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Theoretical predictions for lepton-induced single-pion production (SPP) on $^{12}$C are revisited in order to assess the effect of different treatments of the current operator. On one hand we have the asymptotic approximation, which consists in replacing the particle four-vectors that enter in the operator by their asymptotic values, i.e., their values out of the nucleus. On the other hand we have the full calculation, which is a more accurate approach to the problem. We also compare with results in which the final nucleon is described by a relativistic plane wave, to rate the effect of the nucleon distortion. The study is performed for several lepton kinematics, reproducing inclusive and semi-inclusive cross sections belonging to the low-$Q^2$ region (between 0.05 and 1 GeV$^2$), which is of special interest in charged-current (CC) neutrino-nucleus 1$\pi$ production. Inclusive electron results are compared with experimental data. We find non-trivial corrections comparable in size with the effect of the nucleon distortion, namely, corrections up to 6\%, either increasing or diminishing the asymptotic prediction, and a shift of the distributions towards higher energy transfer. For the semi-inclusive cross sections, we observe the correction to be prominent mainly at low values of the outgoing nucleon kinetic energy. Finally, for CC neutrino-induced 1$\pi^+$ production, we find a reduction at low-$Q^2$ with respect to both the plane-wave approach and the asymptotic case.

We present a detailed study of the contribution from two-body currents to the one-nucleon knockout process induced by electromagnetic interaction. The framework is a relativistic mean-field model (RMF) in which bound and scattering nucleons are consistently described as solutions of Dirac equation with potentials. We show results obtained with the most general expression of the two-body operator, in which the intermediate nucleons are described by relativistic mean-field bound states; then, we propose two approximations consisting in describing the intermediate states as nucleons in a relativistic Fermi gas, preserving the complexity and consistency in the initial and final states. These approximations simplify the calculations considerably, allowing us to provide outcomes in a reasonable computational time. The results obtained under these approximations are validated by comparing with those from the full model. Additionally, the theoretical predictions are compared with experimental data of the longitudinal and transverse responses of carbon 12. The agreement with data is outstanding for the longitudinal response, where the contribution from the two-body operator is negligible. In the transverse sector, the two-body current increases the response from 30 to 15%, depending on the approximations and kinematics, in general, improving the agreement with data., Comment: 11 pages, 5 figures

The interactivism model introduces a dynamic approach to language, communication and cognition. In this work, we explore this fundamental theory in the context of dialogue modelling for spoken dialogue systems (SDS). To extend such a theoretical framework, we present a set of design principles which adhere to central psycholinguistic and communication theories to achieve interactivism in SDS. From these, key ideas are linked to constitute the basis of our proposed design principles.

Longitudinal ($R_L$) and transverse ($R_T$) responses from inclusive electron scattering from carbon 12 and calcium 40 nuclei are computed within a fully relativistic and unfactorized model for the initial and final states, and one- and two-body current operators leading to the one-particle one-hole responses. We find that the two-body contributions have no effect on $R_L$ but they increase $R_T$ by up to 30%, depending on the energy and momentum transfer. Inclusive cross sections have also been computed. In this case, the increase of $R_T$ due to two-body currents will translate into an increase in the cross-sections depending on the degree of transversity of each kinematic. The comparison with carbon data is good for the responses and the cross sections. In the case of calcium, while the model compares well with the cross section data, the agreement with the responses is generally poor. However, the inconsistencies between different data sets for the separate responses in this nucleus points to uncertainties underlying the procedure to extract the responses that are not considered (or largely underestimated) in the experimental error bars. Our calculation is fully relativistic and considers within the full quantum mechanical description both the initial and final nucleon states involved in the process. We also show that it is essential to go beyond the plane-wave approach, since incorporating the distortion of the nucleons while making the initial and final states orthogonal, allows to reproduce both the shape and magnitude of the cross section data and carbon responses. The good agreement with the electron scattering experimental data supports the use of this approach to describe the analogous neutrino-induced scattering reaction., Comment: 21 pages, 8 figures