Coupled-channel Born Approximation Research Articles

The 50th anniversary of the coupled channels Born approximation (CCBA) and the coupled reaction channels (CRC) theories of nucleon transfer reactions (a unique interplay between theory, experiment and computer technology, conducted during the most tumultuous period in modern American society)

Nucleon transfer reactions have played a fundamental role in understanding the single-particle components, shell structure and collective properties of atomic nuclei. The conventional distorted wave Born approximation (DWBA) envisioned the nucleon transfer reaction as a one-step process, which proceeds directly from the ground state of the target nucleus to a state of the residual nucleus. The coupled channels Born approximation (CCBA) and coupled reaction channels (CRC) theories evolved because a number of nucleon transfer reaction cross sections could not be reconciled within the DWBA. These coupled channels models revealed that, in addition to the “one-step” process of the DWBA, “multi-step” nucleon transfer processes involving accessary pathways can participate in populating the final nuclear state. In the CCBA, the auxiliary pathways involved inelastic excitations of the target and/or residual nucleus, whereas, in the CRC, the pathways included sequential nucleon transfer passing through nuclear states of an intermediate partition. Coherent addition of contributions from one-step and multi-step nucleon transfer processes resulted in dramatic alterations in reaction cross sections, which were experimentally confirmed. The CCBA and CRC linked the structure of the nuclei participating in a reaction to modalities of nucleon transfer arising during the relative motion between the interacting ions. These complementary theories inexorably changed physicists’ interpretations of nucleon transfer reactions and, in doing so, heralded in the new field of direct heavy-ion reactions.

Study of the one-neutron transfer reaction in 18O + 76Se collision at 275 MeV in the context of the NUMEN project

Heavy-ion one-nucleon transfer reactions are promising tools to investigate single-particle configurations in nuclear states, with and without the excitation of the core degrees of freedom. An accurate determination of the spectroscopic amplitudes of these configurations is essential for the study of other direct reactions as well as beta-decays. In this context, the 76Se(18O,17O)77Se one-neutron transfer reaction gives a quantitative access to the relevant single particle orbitals and core polarization transitions built on 76Se. This is particularly relevant, since it provides data-driven information to constrain nuclear structure models for the 76Se nucleus.The excitation energy spectrum and the differential cross section angular distributions of this nucleon transfer reaction was measured at 275 MeV incident energy for the first time using the MAGNEX large acceptance magnetic spectrometer. The data are compared with calculations based on distorted wave Born approximation and coupled channel Born approximation adopting spectroscopic amplitudes for the projectile and target overlaps derived by large-scale shell model calculations and interacting boson-fermion model.These reactions are studied in the frame of the NUMEN project. The NUMEN (NUclear Matrix Elements for Neutrinoless double beta decay) project was conceived at the Istituto Nazionale di Fisica Nucleare–Laboratori Nazionali del Sud (INFN-LNS) in Catania, Italy, aiming at accessing information about the nuclear matrix elements (NME) of neutrinoless double beta decay (0νββ) through the study of the heavy-ion induced double charge exchange (DCE) reactions on various 0νββ decay candidate targets. Among these, the 76Se nucleus is under investigation since it is the daughter nucleus of 76Ge in the 0νββ decay process.

Multichannel experimental and theoretical approach to the C12(O18,F18)B12 single-charge-exchange reaction at 275 MeV: Initial-state interaction and single-particle properties of nuclear wave functions

Background: Single-charge-exchange reactions are appropriate tools to study the nuclear response to one-particle/one-hole isospin probes, gaining additional interest from the connection to beta decay. This analogy has been recently extended to second order, connecting double-charge-exchange reactions and double beta decays. Nowadays, the availability of powerful experimental setups and advanced nuclear theories and models allows one to access precious information on key nuclear structure aspects embedded in the widely sought neutrinoless double beta decay. Purpose: We intend to bring to light the main nuclear structure and reaction features involved in the O18+C12 collision at 275 MeV incident energy. In this paper, the main focus is on the role of the initial- and final-state interactions in the overall reaction dynamics and on the single-particle nuclear structure properties accessed via the study of single-nucleon transfer reactions. Forthcoming articles will be devoted to go into the details of the response to one- and two-particle/hole isospin probes. Methods: Cross-section energy spectra and angular distributions were measured in a unique experimental setup for the C12(O18,O18)C12 elastic and inelastic scattering, the C12(O18,O17)C13 one-neutron stripping, the C12(O18,F19)B11 one-proton pickup, and the C12(O18,F18)B12 single-charge-exchange nuclear reactions. A unique comprehensive and coherent theoretical calculation, able to describe the whole network of direct reactions using state-of-the-art nuclear structure and reaction theories, was performed, and it is presented for the first time in this article. This holistic approach, applied both to the experimental and theoretical analysis, is the main feature and worth of the work here presented. Results: The energy and angular resolutions achieved in each reaction channel allowed us to isolate specific transitions and to map the diffraction patterns in the angular distributions. The cross-section calculations describe well the experimental data, both in terms of the absolute values and diffraction patterns. Although the distorted wave Born approximation (DWBA) calculations prove to be accurate in describing all the studied channels, better results are achieved when the couplings to inelastic transitions in both the incoming and outgoing partitions are introduced, as done in the coupled channels Born approximation (CCBA) calculations. Otherwise, no real improvement is found when the coupling effects among different partitions are explicitly taken into account in the coupled reaction channels (CRC) calculations. Conclusions: The multichannel approach proposed in this paper is a promising method for accurate investigations of direct reactions originating in heavy-ion collisions. This is quite appealing for the precise spectroscopy of heavy nuclei proposed in many areas of nuclear physics. An example is the NUMEN project with its challenging commitment to provide valuable information on neutrinoless double beta decay nuclear matrix elements from single- and double-charge-exchange cross-section measurements.1 MoreReceived 18 July 2022Accepted 23 January 2023DOI:https://doi.org/10.1103/PhysRevC.107.024605©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCharge-exchange reactionsCollective modelsDirect reactionsNuclear many-body theoryOptical, coupled-channel & distorted wave modelsShell modelSpectroscopic factors & electromagnetic momentsTransfer reactionsProperties6 ≤ A ≤ 19TechniquesNuclear data analysis & compilationNuclear reactionsSpectrometers & spectroscopic techniquesNuclear Physics

Analysis of the one-neutron transfer reaction in O18+Se76 collisions at 275 MeV

Purpose: We want to analyze transitions to low-lying excited states of the residual and ejectile nuclei in the 76Se(18O, 17O) 77Se one-neutron stripping reaction at 275-MeV incident energy and determine the role of single-particle and core excitation in the description of the measured cross sections. In addition, we explore the sensitivity of the calculated cross section to different nuclear structure models. Methods: The excitation energy spectrum and the differential cross-section angular distributions are measured using the MAGNEX large acceptance magnetic spectrometer for the detection of the ejectiles and the missing mass technique for the reconstruction of the reaction kinematics. The data are compared with calculations based on distorted-wave Born approximation, coupled-channels Born approximation, and coupled reaction channels adopting spectroscopic amplitudes for the projectile and target overlaps derived by large-scale shell-model calculations and interacting boson-fermion model. Results: Peaks in the energy spectra corresponding to groups of unresolved transitions to 77Se and 17O are identified. The experimental cross sections are extracted and compared to theoretical calculations. A remarkable agreement is found, without using any scaling factors, demonstrating that the adopted models for nuclear structure and reaction take into account the relevant aspects of the studied processes. The main transitions which contribute to the cross section of each peak are identified.

Study of the 13C(3He, α)12C reaction at energies of 50 and 60 MeV

Cross sections for the 13C(3He, α)12C reaction were measured for 12C states up to excitation energies of about 20 MeV for 3He energies of 50 and 60 MeV. An analysis of the measured angular distributions was carried out using the Coupled Channels Born Approximation method under the assumption of a direct one-step mechanism of picking up a neutron from the 13C nucleus. In these calculations, the real parts of the implemented potentials were constructed within the framework of the double folding model. This analysis made it possible to extract the values of the spectroscopic factors for the 13C g.s.  → 12C g.s. (12C*) + n configurations, which were found to be in reasonable agreement with theoretical predictions.

Multinucleon transfer in the Cd116(Ne20,O20)Sn116 double charge exchange reaction at 306 MeV incident energy

In heavy-ion collisions at energies above the Coulomb barrier, the multiple nucleon transfer mechanism feeding double charge exchange (DCE) reactions can compete with the meson-induced DCE process once, in both cases, the same final partition is achieved. While the former is a mean field driven process, the latter is generated by second-order isovector components of the nucleon-nucleon interaction. It is particularly interesting to isolate the meson-induced DCE from measured cross sections since their matrix elements can be linked to those controlling the expected double $\ensuremath{\beta}$ decay rates. However, one needs first to isolate the meson-induced DCE contribution, which in turn means that careful scrutiny of the DCE flux from the multinucleon transfer is mandatory. This work presents theoretical results for all the multinucleon transfer routes feeding the $^{116}\mathrm{Cd}(^{20}\mathrm{Ne},^{20}\mathrm{O})^{116}\mathrm{Sn}$ reaction at 306 MeV incident energy. The calculated cross sections are obtained considering the distorted wave Born approximation and coupled channel Born approximation, where the role of the couplings with inelastic states in the initial partition is discussed. Moreover, the spectroscopic amplitudes for the projectile and target overlaps are extracted by considering a large-scale shell-model calculation.

O18 -induced single-nucleon transfer reactions on Ca40 at 15.3A MeV within a multichannel analysis

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 O18+Ca40 system at 15.3A 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-independent description of the single-nucleon transfer reactions. The successful description of the present one-nucleon transfer data is also propaedeutic to the accurate assessment, under the same theoretical description, of higher-order transfer processes, like the sequential nucleon transfer mechanisms which are in competition with the direct charge exchange reactions.Received 14 September 2021Accepted 16 November 2021DOI:https://doi.org/10.1103/PhysRevC.104.064609©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLow & intermediate energy heavy-ion reactionsModels & methods for nuclear reactionsTransfer reactionsTechniquesOptical, coupled-channel & distorted wave modelsNuclear Physics

One-proton transfer reaction for the O18+Ti48 system at 275 MeV

Single-nucleon transfer reactions are processes that selectively probe single-particle components of the populated many-body nuclear states. In this context, recent efforts have been made to build a unified description of the rich nuclear spectroscopy accessible in heavy-ion collisions. An example of this multichannel approach is the study of the competition between successive nucleon transfer and charge exchange reactions, the latter being of particular interest in the context of single and double beta decay studies. To this extent, the one-proton pickup reaction Ti48(O18,F19)Sc47 at 275 MeV was measured for the first time, under the NUMEN experimental campaign. Differential cross-section angular distribution measurements for the F19 ejectiles were performed at INFN-LNS in Catania by using the MAGNEX large acceptance magnetic spectrometer. The data were analyzed within the distorted-wave and coupled-channels Born approximation frameworks. The initial and final-state interactions were described adopting the São Paulo potential, whereas the spectroscopic amplitudes for the projectile and target overlaps were derived from shell-model calculations. The theoretical cross sections are found to be in very good agreement with the experimental data, suggesting the validity of the optical potentials and the shell-model description of the involved nuclear states within the adopted model space.1 MoreReceived 27 May 2021Accepted 8 September 2021DOI:https://doi.org/10.1103/PhysRevC.104.034617©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDirect reactionsDouble beta decayLow & intermediate energy heavy-ion reactionsNuclear reactionsTransfer reactionsTechniquesOptical, coupled-channel & distorted wave modelsSpectrometers & spectroscopic techniquesNuclear Physics

Analysis of two-proton transfer in the Ca40(O18,Ne20)Ar38 reaction at 270 MeV incident energy

Two-nucleon transfer reactions are essential tools to investigate specific features of the nuclear structure, such as the correlation among valence particles in the transfer process. Besides, transfer reactions may be an important channel to take into account in charge-exchange processes since they can represent a competing contribution to the final cross section. The two-proton pickup transfer reaction $^{40}\mathrm{Ca}(^{18}\mathrm{O},^{20}\mathrm{Ne})\phantom{\rule{0.16em}{0ex}}^{38}\mathrm{Ar}$ has been measured at 270 MeV, and the angular distributions for transitions to different excited states extracted. This paper shows the analysis of the data performed by finite-range coupled reaction channel and coupled-channel Born approximation methods. Extensive shell-model calculations are performed to derive the one- and two-proton spectroscopic amplitudes for the projectile and target overlaps. The role of the simultaneous and sequential two-proton transfer mechanisms to populate the measured final states or groups of states, mainly characterized by a high collectivity, is also discussed.

Important Influence of Entrance Channel Reorientation Coupling on Proton Stripping

While it is well established that the ground state reorientation coupling can have a significant influence on the elastic scattering of deformed nuclei, the effect of such couplings on transfer channels has been much less well investigated. In this letter we demonstrate that the ^{208}hbox {Pb}(^7hbox {Li},^6hbox {He})^{209}hbox {Bi} proton stripping reaction at an incident energy of 52 MeV can be well described by the inclusion of the ^7hbox {Li} ground state reorientation coupling within the coupled channels Born approximation formalism. Full finite-range distorted wave Born approximation calculations were previously found to be unable to describe these data. Addition of coupling to the 0.478-MeV 1/2^- excited state of ^7hbox {Li}, together with the associated two-step transfer path, has little or no influence on the shape of the angular distributions (except that for stripping leading to the 1.61-MeV 13/2^+ level of ^{209}hbox {Bi} which is significantly improved) but does affect appreciably the values of the ^{209}mathrm {Bi} rightarrow {^{208}mathrm {Pb}} + p spectroscopic factors. Implications for experiments with weakly-bound light radioactive beams are discussed.

Multistep processes in heavy-ion-induced single-nucleon transfer reactions

It was first noted during the 1970s that finite-range distorted wave Born approximation (FR-DWBA) calculations were unable satisfactorily to describe the shape of the angular distributions of many single-proton (and some single-neutron) transfer reactions induced by heavy ions, with calculations shifted to larger angles by up to ~ 4 degrees compared with the data. These reactions exhibited a significant mismatch, either of the reaction Q value or the grazing angular momentum of the entrance and exit channels, and it was speculated that the inclusion of multi-step transfer paths via excited state(s) of the projectile and/or ejectile could compensate for the effect of this mismatch and yield good descriptions of the data by shifting the calculated peaks to smaller angles. However, to date this has not been explicitly demonstrated for many reactions. In this work we show that inclusion of the two-step transfer path via the 4.44-MeV 2+ excited state of the 12C projectile in coupled channel Born approximation calculations enables a good description of the 208Pb(12C,11B)209Bi single-proton stripping data at four incident energies which could not be described by the FR-DWBA. We also show that inclusion of a similar reaction path for the 208Pb(12C,13C)207Pb single-neutron pickup reaction has a relatively minor influence, slightly improving the already good description obtained with the FR-DWBA.

Analyzing powers and the role of multistep processes in the C12(Li7,t)O16 reaction

The analyzing powers $^{T}T_{10}\phantom{\rule{0.16em}{0ex}},^{T}T_{20}$, and $^{T}T_{30}$ for the $^{12}\mathrm{C}(^{7}\mathrm{Li},t$) reaction were measured and combined with new and previously determined angular distributions to probe the role of multistep processes through coupled channel Born approximation (CCBA) calculations employing new $\ensuremath{\alpha}$-particle spectroscopic amplitudes calculated with the phenomenological shell model in the unrestricted $psd$ space. Good descriptions of the cross-section angular distributions could be obtained except for the larger angles for the 6.05 MeV ${0}^{+}$ and 6.13 MeV ${3}^{\ensuremath{-}}$ states, while the analyzing powers were not generally described. The calculations presented demonstrate the sensitivity of the angular distributions of both the differential cross sections and the analyzing powers to various multistep routes. While the measured analyzing power $^{T}T_{30}$ is roughly zero for all states, the various CCBA calculations produced large and highly oscillatory values for this observable, showing that other multistep processes must be present beyond those taken into account in this work. Standard distorted wave Born approximation (DWBA) calculations were also carried out and these show considerable differences from the CCBA results but the description of the analyzing powers, while slightly improved, is still poor.

Long-range versus short-range correlations in the two-neutron transfer reaction Ni64(O18,O16)Ni66

Recently, various two-neutron transfer studies using the $(^{18}\mathrm{O},^{16}\mathrm{O})$ reaction were performed with a large success. This was achieved because of a combined use of the microscopic quantum description of the reaction mechanism and of the nuclear structure. In the present work we use this methodology to study the two-neutron transfer reaction of the $^{18}\mathrm{O}+^{64}\mathrm{Ni}$ system at 84 MeV incident energy, to the ground and first ${2}^{+}$ excited state of the residual $^{66}\mathrm{Ni}$ nucleus. All the experimental data were measured by the large acceptance MAGNEX spectrometer at the Instituto Nazionale di Fisica Nucleare --Laboratori Nazionali del Sud (Italy). We have performed exact finite range cross section calculations using the coupled channel Born approximation (CCBA) and coupled reaction channel (CRC) method for the sequential and direct two-neutron transfers, respectively. Moreover, this is the first time that the formalism of the microscopic interaction boson model (IBM-2) was applied to a two-neutron transfer reaction. From our results we conclude that for two-neutron transfer to the ground state of $^{66}\mathrm{Ni}$, the direct transfer is the dominant reaction mechanism, whereas for the transfer to the first excited state of $^{66}\mathrm{Ni}$, the sequential process dominates. A competition between long-range and short-range correlations is discussed, in particular, how the use of two different models (Shell model and IBM's) help to disentangle long- and short-range correlations.

Probing surface distributions of a clusters in20Ne via α-transfer reaction

Although several analyses of the α-transfer reaction16O(6Li, d)20Ne using the distorted wave Born approximation have been performed with the aim to clarify the α-cluster structure of20Ne, they have resulted in poor information on the clustering due to insufficiency of models for the analyses. In this work we propose a precise model employing the coupled-channels Born approximation with the microscopically calculated cluster wave function to elucidate the surface manifestation of the α-particle in the ground state of20Ne. Our calculation has shown improvement of the theoretical calculation compared with that in the previous analyses. We have confirmed numerically that the angular distributed cross section at the forward angles probes only the surface region of the α-cluster wave function. The breakup effect of6Li has been investigated and concluded that only the back coupling is important for the (6Li, d) reaction.

Influence of target deformation and deuteron breakup in (d,p) transfer reactions

The effect of core excitations in transfer reactions of the form A(d, p)B has been found to affect significantly the calculated cross sections and to depend strongly and non-linearly on the incident deuteron energy in Faddeev/AGS calculations. Our goal is to investigate these effects within a coupled-channels formulation of the scattering problem which, in addition of being computationally less demanding than the Faddeev counterpart, may help shed some light into the physical interpretation of the cited effects. We use an extended version of the continuum-discretized coupled-channels (CDCC) method with explicit inclusion of target excitations within a coupled-channels Born approximation (CDCC-BA) formulation of the transfer transition amplitude. We compare the calculated transfer cross sections with those obtained with an analogous calculation omitting the effect of target excitation. We consider also an adiabatic coupled channels (ACC) method. Our working example is the 10 Be(d,p) 11 Be reaction. We find that both formalisms are able to reproduce the effects of deformation found in Faddeev calculations, whose origin stems from the interference of the direct one-step transfer, and the two-step transfer following target excitation.

Cluster structure of O17

The transfer reaction $^{13}\mathrm{C}(^{11}\mathrm{B},^{7}\mathrm{Li})^{17}\mathrm{O}$ leading to the ground and several excited states of $^{17}\mathrm{O}$ was investigated at an incident boron beam energy of 45 MeV. The experimental data were analyzed by means of coupled-channel Born approximation calculations and $^{17}\mathrm{O}=\ensuremath{\alpha}+^{13}\mathrm{C}$ spectroscopic factors were extracted from a comparison of the data and the calculations at forward angles. The largest spectroscopic factor obtained was that for the subthreshold 6.356 MeV $1/{2}^{+}$ state, important for the production of neutrons in the stellar environment, and the squared Coulomb modified asymptotic normalization coefficient, ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{C}}^{2}$, is consistent with previous determinations. A significant rise in the experimental data at backward scattering angles suggested the possibility of $^{17}\mathrm{O}=^{6}\mathrm{Li}+^{11}\mathrm{B}$ clustering in some $^{17}\mathrm{O}$ states, including the ground state. However, explicit inclusion of $^{6}\mathrm{Li}$ transfer in the calculations could not explain the observed effect. Compound nucleus calculations suggested that while the backward angle rise could be explained by such processes for two of the populated $^{17}\mathrm{O}$ states other multistep direct processes must contribute significantly to the other two.

Probing transfer to unbound states of the ejectile with weakly boundLi7onNb93

The two-step process of transfer followed by breakup is explored by measuring a rather complete set of exclusive data for reaction channels populating states in the ejectile continua of the $^7$Li+$^{93}$Nb system at energies close to the Coulomb barrier. The cross sections for $\alpha+\alpha$ events from one proton pickup were found to be smaller than those for $\alpha+d$ events from one neutron stripping and $\alpha+t$ events from direct breakup of $^7$Li. Coupled channels Born approximation and continuum discretized coupled channels calculations describe the data well and support the conclusion that the $\alpha+d$ and $\alpha+\alpha$ events are produced by direct transfer to unbound states of the ejectile.

Probing surface distributions ofαclusters inNe20viaα-transferreaction

Direct evidence of the $\alpha$-cluster manifestation in bound states has not been obtained yet, although a number of experimental studies were carried out to extract the information of the clustering. In particular in conventional analyses of $\alpha$-transfer reactions, there exist a few significant problems on reaction models, which are insufficient to qualitatively discuss the cluster structure. We aim to verify the development of the $\alpha$-cluster structure from observables. As the first application, we plan to extract the spatial information of the cluster structure of the $^{20}$Ne nucleus in its ground state through the cross section of the $\alpha$-transfer reaction $^{16}$O($^6$Li,~$d$)$^{20}$Ne. For the analysis of the transfer reaction, we work with the coupled-channel Born approximation (CCBA) approach, in which the breakup effect of $^6$Li is explicitly taken into account by means of the continuum-discretized coupled-channel method based on the three-body $\alpha + d + {}^{16}$O model. The two methods are adopted to calculate the overlap function between $^{20}$Ne and $\alpha + {}^{16}$O; one is the microscopic cluster model (MCM) with the generator coordinate method, and the other is the phenomenological two-body potential model (PM). We show that the CCBA calculation with the MCM wave function gives a significant improvement of the theoretical result on the angular distribution of the transfer cross section, which is consistent with the experimental data. Employing the PM, it is discussed which region of the cluster wave function is probed on the transfer cross section. It is found that the surface region of the cluster wave function is sensitive to the cross section. The present work is situated as the first step in obtaining important information to systematically investigate the cluster structure.

T20Tanalyzing powers fromC12(Li7,α)N15

The transverse analyzing powers $^{T}T_{20}$ were obtained from a polarized beam study of the reaction $^{12}\mathrm{C}(^{7}\mathrm{Li},\ensuremath{\alpha})^{15}\mathrm{N}$ at ${E}_{\text{lab}}({}^{7}\text{Li})=34$ MeV for several well known, strongly populated and isolated states in $^{15}\mathrm{N}$ to determine if they contained a sufficiently distinctive signature to be used to provide a test against which selectively populated and strong, but not well understood states, such as the one at $13.17$ MeV could be used to determine their spins and parities. Unfortunately, current finite range distorted wave Born approximation and coupled channels Born approximation calculations were not able to describe the data to the well-known states. The current work presents these experimental analyzing powers with the expectation that they can be used as a test of future detailed reaction model calculations.

Microscopic double folding potential description of the6He+12Creaction

We investigate the simultaneous explanation of the ${}^{6}\mathrm{He}+{}^{12}\mathrm{C}$ elastic and inelastic scattering and ${}^{6}\mathrm{He}+{}^{12}\mathrm{C}\ensuremath{\rightarrow}{}^{4}\mathrm{He}+{}^{14}\mathrm{C}$ transfer reaction observables at 18.0 MeV within the framework of the coupled-channels Born approximation. In obtaining the microscopic double folding potentials, two different nucleon densities deduced from the no-core shell model and few-body model calculations for the $^{6}\mathrm{He}$ have been used. Although a good agreement between theoretical results and experimental data has been obtained for elastic scattering and transfer reactions data, the theoretical results underestimate the magnitude of the inelastic-${2}^{+}$ state data. We present in this article that the deformation of the imaginary part of the optical potential is very important and it overcomes the magnitude problem for the inelastic data for this system.