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

Abstract

The splitting between the charge-longitudinal and spin-transverse responses is explained in a model whose inputs are the effective interactions in the particle-hole channels in the frame of the first order boson loop expansion. It is shown that the interplay between ω-meson exchange and box diagrams (two-meson exchange with simultaneous excitation of one or two nucleons to ∆'s) mainly rules the longitudinal response, while in the transverse one the direct ∆ excitations almost cancel the one-loop correction and the response is mainly governed by the ρ-meson rescattering inside the nucleus. It is also shown that a small variation in the nuclear densities may explain the observed discrepancies between different nuclei.

The role of the Δ(1232) on the longitudinal response in the inclusive electron scattering reaction

“…Also Pauli matrices must be replaced by the corresponding transitions matrices S and T or S and T , the 3/2-3/2 spin matrices (see ref. [29]); depending on the character of the mesonic vertex. Table I: Effective masses and energies shifts employed in R…”

“…The ∆ is also incorporated in the longitudinal response in the works of Cenni et al. [29] and Amore et al [30] where the Boson Loop Expansion is employed. In Amaro et al [18] (and also in Ref.…”

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

“…Moreover, in eq. (2.3) we have included a monopole form factor for the πΛN vertex: 6) with the same cut-off Λ π = 1.3 GeV used for the πNN strong vertex. In fig.…”

“…On the other hand, as we will see, the RPA automatically appears in this framework as the mean field level. The method has been extensively applied to different processes in nuclear physics [4][5][6]. We will use it for the calculation of the Λ decay rates in nuclear matter, which can be expressed through the nuclear responses to pseudoscalar-isovector and vector-isovector fields.…”

Antisymmetrized Green’s function approach to (e,e′) reactions with a realistic nuclear density

“…Among them, the more recent ones are concerned with the contribution to the inclusive cross section of meson exchange currents and isobar excitations [5][6][7][8], with the effect of correlations [9,10], and the use of a relativistic framework in the calculations [7,11].…”