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This article was published in volume 69, issue 1 of publishing year 2020, with the wrong Figure 1. The correct Figure 1 is the one included in this erratum.

The elastic scattering in the reaction $$^{7}$$ 7 Li+$$^{208}$$ 208 Pb was investigated in the bombarding energy range from 25 to 39 MeV. The real and imaginary parts of the optical potential were analyzed by using a phenomenological potential. A dispersion relation analysis is presented in order to investigate the threshold anomaly effect. It is concluded that $$^{7}$$ 7 Li has an intermediate behavior between the tightly bound nuclei such as $$^{16}$$ 16 O and the loosely bound nuclei such as $$^{6}$$ 6 Li where the lack of the threshold anomaly is unambiguously observed. Reaction cross sections are also extracted from the elastic scattering data and its comparison with the ones of other systems has been performed to draw hints on the effect of the breakup channel.

The quantum shape phase transitions in odd-even nuclei are investigated within the intrinsic frame approach to the interacting boson-fermion model. In this work, the case of a single-j fermion coupled to a bosonic core that performs a transition from prolate to oblate shapes is considered. The focus is on the effect of the coupled fermion on the whole system along the transitional path from prolate to oblate shapes, passing through the ?-unstable shape. One could expect that all the magnetic substates of the coupled single-fermion with j= 9 / 2 would be driven by the shape of the bosonic core. However, the present work shows that the odd-fermion follows some unexpected and unique paths. The five-components of the j= 9 / 2 orbital do show quite interesting and diverse behaviour. Two of them move slowly from the prolate to the oblate shape by venturing into the triaxial region and also show ?-softness around their slow shape-changing region. The other three odd-states show sudden jumps from prolate side to oblate side and shape coexistence appears, although one of them is fairly close to ?-instability. These unexpected situations make this shape phase transition worth of investigation and discussion. © 2021, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature. FIS2017-88410-P, PID2019-104002GB-C22European Commission***Delivered and deleted from Elsevier end because this record is to be no longer updated or in business with Elsevier on Date 10-03-2020***, EC: H2020-INFRAIA-2014-2015, ENSAR2119T127Türkiye Bilimsel ve Teknolojik Araştirma Kurumu, TÜBITAKConsejería de Economía, Conocimiento, Empresas y Universidad, Junta de Andalucía: FQM-160 This work was supported by the Scientific and Technical Research Council of Turkey (TÜBİTAK), under the project number 119T127, by the Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía (Spain) under Group FQM-160, by the Spanish Ministerio de Ciencia e Innovacíon, ref. FIS2017-88410-P and PID2019-104002GB-C22, and by the European Commission, ref. H2020-INFRAIA-2014-2015 (ENSAR2).

The molecular algebraic model based on three and four alpha clusters is used to describe the inelastic scattering of alpha particles populating low-lying states in $^{12}$C and $^{16}$O. Optical potentials and inelastic formfactors are obtained by folding densities and transition densities obtained within the molecular model. One-step and multi-step processes can be included in the reaction mechanism calculation. In spite of the simplicity of the approach the molecular model with rotations and vibrations provides a reliable description of reactions where $\alpha$-cluster degrees of freedom are involved and good results are obtained for the excitation of several low-lying states. Within the same model we briefly discuss the expected selection rules for the $\alpha$-transfer reactions from $^{12}$C and $^{16}$O., Comment: 8 pages, 8 figures; submitted to EPJA special issue Cluster Structure and Dynamics of Nuclei - A Tribute to Mahir Hussein

Liquid fibrinogen is an injectable platelet concentrate rich in platelets, leukocytes, and fibrinogen obtained by blood centrifugation. The aim of this study was to analyze the release of different growth factors in the liquid fibrinogen at different times and to assess possible correlations between growth factors and cell counts. The concentration of transforming growth factor beta 1 (TGF-&beta, 1), platelet-derived growth factor-AB (PDGF-AB), platelet-derived growth factor-BB (PDGF-BB), bone morphogenetic protein 2 (BMP-2), fibroblast growth factor 2 (FGF-2) and vascular endothelial growth factor (VEGF) released by liquid fibrinogen were examined with ELISA at three time points (T0, time of collection, T7, 7 days, T14, 14 days). The cellular content of the liquid fibrinogen and whole blood was also calculated for each volunteer. A mean accumulation of platelets of almost 1.5-fold in liquid fibrinogen compared to whole blood samples was found. An increase of TGF-&beta, 1, PDGF-AB, FGF-2, and VEGF levels was detected at T7. At T14, the level of TGF-&beta, 1 returned to T0 level, PDGF-AB amount remained high, the levels of FGF-2 and VEGF decreased with respect to T7, but remained higher than the T0 levels, PDGF-BB was high at all time points, BMP-2 level was low and remained constant at all time points. TGF-&beta, 1, PDGF-AB, and PDGF-BB showed a correlation with platelet amount, whereas BMP-2, FGF-2, and VEGF showed a mild correlation with platelet amount. Due to the high concentration of platelets, liquid fibrinogen does contain important growth factors for the regeneration of both soft and hard tissue. The centrifugation protocol tested in this study provides a valid solution to stimulate wound healing in oral and periodontal surgery.

The surgical treatment of peri-implantitis is currently based on the removal of biofilms from the implant surface by primary means of mechanical and physical treatments. However, such approaches often determine some alterations of the implant surface with detrimental effects on re-osseointegration. This study aims to evaluate the effects of four different mechanical and physical treatments on titanium samples with moderately rough surface. Air powder abrasion (AP) with glycine powder, a titanium brush (TB) and a diode laser at 3 W (L3) and 4 W (L4) were tested. Surface morphology, roughness and chemical composition were then assessed by scanning electron microscope (SEM), white light interferometer and X-ray photoelectron spectroscopy (XPS), respectively. The microscopic analysis revealed significant alterations in surface morphology on TB samples, while AP and L3 had only a minor or null impact. L4 samples revealed signs of overheating due to the excessive power. Nevertheless, the overall roughness of the samples was not significantly altered in terms of roughness parameters. Similarly, surface chemical composition was not significantly affected by the treatments. Among the treatments tested in this study, air powder abrasion with glycine powder and 3 W diode laser had the lowest impact on surface physicochemical properties.

The aim of this study was to review the histologic evidence of reosseointegration and related influencing factors in experimental induced peri-implantitis.An electronic search was performed on Medline for animal studies that included a histometric evaluation of the amount of regenerated bone in contact with an implant surface. Questions raised in the study focused on the role of implant surfaces, bone regeneration and decontamination treatments in achieving reosseointegration. A detailed electronic search was then conducted on MEDLINE (PubMed) up to July 2017.One hundred and one articles were selected as abstract, thirty-seven articles assessed as full-text and sixteen finally included in the study. Reported measurements of reosseointegration varied significantly in the study, from 0 to 3.37 mm. There is histological evidence that reosseointegration can occur after treatment of ligature-induced peri-implantitis. However regenerated bone in contact with bone is generally restricted to the most apical portion of the peri-implant defect.Animal studies of induced peri-implantitis seem to indicate that rough surfaces can enhance reosseointegration as compared to smooth surfaces. With regard to bone regeneration techniques and materials, submerged healing and barrier membranes have shown a positive effect on reosseointegration. No evidence exists, however, about the specific role of different bone substitutes and their ability to improve bone formation. Growth factors have been shown to improve reosseointegration in animal models, though additional study is required to confirm the data. Several decontamination treatments have been shown to promote reosseointegration compared to control; however no specific procedure has proven superior to others in achieving reosseointegration.

Background: The $^{29}\mathrm{F}$ system is located at the lower-$N$ boundary of the ``island of inversion'' and is an exotic, weakly bound system. Little is known about this system beyond its two-neutron separation energy (${S}_{2n}$) with large uncertainties. A similar situation is found for the low-lying spectrum of its unbound binary subsystem $^{28}\mathrm{F}$.Purpose: We investigate the configuration mixing, matter radius, and neutron-neutron correlations in the ground-state of $^{29}\mathrm{F}$ within a three-body model, exploring the possibility of $^{29}\mathrm{F}$ to be a two-neutron halo nucleus.Method: The $^{29}\mathrm{F}$ ground-state wave function is built within the hyperspherical formalism by using an analytical transformed harmonic oscillator basis. The Gogny-Pires-Tourreil (GPT) $nn$ interaction with central, spin-orbit, and tensor terms is employed in the present calculations, together with different $\text{core}+n$ potentials constrained by the available experimental information on $^{28}\mathrm{F}$.Results: The $^{29}\mathrm{F}$ ground-state configuration mixing and its matter radius are computed for different choices of the $^{28}\mathrm{F}$ structure and ${S}_{2n}$ value. The admixture of $d$ waves with $pf$ components is found to play an important role, favoring the dominance of dineutron configurations in the wave function. Our computed radii show a mild sensitivity to the $^{27}\mathrm{F}+n$ potential and ${S}_{2n}$ values. The relative increase of the matter radius with respect to the $^{27}\mathrm{F}$ core lies in the range 0.1--0.4 fm depending upon these choices.Conclusions: Our three-body results for $^{29}\mathrm{F}$ indicate the presence of a moderate halo structure in its ground state, which is enhanced by larger intruder components. This finding calls for an experimental confirmation.

Weakly bound and unbound three-body nuclei are studied by using the pseudostate method within the hyperspherical formalism. After introducing the theoretical framework, the method is applied first to the $\boldsymbol{^9}$Be nucleus, showing a good agreement with the available data for its low-lying dipole response. Then, recent results on the structure and decay of the two-neutron emitters $\boldsymbol{^{26}}$O and $\boldsymbol{^{16}}$Be are presented. In particular, the role of the $\boldsymbol{n}$-$\boldsymbol{n}$ correlation in shaping their properties is discussed., Proceedings of the 24th European Conference of Few-Body Problems in Physics (EFB24); SciPost contribution

We give an account of the main achievements of the scientific career of Andrea Vitturi so far, that have recently been discussed during the workshop "Theoretical Nuclear Physics in Padova" on the occasion of his retirement from full professor at the University of Padova. He has oftentimes been the driving force behind numerous contributions to nuclear structure and nuclear reactions that are here reviewed: giant resonances, pairing correlations, collective modes, algebraic models, inelastic excitations, electromagnetic response, break-up and transfer reactions, coupled-channel formalism, clustering, subbarrier fusion processes, etc. Among these topics several inspirational works and ideas can be found that we would like to highlight.

We study the two-neutron correlations in the ground state of the weakly-bound two-neutron halo nucleus $^{22}$C sitting at the edge of the neutron-drip line and also in the unbound nucleus $^{26}$O sitting beyond the neutron dripline. For the present study, we employ a three-body (core$+n+n$) structure model designed for describing the two-neutron halo system by explicit inclusion of unbound continuum states of the subsystem (core$+n$). We use either a density-independent or a density-dependent contact-delta interaction to describe the neutron-neutron interaction and its strength is varied to fix the binding energy. We report the configuration mixing in the ground state of these systems for different choices of pairing interactions., 4 Pages, 1 Figure, 2 Tables. 13th International Conference on Nucleus-Nucleus Collisions (NN2018)

The exotic, neutron-rich and weakly-bound isotope 29F stands out as a waymarker on the southern shore of the island of inversion, a portion of the nuclear chart where the effects of nuclear forces lead to a reshuffling of the single particle levels and to a reorganization of the nuclear structure far from stability. This nucleus has become very popular, as new measurements allow to refine theoretical models. We review the latest developments and suggest how to further assess the structure by proposing predictions on electromagnetic transitions that new experiments of Relativistic Coulomb Excitation should soon become able to measure. The neutron-rich, weakly bound fluorine isotope 29F has been extensively investigated theoretically, but its significance has been revived by recent experiments. The authors present the latest developments and make prediction on the electromagnetic transitions occurring in this isotope that may be observed in the near future.

Background: The neutron-rich $^{28,29}\mathrm{F}$ isotopes have been recently studied via knockout and interaction cross-section measurements. The two-neutron halo in $^{29}\mathrm{F}$ has been linked to the occupancy of $pf$ intruder configurations.Purpose: We investigate the bound spectrum and continuum states in $^{29}\mathrm{F}$, focusing on the electric dipole $(E1)$ response of low-lying excitations and the effect of dipole couplings on nuclear reactions.Method: $^{29}\mathrm{F}$ $(^{27}\mathrm{F}+n+n)$ wave functions are built within the hyperspherical harmonics expansion formalism, and total reaction cross sections are calculated using the Glauber theory. Continuum states and $B(E1)$ transition probabilities are described in a pseudostate approach using the analytical transformed harmonic oscillator basis. The corresponding structure form factors are used in continuum-discretized coupled-channels (CDCC) calculations to describe low-energy scattering.Results: Parity inversion in $^{28}\mathrm{F}$ leads to a $^{29}\mathrm{F}$ ground state characterized by 57.5% of ${({p}_{3/2})}^{2}$ intruder components, a strong dineutron configuration, and an increase of the matter radius with respect to the core radius of $\mathrm{\ensuremath{\Delta}}R=0.20$ fm. Glauber-model calculations for a carbon target at 240 MeV/nucleon provide a total reaction cross section of 1370 mb, in agreement with recent data. The model produces also a barely bound excited state corresponding to a quadrupole excitation. $B(E1)$ calculations into the continuum yield a total strength of 1.59 ${e}^{2}$ ${\mathrm{fm}}^{2}$ up to 6 MeV, and the $E1$ distribution exhibits a resonance at $\ensuremath{\approx}0.85$ MeV. Results using a standard shell-model order for $^{28}\mathrm{F}$ lead to a considerable reduction of the $B(E1)$ distribution. The four-body CDCC calculations for $^{29}\mathrm{F}+^{120}\mathrm{Sn}$ around the Coulomb barrier are dominated by dipole couplings, which totally cancel the Fresnel peak in the elastic-scattering cross section.Conclusions: Our three-body calculations for $^{29}\mathrm{F}$, using the most recent experimental information on $^{28}\mathrm{F}$, are consistent with a two-neutron halo. Our predictions show the low-lying enhancement of the $E1$ response expected for halo nuclei and the relevance of dipole couplings for low-energy reactions on heavy targets. These findings may guide future experimental campaigns.

For decades physicists have speculated if ${}^{12}$C could be understood in terms of a cluster arrangement of three $\ensuremath{\alpha}$ particles. This paper suggests a novel experimental way to test these ideas, using polarized $\ensuremath{\gamma}$ rays, as for example in the new EU-funded facility, the Extreme Light Infrastructure or ELI. The work should stimulate both theory and experiment, and possibly address long-standing ideas about clustering in light nuclei.

Making use of an algebraic model for the study of diatomic endofullerenes recently published [Physical Review A 94, 032508 (2016)], we present a possible extension of this framework for the calculation of infrared intensities. We apply the model to the absorption infrared spectrum of H2@C60 at T = 6 K obtaining satisfactory preliminary results.

Form factors for α+12C inelastic scattering are obtained within two theoretical (α+α+α) approaches:The hyperspherical framework for three identical bosons, and the algebraic cluster model assuming the D3h symmetry of an equilateral triangle subject to rotations and vibrations. Results show a good agreement, with form factors involving the Hoyle state having a slightly larger extension within the hyperspherical approach. Coupled-channel calculations using these form factors are ongoing.

The algebraic molecular model is used in $^{12}$C to construct densities and transition densities connecting low-lying states of the rotovibrational spectrum, first and foremost those belonging to the rotational bands based on the ground and the Hoyle states. These densities are then used as basic ingredients to calculate, besides electromagnetic transition probabilities, nuclear potentials and formfactors to describe elastic and inelastic $\alpha$+$^{12}$C scattering processes. The calculated densities and transition densities are also compared with those obtained by directly solving the problem of three interacting alpha's within a three-body approach where continuum effects, relevant in particular for the Hoyle state, are properly taken into account., Comment: Contribution to "Symmetries and Order: Algebraic Methods in Many Body Systems", in honor of F. Iachello

The program diagonalizes the Geometric Collective Model (Bohr Hamiltonian) with generalized Gneuss&ndash, Greiner potential with terms up to the sixth power in &beta, In nuclear physics, the Bohr&ndash, Mottelson model with later extensions into the rotovibrational Collective model is an important theoretical tool with predictive power and it represents a fundamental step in the education of a nuclear physicist. Nuclear spectroscopists might find it useful for fitting experimental data, reproducing spectra, EM transitions and moments and trying theoretical predictions, while students might find it useful for learning about connections between the nuclear shape and its quantum origin. Matrix elements for the kinetic energy operator and for scalar invariants as &beta, 2 and &beta, 3 cos ( 3 &gamma, ) have been calculated in a truncated five-dimensional harmonic oscillator basis with a different program, checked with three different methods and stored in a matrix library for the lowest values of angular momentum. These matrices are called by the program that uses them to write generalized Hamiltonians as linear combinations of certain simple operators. Energy levels and eigenfunctions are obtained as outputs of the diagonalization of these Hamiltonian operators.

Time-dependent calculation has been a suitable method to investigate the quantum dynamical processes. In Ref. [1] = [T. Oishi et al., J. of Phys. G 45, 105101 (2018)], we applied this method to the one-dimensional two-fermion tunneling in the nuclear-physics scale. Beside the specific results presented therein, some basic formalism and methods, which can be helpful for further discussions and developments to investigate time-dependent quantum systems, have been awaiting our description. This note is devoted to describe those supplemental contents. We do not limit the story to the nuclear physics, but keep it applicable to other scales and/or targets.

In this contribution I will review some of the researches that are currently being pursued in Padova (mainly within the In:Theory and Strength projects), focusing on the interdisciplinary applications of nuclear theory to several other branches of physics, with the aim of contributing to show the centrality of nuclear theory in the Italian scientific scenario and the prominence of this fertile field in fostering new physics. In particular, I will talk about: i) the recent solution of the long-standing "electron screening puzzle" that settles a fundamental controversy in nuclear astrophysics between the outcome of lab experiments on earth and nuclear reactions happening in stars; the application of algebraic methods to very diverse systems such as: ii) the supramolecular complex H2@C60, i.e. a diatomic hydrogen molecule caged in a fullerene and iii) to the spectrum of hypernuclei, i.e. systems made of a Lambda particles trapped in (heavy) nuclei., Comment: Based on the talk presented at: TNPI2016 - XV Conference on Theoretical Nuclear Physics in Italy

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

The recent successful application of the Algebraic Cluster Model to the energy spectrum of \(^{12}\)C has brought a new impetus on spectroscopy of this and other \(\alpha -\)conjugate nuclei. In fact, known spectral properties have been reexamined on the basis of vibrations and rotations of three \(\alpha \) particles at the vertexes of an equilateral triangle and new excited states have been measured that fit into this scheme. The analysis of this system entails the application of molecular models for rotational–vibrational spectra to the nuclear context and requires deep knowledge of the underlying group-theoretical properties, based on the \(\mathcal {D}_{3h}\) symmetry, similarly to what is done in quantum chemistry. We have recently analyzed the symmetries of the model and the quantum numbers in great depth, reproducing the all-important results of Wheeler and we have derived electromagnetic selection rules for the system of three \(\alpha \) particles, finding, for instance, that electric dipole E1 and magnetic dipole M1 excitations are excluded from the model. The lowest active modes are therefore E2, E3,\(\cdots \) and M2, M3, \(\cdots \) although there are further restrictions between certain types of bands. The selection rules summarized in the text provide a criterion for assigning of observed lines to the alpha cluster model or not and they might help to further unravel the electromagnetic properties of \(^{12}\)C. With the perspective of new facilities (such as ELI) where photo-excitation and photo-dissociation experiments will play a major role, a complete understanding of e.m. selection rules as a tool to confirm or disprove nuclear structure models, is mandatory.

A simple and yet powerful approach for modeling the structure of endohedrally confined diatomic molecules is introduced. The theory, based on a $\mathrm{u}(4)\ensuremath{\bigoplus}\mathrm{u}(3)$ dynamical algebra, combines $\mathrm{u}(4)$, the vibron model dynamical algebra, with a $\mathrm{u}(3)$ dynamical algebra that models a spherically symmetric three-dimensional potential. The first algebra encompasses the internal rotovibration degrees of freedom of the molecule, while the second takes into account the confined molecule center-of-mass degrees of freedom. A resulting subalgebra chain is connected to the underlying physics and the model is applied to the prototypical case of ${\mathrm{H}}_{2}$ caged in a fullerene molecule. The spectrum of the supramolecular complex ${\mathrm{H}}_{2}@{\mathrm{C}}_{60}$ is described with a few parameters, and predictions for not yet detected levels are made. Our fits suggest that the quantum numbers of a few lines should be reassigned to obtain better agreement with data.

Fortunato, Lorenzo/0000-0003-2137-635X; Arias, Jose M./0000-0001-7363-4328; Alonso, Clara E/0000-0001-9365-4107 WOS: 000289158000003 Shape phase transitions in even and odd systems are reviewed within the frameworks of the Interacting Boson Model(IBM) and the Interacting Boson Fermion Model(IBFM), respectively and compared with geometric models when available. We discuss, in particular, the case of an odd j = 3/2 particle coupled to an even-even boson core that undergoes a transition from the spherical limit U(5) to the gamma-unstable limit O(6). Energy spectrum and electromagnetic transitions, in correspondence of the critical point, display behaviors qualitatively similar to those of the even core and they agree qualitatively with the model based on the E(5/4) boson-fermion symmetry. We describe then the U-BF(5) to SUBF(3) transition when a fermion is allowed to occupy the orbits j = 1/2, 3/2,5/2. The additional particle characterizes the properties at the critical points in finite quantum systems.

We apply here the dicluster model to the evaluation of static properties of 7 Li and 7 Be (e.g.magnetic dipole moment) as well as electromagnetic response to the continuum (in particular E1, E2 and M1). We use Energy Weighted Molecular Sum Rules (EWMSR) to check our calculations and we derive a new expression for the M1 EWMSR. The response functions are then used to evaluate the S -factor for reactions of astrophysical importance, achieving a good agreement.

After recapitulating the procedure to find the bands and the states occurring in the $\mathcal{D}_{3h}$ alpha-cluster model of $^{12}$C in which the clusters are placed at the vertexes of an equilateral triangle, we obtain the selection rules for electromagnetic transitions. While the alpha cluster structure leads to the cancellation of E1 transitions, the approximations carried out in deriving the roto-vibrational hamiltonian lead to the disappearance of M1 transitions. Furthermore, although in general the lowest active modes are E2, E3, $\cdots$ and M2, M3, $\cdots$, the cancellation of M2, M3 and M5 transitions between certain bands also occurs, as a result of the application of group theoretical techniques drawn from molecular physics. These implications can be very relevant for the spectroscopic analysis of $\gamma$-ray spectra of $^{12}$C.

We present an analytic solvable γ -periodic potential of the form μ / sin 2 ( 3 γ ) in the Bohr–Mottelson collective model. The choice allows for a separation in both β , γ and θ ι if the γ -variable in the moments of inertia is approximated by its expectation value γ 0 = π / 6 . Energy spectra, E2 transition rates and subsequent collective bands with their properties are presented. We compare the approximation of γ = γ 0 = π / 6 with a full diagonalisation of the rotational part. These results clearly point out that the approximative analytical treatment describes the full numerical results very well.

New analytic solutions of the quadrupole collective Bohr hamiltonian are proposed, exploiting an approximate separation of the beta and gamma variables to describe gamma-soft prolate axial rotors. The model potential is a sum of two terms: a beta-dependent term taken either with a Coulomb-like or a Kratzer-like form, and a gamma-dependent term taken as an harmonic oscillator. In particular it is possible to give a one parameter paradigm for a beta-soft, gamma-soft axial rotor that can be applied, with a considerable agreement, to the spectrum of 234U.

Properties of collective modes in very neutron-rich nuclei and in weakly-bound nuclei are discussed. In particular the effect of the occurence of neutron skins on the properties of the traditional collective modes, such as the Giant Dipole Resonance and the Giant Quadrupole Resonance, is reviewed. As for the low-lying part of the response, we briefly discuss the occurrence of multipole strength at the continuum threshold in the case of weakly-bound nuclei close to the drip-lines. Application to the multipole response of weakly-bound cluster nuclei, such as 7 Li, is presented.

An analytical solution of the collective Bohr equation with a Coulomb-like and a Kratzer-like $��-$unstable potential in quadrupole deformation space is presented. Eigenvalues and eigenfunctions are given in closed form and transition rates are calculated for the two cases. The corresponding SO(2,1)$\times$SO(5) algebraic structure is discussed., 9 pages, 4 figures in one .ps file

The decay process of the schematic one-dimensional three-body system is considered. A time-dependent approach is used in combination with a one-dimensional three-body model, which is composed of a heavier core nucleus and two nucleons, with the aim of describing its evolution in two-nucleon emission. The process is calculated from the initial state, in which the three ingredient particles are confined. In this process, two different types of emission can be found: the earlier process includes the emission of spatially correlated two-nucleon pair, like a dinucleon, whereas, at a subsequent time, all the particles are separated from each other. The time-dependent method can be a suitable option to investigate the meta-stable and/or open-quantum systems, where the complicated many-body dynamics should necessarily be taken into account., Comment: 8 pages, 4 figures. Final version appears as the proceeding of "XXXV Mazurian Lakes Conference on Physics"

A potential energy surface is constructed for various light nuclei, 3,4He with the Argonne V18 potential and then for alpha- conjugate nuclei like 12C,16O, 20Ne with α – α potentials. Despite the nucleons have large momenta and large fluctuations around the equilibrium points, the minimization suggests the underlying geometric structure. We calculate the Hessian matrix determining the normal modes of vibration. This approach might lead to a new way of fitting the alpha-alpha interactions on the spectroscopic data available for alpha-conjugate nuclei, rather than on scattering phase shift.

Quantum shape-phase transitions in odd-nuclei are investigated within the framework of the interacting boson-fermion model (IBFM). We consider the case of a single-j fermion coupled to an even-even boson core that performs a transition from spherical to oblate shapes varying a control parameter in the boson Hamiltonian. The aim of this work is to see the effect of the coupling of the unpaired fermion on the transition, to understand how the coupled single particle modifies the geometric shape of the system and how each of the odd states behaves when the boson core shifts along the transitional path. Scientific and Technical Research Council of Turkey BIDEB-2224A Ministerio de Economía y Competitividad FIS2011-28738- c02-01, CSD2007-00042 Junta de Andalucía FQM160, P11-FQM-7632

Accurate measurements of nuclear reactions of astrophysical interest within, or close to, the Gamow peak, show evidence of an unexpected effect attributed to the presence of atomic electrons in the target. The experiments need to include an effective "screening" potential to explain the enhancement of the cross sections at the lowest measurable energies. Despite various theoretical studies conducted over the past 20 years and numerous experimental measurements, a theory has not yet been found that can explain the cause of the exceedingly high values of the screening potential needed to explain the data. In this letter we show that instead of an atomic physics solution of the "electron screening puzzle", the reason for the large screening potential values is in fact due to clusterization effects in nuclear reactions, in particular for reaction involving light nuclei., Comment: 6 pages, 2 figures, accepted for publication in Physics Letters B

Giant resonances are collective excitation modes for many-body systems of fermions governed by a mean field, such as the atomic nuclei. The microscopic origin of such modes is the coherence among elementary particle-hole excitations, where a particle is promoted from an occupied state below the Fermi level (hole) to an empty one above the Fermi level (particle). The same coherence is also predicted for the particle–particle and the hole–hole excitations, because of the basic quantum symmetry between particles and holes. In nuclear physics, the giant modes have been widely reported for the particle–hole sector but, despite several attempts, there is no precedent in the particle–particle and hole–hole ones, thus making questionable the aforementioned symmetry assumption. Here we provide experimental indications of the Giant Pairing Vibration, which is the leading particle–particle giant mode. An immediate implication of it is the validation of the particle–hole symmetry., The Giant Pairing Vibration is a collective mode in an atomic nucleus caused by coherence between particle-particle excitations, which has so far eluded detection. Cappuzzello et al. present signatures for its existence via heavy-ion-induced two-neutron transfer reactions in carbon nuclei.

A potential energy surface is constructed for3,4He with the two-body Argonne V18 potential. The minimization suggests a semi-rigid asymmetric top structure for4He, where the appropriate pointgroup symmetry is C 2. We calculate the Hessian matrix, determining the 6 normal modes of vibration (in the range 300-700 MeV). The breathing mode is found to lie at too high an energy to be observable and the nature of the excited states of the alpha particle at 20 MeV should probably be sought elsewhere. Similar investigations have been carried out for the A=3 system, finding a planar Cs configuration (scalene triangle) and three excited vibrational states (in the range 600-1900 MeV).

Quantum phase transitions in odd-nuclei are investigated within the framework of the interacting boson-fermion model with a description based on the concept of intrin- sic states. We consider the case of a single j=9/2 odd-particle coupled to an even-even boson core that performs a transition from spherical to deformed prolate and to deformed gamma-unstable shapes varying a control parameter in the boson Hamiltonian. The effect of the coupling of the odd particle to this core is discussed along the shape transition and, in particular, at the critical point.

Excited states in ${}^{162}$Yb were populated via ${\ensuremath{\beta}}^{+}$/EC decay and were studied via conversion electrons and \ensuremath{\gamma}-ray spectroscopy at the Tandem Accelerator in the INFN Laboratory Nazionali del Sud in Catania, Italy. Conversion electrons were detected by a miniorange spectrometer with a transmission energy window that ranged from 500 to 1300 keV. The $E$0 decay of the first excited state at 1006 keV to the ground state was observed, and a $X$($E$0/$E$2) value was deduced. The value is compared to a few IBM-1 calculations by using the ECQF formalism or the full Hamiltonian in multipole expansion. Calculations turn out to be quite sensitive to properties related to nuclear shape.

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 discretized 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 isotopes 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., Comment: 20 pages, 16 figures, to be submitted

We demonstrate that a realization of the sp(4) symplectic algebra can be used as a spectrum generating algebra for a large class of hamiltonian operators written in two coordinates, r1 and r2, and their conjugate momenta. The physical operators are mapped to step and weight operators of sp(4) and these are mapped to 4-modes boson operators that allow a straightforward exact calculation of matrix elements. Several important three-body quantum hamiltonian can be written using the algebra elements as building blocks. Some cases and applications are discussed.

The modeling of coupled vibrational bending degrees of freedom within the two-dimensional limit of the Vibron Model is presented. The new aspects that arise in this case, in comparison to the single bender case, are examined, with special emphasis on the different geometrical limits embedded in a simple model Hamiltonian and the phase diagram associated to this two-fluid bosonic model.

The algebraic structure of some of the simplest algebraic models u(2), u(3) and u(4), widely used in several branches of physics either as toy models or as working instruments, are reanalyzed under a new perspective that releases the requirement that chains should terminate or pass through the angular momentum algebra. Unitary algebras are non-semisimple, therefore we first apply the Levi-Malcev decomposition. Then we use the theory of weighted Dynkin diagrams to identify conjugacy classes of A1 ~ su(2) ~ so(3) subalgebras: a complete classification of new angular momentum non conserving (AMNC) dynamical symmetries follows that we substantiate with examples.