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We study the $^6$He Borromean nucleus in coordinate representation within a three-body model with two-body potentials derived from cluster effective field theory (EFT). These potentials are originally developed in momentum space and Fourier transformed to provide non-local potentials in configuration space. We use hyperspherical coordinates in combination with the Lagrange-mesh technique to compute the ground state energy, root mean square radius and the E1 strength distribution of $^6$He. We also introduce a three-body interaction to eliminate dependencies on the cutoff parameter of the two-body potentials on the ground state energy. The E1 strength distribution exhibits a low lying resonance as expected. However it is strongly influenced by the choice of the three-body EFT interaction.

We present a semi-microscopic study of the 16C(d,p)17C transfer reaction. The 17C overlap integrals and spectroscopic factors are obtained from a microscopic cluster model, involving many 16C+n configurations. This microscopic model provides a fair description of the 17C bound-state energies. The 16C+d scattering wave functions are defined in the CDCC method, where the deuteron breakup is simulated by pseudostates. The transfer cross sections are in good agreement with recent data. We confirm the 16C(2+)+n structure of the ground state, and show that deuteron breakup effects have a significant influence on the cross sections. We study the 17C(p,d)16C reverse reaction and suggest that the cross section to the 2+ state should be large. A measurement of the ground-state cross section would provide a strong test of the microscopic wave functions., Comment: 8 pages, 5 figures, accepted for publication in Phys. Rev. C

Background: Nuclear transfer reactions are a useful tool to study the structure of a nucleus. For reactions involving weekly bound nuclei, breakup effects can play significant role and theoretical calculations can be computational expensive in such cases. Purpose: To utilize the Lagrange-mesh and R-matrix methods for nuclear transfer reactions. Methods: We use the adiabatic distorted wave approximation (ADWA) method which can approximately treats the breakup effects in a simpler manner. In our approach, we apply the R-matrix method combining it with the Lagrange-mesh method, which is known to provide the fast and accurate computations. Results: As a test case, we calculate the angular distribution of the cross sections for the 54Fe(d, p)55Fe reaction, where deuteron breakup effects play important role. Conclusions: We show that these methods work well in the ADWA framework, and we look forward to applying these methods in coupled channel calculations., Comment: Presented in the online International conference on recent trends in nuclear physics, India

We analyze the $^{16}{\rm C}+p$ and $^{16}{\rm C}+d$ reactions within the four- and five-body Continuum Discretized Coupled Channel (CDCC) method. The $^{16}$C nucleus is described by a $^{14}{\rm C}+n+n$ configuration in hyperspherical coordinates. This description reproduces fairly well several $^{16}$C low-lying states. First we analyze the $2^+\rightarrow 0^+$ $E2$ transition amplitude, which confirms that an effective charge must be introduced to reproduce the experimental value. Then, proton and deuteron elastic and inelastic scattering are investigated by including $^{16}$C pseudostates, which simulate the $^{14}{\rm C}+n+n$ continuum. In $^{16}{\rm C}+d$, the deuteron breakup is taken into account with $p+n$ two-body pseudostates. A fair agreement with experiment is obtained without any fitting parameter. Breakup effects are in general small, but improve the agreement with experiment., Comment: Accepted for publication in Physical Review C

We present a scattering model for nuclei with similar masses. In this three-body model, the projectile has a core+valence structure, whereas the target is identical to the core nucleus. The three-body wave functions must be symmetrized for the exchange of the cores. This property gives rise to non-local potentials, which are computed without approximation. The present model is an extension of the Continuum Discretized Coupled Channel (CDCC) formalism, with an additional treatment of core exchange. We solve the coupled-channel system, including non-local terms, by the $R$-matrix method using Lagrange functions. This model is applied to the $^{13}{\rm C}+^{12}$C, $^{13}{\rm N}+^{12}$C and $^{16}{\rm O}+^{12}$C systems. Experimental scattering cross sections are fairly well reproduced without any parameter fitting. The backward-angle enhancement of the elastic cross sections is due to the non-local potential. We discuss in more detail the various non-local contributions and present effective local potentials., Comment: 13 pages, 11 figures, submitted to Physical Review C

We discuss resonance properties in three-body systems, with examples on $^{12}{\rm C}$ and $^{24}{\rm Mg}$. We use a microscopic cluster model, where the generator coordinate is defined in the hyperspherical formalism. The $^{12}{\rm C}$ nucleus is described by an $\alpha+\alpha+\alpha$ structure, whereas $^{24}{\rm Mg}$ is considered as an $^{16}{\rm O}+\alpha+\alpha$ system. We essentially pay attention to resonances. We review various techniques which may extend variational methods to resonances. We consider $0^+$ and $2^+$ states in $^{12}{\rm C}$ and $^{24}{\rm Mg}$. We show that the r.m.s. radius of a resonance is strongly sensitive to the variational basis. This has consequences for the Hoyle state ($0^+_2$ state in $^{12}{\rm C}$) whose radius has been calculated or measured in several works. In $^{24}{\rm Mg}$, we identify two $0^+$ resonances slightly below the three-body threshold., Comment: 8 pages, 6 figures, accepted for publication at EPJA

We test the sensitivity of transfer reactions to the bound state wave functions within a distorted wave Born approximation formalism. Using supersymmetric transformations, we remove the Pauli-forbidden states from the two-body potentials and generate an equivalent supersymmetric partner. Wave functions from these potentials have the same asymptotics, but they differ in the nuclear interior. This allows us to study the influence of the nuclear interior on transfer cross sections. We apply the calculations to the $^{16}$O($d, p$)$^{17}$O and $^{12}$C($^7$Li, $t$)$^{16}$O reactions, which are typical examples of nucleon and $\alpha$ transfer, respectively. The spectroscopic factors for $^{17}$O are decreased by about 30\% when using supersymmetric potentials. For $^{16}$O, the differences are smaller. However, we show that ambiguities exist in the determination of the spectroscopic factors, due to the choice of the angular range where the fit is performed., Comment: Accepted for publication in Physics Letters B

Given the established 2 alpha structure of 8Be, a realistic model of 4 interacting alpha clusters must be used to obtain a 8Be+8Be interaction potential. Such a four-body problem poses a challenge for the determination of the 8Be+8Be optical potential (OP) that is still unknown due to the lack of the elastic 8Be+8Be scattering data. The main goal of the present study is to probe the complex 8Be+8Be optical potential in the coupled reaction channel (CRC) study of the alpha transfer 12C(alpha,8Be) reaction measured at 65 MeV, and to obtain the spectroscopic information on the alpha+8Be cluster configuration of 12C. The 3- and 4-body Continuum-Discretized Coupled Channel (CDCC) methods are used to calculate the elastic alpha+8Be and 8Be+8Be scattering at the energy around 16 MeV/nucleon, with the breakup effect taken into account explicitly. Using the CDCC-based OP and alpha spectroscopic factors given by the cluster model calculation, a good CRC description of the alpha transfer data without any adjustment of the (complex) potential strength., Comment: Phys. Rev. C {\bf 102}, 024622 (2020)

The 11Li + p and 11Li + d reactions are investigated in the Continuum Discretized Coupled Channel (CDCC) method with a three-body description (9Li + n + n) of 11Li. I first discuss the properties of 11Li, and focus on E1 transition probabilities to the continuum. The existence of a 1- resonance at low excitation energies is confirmed, but the associated E1 transition from the ground state does not have an isoscalar character, as suggested in a recent experiment. In a second step, I study the 11Li + p elastic cross section at Elab = 66 MeV in the CDCC framework. I obtain a fair agreement with experiment, and show that breakup effects are maximal at large angles. The breakup cross section is shown to be dominated by the 1- dipole state in 11Li, but the role of this resonance is minor in elastic scattering. From CDCC equivalent 11Li + p and 11Li + n potentials, I explore the 11Li + d cross section within a standard three-body 11Li +(p + n) model. At small angles, the experimental cross section is close to the Rutherford scattering cross section, which is not supported by the CDCC. A five-body (9Li+n+n)+(p+n) is then performed. Including breakup states in 11Li and in the deuteron represents a numerical challenge for theory, owing to the large number of channels. Although a full convergence could not be reached, the CDCC model tends to overestimate the data at small angles. I suggest that measurements of the 9Li + p elastic scattering would be helpful to determine more accurate optical potentials. The current disagreement between experiment and theory on 11Li + d scattering also deserves new experiments at other energies., Comment: 12 pages, 10 figures, accepted at Phys. Rev. C

The Lagrange-mesh $R$-matrix method is generalized to inhomogeneous equations. This method is numerically stable and efficient. It can be directly used for transfer reactions with the formalism discussed by Ascuitto and Glendenning [Phys. Rev. 181,1396 (1969)] and for inclusive breakup reactions modeled by Ichimura, Austern, and Vincent [Phys. Rev. C 32, 431 (1985)]. We first present a simple example to assess the method. Then the application to the $^{93}$Nb($d$,$pX$) non-elastic breakup is discussed., Comment: 7 pages, 6 figures

We use a microscopic multicluster model to investigate the structure of $^{10}$Be and of $^{11}$Be. These nuclei are described by $\alpha+\alpha+n+n$ and $\alpha+\alpha+n+n+n$ configurations, respectively, within the Generator Coordinate Method (GCM). The 4- and 5-body models raise the problem of a large number of generator coordinates (6 for $^{10}$Be and 9 for $^{11}$Be), which requires specific treatment. We address this issue by using the Stochastic Variational Method (SVM), which is based on an optimal choice of the basis functions, generated randomly. The model provides good energy spectra for low-lying states of both nuclei. We also compute rms radii and densities, as well as electromagnetic transition probabilities. We analyze the structure of $^{10}$Be and of $^{11}$Be by considering energy curves, where one of the generator coordinates is fixed during the minimization procedure.

This white paper reports on the discussions of the 2018 Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program "From bound states to the continuum: Connecting bound state calculations with scattering and reaction theory". One of the biggest and most important frontiers in nuclear theory today is to construct better and stronger bridges between bound state calculations and calculations in the continuum, especially scattering and reaction theory, as well as teasing out the influence of the continuum on states near threshold. This is particularly challenging as many-body structure calculations typically use a bound state basis, while reaction calculations more commonly utilize few-body continuum approaches. The many-body bound state and few-body continuum methods use different language and emphasize different properties. To build better foundations for these bridges, we present an overview of several bound state and continuum methods and, where possible, point to current and possible future connections., Comment: 48 pages, 23 figures; paper from the FRIB Theory Alliance Workshop on "From Bound States to the Continuum", June 11-22, 2018

We apply the $R$-matrix method in Distorted Wave Born Approximation (DWBA) calculations. The internal wave functions are expanded over a Lagrange mesh, which provides an efficient and fast technique to compute matrix elements. We first present an outline of the theory, by emphasizing the $R$-matrix aspects. The model is applied to the 16O(d,p)7Li and 12C(7Li,t)16O reactions, typical of nucleon and of $\alpha$ transfer, respectively. We illustrate the sensitivity of the cross sections with respect to the $R$-matrix parameters, and show that an excellent convergence can be achieved with relatively small bases. We also discuss the effects of the remnant term in DWBA calculations, and address the question of the peripherality in transfer reactions. We suggest that uncertainties on spectroscopic factors could be underestimated in the literature., Comment: 13 pages, 11 figures, accepted for publication at Phys. Rev. C

I develop a microscopic three-cluster model for exotic light nuclei. I use the hyperspherical formalism, associated with the Generator Coordinate Method. This model is well adapted to halo nuclei, since the long-range part of the radial wave functions is accurately reproduced. The core wave functions are described in the shell model, including excited states. This technique provides large bases, expressed in terms of projected Slater determinants. Matrix elements involve seven-dimension integrals, and therefore require long calculation times. I apply the model to 11Li, 14Be, 15B, and 17N described by two neutrons surrounding a 9Li, 12Be, 13B and 15N core, respectively. The 17Ne (as 15O+p+p) and 15Ne (as 13O+p+p) mirror nuclei are briefly discussed. I present the spectra and some spectroscopic properties, such as r.m.s. radii or E2 transition probabilities. I also analyze the importance of core excitations., Comment: Accepted for publication in Phys. Rev. C

We use microscopic 9Be wave functions defined in a alpha+alpha+n multicluster model to compute 9Be+target scattering cross sections. The parameter sets describing 9Be are generated in the spirit of the Stochastic Variational Method (SVM), and the optimal solution is obtained by superposing Slater determinants and by diagonalizing the Hamiltonian. The 9Be three-body continuum is approximated by square-integral wave functions. The 9Be microscopic wave functions are then used in a Continuum Discretized Coupled Channel (CDCC) calculation of 9Be+208Pb and of 9Be+27Al elastic scattering. Without any parameter fitting, we obtain a fair agreement with experiment. For a heavy target, the influence of 9Be breakup is important, while it is weaker for light targets. This result confirms previous non-microscopic CDCC calculations. One of the main advantages of the microscopic CDCC is that it is based on nucleon-target interactions only; there is no adjustable parameter. The present work represents a first step towards more ambitious calculations involving heavier Be isotopes., Comment: Phys. Rev. C in press

The $\beta$-decay process of the $^6$He halo nucleus into the $\alpha+d$ continuum is studied in an updated three-body model. The $^6$He nucleus is described as an $\alpha+n+n$ system in hyperspherical coordinates on a Lagrange-mesh. The shape and absolute values of the transition probability per time and energy units of new experiments are reproduced with a modified $\alpha+d$ potential. The obtained total transition probabilities are $2.48 \times 10^{-6}$ s$^{-1}$ for the full energy region and $2.40 \times 10^{-6}$ s$^{-1}$ for the cut-off $E>150$ keV. The strong cancellation between the internal and halo parts of the $\beta$ decay matrix element is a challenge for future {\it ab initio} calculations., Comment: 4 pages, 3 figures

We present a new reaction model, which permits the description of reactions where both colliding nuclei present a low threshold to breakup. The method corresponds to a four-body extension of the Continuum Discretized Coupled Channel (CDCC) model. We first discuss the theoretical formalism, and then apply the method to 11Be+d scattering at Ecm = 45.5 MeV. The 11Be nucleus and the deuteron are described by 10Be+n and p + n structures, respectively. The model involves very large bases, but we show that an accurate description of elastic-scattering data may be achieved only when continuum states of 11Be and of the deuteron are introduced simultaneously. We also discuss breakup calculations, and show that the cross section is larger for 11Be than for the deuteron. The present theory provides reliable wave functions that may be used in the analysis of (d,p) or (d,n) experiments involving radioactive beams., Comment: 5 pages, 4 figures, accepted for publication at Physics Letters B

We use a three-body Continuum Discretized Coupled Channel (CDCC) model to investigate Coulomb and nuclear effects in breakup and reaction cross sections. The breakup of the projectile is simulated by a finite number of square integrable wave functions. First we show that the scattering matrices can be split in a nuclear term, and in a Coulomb term. This decomposition is based on the Lippmann-Schwinger equation, and requires the scattering wave functions. We present two different methods to separate both effects. Then, we apply this separation to breakup and reaction cross sections of 7Li + 208Pb. For breakup, we investigate various aspects, such as the role of the alpha + t continuum, the angular-momentum distribution, and the balance between Coulomb and nuclear effects. We show that there is a large ambiguity in defining the 'Coulomb' and 'nuclear' breakup cross sections, since both techniques, although providing the same total breakup cross sections, strongly differ for the individual components. We suggest a third method which could be efficiently used to address convergence problems at large angular momentum. For reaction cross sections, interference effects are smaller, and the nuclear contribution is dominant above the Coulomb barrier. We also draw attention on different definitions of the reaction cross section which exist in the literature, and which may induce small, but significant, differences in the numerical values., Comment: 12 pages, 11 figures

A microscopic version of the Continuum Discretized Coupled Channel (CDCC) method is used to investigate $^{6}$He scattering on $^{27}$Al, $^{58}$Ni, $^{120}$Sn, and $^{208}$Pb at energies around the Coulomb barrier. The $^{6}$He nucleus is described by an antisymmetric 6-nucleon wave function, defined in the Resonating Group Method. The $^{6}$He continuum is simulated by square-integrable positive-energy states. The model is based only on well known nucleon-target potentials, and is therefore does not depend on any adjustable parameter. I show that experimental elastic cross sections are fairly well reproduced. The calculation suggests that breakup effects increase for high target masses. For a light system such as $^{6}$He+$^{27}$Al, breakup effects are small, and a single-channel approximation provides fair results. This property is explained by a very simple model, based on the sharp-cut-off approximation for the scattering matrix. I also investigate the $^{6}$He-target optical potentials, which confirm that breakup channels are more and more important when the mass increases. At large distances, polarization effects increase the Coulomb barrier, and provide a long-tail absorption component in the imaginary part of the nucleus-nucleus interaction., Comment: 11 pages, 11 figures, accepted at Phys. Rev. C

Breakup cross sections are determined for the Borromean nucleus 22C by using a four-body eikonal model, including Coulomb corrections. Bound and continuum states are constructed within a 20C + n + n three-body model in hyperspherical coordinates. We compute continuum states with the correct asymptotic behavior through the R-matrix method. For the n+ n potential, we use the Minnesota interaction. As there is no precise experimental information on 21C, we define different parameter sets for the 20C + n potentials. These parameter sets provide different scattering lengths, and resonance energies of an expected 3/2+ excited state. Then we analyze the 22C ground-state energy and rms radius, as well as E1 strength distributions and breakup cross sections. The E1 strength distribution presents an enhancement at low energies. Its amplitude is associated with the low binding energy, rather than with a three-body resonance. We show that the shape of the cross section at low energies is sensitive to the ground-state properties. In addition, we suggest the existence of a low-energy 2+ resonance, which should be observable in breakup experiments.

Primordial or big bang nucleosynthesis (BBN) is one of the three historical strong evidences for the big bang model. Standard BBN is now a parameter free theory, since the baryonic density of the Universe has been deduced with an unprecedented precision from observations of the anisotropies of the cosmic microwave background (CMB) radiation. There is a good agreement between the primordial abundances of 4He, D, 3He and 7Li deduced from observations and from primordial nucleosynthesis calculations. However, the 7Li calculated abundance is significantly higher than the one deduced from spectroscopic observations and remains an open problem. In addition, recent deuterium observations have drastically reduced the uncertainty on D/H, to reach a value of 1.6%. It needs to be matched by BBN predictions whose precision is now limited by thermonuclear reaction rate uncertainties. This is especially important as many attempts to reconcile Li observations with models lead to an increased D prediction. Here, we re-evaluates the D(p,g)3He, D(d,n)3He and D(d,p)3H reaction rates that govern deuterium destruction, incorporating new experimental data and carefully accounting for systematic uncertainties. Contrary to previous evaluations, we use theoretical ab initio models for the energy dependence of the S-factors. As a result, these rates increase at BBN temperatures, leading to a reduced value of D/H = (2.45$\pm0.10)\times10^{-5}$ (2$\sigma$), in agreement with observations., Comment: Submitted to Phys. Rev. D. (without the non-essential Tables IV, IX, X and XI provided here)

We present an $R$-matrix Fortran package to solve coupled-channel problems in nuclear physics. The basis functions are chosen as Lagrange functions, which permits simple calculations of the matrix elements. The main input are the coupling potentials at some nucleus-nucleus distances, specified by the program. The program provides the collision matrix and, optionally, the associated wave function. The present method deals with open and closed channels simultaneously, without numerical instability associated with closed channels. It can also solve coupled-channel problems for non-local potentials. Long-range potentials can be treated with propagation techniques, which significantly speed up the calculations. We first present an overview of the $R$-matrix theory, and of the Lagrange-mesh method. A description of the package and its installation on a UNIX machine is then provided. Finally, five typical examples are discussed., Comment: 28 pages, 6 figures, accepted for publication at Computer Physics Communications

We investigate the $^9$Be + $^{208}$Pb elastic scattering, breakup and fusion at energies around the Coulomb barrier. The three processes are described simultaneously, with identical conditions of calculations. The $^{9}$Be nucleus is defined in an $\alpha + \alpha$ + n three-body model, using the hyperspherical coordinate method. We first analyze spectroscopic properties of $^9$Be, and show that the model provides a fairly good description of the low-lying states. The scattering with $^{208}$Pb is then studied with the Continuum Discretized Coupled Channel (CDCC) method, where the $\alpha+\alpha$ + n continuum is approximated by a discrete number of pseudostates. Optical potentials for the $\alpha$+ $^{208}$Pb and n+ $^{208}$Pb systems are taken from the literature. We present elastic-scattering and fusion cross sections at different energies., Comment: 8 pages, 3 figures, Proceedings of the International Conference on Nucleus-Nucleus Collisions, NN 2015, Catania-Italy. arXiv admin note: substantial text overlap with arXiv:1410.6410

We investigate the 9Be + 208Pb elastic scattering and fusion at energies around the Coulomb barrier. The $^9$Be nucleus is described in a \alpha + \alpha + n three-body model, using the hyperspherical coordinate method. The scattering with $^{208}$Pb is then studied with the Continuum Discretized Coupled Channel (CDCC) method, where the \alpha + \alpha + n continuum is approximated by a discrete number of pseudostates. Optical potentials for the $\alpha+^{208}$Pb and $n+^{208}$Pb systems are taken from the literature. We present elastic-scattering and fusion cross sections at different energies, and investigate the convergence with respect to the truncation of the \alpha + \alpha + n continuum. A good agreement with experiment is obtained, considering that there is no parameter fitting. We show that continuum effects increase at low energies., Comment: 6 pages, 4 figures. Submitted to the proceedings of the "NUBA Conference Series -1: Nuclear Physics and Astrophysics" Adrasan-Antalya, Turkey, September 15-21, 2014

Theoretical estimations for the astrophysical S-factor and the d(alpha,gamma)6Li reaction rates are obtained on the base of the two-body model with the alpha-d potential of a simple Gaussian form, which describes correctly the phase-shifts in the S-, P-, and D-waves, the binding energy and the asymptotic normalization constant in the final S-state. Wave functions of the bound and continuum states are calculated by using the Numerov algorithm of a high accuracy. A good convergence of the results for the E1- and E2- components of the transition is shown when increasing the upper limit of effective integrals up to 40 fm. The obtained results for the S-factor and reaction rates in the temperature interval 10E+6 K < T < 10E+10 K are in a good agreement with the results of Ref. A.M. Mukhamedzhanov, et.al., Phys. Rev., C 83, 055805 (2011), where the authors used the known asymptotical form of wave function at low energies and a complicated potential at higher energies., Comment: 15 pages, 7 figs, 1 table

We employ a microscopic continuum-discretized coupled-channels reaction framework (MCDCC) to study the elastic angular distribution of the $^7$Li$=\alpha+t$ nucleus colliding with $^{12}$C and $^{28}$Si targets at $E_{\text{Lab}}$=350 MeV. In this framework, the $^7$Li projectile is described in a microscopic cluster model and impinges on non-composite targets. The diagonal and coupling potentials are constructed from nucleon-target interactions and $^7$Li microscopic wave functions. We obtain a fair description of the experimental data, in the whole angular range studied, when continuum channels are included. The inelastic and breakup angular distributions on the lightest target are also investigated. In addition, we compute $^{7}$Li$+^{12}$C MCDCC elastic cross sections at energies much higher than the Coulomb barrier and we use them as reference calculations to test the validity of multichannel eikonal cross sections., Comment: 9 Pages, 6 Figures

We propose alternatives to coupled-channels calculations with loosely-bound exotic nuclei (CDCC), based on the the random matrix (RMT) and the optical background (OPM) models for the statistical theory of nuclear reactions. The coupled channels equations are divided into two sets. The first set, described by the CDCC, and the other set treated with RMT. The resulting theory is a Statistical CDCC (CDCC$_S$), able in principle to take into account many pseudo channels., Comment: 15 pages, 4 figures. Contribution to: "4th International Workshop on Compound-Nuclear Reactions and Related Topics (CNR*13)", October 7-11, 2013, Maresias, Brazil

Background: Microscopic description of the projectile, based on an effective NN interaction, in a microscopic CDCC (MCDCC) model [PRL 111, 082701 (2013)] has been successfully applied to the 7Li+208Pb scattering. Purpose: The MCDCC method is applied to the low energy elastic scattering of 17F, 17O and 19F on 58Ni and 208Pb targets. The goal of the calculations is twofold - to test the adequacy and the accuracy of the MCDCC model for the heavier projectiles, and to study the contribution of various channels to the elastic scattering cross sections. Methods: The elastic scattering cross sections are calculated using the MCDCC method. The nucleon-target optical potential is folded with the projectile densities resulting from an effective NN interaction, which includes central nuclear, spin-orbit and Coulomb terms. Discretization of the continuum is achieved via the pseudo state method. Coupled equations are solved using the R-matrix method on a Lagrange mesh. Results: For the test case of 17F at 10 MeV/nucleon, the cross sections are weakly sensitive to the choice of the effective NN interaction, three different energy dependent optical nucleon-target potentials provide a similar reasonable agreement with data. Just below the Coulomb barrier, the MCDCC significantly underestimates the cross sections at larger angles. The coupling to continuum is not significant in most of the assessed cases. Conclusions: The MCDCC is very satisfactory in the sense, that it includes the microscopic properties of the projectile in a reaction model. Well above the Coulomb barrier, the cross sections are in a good agreement with data. The reasons for the discrepancy between the data and the calculated cross sections at the lower energies, which is also observed in a traditional CDCC, are unclear.

We investigate the triple-alpha reaction at low energies, by assuming a direct process. The Coulomb potential of three $\alpha$ particles is examined carefully. The three-body continuum wave functions are generated by calculating an adiabatic potential barrier. We discuss the influence of the $\alpha\alpha$ potential, and compare our reaction rates with the literature. The reaction rate at $T=0.01$\,GK is about 10$^3$ times larger than that of NACRE., Comment: 14 pages, 8 figures, submitted to Phys. Rev. C

We propose an extension of the Continuum Discretized Coupled Channels (CDCC) method, where the projectile is described by a microscopic cluster model. This microscopic generalization (MCDCC) only relies on nucleon-target interactions, and therefore presents an important predictive power. Core excitations can be included without any further parameter. As an example we investigate the $\lipb$ elastic scattering at $E_{lab}=27$ and 35 MeV. The $^7$Li nucleus is known to present an $\alpha+t$ cluster structure, and is well described by the Resonating Group Method. An excellent agreement is obtained for the $\lipb$ elastic cross sections, provided that breakup channels are properly included. We also present an application to inelastic scattering, and discuss future applications of the MCDCC., Comment: 5 pages, 3 figures, Physical Review Letters (2013) in press

We investigate the effect of a variation of fundamental constants on primordial element production in Big Bang nucleosynthesis (BBN). We focus on the effect of a possible change in the nucleon-nucleon interaction on nuclear reaction rates involving the A=5 (5Li and 5He) and A=8 (8Be) unstable nuclei. The reaction rates for 3He(d,p)4He and 3H(d,n)4He are dominated by the properties of broad analog resonances in 5Li and 5He compound nuclei respectively. While the triple-alpha process 4He(aa,g)12C is normally not effective in BBN, its rate is very sensitive to the position of the "Hoyle state" and could in principle be drastically affected if 8Be were stable during BBN. We found that the effect of the variation of constants on the 3He(d,p)4He, 3H(d,n)4He nd 4He(aa,g)12C reaction rates is not sufficient to induce a significant effect on BBN, even with a stable 8Be. The main influences come from the weak rates and the A=2, n(p,g)d, bottleneck reaction., Comment: To appear in proceedings of "XII International Symposium on Nuclei in the Cosmos" August 5-12, 2012, Cairns, Australia, PoS(NIC XII)073

We investigate the effect of a variation of fundamental constants on primordial element production in big bang nucleosynthesis (BBN). We focus on the effect of a possible change in the nucleon-nucleon interaction on nuclear reaction rates involving the A=5 (Li-5 and He-5) and A=8 (Be-8) unstable nuclei and complement earlier work on its effect on the binding energy of deuterium. The reaction rates for He3(d,p)He4 and H3(d,n)He4 are dominated by the properties of broad analog resonances in He-5 and Li-5 compound nuclei respectively. While the triple alpha process is normally not effective in BBN, its rate is very sensitive to the position of the "Hoyle state" and could in principle be drastically affected if Be-8 were stable during BBN. The nuclear properties (resonance energies in He-5 and Li-5 nuclei, and the binding energies of Be-8 and D) are all computed in a consistent way using a microscopic cluster model. The n(p,gamma)d, He3(d,p)He4 and H3(d,n)He4 and triple-alpha reaction rates are subsequently calculated as a function of the nucleon-nucleon interaction that can be related to the fundamental constants. We found that the effect of the variation of constants on the He3(d,p)He4 and H3(d,n)He4 and triple-alpha reaction rates is not sufficient to induce a significant effect on BBN, even if Be-8 was stable. In particular, no significant production of carbon by the triple alpha reaction is found when compared to standard BBN. We also update our previous analysis on the effect of a variation of constants on the n(p,gamma)d reaction rate., Comment: 14 pages, 12 figures

The most intense gamma-ray line observable from novae is likely to be from positron annihilation associated with the decay of 18F. The uncertainty in the destruction rate of this nucleus through the 18F(p,{\alpha})15O reaction presents a limit to interpretation of any future observed gamma-ray flux. Direct measurements of the cross section of both this reaction and the 18F(p,p)18F reaction have been performed between center of mass energies of 0.5 and 1.9 MeV. Simultaneous fits to both data sets with the R-Matrix formalism reveal several resonances, with the inferred parameters of populated states in 19Ne in general agreement with previous measurements. Of particular interest, extra strength has been observed above ECM \sim1.3 MeV in the 18F(p,p)18F reaction and between 1.3-1.7 MeV in the 18F(p,{\alpha})15O reaction. This is well described by a broad 1/2+ state, consistent with both a recent theoretical prediction and an inelastic scattering measurement. The astrophysical implications of a broad sub-threshold partner to this state are discussed., Comment: 7 pages, 4 figures, 2 tables

Elastic-scattering phase shifts for four-nucleon systems are studied in an $ab$-$initio$ type cluster model in order to clarify the role of the tensor force and to investigate cluster distortions in low energy $d+d$ and $t+p$ scattering. In the present method, the description of the cluster wave function is extended from a simple (0$s$) harmonic-oscillator shell model to a few-body model with a realistic interaction, in which the wave function of the subsystems are determined with the Stochastic Variational Method. In order to calculate the matrix elements of the four-body system, we have developed a Triple Global Vector Representation method for the correlated Gaussian basis functions. To compare effects of the cluster distortion with realistic and effective interactions, we employ the AV8$^{\prime}$ potential as a realistic interaction and the Minnesota potential as an effective interaction. Especially for $^1S_0$, the calculated phase shifts show that the $t+p$ and $h+n$ channels are strongly coupled to the $d+d$ channel for the case of the realistic interaction. On the contrary, the coupling of these channels plays a relatively minor role for the case of the effective interaction. This difference between both potentials originates from the tensor term in the realistic interaction. Furthermore, the tensor interaction makes the energy splitting of the negative parity states of $^4$He consistent with experiments. No such splitting is however reproduced with the effective interaction.

The neutron-rich $^{11}$Li halo nucleus is unique among nuclei with known separation energies by its ability to emit a proton and a neutron in a $\beta$ decay process. The branching ratio towards this rare decay mode is evaluated within a three-body model for the initial bound state and with Coulomb three-body final scattering states. The branching ratio should be comprised between two extreme cases, i.e.\ a lower bound $6 \times 10^{-12}$ obtained with a pure Coulomb wave and an upper bound $5 \times 10^{-10}$ obtained with a plane wave. A simple model with modified Coulomb waves provides plausible values between between $0.8 \times 10^{-10}$ and $2.2 \times 10^{-10}$ with most probable total energies of the proton and neutron between 0.15 and 0.3 MeV., Comment: 15 pages, 3 figures

The beta-decay of the 6He halo nucleus and the M1-transition processes of the excited 6Li(0+) state into the alpha + d continuum are studied in a three-body model. The initial nuclear states are described as an alpha + 2N system in hyperspherical coordinates on a Lagrange mesh. The energy dependence and absolute values of the beta-transition probability per time and energy units of a recent experiment can be reproduced very well with an appropriate alpha + d potential. A total transition probability of 2.04E-6 s^(-1) is obtained in agreement with the experiment. Due to a strong cancellation of the internal and halo components of the matrix elements, halo effects are shown to be very important. For the M1 transition process the halo structure of the excited 6Li(0+) isobaric analog state is confirmed. The cancellation effects, however, are not so strong. The transition probability is strongly sensitive to the description of the alpha + d phase shifts. Charge symmetry is analyzed through a comparison of the two processes. The present branching ratio Gamma(0^+ --> alpha + d)/Gamma(0^+ --> 1+) is of the order 1.0E-4, and is expected to be observable in current experiments., Comment: 14 pages, 5 figures

The different facets of the $R$-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: $(i)$ The "calculable" $R$-matrix method is a calculational tool to derive scattering properties from the Schr\"odinger equation in a large variety of physical problems. It was developed rather independently in atomic and nuclear physics with too little mutual influence. $(ii)$ The "phenomenological" $R$-matrix method is a technique to parametrize various types of cross sections. It was mainly (or uniquely) used in nuclear physics. Both directions are explained by starting from the simple problem of scattering by a potential. They are illustrated by simple examples in nuclear and atomic physics. In addition to elastic scattering, the $R$-matrix formalism is applied to transfer and radiative-capture reactions. We also present more recent and more ambitious applications of the theory in nuclear physics., Comment: 93 pages, 26 figures. Rep. Prog. Phys., in press

A variation of the fundamental constants is expected to affect the thermonuclear rates important for stellar nucleosynthesis. In particular, because of the very small resonant energies of Be8 and C12, the triple $\alpha$ process is extremely sensitive to any such variations. Using a microscopic model for these nuclei, we derive the sensitivity of the Hoyle state to the nucleon-nucleon potential allowing for a change in the magnitude of the nuclear interaction. We follow the evolution of 15 and 60 solar mass, zero metallicity stellar models, up to the end of core helium burning. These stars are assumed to be representative of the first, Population III stars. We derive limits on the variation of the magnitude of the nuclear interaction and model dependent limits on the variation of the fine structure constant based on the calculated oxygen and carbon abundances resulting from helium burning. The requirement that some C12 and O16 be present are the end of the helium burning phase allows for permille limits on the change of the nuclear interaction and limits of order 10^{-5} on the fine structure constant relevant at a cosmological redshift of z ~ 15-20., Comment: 14 pages, 12 figures

The 16O(p,gamma)17F reaction rate is revisited with special emphasis on the stellar temperature range of T=60-100 MK important for hot bottom burning in asymptotic giant branch (AGB) stars. We evaluate existing cross section data that were obtained since 1958 and, if appropriate, correct published data for systematic errors that were not noticed previously, including the effects of coincidence summing and updated effective stopping powers. The data are interpreted by using two different models of nuclear reactions, that is, a potential model and R-matrix theory. A new astrophysical S-factor and recommended thermonuclear reaction rates are presented. As a result of our work, the 16O(p,gamma)17F reaction has now the most precisely known rate involving any target nucleus in the mass A >= 12 range, with reaction rate errors of about 7% over the entire temperature region of astrophysical interest (T=0.01-2.5 GK). The impact of the present improved reaction rate with its significantly reduced uncertainties on the hot bottom burning in AGB stars is discussed. In contrast to earlier results we find now that there is not clear evidence to date for any stellar grain origin from massive AGB stars., Comment: 14 pages, 9 figures, PRC, accepted

A generalized optical potential for elastic scattering induced by light nuclei is calculated within the Feshbach projection operator method. The model explicitly takes into account the contribution of the projectile break-up continuum treated within a microscopic few-cluster model. In this work we formulate the model, deriving an explicit expression for the optical potential, and show ability of the model applying it to deuteron elastic scattering., Comment: 35 pages, 11 figures

M1 transitions from the $^6$Li($0^+;T=1$) state at 3.563 MeV to the $^6$Li($1^+$) ground state and to the $\alpha+d$ continuum are studied in a three-body model. The bound states are described as an $\alpha+n+p$ system in hyperspherical coordinates on a Lagrange mesh. The ground-state magnetic moment and the gamma width of the $^6$Li(0$^+$) resonance are well reproduced. The halo-like structure of the $^6$Li$(0^+)$ resonance is confirmed and is probed by the M1 transition probability to the $\alpha+d$ continuum. The spectrum is sensitive to the description of the $\alpha+d$ phase shifts. The corresponding gamma width is around 1.0 meV, with optimal potentials. Charge symmetry is analyzed through a comparison with the $\beta$-delayed deuteron spectrum of $^6$He. In $^6$He, a nearly perfect cancellation effect between short-range and halo contributions was found. A similar analysis for the $^6$Li($0^+;T=1$) $\gamma$ decay is performed; it shows that charge-symmetry breaking at large distances, due to the different binding energies and to different charges, reduces this effect. The present branching ratio $\Gamma_{\gamma}(0^+\to \alpha+d)/\Gamma_{\gamma}(0^+\to1^+)\approx 1.3\times 10^{-4}$ should be observable with current experimental facilities., Comment: 20 pages, 5 figures. Accepted for publication in Nucl. Phys. A., 2007

Local $\alpha \alpha$ potentials fail to describe $^{12}$C as a $3\alpha$ system. Nonlocal $\alpha \alpha$ potentials that renormalize the energy-dependent kernel of the resonating group method allow interpreting simultaneously the ground state and $0^+_2$ resonance of $^{12}$C as $3\alpha$ states. A comparison with fully microscopic calculations provides a measure of the importance of three-cluster exchanges in those states., Comment: The tar.gz file has 1 tex file and 1 eps file

The beta decay process of the 11Li halo nucleus into 9Li and d is studied in a three-body model. The 11Li nucleus is described as a 9Li+n+n system in hyperspherical coordinates on a Lagrange mesh. Various 9Li+d potentials are compared involving a forbidden state, a physical bound state, and a resonance near 0.25 MeV in the s-wave. With an added surface absorption, they are compatible with elastic scattering data. The transition probability per time unit is quite sensitive to the location of the resonance. For a fixed resonance location, it does not depend much on the potential choice at variance with the 6He delayed deuteron decay. The calculated transition probability per time unit is larger than the experimental value but the difference can be explained by a slightly higher resonance location and/or by absorption from the 9Li+d final channel., Comment: 14 pages, 7 figures, 3 tables

We show that a consequence of isospin symmetry, recently discovered in mirror conjugated one-nucleon decays, can be extended to mirror-conjugated $\alpha$-particles decays, both virtual and real. For virtual $\alpha$-decays of bound mirror pairs this symmetry manifests itself as a relation between the Asymptotic Normalization Coefficients (ANCs) of $\alpha$-particle overlap integrals. This relation is given by a simple analytical formula which involves $\alpha$-particle separation energies and charges of residual nuclei. For bound-unbound mirror pairs, the ANC of a bound nucleus is related to the $\alpha$-width of the mirror unbound level. For unbound mirror pairs we get a new analytical formula that relates the widths of mirror resonances. We test the validity of these analytical formuli against the predictions of a two-body potential and of a many-body microscopic cluster model for several mirror states in $^7$Li-$^7$Be, $^{11}$B-$^{11}$C and $^{19}$F-$^{19}$Ne isotopes. We show that these analytical formulae are valid in many cases but that some deviations can be expected for isotopes with strongly deformed and easily excited cores. In general, the results from microscopic model are not very sensitive to model assumptions and can be used to predict unknown astrophysically relevant cross sections using known information about mirror systems., Comment: 15 pages, 6 figures, submitted to Phys. Rev. C

Three-body continuum states are investigated with the hyperspherical method on a Lagrange mesh. The $R$-matrix theory is used to treat the asymptotic behaviour of scattering wave functions. The formalism is developed for neutral as well as for charged systems. We point out some specificities of continuum states in the hyperspherical method. The collision matrix can be determined with a good accuracy by using propagation techniques. The method is applied to the $^6$He (=$\alpha$+n+n) and $^6$Be (=$\alpha$+p+p) systems, as well as to $^{14}$Be (=$^{12}$Be+n+n). For $^6$He, we essentially recover results of the literature. Application to $^{14}$Be suggests the existence of an excited $2^+$ state below threshold. The calculated B(E2) value should make this state observable with Coulomb excitation experiments., Comment: 17 pages, 8 figures. Accepted for publication in Nucl.Phys.A