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The role of initial state (ISI) and final state (FSI) ion–ion interactions in heavy-ion doublecharge-exchange (DCE) reactions A(Z, N) → A(Z ± 2, N ∓ 2) are studied for double single-chargeexchange (DSCE) reactions given by sequential actions of the isovector nucleon–nucleon (NN) T-matrix. In momentum representation, the second-order DSCE reaction amplitude is shown to be given in factorized form by projectile and target nuclear matrix elements and a reaction kernel containing ISI and FSI. Expanding the intermediate propagator in a Taylor series with respect to auxiliary energy allows us to perform the summation in the leading-order term over intermediate nuclear states in closure approximation. The nuclear matrix element attains a form given by the products of two-body interactions directly exciting the n 2 p −2 and p 2n −2 DCE transitions in the projectile and the target nucleus, respectively. A surprising result is that the intermediate propagation induces correlations between the transition vertices, showing that DSCE reactions are a two-nucleon process that resembles a system of interacting spin–isospin dipoles. Transformation of the DSCE NN T-matrix interactions from the reaction theoretical t-channel form to the s-channel operator structure required for spectroscopic purposes is elaborated in detail, showing that, in general, a rich spectrum of spin scalar, spin vector and higher-rank spin tensor multipole transitions will contribute to a DSCE reaction. Similarities (and differences) to two-neutrino double-beta decay (DBD) are discussed. ISI/FSI distortion and absorption effects are illustrated in black sphere approximation and in an illustrative application to data.

We explore two-particle transfer reactions as a crucial probe of the occurrence of shape coexistence in shape phase transitions. The (t,p) reactions to the ground state and to excited 0+ states are calculated for the isotope chain of even-even Zirconium isotopes starting from stable nuclei up to beyond current experimental limits. Two-particle spectroscopic factors derived from Monte Carlo Shell Model calculations are used, together with the sequential description of the two-particle transfer reaction mechanism. The calculation shows a clear signature for a shape phase transition between 98Zr and 100Zr, which displays coexistence of a deformed ground state with an excited spherical 0+ state. Furthermore, we show that there is a qualitative difference with respect to the case of a normal shape phase transition that can be discriminated with two-neutron transfer reactions.

Background: Reactions with halo nuclei from deformed regions exhibit important deviations from the inert core + valence picture. Structure and reaction formalisms have recently been extended or adapted to explore the possibility of exciting the underlying core. Purpose: We will study up to what extent transfer reactions involving halo nuclei 11 Be and 17 C can be reproduced with two different models that have previously shown a good success reproducing the role of the core in light halo nuclei. Methods: We focus on the structure of 11 Be and 17 C with two core + valence models: Nilsson and a semimicroscopic particle-rotor model using antisymmetrized molecular dynamic calculations of the cores. These models are later used to study 16 C ( d ,p) 17 C and 11 Be ( d) 10 Be transfer reactions within the adiabatic distorted wave approximation. Results are compared with three different experimental data sets. Results: A good reproduction of both the structure and transfer reactions of 11 Be and 17 C is found. The Nilsson model provides an overall better agreement for the spectrum and reactions involving 17 C while the semimicroscopic model is more adequate for 11 Be , as expected, since the 17 C core is closer to an ideal rotor. Conclusions: Both models show promising results for the study of transfer reactions with halo nuclei. We expect that including microscopic information in the Nilsson model, following the spirit of the semimicroscopic model, can provide a useful, yet simple framework for studying newly discovered halo nuclei.

Double charge exchange (DCE) reactions induced by heavy ions are crucial tools to access information relevant for neutrinoless double beta decay nuclear matrix elements. In this context the NUMEN project aims to investigate, for each system of interest, the DCE reaction channel together with the whole set of reactions promoted by the same projectile/target interaction in the same experimental conditions and within the same theoretical framework.

Different reactions channels induced by the 18O + 40Ca collisions at 275 MeV incident energy are simultaneously measured and analysed consistently within the same reaction and structure frameworks within the NUMEN project. The project aims to provide data-driven information for the determination of the nuclear matrix elements involved in the neutrinoless double beta decay. In particular, the elastic and inelastic scattering, one- and two-proton transfer, one-neutron transfer, and single charge exchange reactions are explored. The full quantum-mechanical calculations, performed by including microscopic nuclear structure inputs, describe well all the experimental data, giving support to a multi-channel strategy for the analysis of heavy-ion induced direct reactions.

The broad network of nuclear reactions populated in the 18O + 12C collision was studied to test the capability of state-of-art nuclear structure and reaction theories to describe both the direct and sequential components of the (18O, 18F) single charge exchange nuclear reaction. The experiment was performed using the 18O beam at 275 MeV incident energy produced by the K800 superconducting cyclotron and the MAGNEX magnetic spectrometer at the Laboratori Nazionali del Sud of the Istituto Nazionale di Fisica Nucleare. A unique comprehensive and coherent theoretical calculation, able to describe the whole network of direct reactions, is the approach proposed for the first time to analyse this large set of experimental data. This holistic approach, applied both to the experimental and theoretical analysis, is the main feature and novelty of the work here presented.

Double charge exchange (DCE) reactions induced by heavy ions and other direct reactions characterized by same projectile and target are crucial tools to access information relevant for neutrinoless double beta decay nuclear matrix elements. In this context the NUMEN project aims to investigate, for each system of interest, not only the DCE channel but also the whole set of reactions promoted by the same projectile/target interaction in the same experimental conditions and within the same theoretical framework. An example of the application of such a multi-channel approach is presented here.

This work is concerned with the theoretical study of nuclear reactions between light charged ions at incident energies around and below the reactants Coulomb barrier, with a focus on the energy range of astrophysical interest for Big Bang and quiescent stellar processes. The main goal of the analysis is to investigate the sensitivity of nuclear reaction dynamics, and more specifically the cross-section predictions, to the description of the structure of each reactant, and in particular to clustering phenomena. The case of the 6Li + p -> 3He + 4He reaction was investigated explicitly, treating the process as a direct deuteron transfer in first- or second-order distorted-wave Born approximation (DWBA) and through a coupled reaction channels (CRC) approach. The penetrability of the Coulomb barrier in the initial state was also analysed phenomenologically from available experimental data, and studied theoretically taking into account the 6Li ground-state deformation. Chapter 1 of this thesis treats some phenomenological aspects of the class of nuclear reactions of interest, both taking place in vacuum (``bare-nuclei'') or immersed in an external medium. The tools developed in this chapter, in spite of (and thanks to) their simplicity, allow to understand the main features of the non-resonant sub-Coulomb reaction cross-section, providing analytical expressions that can be compared to the results of more advanced computations to discuss their qualitative meaning and implications. Section 1.2 includes a quantitative analysis on the electron screening anomalies observed in the 6Li + p -> 3He + 4He reaction. Chapter 2 is a dissertation on some characteristics of the static structure of an isolated nucleus, with a focus on clustered systems. In particular, section 2.2 presents the formalism of overlap functions, which are important for treating direct transfer reactions and encode the required information to represent reactants within a cluster model. Section 2.3 instead is d

We investigate the impact of the 6Li ground-state deformation on Coulomb-barrier penetrability in nuclear reactions between 6Li and a structureless projectile. The 6Li ground state is described through a quantum di-cluster model, including a quadrupolar component which induces a tensor term in the projectiletarget interaction. The corresponding ground-state form factor, for each possible 6Li orientation, is employed as a potential barrier in a Wentzel-Kramers-BrillouinJeffreys (WKB) radial penetrability calculation. The formalism was applied to the 6Li–p scattering. Throughout the sub-Coulomb energy range, we find no significant influence of the tensor interaction on the overall penetrability.

We introduce the concept of neutron-proton two-particle units (np-Weisskopf units) to be used in the analysis of the (3He,p) and (p,3He) reactions on nuclei along the N=Z line. These are presented for the conditions relevant to the (n, j, ) orbits expected from 16O to 100Sn. As is the case of the Weisskopf units for electromagnetic transitions, the np-WU’s will provide a simple, yet robust, measure of isoscalar and isovector np pairing collective effects

Background: Charge-exchange (CE) reactions offer a major opportunity to excite nuclear isovector modes, providing important clues about the nuclear interaction in the medium. Moreover, double charge-exchange reactions are proving to be a tempting tool to access nuclear transition matrix elements (NMEs) related to double beta-decay processes. The latter are also of crucial importance to extract neutrino properties from the half-life of the hypothetical neutrinoless double beta decay and to search for physics beyond the standard model. Purpose: Through a multichannel experimental analysis and a consistent theoretical approach of the 116 Cd ( 20 Ne , 20 F ) 116 In single charge-exchange (SCE) reaction at 306 MeV, we aim at disentangling from the experimental cross section the contribution of the competing mechanisms associated with second- or higher-order sequential transfer and/or inelastic processes. Methods: We measured excitation energy spectra and absolute cross sections for elastic + inelastic, one-proton transfer and SCE channels by using the MAGNEX large acceptance magnetic spectrometer to detect the ejectiles. For the first two channels, we also extracted the experimental cross-section angular distributions. The experimental data are compared with theoretical predictions obtained by performing two-step distorted-wave Born approximation and coupled reaction channel calculations. We employ spectroscopic amplitudes for single-particle transitions derived within a large-scale shell-model approach and different optical potentials for modeling the initial- and the final-state interactions. Results: The present study significantly mitigates the possible model dependence existing in the description of these complex reaction mechanisms thanks to the satisfactory reproduction of several channels at once. In particular, our work demonstrates that the two-step transfer mechanisms produce a non-negligible contribution to the total cross section of the 116 Cd ( 20 Ne , 20 F

The use of double charge exchange reactions is discussed in view of their application to extract information that may be helpful to determinate the nuclear matrix elements entering in the expression of neutrinoless double beta decay half-life. The strategy adopted in the experimental campaigns performed at INFN - Laboratori Nazionali del Sud and in the analysis methods within the NUMEN project is briefly described, emphasizing the advantages of the multi-channel approach to nuclear reaction data analysis. An overview on the research and development activities on the MAGNEX magnetic spectrometer is also given, with a focus on the chosen technological solutions for the focal plane detector which will guarantee the performances at high-rate conditions.

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 = 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.

We report on systematical optical model (OM) and continuum discretized coupled channel (CDCC) calculations applied to describe the elastic scattering angular distributions of exotic and stable nuclei projectiles on heavy targets. Our optical potential (OP) is composed of the nuclear microscopic double folding São Paulo potential (SPP), derived from the nonlocal nature of the interaction, and the Coulomb dipole polarization (CDP) potential, derived from the semiclassical theory of Coulomb excitation. The OP is compared to the trivial equivalent local potential (TELP), extracted from CDCC calculations. The OM and CDCC predictions corroborate each other and account for important differences in the nuclei reaction mechanisms, which are directly related to their structural properties. Thus, OM and CDCC establish a common basis for analyzing or even predicting exotic and stable nuclei reactions.

Background: Nucleon transfer reactions are selective tools for nuclear physics investigations. The theoretical and computational limits affecting in the past their data analysis could be nowadays surmounted thanks to the advent of methods with refined approximations and constraints, even when heavy-ion collisions are considered. Purpose: Modern microscopic calculations of heavy-ion-induced transfer reactions combined with precise experimental data offer the chance for accurately testing different reaction models as well as the nuclear structure description of the involved nuclear states. Method: Single proton and neutron transfer reactions were measured with the MAGNEX magnetic spectrometer for the 18 O + 40 Ca system at 15.3 A MeV. Excitation energy spectra and angular differential cross section distributions were extracted. The experimental results are compared with theoretical calculations performed in distorted wave and coupled channel Born approximation. The use of a coupled channel equivalent polarization potential to effectively describe the coupling effects affecting the initial state interaction is also considered. Spectroscopic amplitudes derived from a large-scale shell model with appropriate interactions adapted for the involved nuclei are employed. Results: Our theoretical calculations are in good agreement with experimental data, without the need for any scaling factor, validating the adopted reaction and nuclear structure parameters. Moreover, under the present experimental conditions, a weak dependence of the obtained results on the choice of the reaction models was observed. Conclusions: The good agreement between experimental and theoretical results validates the reliability of the parameter sets entering the calculations. They are extracted from or tested in complementary analyses of other reaction channels under the same experimental conditions. Such a multichannel approach represents the best option to pursue a solid, comprehensive, and model-in

Este trabajo se estudian núcleos exóticos ligeros débilmente ligados. En concreto, se centra en los núcleos 17C, 19C y 11Be. Se considera un problema de dos cuerpos: el neutrón menos ligado y el resto de nucleones, que forma una estructura compacta llamada core. Estos núcleos tienen una desviación importante respecto a la simetría esférica. Suponemos que el neutrón se mueve bajo la ación de un potencial elipsoidal, aplicando el modelo de Nilsson para núcleos deformados. Para el core solo se considera un grado de libertad rotacional colectivo. Mediante la diagonalización del hamiltoniano, se obtienen los niveles energéticos y funciones de onda de los distintos estados para los núcleos considerados. Este proceso se ha realizado utilizando un programa en Fortran, creado desde cero para este trabajo. Utilizando la función de onda obtenida para los núcleos 11Be y 17C, se calcula la sección eficaz diferencial para las reacciones 11Be(p,d) 10 Be y 16C(d,p) 17C. Los resultados obtenidos se comparan con los datos experimentales.

A novel method to extract the B(E1) strength of a weakly bound nucleus from experimental Coulomb dissociation data is proposed. The method makes use of continuum discretized coupled channels (CDCC) calculations, in which both nuclear and Coulomb forces are taken into account to all orders. This is a crucial advantage with respect to the standard procedure based on the Equivalent Photon Method (EPM) which does not properly take into account nuclear distortion, higher order coupling effects, or Coulomb- nuclear interference terms. The systematic and statistical uncertainties of this procedure are evaluated. The procedure is applied to the 11Be nucleus using two sets of available experimental data at different energies, for which seemingly incompatible B(E1) have been reported using the EPM. We show that the present procedure gives consistent B(E1) strengths, thus solving the aforementioned long-standing discrepancy between the two measurements.

Los núcleos halo, son núcleos con uno o varios nucleones débilmente ligados, llamados de valencia. Estos nucleones pueden alejarse en gran medida del resto del núcleo, que forma una estructura compacta llamada core. Este trabajo se centra en el estudio del 11Be, núcleo halo de un neutrón. Utilizamos un modelo sencillo en el que el core es un solo cuerpo inerte, y el neutrón de valencia, solo siente un potencial nuclear modelado como un pozo esférico finito. Las soluciones dentro y fuera del pozo son analíticas. Por lo tanto, imponiendo continuidad y derivabilidad entre las dos soluciones, somos capaces de obtener las funciones de onda del neutrón de valencia para estados ligados y no ligados, que llamaremos del continuo. Obtenidas dichas funciones, se calculan las probabilidades de transición dipolar eléctrica del estado fundamental a otros estados ligados o del continuo. Estas probabilidades se relacionan con la llamada regla de suma, que comprobaremos con nuestro modelo. Finalmente, sumando las transiciones al continuo, se obtiene la probabilidad de desligar el neutrón halo del resto del núcleo bajo la acción de un campo eléctrico dipolar.

The possibility to use a special class of heavy-ion induced direct reactions, such as double charge exchange reactions, is discussed in view of their application to extract information that may be helpful to determinate the nuclear matrix elements entering in the expression of neutrinoless double beta decay half-life. The methodology of the experimental campaign presently running at INFN - Laboratori Nazionali del Sud is reported andthe experimental challenges characterizing such activity are described.

There is a recently renewed interest on the study of single and double charge exchange reactions with heavy ions. We report here a preliminary theoretical study of double charge exchange reactions in terms of two successive charge exchanges in 2nd order Distorted Wave Born approximation. This allows us to include the effect of the different transfer channels in an approximate way. Evidences show that the charge exchange process is dominant. The following one in importance is the combination of one single charge exchange, one neutron pick-up and one proton stripping. This particular process calls for further investigation.

To access information on neutrinoless double beta decay (0νββ) nuclear matrix elements, it has been proposed by the NUMEN collaboration to exploit the analogies between double beta decay processes and double charge exchange (DCE) nuclear reactions, looking in particular at the conditions where the corresponding cross section can be factorized into nuclear reaction and nuclear structure terms. DCE reactions can be treated as a convolution of two correlated or uncorrelated single charge exchange (SCE) processes, resembling 0νββ and 2νββ, respectively. Thus it is important to model first SCE processes, to get a deeper insight into the possibility to factorize the corresponding cross section, so one can gain a better understanding of DCE cross section factorization. In this contribution, DCE reactions are discussed in terms of the convolution of two uncorrelated SCE processes, which should allow one to extract information on 2νββ nuclear matrix elements. These theoretical investigations are performed in close synergy with the experimental activity running at INFN-LNS within the NUMEN project.

El presente trabajo se centra en el estudio de núcleos exóticos ligeros, en concreto, en algunos núcleos denominados núcleos halo. En el caso de los núcleos estables ligeros, éstos se caracterizan por tener un número similar de protones y de neutrones mientras que en el caso de los núcleos exoticos ligeros, el número de uno u otro es significativamente mayor. Esta descompensación en el número de protones o de neutrones da lugar a la desestabilización del núcleo y, de aquí, que este tipo de núcleos se encuentren alejados del valle de estabilidad en el diagrama de Segré.

The article describes the main achievements of the NUMEN project together with an updated and detailed overview of the related R&D activities and theoretical developments. NUMEN proposes an innovative technique to access the nuclear matrix elements entering the expression of the lifetime of the double beta decay by cross section measurements of heavy-ion induced Double Charge Exchange (DCE) reactions. Despite the two processes, namely neutrinoless double beta decay and DCE reactions, are triggered by the weak and strong interaction respectively, important analogies are suggested. The basic point is the coincidence of the initial and final state many-body wave-functions in the two types of processes and the formal similarity of the transition operators. First experimental results obtained at the INFN-LNS laboratory for the 40Ca(18O,18Ne)40Ar reaction at 270 MeV, give encouraging indication on the capability of the proposed technique to access relevant quantitative information. The two major aspects for this project are the K800 Superconducting Cyclotron and MAGNEX spectrometer. The former is used for the acceleration of the required high resolution and low emittance heavy ion beams and the latter is the large acceptance magnetic spectrometer for the detection of the ejectiles. The use of the high-order trajectory reconstruction technique, implemented in MAGNEX, allows to reach the experimental resolution and sensitivity required for the accurate measurement of the DCE cross sections at forward angles. However, the tiny values of such cross sections and the resolution requirements demand beam intensities much larger than manageable with the present facility. The on-going upgrade of the INFN-LNS facilities in this perspective is part of the NUMEN project and will be discussed in the article.

This work reports on the scattering of 11Be on 197Au at energies around and below the Coulomb barrier. By experimentally identifying the elastic scattering, inelastic scattering and breakup channels, and comparing them with different calculations, valuable information on the 11Be structure and its B(E1) distribution to the continuum are obtained. On top of that, a deeper understanding of the scattering process at low energies is achieved for reactions of this kind, making these studies extendable to other loosely-bound systems like 17,19C

The program TFF calculates stripping single-particle form factors for one-neutron transfer in prior representation with appropriate perturbative treatment of recoil. Coupled equations are then integrated along a semiclassical trajectory to obtain one- and two-neutron transfer amplitudes and probabilities within first- and second-order perturbation theory. Total and differential cross-sections are then calculated by folding with a transmission function (obtained from a phenomenological imaginary absorption potential). The program description, user instructions and examples are discussed. View Full-Text

Neutron-proton pairing correlations are investigated in detail via np transfer reactions in N = Z sd-shell nuclei. In particular, we study the cross-section ratio of the lowest 0+ and 1+ states as an observable to quantify the interplay between T = 0 (isoscalar) and T = 1 (isovector) pairing strengths. The experimental results are compared to second-order distorted-wave Born approximation calculations with proton-neutron amplitudes obtained in the shell-model formalism using the universal sd-shell interaction B. Our results suggest underestimation of the nonneglible isoscalar pairing strength in the shell-model descriptions at the expense of the isovector channel.

Within the frame of the commissioning of a new experimental apparatus EXPADES we undertook the measurement of the elastic scattering angular distribution for the system O-17+Pb-208 at energy around the Coulomb barrier. The reaction dynamics induced by loosely bound Radioactive Ion Beams is currently being extensively studied [4]. In particular the study of the elastic scattering process allows to obtain direct information on the total reaction cross section of the exotic nuclei. In order to understand the effect of the low binding energy on the reaction mechanism it is important to compare radioactive weakly bound nuclei with stable strongly-bound nuclei. In this framework the study of the O-17+Pb-208 elastic scattering can be considered to be complementary to a previous measurement of the total reaction cross section for the system F-17+Pb-208 at energies of 86, 90.4 MeV [5, 6]. The data will be compared with those obtained for the neighboring systems O-16,O-18+Pb-208 and others available in literature.

The resonant breakup of 19C on protons measured at RIKEN [Y. Satou et al., Phys. Lett. B 660, 320 (2008)] is analyzed in terms of a valence-core model for 19C that includes possible core excitations. The analysis of the angular distribution of a prominent peak appearing in the relative-energy spectrum could be well described with this model and is consistent with the previous assignment of 5/2+ for this state. Inclusion of core-excitation effects are found to be essential to giving the correct magnitude of the cross section for this state. By contrast, the calculation assuming an inert 18C core is found to largely underestimate the data.

The Bardeen-Cooper-Schrieffer (BCS) formalism is extended by including the single-particle continuum in order to analyse the evolution of pairing in an isotopic chain from stability up to the drip line. We propose a continuum discret ized generalized BCS based on single-particle pseudostates (PS). These PS are generated from the diagonalization of the single-particle Hamiltonian within a Transformed Harmonic Oscillator (THO) basis. The consistency of the results versus the size of the basis is studied. The method is applied to neutron rich Oxygen and Carbon is otopes and compared with similar previous works and available experimental data. We make use of the flexibility of the proposed model in order to study the evolution of the occupation of the low-energy continuum when the system becomes weakly bound. We find a larger influence of the non-resonant continuum as long as the Fermi level approaches zero.