arXiv subjects

Do Cong Cuong

Publications and source records attributed to Do Cong Cuong.

12 recordsLinked to original sources

arXiv2024

Systematics of supernumerary nuclear rainbow in inelastic $^{16}$O+$^{12}$C scattering

We perform a systematic study of inelastic nuclear rainbow scattering for the \oc system to the 2$^+$ (4.44 MeV) state of $^{12}$C at incident energies of 100--608 MeV with the coupled-channels method. The recently generalized nearside-farside decomposition for inelastic scattering was applied in combination with the multichannel deflection function analysis to elucidate the origin of the nuclear rainbow phenomenon and the suppression of the primary and supernumerary Airy minima in the inelastic scattering cross section. The systematic evolution of the Airy minima for the excited 2$^+$ (4.44 MeV) state of $^{12}$C was unambiguously determined. Our work suggests that there is no clear shift in the positions of the first Airy minima and a small shift at low energies for the second and third Airy minima between the inelastic and elastic scattering cross sections. Using the $K$-subamplitudes splitting technique combined with the generalized nearside-farside decomposition and deflection function, the distinct refractive pattern commonly suppressed in the inelastic heavy-ion scattering can be interpreted and provides new insights into the relationship between elastic and inelastic nuclear rainbow scattering.

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arXiv2021

Study of nonlocality effects in direct capture reactions with Lagrange-mesh $R$-matrix method

We apply the Lagrange-mesh $R$-matrix method to calculate the $S$-factor for the $^{13}$C$(p,γ)^{14}$N and $^{16}$O$(p,γ)^{17}$F direct radiative capture reactions. By comparing the astrophysical $S$-factors calculated with nonlocal and local potentials, we investigate the nonlocality effects coming from the nuclear potentials in the direct capture reactions. Our calculations are in good agreement with the experimental data and indicate a nonnegligible difference in the results of local and nonlocal potentials. The use of small diffuseness narrow potentials also provides a remarkably good fit in the case with multiple broad resonances. Our findings suggest that the nonlocal potential improves the calculated results although the difference between the local and nonlocal potentials is smaller than uncertainties from other sources. We propose the nonlocality potential should be used in the potential model calculation of future astrophysics rates evaluation.

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arXiv2021

Suppression of the nuclear rainbow in the inelastic nucleus-nucleus scattering

The nuclear rainbow observed in the elastic $α$-nucleus and light heavy-ion scattering is proven to be due to the refraction of the scattering wave by a deep, attractive real optical potential. The nuclear rainbow pattern, established as a broad oscillation of the Airy minima in the elastic cross section, originates from an interference of the refracted far-side scattering amplitudes. It is natural to expect a similar rainbow pattern also in the inelastic scattering of a nucleus-nucleus system that exhibits a pronounced rainbow pattern in the elastic channel. Although some feature of the nuclear rainbow in the inelastic nucleus-nucleus scattering was observed in experiment, the measured inelastic cross sections exhibit much weaker rainbow pattern, where the Airy oscillation is suppressed and smeared out. To investigate this effect, a novel method of the near-far decomposition of the inelastic scattering amplitude is proposed to explicitly reveal the coupled partial-wave contributions to the inelastic cross section. Using the new decomposition method, our coupled channel analysis of the elastic and inelastic $^{12}$C+$^{12}$C and $^{16}$O+$^{12}$C scattering at the refractive energies shows unambiguously that the suppression of the nuclear rainbow pattern in the inelastic scattering cross section is caused by a destructive interference of the partial waves of different multipoles. However, the inelastic scattering remains strongly refractive in these cases, where the far-side scattering is dominant at medium and large angles like that observed in the elastic scattering.

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arXiv2020

Coupled reaction channel study of the 12C(alpha,8Be) reaction, and the 8Be+8Be optical potential

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.

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arXiv2018

Consistent mean-field description of the $^{12}$C+$^{12}$C optical potential at low energies and the astrophysical $S$ factor

The nuclear mean-field potential built up by the $^{12}$C+$^{12}$C interaction at energies relevant for the carbon burning process is calculated in the double-folding model (DFM) using the realistic ground-state density of $^{12}$C and the CDM3Y3 density dependent nucleon-nucleon (NN) interaction, with the rearrangement term properly included. To validate the use of a density dependent NN interaction in the DFM calculation in the low-energy regime, an adiabatic approximation is suggested for the nucleus-nucleus overlap density. The reliability of the nuclear mean-field potential predicted by this low-energy version of the DFM is tested in a detailed optical model analysis of the elastic $^{12}$C+$^{12}$C scattering data at energies below 10 MeV/nucleon. The folded mean-field potential is then used to study the astrophysical $S$ factor of the $^{12}$C+$^{12}$C fusion in the barrier penetration model. Without any adjustment of the potential strength, our results reproduce very well the non-resonant behavior of the $S$ factor of the $^{12}$C+$^{12}$C fusion over a wide range of energies.

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arXiv2016

Mean-field study of $^{12}$C+$^{12}$C fusion

The nuclear mean-field potential arising from the $^{12}$C+$^{12}$C interaction at the low energies relevant for the astrophysical carbon burning process has been constructed within the double-folding model, using the realistic nuclear ground-state density of the $^{12}$C nucleus and the effective M3Y nucleon-nucleon (NN) interaction constructed from the G-matrix of the Paris (free) NN potential. To explore the nuclear medium effect, both the original density independent M3Y-Paris interaction and its density dependent CDM3Y6 version have been used in the folding model calculation of the $^{12}$C+$^{12}$C potential. The folded potentials at the different energies were used in the optical model description of the elastic $^{12}$C+$^{12}$C scattering at the energies around and below the Coulomb barrier, as well as in the barrier penetration model to estimate the fusion cross section and astrophysical $S$ factor of the $^{12}$C+$^{12}$C reactions at the low energies. The obtained results are in good agreement with experimental data over a wide range of energies.

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arXiv2013

Folding model analysis of the inelastic $α+^{12}$C scattering at medium energies, and the isoscalar transition strengths of the cluster states of $^{12}$C

The complex optical potential and inelastic form factor given by the folding model for the $α+^{12}$C scattering are used to calculate the ($α,α'$) cross sections for the known isoscalar states of $^{12}$C in an elaborate coupled channel approach. The strengths of the form factors for these states are then fine tuned against the ($α,α'$) data to deduce the corresponding $Eλ$ transition strengths. A significant $E2$ transition strength has been obtained for the $2^+_2$ state from the present analysis of the ($α,α'$) data measured at $E_α=240$ and 386 MeV. The $Eλ$ transition strengths of the $0^+_2,\ 3^-_1,\ 0^+_3,$ and $1^-_1$ states were also carefully deduced, and some difference from the results of earlier analyses has been found and qualitatively understood.

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arXiv2010

Hindrance of the excitation of the Hoyle state and the ghost of the $2^+_2$ state in $^{12}$C

While the Hoyle state (the isoscalar $0^+_2$ excitation at 7.65 MeV in $^{12}$C) has been observed in almost all the electron and $α$ inelastic scattering experiments, the second $2^+$ excited state of $^{12}$C at $E_{\rm x}\approx 10$ MeV, believed to be an excitation of the Hoyle state, has not been clearly observed in these measurements excepting the high-precision \aap experiments at $E_α=240$ and 386 MeV. Given the (spin and isospin zero) $α$-particle as a good probe for the nuclear isoscalar excitations, it remains a puzzle why the peak of the $2^+_2$ state could not be clearly identified in the measured \aap spectra. To investigate this effect, we have performed a microscopic folding model analysis of the \ac scattering data at 240 and 386 MeV in both the Distorted Wave Born Approximation (DWBA) and coupled-channel (CC) formalism, using the nuclear transition densities given by the antisymmetrized molecular dynamics (AMD) approach and a complex CDM3Y6 density dependent interaction. Although AMD predicts a very weak transition strength for the direct $(0^+_1\to 2^+_2)$ excitation, our detailed analysis has shown evidence that a weak \emph{ghost} of the $2^+_2$ state could be identified in the 240 MeV \aap data for the $0^+_3$ state at 10.3 MeV, when the CC effects by the indirect excitation of the $2^+_2$ state are taken into account. Based on the same AMD structure input and preliminary \aap data at 386 MeV, we have estimated relative contributions from the $2^+_2$ and $0^+_3$ states to the excitation of $^{12}$C at $E_{\rm x}\approx 10$ MeV as well as possible contamination by $3^-_1$ state.

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arXiv2009

Microscopic study of the isoscalar giant resonances in 208Pb induced by inelastic alpha scattering

The energetic beam of (spin and isospin zero) $α$-particles remains a very efficient probe for the nuclear isoscalar giant resonances. In the present work, a microscopic folding model study of the isoscalar giant resonances in $^{208}$Pb induced by inelastic \aPb scattering at $E_{\rm lab}=240$ and 386 MeV has been performed using the (complex) CDM3Y6 interaction and nuclear transition densities given by both the collective model and Random Phase Approximation (RPA) approach. The fractions of energy weighted sum rule around the main peaks of the isoscalar monopole, dipole and quadrupole giant resonances were probed in the Distorted Wave Born Approximation analysis of inelastic \aPb scattering using the double-folded form factors given by different choices of the nuclear transition densities. The energy distribution of the $E0, E1$ and $E2$ strengths given by the multipole decomposition {analyses} of the \aap data under study are compared with those predicted by the RPA calculation.

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arXiv2007

Missing monopole strength of the Hoyle state in the inelastic $α$+$^{12}$C scattering

Analyses of the inelastic $α$+$^{12}$C scattering at medium energies have indicated that the strength of the Hoyle state (the isoscalar 0$^+_2$ excitation at 7.65 MeV in $^{12}$C) seems to exhaust only 7 to 9% of the monopole energy weighted sum rule (EWSR), compared to about 15% of the EWSR extracted from inelastic electron scattering data. The full monopole transition strength predicted by realistic microscopic $α$-cluster models of the Hoyle state can be shown to exhaust up to 22% of the EWSR. To explore the missing monopole strength in the inelastic $α$+$^{12}$C scattering, we have performed a fully microscopic folding model analysis of the inelastic $α$+$^{12}$C scattering at $E_{\rm lab}=104$ to 240 MeV using the 3-$α$ resonating group wave function of the Hoyle state obtained by Kamimura, and a complex density-dependent M3Y interaction newly parametrized based on the Brueckner Hartree Fock results for nuclear matter. Our folding model analysis has shown consistently that the missing monopole strength of the Hoyle state is not associated with the uncertainties in the analysis of the $α$+$^{12}$C scattering, but is most likely due to the short lifetime and weakly bound structure of this state which significantly enhances absorption in the exit $α$+$^{12}$C$^*(0^+_2)$ channel.

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arXiv2007

Mean-field description of the nucleus-nucleus optical potential

A new finite-range representation of the JLM effective nucleon-nucleon interaction is suggested based on the CDM3Y density dependent functional and M3Y-Paris interaction. The density dependence has been carefully adjusted at each energy so that the nucleon optical potential (OP) given by the new density dependent interaction in the Hartree-Fock calculation of nuclear matter closely matches the JLM nucleon OP given by the Brueckner-Hatree-Fock calculation. The new interaction has been used in the double-folding model to calculate the OP for the elastic $^{6}$Li,$^{6}$He,$^{12}$C + $^{12}$C scattering at different energies.

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arXiv2007

Folding model study of the isobaric analog excitation: isovector density dependence, Lane potential and nuclear symmetry energy

A consistent folding model analysis of the ($ΔS=0, ΔT=1$) charge exchange \pn reaction measured with $^{48}$Ca, $^{90}$Zr, $^{120}$Sn and $^{208}$Pb targets at the proton energies of 35 and 45 MeV is done within a two-channel coupling formalism. The nuclear ground state densities given by the Hartree-Fock-Bogoljubov formalism and the density dependent CDM3Y6 interaction were used as inputs for the folding calculation of the nucleon optical potential and \pn form factor. To have an accurate isospin dependence of the interaction, a complex isovector density dependence of the CDM3Y6 interaction has been carefully calibrated against the microscopic Brueckner-Hatree-Fock calculation by Jeukenne, Lejeune and Mahaux before being used as folding input. Since the isovector coupling was used to explicitly link the isovector part of the nucleon optical potential to the cross section of \pn reaction exciting the 0$^+$ isobaric analog states in $^{48}$Sc, $^{90}$Nb, $^{120}$Sb and $^{208}$Bi, the newly parameterized isovector density dependence could be well tested in the folding model analysis of the \pn reaction. The isospin- and density dependent CDM3Y6 interaction was further used in the Hartree-Fock calculation of asymmetric nuclear matter, and a realistic estimation of the nuclear symmetry energy has been made.

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