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A. Molinari

Publications and source records attributed to A. Molinari.

At least 73 records · Page 4Linked to original sources
arXiv2001

Consistent one-pion exchange currents in electron scattering from a relativistic Fermi gas

A set of fully relativistic one-pion-exchange electromagnetic operators is developed for use in one-particle emission reactions induced by electrons. To preserve the gauge invariance of the theory additional pionic correlation operators are required beyond the usual meson-exchange current operators. Of these, in the present work emphasis is placed on the self-energy current which is infinite and needs to be renormalized. The renormalized current is expanded to first order to obtain a genuine one-pion-exchange contribution to the inclusive responses.

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arXiv2001

Relativistic pionic effects in quasielastic electron scattering

The impact of relativistic pionic correlations and meson-exchange currents on the response functions for electromagnetic quasielastic electron scattering from nuclei is studied in detail. Results in first-order perturbation theory are obtained for one-particle emission electronuclear reactions within the context of the relativistic Fermi gas model. Improving upon previous analyses where non-relativistic reductions of the currents were performed, here a fully relativistic analysis in which both forces and currents are treated consistently is presented. Lorentz covariance is shown to play a crucial role in enforcing the gauge invariance of the theory. Effects stemming uniquely from relativity in the pionic correlations are identified and, in particular, a comprehensive study of the self-energy contributions and of the currents associated with the pion is presented. First- and second-kind scaling for high momentum transfer is investigated.

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arXiv2001

The pairing Hamiltonian for one pair of identical nucleons bound in a potential well

The problem of one pair of identical nucleons sitting in ${\cal N}$ single particle levels of a potential well and interacting through the pairing force is treated introducing even Grassmann variables. The eigenvectors are analytically expressed solely in terms of these with coefficients fixed by the eigenvalues and the single particle energies. When the latter are those of an harmonic oscillator well an accurate expression is derived for both the collective eigenvalue and for those trapped in between the single particle levels, for any strength of the pairing interaction and for any number of levels. Notably the trapped solutions are labelled through an index upon which they depend parabolically.

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arXiv2000

The pairing Hamiltonian for one pair of nucleons bound in a potential well

The problem of one pair of identical nucleons sitting in ${\cal N}$ single particle levels of a potential well and interacting through the pairing force is treated introducing, in the Hamiltonian formalism, even Grassmann variables. The eigenvectors are analytically expressed solely in terms of these with coefficients fixed by the eigenvalues and the single particle energies. For these a specific model is needed: in the case of the harmonic oscillator well, for any strength of the pairing interaction, an accurate expression is derived for both the collective eigenvalue and for those trapped in between the single particle levels. Notably the latter are labelled through an index upon which they depend parabolically.

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arXiv2000

Contrasting N Delta and N N parity-violating asymmetries in nuclei

Several perspectives that can be opened by studying the electroexcitation of the delta via parity-violating electron scattering from nuclei are examined, working within the context of the relativistic Fermi gas model. A strong enhancement of the left-right asymmetry in the delta sector compared with that in the quasi-elastic regime is found and the potential to find clear signatures for the axial-vector contributions of the nucleon-to-delta transition to the asymmetry identified at specific low momentum transfer kinematics. Possibilities of probing the deformation of the delta are also explored, and using both the proton and nuclei as targets, the abilitiy to study the asymmetry on neutrons is studied.

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arXiv2000

Influence of nucleonic motion in Relativistic Fermi Gas inclusive responses

Impulsive hadronic descriptions of electroweak processes in nuclei involve two distinctly different elements: one stems from the nuclear many-body physics --- the medium --- which is rather similar for the various inclusive response functions, and the other embodies the responses of the hadrons themselves to the electroweak probe and varies with the channel selected. In this letter we investigate within the context of the relativistic Fermi gas in both the quasi-elastic and $N\toΔ$ regimes the interplay between these two elements. Specifically, we focus on expansions in the one small parameter in the problem, namely, the momentum of a nucleon in the initial wave function compared with the hadronic scale, the nucleon mass. Both parity-conserving and -violating inclusive responses are studied and the interplay between longitudinal ($L$) and transverse ($T$ and $T'$) contributions is highlighted.

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arXiv2000

Bosonization of the pairing Hamiltonian

The problem of the pairing interaction is dealt with even Grassmann variables in the hamiltonian framework. Eigenfunctions of given energy, seniority and zero third component of angular momentum are given in terms of single particle and collective bosonic fields.

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arXiv2000

A composite bosons minimal basis for the pairing Hamiltonian

The pairing interaction among identical nucleons in a single-particle level is treated in the hamiltonian formalism using even Grassmann variables. A minimal (irreducible) basis having a remarkable symmetry property is set up using composite, commuting variables with a finite index of nilpotency. Eigenvalues and eigenfunctions of given energy, seniority and zero third component of the angular momentum of the pairing hamiltonian are then found. The eigenvectors, which cannot be cast solely in terms of composite bosons with angular momentum zero and two, are expanded in the minimal basis with coefficients analytically expressed in terms of a generalized hypergeometric function.

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arXiv1999

Ground state energy fluctuations in nuclear matter II

Improvements are performed on a recently proposed statistical theory of the mean field of a many-fermion system. The dependence of the predictions of the theory upon its two basic ingredients, namely the Hartree-Fock energy and the average energy of the two particle-two hole excitations, is explored.

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arXiv1999

Relativistic effects in electromagnetic nuclear responses in the quasi-elastic delta region

A new non-relativistic expansion in terms of the nucleon's momentum inside nuclear matter of the current for isobar electro-excitation from the nucleon is performed. Being exact with respect to the transferred energy and momentum, this yields new current operators which retain important aspects of relativity not taken into account in the traditional non-relativistic reductions. The transition current thus obtained differs from the leading order of the traditional expansion by simple multiplicative factors. These depend on the momentum and energy transfer and can be easily included together with relativistic kinematics in non-relativistic, many-body models of isobar electro-excitation in nuclei. The merits of the new current are tested by comparing with the unexpanded electromagnetic nuclear responses in the isobar peak computed in a relativistic Fermi gas framework. The sensitivity of the relativistic responses to the isobar's magnetic, electric and Coulomb form factors and the finite width of the isobar is analyzed.

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arXiv1998

Relativistic Effects in Electromagnetic Meson-Exchange Currents for One-Particle Emission Reactions

Following recent studies of non-relativistic reductions of the single-nucleon electromagnetic current operator, here we extend the treatment to include meson exchange current operators. We focus on one-particle emission electronuclear reactions. In contrast to the traditional scheme where approximations are made for the transferred momentum, transferred energy and momenta of the initial-state struck nucleons, we treat the problem exactly for the transferred energy and momentum, thus obtaining new current operators which retain important aspects of relativity not taken into account in the traditional non-relativistic reductions. We calculate the matrix elements of our current operators between the Fermi sphere and a particle-hole state for several choices of kinematics. We present a comparison between our results using approximate current operators and those obtained using the fully-relativistic operators, as well as with results obtained using the traditional non-relativistic current operators.

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arXiv1998

Relativistic y-scaling and the Coulomb sum rule in nuclei

In this paper dividing factors GL and GT are constructed for the longitudinal and transverse responses of the relativistic Fermi gas in such a way that the reduced responses so obtained scale. These factors parallel another dividing factor studied previously, HL, that yields a (different) reduced response which fulfills the Coulomb sum rule. GL, GT and HL are all found to be only very weakly model-dependent, thus providing essentially universal dividing factors. To explore the residual degree of dependence which remains, the scaling and sum rule properties of several specific models have been considered. It is seen that the relativistic Fermi gas (by construction) and also typical shell-model reduced responses successfully scale and satisfy the Coulomb sum rule, as do experimental results at medium to high momentum transfers. On the other hand, it is observed that the quantum hadrodynamic model does so only if interaction effects become weaker with increasing momentum transfer, as predicted in the most recent versions of that model.

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arXiv1997

A statistical approach to the theory of the mean field

We develop a statistical theory of the mean field. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction are random with the average value of zero. Explicit expressions for the mean field and the fluctuation away from the average are obtained. The fluctuation is expanded in terms of more and more complex excitations. Using the randomness of the matrix elements one can then obtain formulas for the contribution to the error from each class of complex excitations and a general condition for the convergence of the expansion is derived. Making some simplifying assumptions a schematic model is developed and applied to the problem of nuclear matter. It yields a measure of the strength of the effective interaction. The latter turns out to be three orders of magnitude less than that calculated using a potential which gives a binding energy of about -7 MeV/nucleon demonstrating the strong damping of the interaction strength induced by the averaging process.

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arXiv1997

The semi-classical approach to the exclusive electron scattering

The semiclassical approach, successfully applied in the past to the inelastic, inclusive electron scattering off nuclei, is extended to the treatment of exclusive processes. The final states interaction is accounted for in the mean field approximation, respecting the Pauli principle. The impact on the exclusive cross section of the shape of the potential binding the nucleons into the nucleus and of the distortion of the outgoing nucleon wave are explored. The exclusive scattering is found to be quite sensitive to the mean field final states interaction, unlike the inclusive one. Indeed we verify that the latter is not affected, as implied by unitarity, by the distortion of the outgoing nucleon wave except for the effect of relativity, which is modest in the range of momenta up to about 500 MeV/c. Furthermore, depending upon the correlations between the directions of the outgoing and of the initial nucleon, the exclusive cross-section turns out to be remarkably sensitive to the shape of the potential binding the nucleons. These correlations also critically affect the domain in the missing energy-- missing momentum plane where the exclusive process occurs.

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arXiv1997

A statistical theory of the mean field

A statistical theory of the mean field is developed. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction, obtained after the average interaction is removed, are random with the average value of zero. With these two assumptions one obtains explicit expressions for the mean field and the fluctuation away from the average. The fluctuation is expanded in terms of more and more complex excitations. Using the randomness of the matrix elements one can then obtain formulas for the contribution to the error from each class of complex excitations and a general condition for the convergence of the expansion is derived. It is to be emphasized that no conditions on the nature of the system being studied are made. Making some simplifying assumptions a schematic model is developed. This model is applied to the problem of nuclear matter. The model yields a measure of the strength of the effective interaction. It turns out to be three orders of magnitude less than that calculated using a potential which gives a binding energy of about -7 MeV/nucleon demonstrating the strong damping of the interaction strength induced by the averaging process.

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arXiv1996

On the Coulomb and higher-order sum rules in the relativistic Fermi gas

Two different methods for establishing a space-like Coulomb sum rule for the relativistic Fermi gas are compared. Both of them divide the charge response by a normalizing factor such that the reduced response thus obtained fulfills the sum rule at large momentum transfer. To determine the factor, in the first approach one exploits the scaling property of the longitudinal response function, while in the second one enforces the completeness of the states in the space-like domain via the Foldy-Wouthuysen transformation. The energy-weighted and the squared-energy-weighted sum rules for the reduced responses are explored as well and the extension to momentum distributions that are more general than a step-function is also considered. The two methods yield reduced responses and Coulomb sum rules that saturate in the non-Pauli-blocked region, which can hardly be distinguished for Fermi momenta appropriate to atomic nuclei. Notably the sum rule obtained in the Foldy-Wouthuysen approach coincides with the well known non-relativistic one. Only at quite large momentum transfers (say 1 GeV/c) does a modest softening of the Foldy-Wouthuysen reduced response with respect to that obtained in the scaling framework show up. The two responses have the same half-width to second order in the Fermi momentum expansion. However, when distributions extending to momenta larger than that at the Fermi surface are employed, then in both methods the Coulomb sum rule saturates only if the normalizing factors are appropriately modified to account for the high momentum components of the nucleons.

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arXiv1996

Bosonization and even Grassmann variables

A new approach to bosonization in relativistic field theories and many-body systems, based on the use of fermionic composites as integration variables in the Berezin integral defining the partition function of the system, is tested. The method is applied to the study of a simplified version of the BCS model.

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