# Dr Matteo Vorabbi

## Academic and research departments

Theoretical Nuclear Physics Group, School of Mathematics and Physics.## Teaching

- Quantum Physics (PHY2069) module.
- Part B - Analogue Electronics of the Electronic Circuit (EEE1025) module.
- Tutorials of Programming in C (EEE1035) module.

## Publications

In this work we use microscopic Nucleon–Nucleus Optical Potentials (OP) to analyze elastic scattering data for the differential cross section of the 78 Kr (p,p) 78 Kr reaction, with the goal of extracting the matter radius and estimating the neutron skin, quantities that are both needed to determine the slope parameter L of the nuclear symmetry energy. Our analysis is performed with the factorized version of the microscopic OP obtained in a previous series of papers within the Watson multiple scattering theory at the first order of the spectator expansion, which is based on the underlying nucleon–nucleon dynamics and is free from phenomeno-logical inputs. Differently from our previous applications, the proton and neutron densities are described with a two-parameter Fermi (2pF) distribution, which makes the extraction of the matter radius easier and allows us to make a meaningful comparison with the original analysis, that was performed with the Glauber model. With standard minimization techniques we performed data analysis and extracted the matter radius and the neutron skin. Our analysis produces a matter radius of R (rms) m = 4.12 fm, in good agreement with previous matter radii extracted from 76 Kr and 80 Kr, and a neutron skin of R np −0.1 fm, compatible with a previous analysis. Our factorized microscopic OP, supplied with 2pF densities, is a valuable tool to perform the analysis of the experimental differential cross section and extract information such as matter radius and neutron skin. Without any free parameters it provides a reasonably good description of the experimental differential cross section for scattering angles up to ≈ 40 degrees. Compared to the Glauber model our OP can be applied to a wider range of scattering angles and allows one to probe the nuclear systems in a more internal region.

A measurement of proton inelastic scattering of 8He at 8.25A MeV at TRIUMF shows a resonance at 3.54(6) MeV with a width of 0.89(11) MeV. The energy of the state is in good agreement with coupled cluster and no-core shell model with continuum calculations, with the latter successfully describing the measured resonance width as well. Its differential cross section analyzed with phenomenological collective excitation form factor and microscopic coupled reaction channels framework consistently reveals a large deformation parameter β2 = 0.40(3), consistent with no-core shell model predictions of a large neutron deformation. This deformed double-closed shell at the neutron drip-line opens a new paradigm.

The understanding of astrophysics processes and the performance of nuclear reactors and other nuclear systems depend on a precise description of the neutron interaction cross sections for materials and nuclei present in these environments. At low neutron energies, these cross sections exhibit resonance structure represented by sharp enhancements when the neutron energy is sufficiently close to excited levels in a compound nucleus. Such resonances can be characterized by their quantum numbers relative to angular momenta, which are often deduced in an ad hoc and irreproducible manner from the shape of the cross sections. The correct assignment of the quantum numbers of neutron resonances is therefore of paramount importance. To address this we have developed a machine-learning method to automate the identification and correction of these spin assignments. The algorithm is trained from simulated data, generated from statistical properties of resonance data for a given nucleus, to mimic the errors found in real data. In this project we describe five independent approaches to further develop and expand the applicability of the machine-learning spin classifier: i) Feature impact; ii) Integration with the Atlas; iii) Training optimization; iv) Spacings systematics; and v) Validation with polarized data. The premises, methods, results, and future perspectives are discussed.

The level density distribution of near closed-shell nuclei is much lower than the typical nucleus, therefore, the cross sections show significant fluctuations, and these fluctuations are not predictable. The current methodology used to describe such behavior and construct the probability table of the cross section is based on the extrapolation of the average resonance widths and average resonance spacings from the resonance region and use these parameters to construct the probability table. Although this is a standard and widely used technique, it does not take into account the existing experimental data, such for total and the elastic cross section. Our goal is to extend the current theory and provide a more general approach to compute the probability distribution function of the cross section combining the existing probability tables and the available experimental data. Results will be presented for ⁹⁰Zr.

The cross sections of neutron-induced reactions can be divided into three energy ranges: the resolved resonance region (RRR), the unresolved resonance region (URR), and the fast region. In general, the cross sections in the URR show significant fluctuations that cannot be predicted and cannot be experimentally resolved, thus, it is commonly assumed that the cross section at a specific energy is given by a probability distribution function (PDF) over a range of values that can span several orders of magnitude. The current methodology used to describe such behavior is to construct the PDF by stochastically generating resonance ladders and numerically measuring the PDF. The resonance ladders are sampled using known resonance statistical properties and average resonance widths and spacings extrapolated from the RRR. Although this is a standard and widely used technique, it is computationally very expensive, therefore, an alternative, analytical, approach would be preferable due to the considerable speed up of the computational time in real life applications. Moreover, the current methodology does not take into account existing experimental data, such for total and capture cross sections, that are available for many nuclei. Finally, this approach was developed to be used in reactor-scale applications and it is not suited for use in single-event applications. In this work we will rethink the entire approach to the PDF construction using a Bayesian mindset. This will allow us to provide a different definition of the PDF that allows a much faster calculation of the higher-temperature PDFs and a proper combination of theoretical and experimental PDFs following the probability theory. We will also show that our definition is well suited for single-event applications and we will make an explicit connection between our method and the standard approach. We do this by showing that the central limit theorem applies and our method leads to the same PDF obtained with the standard methodology, for a large number of events per history.

The National Ignition Facility at Lawrence Livermore National Laboratory uses ⁸⁶Kr as a diagnostic tool to measure the neutron flux produced by fusion reactions. As krypton is chemically inert, it can be implanted directly into the fuel capsule, and the reaction products can be measured to determine the flux of fusion neutrons. ⁸⁶Kr cross sections also provide model constraints for the ⁸⁵Kr branching point in the s-process and the neutron flux in stars. In this work, experimental data on the neutron production, radiative capture, inelastic scattering, and total cross sections of ⁸⁶Kr were used in conjunction with the fast region nuclear reaction code EMPIRE and a new resonance-region evaluation to produce a new evaluation of neutron-induced reactions on ⁸⁶Kr. For the EMPIRE calculations, we fitted the optical model potential up to 12 MeV to simultaneously reproduce the experimental data for the total cross section and the main inelastic gamma transition from the 2⁺ state to the 0⁺ ground state. For energies above 12 MeV, due to large fluctuations and uncertainties in the total cross section data, we preferred to adopt the Koning-Delaroche global spherical optical model potential. With these models and corrections to the structure of ⁸⁶Kr, the evaluated cross sections matched the experimental data. The new evaluation has been submitted for incorporation in the next release of the ENDF/B nuclear reaction library.

We perform a first-principle calculation of optical potentials for nucleon elastic scattering off medium-mass isotopes. Fully based on a saturating chiral Hamiltonian, the optical potentials are derived by folding nuclear density distributions computed with ab initio self-consistent Green's function theory with a nucleon-nucleon $t$ matrix computed with a consistent chiral interaction. The dependence on the folding interaction as well as the convergence of the target densities are investigated. Numerical results are presented and discussed for differential cross sections and analyzing powers, with focus on elastic proton scattering off Calcium and Nickel isotopes. Our optical potentials generally show a remarkable agreement with the available experimental data for laboratory energies in the range 65-200 MeV. We study the evolution of the scattering observables with increasing proton-neutron asymmetry by computing theoretical predictions of the cross section and analyzing power over the Calcium and Nickel isotopic chains.

Few years ago we started the investigation of microscopic Optical Potentials (OP) in the framework of chiral effective field theories [1, 2] and published our results in a series of manuscripts. Starting from the very first work [3], where a microscopic OP was introduced following the multiple scattering procedure of Watson [4], and then followed by Refs. [5, 6], where the agreement with experimental data and phenomenological approaches was successfully tested, we finally arrived at a description of elastic scattering processes off non-zero spin nuclei [7]. Among our achievements, it is worth mentioning the partial inclusion of three-nucleon forces [8], and the extension of our OP to antiproton-nucleus elastic scattering [9]. Despite the overall good agreement with empirical data obtained so far, we do believe that several improvements and upgrades of the present approach are still to be achieved.

We review recent progress and motivate the need for further developments in nuclear optical potentials that are widely used in the theoretical analysis of nucleon elastic scattering and reaction cross sections. In regions of the nuclear chart away from stability, which represent a frontier in nuclear science over the coming decade and which will be probed at new rare-isotope beam facilities worldwide, there is a targeted need to quantify and reduce theoretical reaction model uncertainties, especially with respect to nuclear optical potentials. We first describe the primary physics motivations for an improved description of nuclear reactions involving short-lived isotopes, focusing on its benefits for fundamental science discoveries and applications to medicine, energy, and security. We then outline the various methods in use today to build optical potentials starting from phenomenological, microscopic, and ab initio methods, highlighting in particular, the strengths and weaknesses of each approach. We then discuss publicly-available tools and resources facilitating the propagation of recent progresses in the field to practitioners. Finally, we provide a set of open challenges and recommendations for the field to advance the fundamental science goals of nuclear reaction studies in the rare-isotope beam era. This paper is the outcome of the Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program ‘Optical Potentials in Nuclear Physics’ held in March 2022 at FRIB. Its content is non-exhaustive, was chosen by the participants and reflects their efforts related to optical potentials.

We derived microscopic optical potentials (OPs) for elastic nucleon-nucleus scattering within the framework of chiral effective field theories at the first-order term of the spectator expansion of the Watson multiple-scattering theory and adopting the impulse approximation. Our OPs are derived by folding ab initio nuclear densities with a nucleon-nucleon (N N) t matrix computed with a consistent chiral interaction. The results of our OPs are in good agreement with the experimental data. Recent achievements of our work are reviewed in this contribution.

Background: Elastic scattering is probably the main event in the interactions of nucleons with nuclei. Even if this process has been extensively studied in the past years, a consistent description, i.e., starting from microscopic two-and many-body forces connected by the same symmetries and principles, is still under development. Purpose: In a previous paper [M. Vorabbi, P. Finelli, and C. Giusti, Phys. Rev. C 93, 034619 (2016)] we derived a theoretical optical potential from NN chiral potentials at fourth order ((NLO)-L-3). In the present work we use NN chiral potentials at fifth order ((NLO)-L-4), with the purpose to check the convergence and to assess the theoretical errors associated with the truncation of the chiral expansion in the construction of an optical potential. Methods: Within the same framework and with the same approximations as the previous paper [M. Vorabbi, P. Finelli, and C. Giusti, Phys. Rev. C 93, 034619 (2016)], the optical potential is derived as the first-order term within the spectator expansion of the nonrelativistic multiple scattering theory and adopting the impulse approximation and the optimum factorization approximation. Results: The pp and np Wolfenstein amplitudes and the cross section, analyzing power, and spin rotation of elastic proton scattering from O-16, C-12, and Ca-40 nuclei are presented at an incident proton energy of 200 MeV. The results obtained with different versions of chiral potentials at (NLO)-L-4 are compared. Conclusions: Our results indicate that convergence has been reached at (NLO)-L-4. The agreement with the experimental data is comparable with the agreement obtained in the previous paper [M. Vorabbi, P. Finelli, and C. Giusti, Phys. Rev. C 93, 034619 (2016)]. We confirm that building an optical potential within chiral perturbation theory is a promising approach for describing elastic proton-nucleus scattering.

We present theoretical predictions for electron scattering on oxygen and calcium isotopic chains. The calculations are done within the framework of the distorted-wave Born approximation and the proton and neutron density distributions are evaluated adopting a relativistic Dirac-Hartree model. We present results for the elastic and quasi-elastic cross sections and for the parity-violating asymmetry. As a first step, the results of the models are tested in comparison with some of the data available for elastic and quasi-elastic scattering on O-16 and Ca-40 nuclei. Then, the evolution of some nuclear properties is investigated as a function of the neutron number. We also present a comparison with the parity-violating asymmetry parameter obtained by the PREX Collaboration on Pb-208 and give a prediction for the future experiment CREX on Ca-48.

Background: Elastic scattering is probably the main event in the interactions of nucleons with nuclei. Even if this process has been extensively studied over the last years, a consistent description, i.e., starting from microscopic two- and many-body forces connected by the same symmetries and principles, is still under development. Purpose: In this work we study the domain of applicability of microscopic two-body chiral potentials in the construction of an optical potential. Methods: We basically follow the Kerman, McManus, and Thaler approach [Ann. Phys. (NY) 8, 551 (1959)] to build a microscopic complex optical potential, and then we perform some test calculations on O-16 at different energies. Results:. Our conclusion is that a particular set of potentials with a Lippmann-Schwinger cutoff at relatively high energies (above 500 MeV) reproduces best the scattering observables. Conclusions: Our work shows that building an optical potential within chiral perturbation theory is a promising approach for describing elastic proton scattering; in particular, in view of the future inclusion of many-body forces that naturally arises in such a framework.

The analysis of the recent charged-current neutrino-nucleus scattering cross sections measured by the ArgoNeuT Collaboration requires relativistic theoretical descriptions also accounting for the role of final-state interactions. In this work, we evaluate differential neutrino-nucleus cross sections with the relativistic Green's function model, where final-state interactions are described in the inclusive scattering consistently with the exclusive scattering using a complex optical potential. The sensitivity to the parametrization adopted for the phenomenological optical potential is discussed. The predictions of the relativistic Green's function model are compared with the results of different descriptions of final-state interactions.

We present and discuss numerical predictions for the neutron density distribution of Pb-208 using various nonrelativistic and relativistic mean-field models for the nuclear structure. Our results are compared with the very recent pion photoproduction data from Mainz. The parity-violating asymmetry parameter for elastic electron scattering at the kinematics of the PREX experiment at JLab and the neutron skin thickness are compared with the available data. We consider also the dependence between the neutron skin and the parameters of the expansion of the symmetry energy.

We present theoretical predictions for electron scattering on the N = 14,20, and 28 isotonic chains from proton-deficient to proton-rich nuclei. The calculations are performed within the framework of the distortedwave Born approximation and the proton and neutron density distributions are evaluated adopting a relativistic Hartree-Bogoliubov (RHB) approach with a density dependent meson-exchange interaction. We present results for the elastic and quasi-elastic cross sections and for the parity-violating asymmetry parameter. Owing to the correlations between the evolution of the electric charge form factors along each chain with the underlying proton shell structure of the isotones, elastic electron scattering experiments on isotones can provide useful information about the occupation and filling of the single-particle levels of protons.

Elastic scattering of antiprotons off He-4, C-12, and O-16,O-18 is described for the first time with a consistent microscopic approach based on the calculation of an optical potential (OP) describing the antiproton-target interaction. The OP is derived using the recent antiproton-nucleon ((p) over barN) chiral interaction to calculate the (p) over barN t matrix, while the target densities are computed with the ab initio no-core shell model using chiral interactions as well. Our results are in good agreement with the existing experimental data and the results computed at different chiral orders of the (p) over barN interaction display a well-defined convergence pattern.

Background: Elastic scattering is a very important process to understand nuclear interactions in finite nuclei. Despite decades of efforts, the goal of reaching a coherent description of this physical process in terms of microscopic forces is still far from being completed. Purpose: In previous papers we derived a nonrelativistic theoretical optical potential from nucleon-nucleon chiral potentials at fourth ((NLO)-L-3) and fifth order ((NLO)-L-4). We checked convergence patterns and established theoretical error bands. With this work we study the performances of our optical potential in comparison with those of a successful nonrelativistic phenomenological optical potential in the description of elastic proton scattering data on several isotopic chains at energies around and above 200 MeV. Methods: We use the same framework and the same approximations as adopted in our previous papers, where the nonrelativistic optical potential is derived at the first-order term within the spectator expansion of the multiple scattering theory and adopting the impulse approximation and the optimum factorization approximation. Results: The cross sections and analyzing powers for elastic proton scattering off calcium, nickel, tin, and lead isotopes are presented for several incident proton energies, exploring the range 156

Background: The nuclear optical potential is a successful tool for the study of nucleon-nucleus elastic scattering and its use has been further extended to inelastic scattering and other nuclear reactions. The nuclear density of the target nucleus is a fundamental ingredient in the construction of the optical potential and thus plays an important role in the description of the scattering process. Purpose: In this paper we derive a microscopic optical potential for intermediate energies using ab initio translationally invariant nonlocal one-body nuclear densities computed within the no-core shell model (NCSM) approach utilizing two- and three-nucleon chiral interactions as the only input. Methods: The optical potential is derived at first order within the spectator expansion of the nonrelativistic multiple scattering theory by adopting the impulse approximation. Nonlocal nuclear densities are derived from the NCSM one-body densities calculated in the second quantization. The translational invariance is generated by exactly removing the spurious center-of-mass (COM) component from the NCSM eigenstates. Results: The ground-state local and nonlocal densities of He-4,He-6,He-8, C-12, and O-16 are calculated and applied to optical potential construction. The differential cross sections and the analyzing powers for the elastic proton scattering off these nuclei are then calculated for different values of the incident proton energy. The impact of nonlocality and the COM removal is discussed. Conclusions: The use of nonlocal densities has a substantial impact on the differential cross sections and improves agreement with experiment in comparison to results generated with the local densities especially for light nuclei. For the halo nuclei He-6 and He-8, the results for the differential cross section are in a reasonable agreement with the data although a more sophisticated model for the optical potential is required to properly describe the analyzing powers.

Background: In a previous series of papers we investigated the domain of applicability of chiral potentials to the construction of a microscopic optical potential (OP) for elastic nucleon-nucleus scattering. The OP was derived at the first order of the spectator expansion of the Watson multiple scattering theory and its final expression was a folding integral between the nucleon-nucleon (NN) t matrix and the nuclear density of the target. In the calculations NN and three-nucleon (3N) chiral interactions were used for the target density and only the NN interaction for the NN t matrix. Purpose: The purpose of this work is to achieve another step towards the calculation of a more consistent OP introducing the 3N force also in the dynamic part of the OP. Methods: The full treatment of the 3N interaction is beyond our present capabilities. Thus, in the present work it is approximated with a density dependent NN interaction obtained after the averaging over the Fermi sphere. In practice, in our model the 3N force acts as a medium correction of the bare NN interaction used to calculate the t matrix. Even if the 3N force is treated in an approximate way, this method naturally extends our previous model of the OP and allows a direct comparison of our present and previous results. Results: We consider as case studies the elastic scattering of nucleons off C-12 and O-16. We present results for the differential cross section and the spin observables for different values of the projectile energy. From the comparison with the experimental data and with the results of our previous model we assess the importance of the 3N interaction in the dynamic part of the OP. Conclusions: Our analysis indicates that the contribution of the 3N force in the t matrix is small for the differential cross section and it is sizable for the spin observables, in particular, for the analyzing power. We find that the two-pion exchange term is the major contributor to the 3N force. A chiral expansion order-by-order analysis of the scattering observables confirms the convergence of our results at the next-to-next-to-next-to-leading-order, as already established in our previous work.

Background: The production of Be-7 and Li-7 nuclei plays an important role in primordial nucleosynthesis, nuclear astrophysics, and fusion energy generation. The He-3(alpha, gamma)Be-7 and H-3(alpha, gamma)Li-7 radiative-capture processes are important to determine the Li-7 abundance in the early universe and to predict the correct fraction of pp-chain branches resulting in Be-7 versus B-8 neutrinos. The Li-6(p, gamma)Be-7 has been investigated recently hinting at a possible cross section enhacement near the thershold. The Li-6(n, H-3)He-4 process can be utilized for tritium breeding in machines dedicated to fusion energy generation through the deuteron-tritium reaction, and is a neutron cross section standard used in the measurement and evaluation of fission cross sections. Purpose: In this work we study the properties of Be-7 and Li-7 within the no-core shell model with continuum (NCSMC) method, using chiral nucleon-nucleon interactions as the only input, and analyze all the binary mass partitions involved in the formation of these systems. Methods: The NCSMC is an ab initio method applicable to light nuclei that provides a unified description of bound and scattering states and thus is well suited to investigate systems with many resonances and pronounced clustering like Be-7 and Li-7. Results: Our calculations reproduce all the experimentally known states of the two systems and provide predictions for several new resonances of both parities. Some of these new possible resonances are built on the ground states of Li-6 and He-6, and thus represent a robust prediction. We do not find any resonance in the p + Li-6 mass partition near the threshold. On the other hand, in the p + He-6 mass partition of Li-7 we observe an S-wave resonance near the threshold producing a very pronounced peak in the calculated S factor of the He-6(p, gamma)Li-7 radiative-capture reaction. Conclusions: While we do not find a resonance near the thershold in the p + Li-6 channel, in the case of He-6 + p reaction a resonant S-wave state is predicted at a very low energy above the reaction threshold, which could be relevant for astrophysics and its implications should be investigated. We note though that this state lies above the three-body breakup threshold not included in our method and may be influenced by three-body continuum correlations.

Background: In recent years, we constructed a microscopic optical potential (OP) for elastic nucleon-nucleus (NA) scattering using modern approaches based on chiral theories for the nucleon-nucleon (NN) interaction. The OP was derived at first order of the spectator expansion in Watson multiple scattering theory and its final expression was a folding integral between the NN t matrix and the nuclear density of the target. Two- and three-body forces are consistently included both in the target and in the projectile description. Purpose: The purpose of this work is to apply our microscopic OP to nuclei characterized by a ground state of spin-parity quantum numbers J(pi) not equal 0(+). Methods: We extended our formalism to include the spin of the target nucleus. The full amplitudes of the NN reaction matrix are retained in the calculations starting from two- and three-body chiral forces. Results: The microscopic OP can be applied in the energy range 100

Background: The exotic He-9 nucleus, which presents one of the most extreme neutron-to-proton ratios, belongs to the N = 7 isotonic chain famous for the phenomenon of ground-state parity inversion with decreasing number of protons. Consequently, it would be expected to have an unnatural (positive) parity ground state similar to Be-11 and Li-10. Despite many experimental and theoretical investigations, its structure remains uncertain. Apart from the fact that it is unbound, other properties including the spin and parity of its ground state, and the very existence of additional low-lying resonances are still a matter of debate. Purpose: In this work, we study the properties of He-9 by analyzing the n + He-8 continuum in the context of the ab initio no-core shell model with continuum (NCSMC) formalism with chiral nucleon-nucleon interactions as the only input. Methods: The NCSMCis a state-of-the-art approach for the ab initio description of light nuclei. With its capability to predict properties of bound states, resonances, and scattering states in a unified framework, the method is particularly well suited for the study of unbound nuclei such as He-9. Results: Our analysis produces an unbound He-9 nucleus. Two resonant states are found at the energies of similar to 1 and similar to 3.5MeV, respectively, above the n + 8He breakup threshold. The first state has a spin-parity assignment of J(pi) = 1/2(-) and can be associated with the ground state of He-9, while the second, broader state has a spin parity of 3/2(-). No resonance is found in the 1/2(+) channel, only a very weak attraction. Conclusions: We find that the He-9 ground-state resonance has a negative parity and thus breaks the parity-inversion mechanism found in the Be-11 and Li-10 nuclei of the same N = 7 isotonic chain.

The only available electroweak measurement of the Pb-208 neutron skin Delta R-np, performed by the PREX-II Collaboration through polarized electron-lead scattering, shows a mild tension with respect to both the theoretical nuclear-model predictions and a host of measurements. However, the dependence on the weak mixing angle should be incorporated in the calculation, since its low-energy value is experimentally poorly known. We first repeat the PREX-II analysis confirming their measurement by fixing the weak mixing angle to its standard model value. Then, we show the explicit dependence of the PREX-II measurement on the weak mixing angle, obtaining that it is fully degenerate with the neutron skin. To break this degeneracy, we exploit the weak mixing angle measurement from atomic parity violation on lead, obtaining a slightly thinner neutron skin but with about doubled uncertainties, possibly easing the PREX tension. Relying on the theoretical prediction, Delta R-np(th) approximate to 0.13-0.19 fm, and using it as a prior in the fit, we find a weak mixing angle value about 1.2 sigma smaller than the standard model prediction. Thus, we suggest a possible solution of the PREX-II tension by showing that, considering its underlying dependence on the weak mixing angle, the PREX-II neutron skin determination could be in agreement with the other available measurements and predictions if the weak mixing angle at the proper energy scale is smaller than the standard model prediction.

We present the first ab initio calculations for open-shell nuclei past the tin isotopic line, focusing on Xe isotopes as well as doubly magic Sn isotopes. We show that, even for moderately hard interactions, it is possible to obtain meaningful predictions and that the NNLOsat, chiral interaction predicts radii and charge density distributions close to the experiment. We then make a new prediction for Sn-100. This paves the way for ab initio studies of exotic charge density distributions at the limit of the present ab initio mass domain, where experimental data is becoming available. The present study closes the gap between the largest isotopes reachable by ab initio methods and the smallest exotic nuclei accessible to electron scattering experiments.