arXiv subjects

P. Descouvemont

Publications and source records attributed to P. Descouvemont.

At least 19 recordsLinked to original sources

arXiv2026

Towards a microscopic description of 12C+12C fusion at stellar energies

I present a fully microscopic description of the 12C+12C fusion reaction at stellar energies. Utilizing the multichannel Resonating Group Method (RGM), my model explicitly includes 12C+12C and alpha+20Ne reaction channels (with excited states). This approach provides a consistent, simultaneous, description of fusion, elastic scattering, and 24Mg spectroscopy. Results for 12C+12C elastic scattering show excellent agreement with experimental data, significantly improving the single-channel approximations. Spectroscopic analysis reveals that 24Mg states and resonances are highly mixed configurations, contradicting the concept of pure "molecular states." The calculated fusion S-factor is consistent with available experimental data and predicts both narrow and broad resonances near the Coulomb barrier. Main resonance widths originate primarily from the alpha+20Ne exit channels. The S-factor exhibits a decrease at low energies, providing a microscopic support for the hypothesis of fusion hindrance. This work is a first step towards a reliable theoretical extrapolation of the 12C+12C reaction to deep stellar burning temperatures. Future works should include the neutron and proton channels to provide a complete description of the 12C+12C fusion.

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arXiv2025

Three-body model of $^{6}$He with non-local halo effective field theory potentials

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.

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arXiv2022

Application of R-matrix and Lagrange-mesh methods to nuclear transfer reactions

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.

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arXiv2022

Breakup effects in the $^{16}{\rm C}+p$ and $^{16}{\rm C}+d$ reactions

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.

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arXiv2021

Exchange effects in nucleus-nucleus reactions

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.

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arXiv2021

Resonances in $^{12}$C and $^{24}$Mg: what do we learn from a microscopic cluster theory?

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 $α+α+α$ structure, whereas $^{24}{\rm Mg}$ is considered as an $^{16}{\rm O}+α+α$ 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.

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arXiv2020

Sensitivity of transfer cross sections to the bound-state wave functions

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 $α$ 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.

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arXiv2019

Transfer reactions with the Lagrange-mesh method

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 $α$ 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.

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arXiv2019

Microscopic three-cluster study of light exotic nuclei

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.

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arXiv2018

9Be scattering with microscopic wave functions and the CDCC method

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.

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arXiv2017

Updated three-body model of $^6$He $β$ decay into the $α$ + $d$ continuum

The $β$-decay process of the $^6$He halo nucleus into the $α+d$ continuum is studied in an updated three-body model. The $^6$He nucleus is described as an $α+n+n$ 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 $α+d$ 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 $β$ decay matrix element is a challenge for future {\it ab initio} calculations.

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arXiv2016

Low-energy $^{6}$He scattering in a microscopic model

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.

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arXiv2016

Coulomb breakup of 22C in a four-body model

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.

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arXiv2015

An R-matrix package for coupled-channel problems in nuclear physics

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.

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arXiv2015

A consistent four-body CDCC model of low-energy reactions: Application to 9Be + 208Pb

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 $α+ α$ + 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 $α+α$ + n continuum is approximated by a discrete number of pseudostates. Optical potentials for the $α$+ $^{208}$Pb and n+ $^{208}$Pb systems are taken from the literature. We present elastic-scattering and fusion cross sections at different energies.

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arXiv2014

Four-body effects on 9Be + 208Pb scattering and fusion around the Coulomb barrier

We investigate the 9Be + 208Pb elastic scattering and fusion at energies around the Coulomb barrier. The $^9$Be nucleus is described in a α+ α+ 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 α+ α+ n continuum is approximated by a discrete number of pseudostates. Optical potentials for the $α+^{208}$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 α+ α+ 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.

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arXiv2014

Elastic scattering of 17F, 17O and 19F on a heavy target in microscopic continuum discretized coupled-channels method

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.

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arXiv2014

Theoretical analysis of the astrophysical S-factor for the alpha+d -->6Li + gamma capture reaction in the two body model

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.

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