Dr Laura Moschini

The next years will see the completion of the radioactive ion beam facility SPES (Selective Production of Exotic Species) and the upgrade of the accelerators complex at Istituto Nazionale di Fisica Nucleare – Legnaro National Laboratories (LNL) opening up new possibilities in the fields of nuclear structure, nuclear dynamics, nuclear astrophysics, and applications. The nuclear physics community has organised a workshop to discuss the new physics opportunities that will be possible in the near future by employing state-of-the-art detection systems. A detailed discussion of the outcome from the workshop is presented in this report.

In this work we study one-neutron halo nuclei, and in particular Be-11 and C-15, which can be seen as an inert core of Be-10 or C-14 plus a loosely bound neutron. During the last decades several transfer and breakup reactions involving these systems have been measured on different targets and energies. We study these processes using one single structure model for each nucleus applying the halo effective field theory (Halo EFT) at next-to-leading order NLO. The main parameters of this EFT are adjusted on nuclear-structure data and/or ab initio predictions. We model the transfer reaction within the Adiabatic Distorted Wave Approximation (ADWA) and the breakup process applying an eikonal model with a consistent treatment of nuclear and Coulomb interactions at all orders. At high energy, our model includes a proper treatment of special relativity Our theoretical calculations are in good agreement with experiment for a variety of reaction observables, thus assessing the robustness of the structure model provided for these nuclei. This new idea enables us also to reliably estimate the nuclear-structure observables that actually affect the reaction process, and hence that can be inferred from such measurements.

Be-11 is the archetypical one-neutron halo nucleus. Due to its short lifetime, one of the only way to infer information about its exotic structure is to study reactions involving that nucleus, like breakup. When performed on a heavy target, like lead, breakup is dominated by the E1 transition from the bound state to the continuum, which is characterized by the dB(E1)/dE. This strength has been inferred from two experiments, one performed at 520A MeV at GSI and the other at 69A MeV at RIKEN. Strangely the analyses of both experiments provide different E1 strengths. In this work, we reanalyze them using the eikonal approximation to study this discrepancy. In particular, we properly take into account relativistic effects, and include a consistent treatment of both nuclear and Coulomb interactions and their interference at all orders. The description of the 11 Be structure is provided by halo effective field theory (Halo-EFT). Our cross sections for the 11 Be breakup are in good agreement with both RIKEN and GSI data. The dB(E1)1dE extracted from our 11 Be model is in agreement with the RIKEN result and ab initio predictions. We can conclude that the discrepancy between GSI and RIKEN dB(E1)/dE arises from the method applied to extract this quantity. From our detailed analysis of the reaction, it seems that the most efficient way to extract the dB(E1)/dE from the breakup cross section is to select the data at small angles, where the reaction is dominated by the Coulomb interaction.

In this note we illustrate some applications of a simple model which has been devised to clarify the reaction mechanism and the interplay of different reaction channels (elastic, inelastic, transfer, break-up) in heavy-ion collisions. The model involves two potential wells moving in one dimension and few active particles; in spite of its simplicity, it is supposed to maintain the main features, the properties and the physics of the full three-dimensional case. Special attention is given to the role of continuum states in reactions involving weakly-bound systems, and different approximation schemes (as first-order or coupled-channels) as well as different continuum discretization procedures are tested. In the case of two active particles the reaction mechanism associated with two-particle transfer and the effect of pairing intearction are investigated.

We discuss the reaction mechanism associated with two-particle transfer reactions in a simple one-dimensional model. The reaction process is generated by two colliding wells and we follow in time the evolution of the two-particle wave function, initially concentrated in one of the two wells. At the end of the process one can single out the population of the different final channels, including one and two-particle transfer. When a residual short-ranged pairing interaction among the two particles is included in addition to the moving potentials, one observes a clear enhancement of the pair transfer as compared to the expectation of a pure sequential one-particle transfers. The final "exact" solution can be compared to the one obtained within different reaction and structure models (as coupled-channels, first-order approximation, approximate treatment of the continuum, etc), so providing important information on the reaction mechanism associated with the different processes.

A line of research has been developed to describe the structure and the dynamics of weakly-bound systems with one or more valence particles. To simplify the problem we are assuming particles moving in one dimension. Within this model one can describe, for example, direct reactions involving one or two valence neutrons: inelastic scattering, breakup and transfer processes. Exact solutions obtained by directly solving the many-body time-dependent Schrodinger equation can be compared with the results obtained with different approximate schemes (first-order, coupled channels, continuum discretization, etc.). In this contribution we concentrate on inelastic scattering.

The competition among reaction processes of a weakly-bound projectile at intermediate times of a slow collision has been unraveled. This has been done using a two-center molecular continuum within a semiclassical, time-dependent coupled-channel reaction model. Dynamical probabilities of elastic scattering, transfer and breakup agree with those derived from the direct integration of the time-dependent Schrödinger equation, demonstrating the usefulness of a two-center molecular continuum for gaining insights into the reaction dynamics of exotic nuclei.

Aside from being a one-neutron halo nucleus, $^{15}$C is interesting because it is involved in reactions of relevance for several nucleosynthesis scenarios. The aim of this work is to analyze various reactions involving $^{15}$C, using a single structure model based on Halo EFT. To develop a Halo-EFT model of $^{15}$C at NLO, we first extract the ANC of its ground state by analyzing $^{14}$C(d,p)$^{15}$C transfer data at low energy. Using this Halo-EFT description, we study the $^{15}$C Coulomb breakup at high (605AMeV) and intermediate (68AMeV) energies using eikonal models with a consistent treatment of nuclear and Coulomb interactions at all orders, and proper relativistic corrections. Finally, we study the $^{14}$C(n,$\gamma$)$^{15}$C radiative capture. Our theoretical cross sections are in good agreement with experimental data for all reactions, thereby assessing the robustness of the $^{15}$C Halo-EFT model. Since a simple NLO description is enough to reproduce all data, the only nuclear-structure observables that matter are the binding energy and its ANC, showing that all the reactions considered are purely peripheral. In particular, it confirms the ANC value obtained for the $^{15}$C ground state: 1.59$\pm$0.06fm$^{-1}$. Our model provides also a new estimate of the radiative-capture cross section at astrophysical energy (23.3keV): 4.66$\pm$0.14$\mu$b. Including a Halo-EFT description of $^{15}$C within precise models of reactions is confirmed to be an excellent way to relate the nucleus reaction cross sections and structure. Its systematic expansion enables us to deduce which nuclear-structure observables are actually probed in the collision. From this, we can infer valuable information on both the structure of $^{15}$C and its synthesis through the $^{14}$C(n,$\gamma$)$^{15}$C radiative capture at astrophysical energies.

The direct reaction theory widely used to study single-particle spectroscopic strength in nucleon transfer experiments is based on a Hamiltonian with two-nucleon interactions only. We point out that in reactions with a loosely-bound projectile, where clustering and breakup effects are important, an additional three-body force arises due to three-nucleon (3N) interaction between two nucleons belonging to different clusters in the projectile and a target nucleon. We study the effects of this force on nucleon transfer in (d,p) and (d,n) reactions on 56Ni, 48Ca, 26mAl and 24O targets at deuteron incident energies between 4 and 40 MeV/nucleon. Deuteron breakup is treated exactly within a continuum discretized coupled-channel approach. It was found that an additional three-body force can noticeably alter the angular distributions at forward angles, with consequences for spectroscopic factors' studies. Additional study of transfer to 2p continuum in the 25F(p,2p)24O reaction, involving the same overlap function as in the 24O(d,n)25F case, revealed that 3N force affects the (d,n) and (p,2p) reactions in a similar way, increasing the cross sections and decreasing spectroscopic factors, although its influence at the main peak of (p,2p) is weaker. The angle-integrated cross sections are found to be less sensitive to the 3N force contribution, they increase by less than 20%. Including 3N interactions in nucleon removal reactions makes an essential step towards bringing together nuclear structure theory, where 3N force is routinely used, and nuclear direct reaction theory, based on two-nucleon interactions only.

Background: The problem of the scattering of a one-neutron halo nucleus by another nucleus might involve an extremely complicated solution, particularly when breakup and rearrangement channels are to be considered. Purpose: We construct a simple model to study the evolution of a single-particle wave function during the collision of a one-dimensional potential well by another well. Method: Our one-dimensional model provides the essential three-body nature of this problem, and allows for a much simpler application and assessment of different methods of solution. To simplify further the problem, we assume that the potential well representing the projectile moves according to a predetermined classical trajectory, although the internal motion of the “valence” particle is treated fully quantum mechanically. This corresponds to a semiclassical approach of the scattering problem, applicable in the case of heavy projectile and target. Different approaches are investigated to understand the dynamics involving one-body halo-like systems: the “exact” time-dependent solution of the Schrödinger equation is compared to a numerical continuum-discretized coupled-channels (CC) calculation presenting various model cases including different reaction channels. Results: This framework allows us to discuss the reaction mechanism and the role of the continuum, the inclusion of which in the CC calculation results to be crucial to reproduce the exact solution, even when the initial and final states are well bound. Conclusions: The dynamical situations under study can be linked to analogous problems solved in a three-dimensional (3D) CC framework, so the present model provides a simple tool to understand the main challenges experienced in the usual 3D models with the treatment of the continuum.

The adiabatic distorted wave approximation (ADWA) is widely used by the nuclear community to analyse deuteron stripping ($d$,$p$) experiments. It provides a quick way to take into account an important property of the reaction mechanism: deuteron breakup. In this work we provide a numerical quantification of a perturbative correction to this theory, recently proposed in [R.C. Johnson, J. Phys. G: Nucl. Part. Phys. 41 (2014) 094005] for separable rank-one nucleon-proton potentials. The correction involves an additional, nonlocal, term in the effective deuteron-target ADWA potential in the entrance channel. We test the calculations with perturbative corrections against continuum-discretized coupled channel predictions which treat deuteron breakup exactly.

We analyze the breakup of the one-neutron halo nucleus 11Be measured at 520 MeV/nucleon at GSI on Pb and C targets within an eikonal description of the reaction including a proper treatment of special relativity. The Coulomb term of the projectile-target interaction is corrected at first order, while its nuclear part is described at the optical limit approximation. Good agreement with the data is obtained using a description of 11Be, which fits the breakup data of RIKEN. This solves the apparent discrepancy between the dB(E1)/dE estimations from GSI and RIKEN for this nucleus.