conjunction with the Single Operator Chain approximation, we evaluate the ground state energy, one- and two-body densities and electromagnetic and spin static responses for both nuclei. In $^{16}$O we compare our results with the available Monte Carlo and Coupled Cluster ones and find a satisfying agreement. As in the nuclear matter case with similar interactions and wave functions, the nuclei result under-bound by 2--3 MeV/A.

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