arXiv subjects

Nguyen Hoang Phuc

Publications and source records attributed to Nguyen Hoang Phuc.

At least 19 recordsLinked to original sources

arXiv2026

Comparative folding-model study of low-energy elastic scattering and fusion of the $^{12}$C+$^{12}$C and $^{16}$O+$^{16}$O systems

A density dependent nucleon-nucleon interaction (CDM3YR) has been parametrized based on the original M3Y-Reid interaction, to properly reproduce the saturation properties of symmetric nuclear matter (NM) in the nonrelativistic Hartree-Fock calculation, with the energy of NM in a good agreement with the microscopic \emph{ab-initio} results over densities up to three times the saturation density. The real optical potential (OP) of symmetric $^{12}$C+$^{12}$C and $^{16}$O+$^{16}$O systems is then calculated within the double-folding model (DFM), using the realistic densities of $^{12}$C and $^{16}$O nuclei and CDM3YR interaction, for the optical model analysis of elastic scattering at low energies and determination of the astrophysical $S$ factor of $^{12}$C+$^{12}$C and $^{16}$O+$^{16}$O fusion in the barrier penetration model. The DFM calculation of the real OP for these two symmetric systems was also done using the original (density independent) M3Y-Reid interaction, and that added by a repulsive core suggested by Esbensen {\it et al.} to explore the impact of medium effects that are effectively encoded in the density dependence of the CDM3YR interaction.

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arXiv2026

Nuclear Rainbow of Core-Symmetric Systems

The nearside-farside (NF) decomposition method developed originally by Fuller for elastic scattering of a nonidentical nucleus-nucleus system was generalized to study the nuclear rainbow pattern in a symmetric or core-symmetric dinuclear system. It has been shown that the projectile-target identity of an identical system implies a symmetric interchange of the nearside and farside components of elastic scattering amplitude around $θ_{\mathrm{c.m.}}=90^\circ$. A similar interchange appears also in a nonidentical core-symmetric system due to elastic transfer of cluster or nucleon between two identical cores. The analysis of the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$, and ${}^{13}\mathrm{C}+{}^{12}\mathrm{C}$ systems shows how the generalized NF decomposition method reveals the nuclear rainbow pattern in these systems, which can be helpful in probing the real optical potential and nuclear clustering.

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arXiv2025

Collective excited states at small amplitude in neutron elastic scattering at low-energies

We investigate the contributions of isoscalar and isovector collective excitations in the neutron elastic scattering of $^{16}$O, $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb nuclei by using a microscopic optical potential (MOP) derived from nuclear structure models based on self-consistent mean-field approaches. Particular attention is given to the role of these collective modes in shaping the imaginary part of the MOP and the resulting angular distributions. Our analysis indicates that both isoscalar and isovector contributions are significant for all considered targets, especially for light and medium targets. Furthermore, the Coulomb interaction is found to play an important role in describing absorption mechanisms and reproducing the experimental angular distributions.

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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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arXiv2024

Pauli nonlocality and the nucleon effective mass

A study of the nucleon mean-field potential in nuclear matter (NM) is done within an extended Hartree-Fock (HF) formalism, using the CDM3Y6 density dependent version of the M3Y interaction which is associated with the nuclear incompressibility $K\simeq 252$ MeV. The momentum dependence of nucleon optical potential (OP) in NM at the saturation density $ρ_0$ is shown to be due mainly to its exchange term up to $k\approx 2$ fm$^{-1}$, so that the Pauli nonlocality is expected to be the main origin of the nucleon effective mass at low momenta. Because nucleons in neutron-rich NM at $ρ\approx ρ_0$ are either weakly bound or unbound by the in-medium nucleon-nucleon interaction, the determination of the effective mass of nucleon scattered on targets with neutron excess at low energies should be of interest for the mean-field studies of neutron star matter. For this purpose, the folding model is used to calculate the nonlocal nucleon OP for the optical model analysis of elastic nucleon scattering on $^{40,48}$Ca, $^{90}$Zr, and $^{208}$Pb targets at energies $E<50$ MeV, to probe the model reliability and validate the WKB local approximation to obtain the local folded nucleon OP. The nucleon effective mass $m^*$ is then carefully deduced from the momentum dependence of the local folded nucleon OP which is resulted from the Pauli nonlocality of the exchange term. The neutron-proton effective mass splitting determined at $ρ\approxρ_0$ from the central strength of the real folded nucleon OP for $^{48}$Ca, $^{90}$Zr, and $^{208}$Pb targets has been found to depend linearly on the neutron-proton asymmetry parameter as $m^*_{n-p}\approx (0.167\pm 0.018)δ$, in a good agreement with the recent empirical constraints.

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arXiv2024

Nuclear rainbow of the symmetric nucleus-nucleus system: Interchange of the nearside and farside scattering

Extensive elastic scattering data measured at energies around 10 to 20 MeV/nucleon for some identical systems, like 12C+12C and 16O+16O, exhibit the nuclear rainbow pattern of broad Airy oscillations of the cross section at medium and large angles. Due to the identity of the scattered projectile and recoiled target, the rainbow pattern at angles around and beyond $θ_{\rm c.m.}\approx 90^\circ$ is strongly deteriorated by the boson exchange. The nuclear rainbow features in the identical-particles elastic scattering discussed so far are based on the nearside-farside (NF) decomposition of the scattering amplitude given by an optical model calculation neglecting the projectile-target exchange symmetry. Moreover, the NF decomposition method was developed in the 70s by Fuller for nonidentical systems only, and the details of how the exchange symmetry of an identical system affects the evolution of nuclear rainbow remain unexplored. Therefore, the Fuller method is generalized in this work for the elastic scattering of two identical (spin-zero) nuclei, with the projectile-target exchange symmetry taken explicitly into account. The results obtained for elastic 12C+12C and 16O+16O scattering at low energies show the exchange symmetry results in a symmetric interchange of the nearside and farside patterns at angles passing $θ_{\rm c.m.}=90^\circ$, which requires a more subtle interpretation of nuclear rainbow. We also found that a similar NF interchange occurs in a nonidentical nucleus-nucleus system with the core-core symmetry, where the elastic cross section at backward angles is due mainly to the elastic transfer of cluster or nucleon between two identical cores. This interesting effect is illustrated in the elastic 16O+12C scattering at low energies where the elastic $α$ transfer between two 12C cores has been proven to enhance the elastic cross section at backward angles.

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arXiv2021

Ambiguities from nuclear interactions in the $^{12}$C($p,2p$)$^{11}$B reaction

We investigate the impact of ambiguities coming from the choice of optical potentials and nucleon-nucleon scattering cross sections on the spectroscopic factors extracted from the $^{12}$C($p,2p$)$^{11}$B reaction. These ambiguities are evaluated by analyzing the cross sections of the $^{12}$C($p,2p$)$^{11}$B reaction at 100 and 200 MeV within the framework of the distorted-wave impulse approximation with realistic choices of nuclear inputs. The results show that the studied ambiguities are considerably large in this energy region and careful choices of nuclear inputs used in the reaction calculations are required to extract reliable structure information.

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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

Elastic and inelastic alpha transfer in the $^{16}$O+$^{12}$C scattering

The elastic scattering cross section measured at energies $E\lesssim 10$ MeV/nucleon for some light heavy-ion systems having two identical cores like $^{16}$O+$^{12}$C exhibits an enhanced oscillatory pattern at the backward angles. Such a pattern is known to be due to the transfer of the valence nucleon or cluster between the two identical cores. In particular, the elastic $α$ transfer has been shown to originate directly from the core-exchange symmetry in the elastic $^{16}$O+$^{12}$C scattering. Given the strong transition strength of the $2^+_1$ state of $^{12}$C and its large overlap with the $^{16}$O ground state, it is natural to expect a similar $α$ transfer process (or inelastic $α$ transfer) to take place in the inelastic $^{16}$O+$^{12}$C scattering. The present work provides a realistic coupled channel description of the $α$ transfer in the inelastic $^{16}$O+$^{12}$C scattering at low energies. Based on the results of the 4 coupled reaction-channels calculation, we show a significant contribution of the $α$ transfer to the inelastic $^{16}$O+$^{12}$C scattering cross section at the backward angles. These results suggest that the explicit coupling to the $α$ transfer channels is crucial in the studies of the elastic and inelastic scattering of a nucleus-nucleus system with the core-exchange symmetry.

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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

Elastic $α$ transfer in the $^{16}$O+$^{12}$C scattering and its impact on the nuclear rainbow

Elastic $^{16}$O+$^{12}$C scattering is known to exhibit the nuclear rainbow pattern at incident energies $E_\text{lab}\gtrsim 200$ MeV, with the Airy structure of the far-side scattering cross section clearly seen at medium and large angles. Such a rainbow pattern is well described by the deep real optical potential (OP) given by the double-folding model (DFM). At lower energies, the extensive elastic $^{16}$O+$^{12}$C scattering data show consistently that the nuclear rainbow pattern at backward angles is deteriorated by an oscillating enhancement of elastic cross section that is difficult to describe in the conventional optical model (OM). Given a significant $α$ spectroscopic factor predicted for the dissociation $^{16}$O$\toα+^{12}$C by the shell model and $α$-cluster models, the contribution of the elastic $α$ transfer (or the core-core exchange) to the elastic $^{16}$O+$^{12}$C scattering should not be negligible and is expected to account for the enhanced elastic cross section at backward angles. To reveal the impact of the elastic $α$ transfer, a systematic coupled reaction channels analysis of the elastic $^{16}$O+$^{12}$C scattering has been performed, with the coupling between the elastic scattering and elastic $α$ transfer channels treated explicitly, using the real OP given by the DFM. We found that the elastic $α$ transfer enhances the near-side scattering significantly at backward angles, giving rise to an oscillating distortion of the smooth Airy structure. The dynamic polarization of the OP by the coupling between the elastic scattering and elastic $α$ transfer channels can be effectively taken into account in the OM calculation by an angular-momentum (or parity) dependent potential added to the imaginary OP, as suggested by Frahn and Hussein 40 years ago.

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arXiv2020

Folding model approach to the elastic $p+^{12,13}$C scattering at low energies and radiative capture $^{12,13}$C$(p,γ)$ reactions

The proton radiative capture $^{12,13}$C$(p,γ)$ reactions at astrophysical energies, key processes in the CNO cycle, are revisited in the potential model with the proton-nucleus potential for both the scattering and bound states obtained in the folding model, using a realistic density dependent nucleon-nucleon interaction. For the consistency, this same folding model is also used to calculate the optical potential of the elastic $p+^{12,13}$C scattering at energies around the Coulomb barrier. The folded $p+^{12,13}$C optical potentials are shown to account well for both the elastic $p+^{12,13}$C3 scattering and astrophysical $S$ factors of the radiative capture $^{12,13}$C$(p,γ)$ reactions.

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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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arXiv2019

Rearrangement term in the nonlocal folding model of the nucleon optical potential

Based on the mean-field determination of the single-particle energy in nuclear matter that contains naturally a rearrangement term (RT) implied by the Hugenholtz-van Hove theorem, the folding model of the nucleon optical potential (OP) is extended to take into account the RT using the effective, density dependent CDM3Yn interaction. With the exchange part of the nucleon folded OP treated exactly in the Hartree-Fock manner, a compact nonlocal version of the folding model is suggested in the present work to determine explicitly the isospin-dependent, nonlocal central term of the nucleon OP. To solve the optical model (OM) equation with a complex nonlocal OP, the calculable $R$-matrix method is used to analyse the elastic neutron and proton scattering on $^{40,48}$Ca, $^{90}$Zr, and $^{208}$Pb targets at low energies. The inclusion of the RT into the folding model calculation of the nonlocal nucleon OP was shown to be essential for the overall good OM description of elastic nucleon scattering. To validate the nonlocal version of the folding model, the OM results given by the nonlocal folded nucleon OP are also compared with those given by the global parametrization of the nonlocal OP using the analytical nonlocal form factor suggested by Perey and Buck.

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arXiv2019

Elastic transfer and parity dependence of the nucleus-nucleus optical potential

Background: A recent coupled reaction channel (CRC) study shows that the enhanced oscillation of the elastic $^{16}$O+$^{12}$C cross section at backward angles is due mainly to the elastic $α$ transfer or the core exchange. Such a process gives rise to a parity-dependent term in the total elastic $S$-matrix, an indication of the parity dependence of the $^{16}$O+$^{12}$C optical potential (OP). Purpose: To explicitly determine the core exchange potential (CEP) induced by the symmetric exchange of the two $^{12}$C cores in the elastic $^{16}$O+$^{12}$C scattering at $E_{\rm lab}= 132$ and 300 MeV, and explore its parity dependence. Method: $S$-matrix generated by CRC description of the elastic $^{16}$O+$^{12}$C scattering is used as the input for the inversion calculation to obtain the effective local OP that contains both the Wigner and Majorana terms. Results: The high-precision inversion results show a strong contribution by the complex Majorana term in the total OP of the $^{16}$O+$^{12}$C system, and thus provide for the first time a direct estimation of the parity-dependent CEP. Conclusions: The elastic $α$ transfer or exchange of the two $^{12}$C cores in the $^{16}$O+$^{12}$C system gives rise to a complex parity dependence of the total OP. This should be a general feature of the OP for the light heavy-ion systems that contain two identical cores.

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arXiv2019

R-matrix method and the nonlocal nucleon optical potential

The calculable R-matrix method is applied to solve the Schrödinger equation in the optical model (OM) analysis of the elastic nucleon-nucleus scattering using a nonlocal nucleon optical potential (OP). The phenomenological nonlocal nucleon OP proposed by Perey and Buck (PB), and the two recent versions of the PB parametrization were used in the present OM study of the elastic nucleon scattering on $^{27}$Al, $^{40}$Ca, $^{48}$Ca, $^{90}$Zr, and $^{208}$Pb targets at different energies. The comparison of the OM results given by the calculable $R$-matrix method with those given by other methods confirms that the calculable $R$-matrix method is an efficient tool for the OM study of the elastic nucleon-nucleus scattering using a nonlocal nucleon OP.

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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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arXiv2018

Direct and indirect $α$ transfer in the elastic $^{16}$O+$^{12}$C scattering

The extensive elastic $^{16}$O+$^{12}$C scattering data measured at low energies show consistently an oscillating enhancement of the elastic cross section at backward angles that is difficult to describe within the conventional optical model. Given the significant $α$ spectroscopic factors predicted for the dissociation $^{16}$O$\toα+^{12}$C by the shell model (SM) and $α$-cluster model calculations, the contribution of the $α$ transfer channels to the elastic $^{16}$O+$^{12}$C scattering should not be negligible, and is expected to account for the enhanced oscillation of the elastic cross section at backward angles. To reveal the impact of the $α$ transfer, a systematic coupled reaction channels (CRC) analysis of the elastic $^{16}$O+$^{12}$C scattering has been performed where the multistep couplings between the elastic and inelastic scattering channels, the direct and indirect $α$ transfer channels were treated explicitly, using the real optical potentials and inelastic scattering form factors determined by the double-folding model. We show that a consistent CRC description of the elastic $^{16}$O+$^{12}$C data at different energies can be obtained over the whole angular region, using the $α$ spectroscopic factors determined recently in the large scale SM calculation. The present CRC results are, therefore, of interest not only for the nuclear scattering studies but also provide an important spectroscopic information on the cluster dissociation of $^{16}$O.

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