R. Cenni

Evaluation of a class of diagrams useful in many-body calculations

Abstract A recent functional approach to the many-body theory has put in evidence the relevance of the diagrams containing one fermion loop only. We shall prove here a relevant theorem which shows that all (but one) of the γ-functions are irrelevant, the contained information being transferred to analyticity properties. The simplest diagrams are explicitly evaluated and some useful limits are discussed. However, some of these diagrams have been considered also in different approaches to the many-body problem, so their evaluation is of general interest. The low-density behaviour is also considered.

Orthogonality, antisymmetry and c.m. effects in direct photoreactions

Abstract The relevance of different approximations usually adopted in the description of direct knockout of nucleons in photoreactions at medium energies is investigated. Orthogonality between initial and final states in DWIA and antisymmetrization of the outgoing particle are studied in the presence of recoil terms arising from a correct treatment of the c.m. motion. The different effects are discussed in the specific example of the 12 C target nucleus for different combinations of bound and scattering states. Whereas orthogonality and antisymmetrization appear to play a rather relevant role only at backward angles, the recoil term is particularly important for the (γ, n) reaction and cannot be simulated by the use of multipole energy-independent effective charges.

Relativistic γ-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.

Functional Treatment of the Meson Exchange Currents

Abstract Two alternative formulations of the meson exchange currents (MEC) and of the associated response to an electromagnetic field are derived in the path integral framework for a system of nucleons and pion with either a pseudoscalar or a pseudovector interaction. In the first approach, by integrating out the pionic and the electromagnetic fields configurations, we deduce a fermionic effective action SeffF leading, in conventional perturbation theory, to the standard expression for the MEC. In the second one, instead, by integrating out the fermions and electromagnetic fields configuration, we obtain a bosonic effective action SeffB. We evaluate the functional generator ZC associated to the latter in the stationary phase approximation (mean field) plus leading order quantum fluctuations. The corresponding response, most suited to deal with the physics at high energies and densities, includes RPA dressed pion propagators, the exchange interaction between the particle and the hole, the full variety of the two particles-two holes diagrams as well as the so-called bubbles into bubble (to leading order) and the nucleon self-energy (to infinite order). Thus the functional expansion, closely related to the loop expansion of the field theory, yields an unambiguous prescription for the diagrams to be kept in order to achieve a consistent many-body description of the response of a system of pions and nucleons to an electromagnetic field.

Functional approach to the non-mesonic decay of Λ-hypernuclei

Abstract We present an evaluation of the non-mesonic decay widths for Λ -hypernuclei ( ΛN → NN , ΛNN → NNN ) within the framework of the polarization propagator method. The full Λ self-energy is evaluated microscopically in nuclear matter by using the functional approach, which supplies a theoretically well grounded approximation scheme for the classification of the relevant diagrams, according to the prescriptions of the bosonic loop expansion. We employ average Fermi momenta, suitably adapted to different mass number regions (medium-light, medium and heavy hypernuclei). Moreover, we study the dependence of the decay rates on the NN and ΛN short range correlations. With a proper choice of the parameters which control these correlations in the new approximation scheme, it is possible to reproduce the experimental decay widths for A ≳10 hypernuclei.

Relativistic electromagnetic charge response: Finite versus infinite systems, exclusive versus inclusive processes

Connections are explored between exclusive and inclusive electron scattering within the framework of the relativistic plane-wave impulse approximation, beginning with an analysis of the model-independent kinematical constraints to be found in the missing energy--missing momentum plane. From the interplay between these constraints and the spectral function basic features of the exclusive and inclusive nuclear responses are seen to arise. In particular, the responses of the relativistic Fermi gas and of a specific hybrid model with confined nucleons in the initial state are compared in this work. As expected, the exclusive responses are significantly different in the two models, whereas the inclusive ones are rather similar. By extending previous work on the relativistic Fermi gas, a reduced response is introduced for the hybrid model such that it fulfills the Coulomb and the higher-power energy-weighted sum rules. While incorporating specific classes of off-shellness for the struck nucleons, it is found that the reducing factor required is largely model-independent and, as such, yields a reduced response that is useful for extracting the Coulomb sum rule from experimental data. Finally, guided by the difference between the energy-weighted sum rules of the two models, a version of the relativistic Fermi gas is devised which has the 0

The longitudinal and transverse responses in the inclusive electron scattering A functional approach

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Dynamical model for π-photoproduction in the Δ-channel

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Δ photoexcitation in nuclei

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

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