arXiv subjects

Michele Viviani

Publications and source records attributed to Michele Viviani.

27 records · Page 2Linked to original sources

arXiv2019

Embedding nuclear physics inside the unitary window

The large values of the singlet and triplet scattering lengths locate the two-nucleon system close to the unitary limit, the limit in which these two values diverge. As a consequence, the system shows a continuous scale invariance which strongly constrains the values of the observables, a well-known fact already noticed a long time ago. The three-nucleon system shows a discrete scale invariance that can be observed by correlations of the triton binding energy with other observables as the doublet nucleon-deuteron scattering length or the alpha-particle binding energy. The low-energy dynamics of these systems is universal; it does not depend on the details of the particular way in which the nucleons interact. Instead, it depends on a few control parameters, the large values of the scattering lengths and the triton binding energy. Using a potential model with variable strength set to give values to the control parameters, we study the spectrum of $A=2,3,4,6$ nuclei in the region between the unitary limit and their physical values. In particular, we analyze how the binding energies emerge from the unitary limit forming the observed levels.

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arXiv2018

Coherent deeply virtual Compton scattering off $^4$He

Coherent Deeply virtual Compton scattering off the $^4$He nucleus is studied in impulse approximation. A convolution formula for the nuclear Generalized Parton Distribution (GPD) is derived in terms of the $^4$He non-diagonal spectral function and of the GPD of the struck nucleon. A model of the nuclear non diagonal spectral function, based on the momentum distribution corresponding to the AV18 nucleon-nucleon interaction, is used in the actual calculation. Typical impulse approximation results are reproduced, in proper limits, for the nuclear form factor and for nuclear parton distributions. The nuclear generalized parton distribution and the Compton form factor are evaluated using, as nucleonic ingredient, a well known generalized parton distribution model. An overall very good agreement is found with the data recently published by the EG6 experiment at the Jefferson Laboratory (JLab). More refined nuclear calculations are addressed and will be necessary for the expected improved accuracy of the next generation of experiments at JLab, with the 12 GeV electron beam and high luminosity.

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arXiv2017

Two-fermion Bethe-Salpeter Equation in Minkowski Space: the Nakanishi Way

The possibility of solving the Bethe-Salpeter Equation in Minkowski space, even for fermionic systems, is becoming actual, through the applications of well-known tools: i) the Nakanishi integral representation of the Bethe-Salpeter amplitude and ii) the light-front projection onto the null-plane. The theoretical background and some preliminary calculations are illustrated, in order to show the potentiality and the wide range of application of the method.

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arXiv2016

Local chiral potentials and the structure of light nuclei

We present fully local versions of the minimally non-local nucleon-nucleon potentials constructed in a previous paper [M.\ Piarulli {\it et al.}, Phys.\ Rev.\ C {\bf 91}, 024003 (2015)], and use them in hypersperical-harmonics and quantum Monte Carlo calculations of ground and excited states of $^3$H, $^3$He, $^4$He, $^6$He, and $^6$Li nuclei. The long-range part of these local potentials includes one- and two-pion exchange contributions without and with $Δ$-isobars in the intermediate states up to order $Q^3$ ($Q$ denotes generically the low momentum scale) in the chiral expansion, while the short-range part consists of contact interactions up to order $Q^4$. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database in two different ranges of laboratory energies, either 0--125 MeV or 0--200 MeV, and to the deuteron binding energy and $nn$ singlet scattering length. Fits to these data are performed for three models characterized by long- and short-range cutoffs, $R_{\rm L}$ and $R_{\rm S}$ respectively, ranging from $(R_{\rm L},R_{\rm S})=(1.2,0.8)$ fm down to $(0.8,0.6)$ fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential.

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arXiv2014

Solutions of the Bethe-Salpeter Equation in Minkowski space: a comparative study

The Bethe-Salpeter Equation for a two-scalar, S-wave bound system, interacting through a massive scalar, is investigated within the ladder approximation. By assuming a Nakanishi integral representation of the Bethe-Salpeter amplitude, one can deduce new integral equations that can be solved and quantitatively studied, overcoming the analytic difficulties of the Minkowski space. Finally, it is shown that the Light-front distributions of the valence state, directly obtained from the Bethe-Salpeter amplitude, open an effective window for studying the two-body dynamics.

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arXiv2013

Quantitative studies of the homogeneous Bethe-Salpeter Equation in Minkowski space

The Bethe-Salpeter Equation for a bound system, composed by two massive scalars exchanging a massive scalar, is quantitatively investigated in ladder approximation, within the Nakanishi integral representation approach. For the S-wave case, numerical solutions with a form inspired by the Nakanishi integral representation, have been calculated. The needed Nakanishi weight functions have been evaluated by solving two different eigenequations, obtained directly from the Bethe-Salpeter equation applying the Light-Front projection technique. A remarkable agreement, in particular for the eigenvalues, has been achieved, numerically confirming that the Nakanishi uniqueness theorem for the weight functions, demonstrated in the context of the perturbative analysis of the multi-leg transition amplitudes and playing a basic role in suggesting one of the two adopted eigenequations, can be extended to a non perturbative realm. The detailed, quantitative studies are completed by presenting both probabilities and Light-Front momentum distributions for the valence component of the bound state.

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arXiv2011

Two-body scattering states in Minkowski space and the Nakanishi integral representation onto the null plane

The Nakanishi perturbative integral representation of the four-dimensional T-matrix is investigated in order to get a workable treatment for scattering states, solutions of the inhomogeneous Bethe-Salpeter Equation, in Minkowski space. The projection onto the null-plane of the four-dimensional inhomogeneous Bethe-Salpeter Equation plays a key role for devising an equation for the Nakanishi weight function (a real function), as in the homogeneous case that corresponds to bound states and it has been already studied within different frameworks. In this paper, the whole formal development is illustrated in detail and applied to a system, composed by two massive scalars interacting through the exchange of a massive scalar. The explicit expression of the scattering integral equations are also obtained in ladder approximation, and, as simple applications of our formalism, some limiting cases, like the zero-energy limit and the Wick-Cutkosky model in the continuum, are presented.

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arXiv2010

Nonsymmetrized Hyperspherical Harmonics approach to A=6 system

The Hyperspherical Harmonics basis, without a previous symmetrization step, is used to calculate binding energies of the nuclear A=6 systems using a version of the Volkov potential acting only on s-wave. The aim of this work is to illustrate the use of the nonsymmetrized basis to deal with permutational-symmetry-breaking term in the Hamiltonian, in the present case the Coulomb interaction.

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arXiv2007

Spin effects in elastic backward P-D scattering

The elastic backward proton-deuteron scattering is analyzed including both relativistic effects in the deuteron and the reaction mechanism. It is shown that inclusion of the graphs corresponding to the emission, rescattering and absorption of the virtual pion by a deuteron nucleon in addition to the one-nucleon exchange graph allows a rather satisfactory description of all the experimental data on the differential cross section, tensor analyzing power of the deuteron and transfer polarization in this reaction.

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