Solving the inhomogeneous Bethe-Salpeter Equation in Minkowski space: the zero-energy limit

For the first time, the inhomogeneous Bethe-Salpeter Equation for an interacting system, composed by two massive scalars exchanging a massive scalar, is numerically investigated in ladder approximation, directly in Minkowski space, by using an approach based on the Nakanishi integral representation. In this paper, the limiting case of zero-energy states is considered, extending the approach successfully applied to bound states. The numerical values of scattering lengths, are calculated for several values of the Yukawa coupling constant, by using two different integral equations that stem within the Nakanishi framework. Those low-energy observables are compared with (i) the analogous quantities recently obtained in literature, within a totally different framework and (ii) the non relativistic evaluations, for illustrating the relevance of a non perturbative, genuine field theoretical treatment in Minkowski space, even in the low-energy regime. Moreover, dynamical functions, like the Nakanishi weight functions and the distorted part of the zero-energy Light-front wave functions are also presented. Interestingly, a highly non trivial issue related to the abrupt change in the width of the support of the Nakanishi weight function, when the zero-energy limit is approached, is elucidated, ensuring a sound basis to the forthcoming evaluation of phase-shifts.Comment: 23 pages and 4 figures. Minor changes in the abstract, typos fixed and added a figure. Submitted for publicatio

Neutron electromagnetic form factors and inclusive scattering of polarized electrons by polarized 3^{3}He and 3^{3}H targets

The electromagnetic inclusive responses of polarized $^{3}$He and $^{3}$H are thoroughly investigated at the quasielastic peak for squared momentum transfers up to $2 (GeV/c)^2$, within the plane wave impulse approximation. Great emphasys is put on the effects in the bound-state due to different two- and three-body nuclear forces, and to the Coulomb interaction as well. A careful analysis of the polarized responses allows to select possible experiments for minimizing the model dependence in the extraction of the neutron electromagnetic form factors. In particular, the relevant role played by the proton in the transverse-longitudinal response of polarized $^{3}$He, at low momentum transfer, can be utilized for obtaining valuable information on the proton contribution to the total polarized response and eventually on the neutron charge form factor.Comment: 27 pages, Latex, 9 Postscript figures. To appear in Phys. Rev. C (July '97

Implication of the proton-deuteron radiative capture for Big Bang Nucleosynthesis

The astrophysical $S$-factor for the radiative capture $d(p,\gamma)^3$He in the energy-range of interest for Big Bang Nucleosynthesis (BBN) is calculated using an {\it ab-initio} approach. The nuclear Hamiltonian retains both two- and three-nucleon interactions - the Argonne $v_{18}$ and the Urbana IX, respectively. Both one- and many-body contributions to the nuclear current operator are included. The former retain for the first time, besides the $1/m$ leading order contribution ($m$ is the nucleon mass), also the next-to-leading order term, proportional to $1/m^3$. The many-body currents are constructed in order to satisfy the current conservation relation with the adopted Hamiltonian model. The hyperspherical harmonics technique is applied to solve the $A=3$ bound and scattering states. A particular attention is used in this second case in order to obtain, in the energy range of BBN, an uncertainty on the astrophysical $S$-factor of the order or below $\sim$1 %. Then, in this energy range, the $S$-factor is found to be $\sim$10 % larger than the currently adopted values.Part of this increase (1-3 %) is due to the $1/m^3$ one-body operator, while the remaining is due to the new more accurate scattering wave functions. We have studied the implication of this new determination for the $d(p,\gamma)^3$He $S$-factor on deuterium primordial abundance. We find that the predicted theoretical value for $^2$H/H is in excellent agreement with its experimental determination, using the most recent determination of baryon density of Planck experiment, and with a standard number of relativistic degrees of freedom $N_{\rm eff}=3.046$ during primordial nucleosynthesis.Comment: 5 pages, 2 figures, submitted to Phys. Rev. Let

Fermionic bound states in Minkowski-space: Light-cone singularities and structure

The Bethe-Salpeter equation for two-body bound system with spin $1/2$ constituent is addressed directly in the Minkowski space. In order to accomplish this aim we use the Nakanishi integral representation of the Bethe-Salpeter amplitude and exploit the formal tool represented by the exact projection onto the null-plane. This formal step allows one i) to deal with end-point singularities one meets and ii) to find stable results, up to strongly relativistic regimes, that settles in strongly bound systems. We apply this technique to obtain the numerical dependence of the binding energies upon the coupling constants and the light-front amplitudes for a fermion-fermion $0^+$ state with interaction kernels, in ladder approximation, corresponding to scalar-, pseudoscalar- and vector boson exchanges, respectively. After completing the numerical survey of the previous cases, we extend our approach to a quark-antiquark system in $0^-$ state, taking both constituent-fermion and exchanged boson masses, from lattice calculations. Interestingly, the calculated light-front amplitudes for such a mock pion show peculiar signatures of the spin degrees of freedom.Comment: 22 pages, 7 figures, bst file include

Restricted infinitesimal deformations of restricted simple Lie algebras

We compute the restricted infinitesimal deformations of the restricted simple Lie algebras over an algebraically closed field of characteristic different from 2 and 3.Comment: 15 pages; final version, to appear in Journal of Algebra and Its Application

Micropollutants throughout an integrated urban drainage model: Sensitivity and uncertainty analysis

The paper presents the sensitivity and uncertainty analysis of an integrated urban drainage model which includes micropollutants. Specifically, a bespoke integrated model developed in previous studies has been modified in order to include the micropollutant assessment (namely, sulfamethoxazole \ue2\u80\u93 SMX). The model takes into account also the interactions between the three components of the system: sewer system (SS), wastewater treatment plant (WWTP) and receiving water body (RWB). The analysis has been applied to an experimental catchment nearby Palermo (Italy): the Nocella catchment. Overall, five scenarios, each characterized by different uncertainty combinations of sub-systems (i.e., SS, WWTP and RWB), have been considered applying, for the sensitivity analysis, the Extended-FAST method in order to select the key factors affecting the RWB quality and to design a reliable/useful experimental campaign. Results have demonstrated that sensitivity analysis is a powerful tool for increasing operator confidence in the modelling results. The approach adopted here can be used for blocking some non-identifiable factors, thus wisely modifying the structure of the model and reducing the related uncertainty. The model factors related to the SS have been found to be the most relevant factors affecting the SMX modeling in the RWB when all model factors (scenario 1) or model factors of SS (scenarios 2 and 3) are varied. If the only factors related to the WWTP are changed (scenarios 4 and 5), the SMX concentration in the RWB is mainly influenced (till to 95% influence of the total variance for SSMX,max) by the aerobic sorption coefficient. A progressive uncertainty reduction from the upstream to downstream was found for the soluble fraction of SMX in the RWB

BioMAc 2016 Bioreattori a membrane (MBR) e trattamenti avanzati per la depurazione delle acque

Questo volume raccoglie i contributi presentati nella manifestazione BioMAc 2016: Bioreattori a Membrane (MBR) e trattamenti avanzati per la depurazione delle Acque, che ha avuto luogo presso il Dipartimento di Ingegneria Civile, Ambientale, Aerospaziale, dei Materiali dell'Universit\ue0 degli Studi di Palermo, Aula G. Capit\uf2, nei giorni 27 e 28 ottobre 2016

Bethe-Salpeter bound-state structure in Minkowski space

The quantitative investigation of the scalar Bethe-Salpeter equation in Minkowski space, within the ladder-approximation framework, is extended to include the excited states. This study has been carried out for an interacting system composed by two massive bosons exchanging a massive scalar, by adopting (i) the Nakanishi integral representation of the Bethe-Salpeter amplitude, and (ii) the formally exact projection onto the null plane. Our analysis, on one hand, confirms the reliability of the method already applied to the ground state and, on the other one, extends the investigation from the valence distribution in momentum space to the corresponding quantity in the impact-parameter space, pointing out some relevant features, like (i) the equivalence between Minkowski and Euclidean transverse-momentum amplitudes, and (ii) the leading exponential fall-off of the valence wave function in the impact-parameter space.Comment: 15 pages, 7 figure

Simplified model to evaluate the fate of micropollutants in an integrated urban drainage system: sensitivity analysis

The paper presents the sensitivity analysis of an integrated urban water quality system by means of the global sensitivity analysis (GSA). Specifically, an home-made integrated model developed in previous studies has been modified in order to include the micropollutant assessment (namely, sulfamethoxazole - SMX). The model takes into account also the interactions between the three components of the system: sewer system (SS), wastewater treatment plant (WWTP) and the receiving water body (RWB). The analysis has been applied to an experimental catchment nearby Palermo (Italy): the Nocella catchment. Five scenarios each characterized by different combinations of sub-systems (i.e., SS, WWTP and RWB) have been considered applying the Extended-FAST method in order to select the key factors affecting the RWB quality and to design a reliable/useful experimental campaign. Results demonstrated that GSA is a powerful tool for increasing operator confidence in the modelling results; the approach can be used for blocking some non-identifiable parameters thus wisely modifying the structure of the model and reducing the related uncertainty. The model factors related to the SS have been found to be the most relevant factors affecting the SMX modelin