arXiv subjects

Dao T. Khoa

Publications and source records attributed to Dao T. Khoa.

At least 37 records · Page 2Linked to original sources

arXiv2016

Nuclear mean field and double-folding model of the nucleus-nucleus optical potential

Realistic density dependent CDM3Yn versions of the M3Y interaction have been used in an extended Hartree-Fock (HF) calculation of nuclear matter (NM), with the nucleon single-particle potential determined from the total NM energy based on the Hugenholtz-van Hove theorem that gives rise naturally to a rearrangement term (RT). Using the RT of the single-nucleon potential obtained exactly at different NM densities, the density- and energy dependence of the CDM3Yn interactions was modified to account properly for both the RT and observed energy dependence of the nucleon optical potential. Based on a local density approximation, the double-folding model of the nucleus-nucleus optical potential has been extended to take into account consistently the rearrangement effect and energy dependence of the nuclear mean-field potential, using the modified CDM3Yn interactions. The extended double-folding model was applied to study the elastic $^{12}$C+$^{12}$C and $^{16}$O+$^{12}$C scattering at the refractive energies, where the Airy structure of the nuclear rainbow has been well established. The RT was found to affect significantly the real nucleus-nucleus optical potential at small internuclear distances, giving the potential strength close to that implied by the realistic optical model description of the Airy oscillation.

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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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arXiv2016

Mean-field study of hot beta-stable protoneutron star matter: Impact of the symmetry energy and nucleon effective mass

A consistent Hartree-Fock study of the equation of state (EOS) of asymmetric nuclear matter at finite temperature has been performed using realistic choices of the effective, density dependent nucleon-nucleon (NN) interaction, which were successfully used in different nuclear structure and reaction studies. Given the importance of the nuclear symmetry energy in the neutron star formation, EOS's associated with different behaviors of the symmetry energy were used to study hot asymmetric nuclear matter. The slope of the symmetry energy and nucleon effective mass with increasing baryon density was found to affect the thermal properties of nuclear matter significantly. Different density dependent NN interactions were further used to study the EOS of hot protoneutron star (PNS) matter of the $npeμν$ composition in $β$-equilibrium. The hydrostatic configurations of PNS in terms of the maximal gravitational mass $M_{\rm max}$ and radius, central density, pressure and temperature at the total entropy per baryon $S/A= 1,2$ and 4 have been determined in both the neutrino-free and neutrino-trapped scenarios. The obtained results show consistently a strong impact of the symmetry energy and nucleon effective mass on thermal properties and composition of hot PNS matter. $M_{\rm max}$ values obtained for the (neutrino-free) $β$-stable PNS at $S/A=4$ were used to assess time $t_{\rm BH}$ of the collapse of 40 $M_\odot$ protoneutron progenitor to black hole, based on a correlation between $t_{\rm BH}$ and $M_{\rm max}$ found from the hydrodynamic simulation by Hempel {\it et al.}.

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arXiv2015

Elastic proton scattering at intermediate energies as a probe of the $^{6,8}$He nuclear matter densities

The Glauber model analysis of the elastic $^{6,8}$He+$p$ scattering data at energies around 700 MeV/nucleon, measured in two separate experiments at GSI-Darmstadt, has been done using several phenomenological parametrizations of the nuclear matter density. By taking into account the new data points measured at the high momentum transfer, the nuclear matter radii of $^{6,8}$He were accurately determined from the Glauber model analysis of the data, with the spin-orbital interaction explicitly taken into account. The well-known geometry for the core and dineutron halo has been used with the new parametrizations of the $^{6}$He density to extract the detailed information on the structure of $^{6}$He in terms of the core and dineutron halo radii. An enhanced sensitivity of the data measured at the high momentum transfer to the core part of the $^{6,8}$He densities has been found.

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arXiv2015

Extended Hartree-Fock study of the single-particle potential: the nuclear symmetry energy, nucleon effective mass, and folding model of the nucleon optical potential

The nucleon mean-field potential has been thoroughly investigated in an extended Hartree-Fock (HF) calculation of nuclear matter (NM) using the CDM3Y3 and CDM3Y6 density dependent versions of the M3Y interaction. The single-particle (s/p) energies of nucleons in NM are determined according to the Hugenholtz-van Hove theorem, which gives rise naturally to a rearrangement term (RT) of the s/p potential at the Fermi momentum. Using the RT obtained exactly at the different NM densities and neutron-proton asymmetries, a consistent method is suggested to take into account effectively the momentum dependence of the RT of the s/p potential within the standard HF scheme. To obtain a realistic momentum dependence of the nucleon optical potential (OP), the high-momentum part of the s/p potential was accurately readjusted to reproduce the observed energy dependence of the nucleon OP over a wide range of energies. The impact of the RT and momentum dependence of the s/p potential on the density dependence of the nuclear symmetry energy and nucleon effective mass has been studied in details. The high-momentum tail of the s/p potential was found to have a sizable effect on the slope of the symmetry energy and the neutron-proton effective mass splitting at supranuclear densities of the NM. Based on a local density approximation, the folding model of the nucleon OP of finite nuclei has been extended to take into account consistently the RT and momentum dependence of the nucleon OP in the same mean-field manner, and successfully applied to study the elastic neutron scattering on the lead target at the energies around the Fermi energy.

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arXiv2014

Folding model study of the elastic $α+ α$ scattering at low energies

The folding model analysis of the elastic $α+ α$ scattering at the incident energies below the reaction threshold of 34.7 MeV (in the lab system) has been done using the well-tested density dependent versions of the M3Y interaction and realistic choices for the $^4$He density. Because the absorption is negligible at the energies below the reaction threshold, we were able to probe the $α+ α$ optical potential at low energies quite unambiguously and found that the $α+ α$ overlap density used to construct the density dependence of the M3Y interaction is strongly distorted by the Pauli blocking. This result gives possible explanation of a long-standing inconsistency of the double-folding model in its study of the elastic $α+ α$ and $α$-nucleus scattering at low energies using the same realistic density dependent M3Y interaction.

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arXiv2014

Charge-exchange scattering to the isobaric analog state at medium energies as a probe of the neutron skin

The charge-exchange (3He,t) scattering to the isobaric analog state (IAS) of the target can be considered as "elastic" scattering of 3He by the isovector term of the optical potential (OP) that flips the projectile isospin. Therefore, the accurately measured charge-exchange scattering cross- section for the IAS can be a good probe of the isospin dependence of the OP, which is determined exclusively within the folding model by the difference between the neutron and proton densities and isospin dependence of the nucleon-nucleon interaction. Given the neutron skin of the target is related directly to the same density difference, it can be well probed in the analysis of the charge- exchange (3He,t) reactions at medium energies when the two-step processes can be neglected and the t-matrix interaction can be used in the folding calculation. For this purpose, the data of the (3He,t) scattering to the IAS of 90Zr and 208Pb targets at Elab = 420 MeV have been analyzed in the distorted wave Born approximation using the double-folded charge-exchange form factor. The neutron skin deduced for these two nuclei turned out to be in a good agreement with the existing database.

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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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arXiv2013

Folding model study of the charge-exchange scattering to the isobaric analog state and implication for the nuclear symmetry energy

The Fermi transition (ΔL=ΔS=0 and ΔT=1) between the nuclear isobaric analog states (IAS), induced by the charge-exchange (p,n) or (3He,t) reaction, can be considered as "elastic" scattering of proton or 3He by the isovector term of the optical potential (OP) that flips the projectile isospin. The accurately measured (p,n) or (3He,t) scattering cross-section to the IAS can be used, therefore, to probe the isospin dependence of the proton or 3He optical potential. Within the folding model, the isovector part of the OP is determined exclusively by the neutron-proton difference in the nuclear densities and the isospin dependence of the effective nucleon-nucleon (NN) interaction. Because the isovector coupling explicitly links the isovector part of the proton or 3He optical potential to the cross section of the charge-exchange (p,n) or (3He,t) scattering to the IAS, the isospin dependence of the effective (in-medium) NN interaction can be well tested in the folding model analysis of these charge-exchange reactions. On the other hand, the same isospin- and density dependent NN interaction can also be used in a Hartree-Fock calculation of asymmetric nuclear matter, to estimate the nuclear matter energy and its asymmetry part (the nuclear symmetry energy). As a result, the fine-tuning of the isospin dependence of the effective NN interaction against the measured (p,n) or (3He,t) cross sections should allow us to make some realistic prediction of the nuclear symmetry energy and its density dependence.

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arXiv2012

Neutron scattering from 208Pb at 30.4 and 40.0 MeV and isospin dependence of the nucleon optical potential

Analysis of data involving nuclei far from stability often requires optical potential (OP) for neutron scattering. Since neutron data is seldom available, while proton scattering data is more abundant, it is useful to have estimates of the difference of the neutron and proton optical potentials. This information is contained in the isospin dependence of the nucleon OP. Here we attempt to provide it for the nucleon-208Pb system. The goal of this paper is to obtain accurate n+208Pb scattering data, and use it, together with existing p+208Pb and 208Pb(p,n)208$Bi*_{IAS} data, to obtain an accurate estimate of the isospin dependence of the nucleon OP at energies in the 30-60 MeV range. Cross sections for n+208Pb scattering were measured at 30.4 and 40.0 MeV, with a typical relative (normalization) accuracy of 2-4% (3%). An angular range of 15 to 130 degrees was covered using the beam-swinger time of flight system at Michigan State University. These data were analyzed by a consistent optical model study of the neutron data and of elastic p+208Pb scattering at 45 MeV and 54 MeV. These results were combined with a coupled-channel analysis of the 208Pb(p,n) reaction at 45 MeV, exciting the 0^+ isobaric analog state in 208Bi. The new data and analysis give an accurate estimate the isospin impurity of the nucleon-208Pb OP at 30.4 MeV, caused by the Coulomb correction to the proton OP. The corrections to the real proton OP given by the CH89 global systematics was found to be only few percent, while for the imaginary potential it was over 20% at the nuclear surface. Based on the analysis of the measured elastic p+208Pb data at 40 MeV, a Coulomb correction of similar strength and shape was also predicted for the p+208Pb OP at energy around 54 MeV.

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arXiv2011

Equation of state of the neutron star matter, and the nuclear symmetry energy

The nuclear mean-field potentials obtained in the Hartree-Fock method with different choices of the in-medium nucleon-nucleon (NN) interaction have been used to study the equation of state (EOS) of the neutron star (NS) matter. The EOS of the uniform NS core has been calculated for the np$eμ$ composition in the $β$-equilibrium at zero temperature, using version Sly4 of the Skyrme interaction as well as two density-dependent versions of the finite-range M3Y interaction (CDM3Y$n$ and M3Y-P$n$), and versions D1S and D1N of the Gogny interaction. Although the considered effective NN interactions were proven to be quite realistic in numerous nuclear structure and/or reaction studies, they give quite different behaviors of the symmetry energy of nuclear matter at supranuclear densities that lead to the \emph{soft} and \emph{stiff} scenarios discussed recently in the literature. Different EOS's of the NS core and the EOS of the NS crust given by the compressible liquid drop model have been used as input of the Tolman-Oppenheimer-Volkov equations to study how the nuclear symmetry energy affects the model prediction of different NS properties, like the cooling process as well as the gravitational mass, radius, and moment of inertia.

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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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arXiv2009

Neutron star cooling - a challenge to the nuclear mean field

The two recent density-dependent versions of the finite-range M3Y interaction (CDM3Y$n$ and M3Y-P$n$) have been probed against the bulk properties of asymmetric nuclear matter (NM) in the nonrelativistic Hartree Fock (HF) formalism. The same HF study has also been done with the famous Skyrme (SLy4) and Gogny (D1S and D1N) interactions which were well tested in the nuclear structure calculations. Our HF results are compared with those given by other many-body calculations like the Dirac-Brueckner Hartree-Fock approach or ab-initio variational calculation using free nucleon-nucleon interaction, and by both the nonrelativistic and relativistic mean-field studies using different model parameters. Although the two considered density-dependent versions of the M3Y interaction were proven to be quite realistic in the nuclear structure or reaction studies, they give two distinct behaviors of the NM symmetry energy at high densities, like the Asy-soft and Asy-stiff scenarios found earlier with other mean-field interactions. As a consequence, we obtain two different behaviors of the proton fraction in the $β$-equilibrium which in turn can imply two drastically different mechanisms for the neutron star cooling. While some preference of the Asy-stiff scenario was found based on predictions of the latest microscopic many-body calculations or empirical NM pressure and isospin diffusion data deduced from heavy-ion collisions, a consistent mean-field description of nuclear structure database is more often given by some Asy-soft type interaction like the Gogny or M3Y-P$n$ ones. Such a dilemma poses an interesting challenge to the modern mean-field approaches.

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arXiv2009

Neutron transition strengths of $2^+_1$ states in the neutron rich Oxygen isotopes determined from inelastic proton scattering

A coupled-channel analysis of the $^{18,20,22}$O$(p,p')$ data has been performed to determine the neutron transition strengths of 2$^+_1$ states in Oxygen targets, using the microscopic optical potential and inelastic form factor calculated in the folding model. A complex density- and \emph{isospin} dependent version of the CDM3Y6 interaction was constructed, based on the Brueckner-Hatree-Fock calculation of nuclear matter, for the folding model input. Given an accurate isovector density dependence of the CDM3Y6 interaction, the isoscalar ($δ_0$) and isovector ($δ_1$) deformation lengths of 2$^+_1$ states in $^{18,20,22}$O have been extracted from the folding model analysis of the $(p,p')$ data. A specific $N$-dependence of $δ_0$ and $δ_1$ has been established which can be linked to the neutron shell closure occurring at $N$ approaching 16. The strongest isovector deformation was found for 2$^+_1$ state in $^{20}$O, with $δ_1$ about 2.5 times larger than $δ_0$, which indicates a strong core polarization by the valence neutrons in $^{20}$O. The ratios of the neutron/proton transition matrix elements ($M_n/M_p$) determined for 2$^+_1$ states in $^{18,20}$O have been compared to those deduced from the mirror symmetry, using the measured $B(E2)$ values of 2$^+_1$ states in the proton rich $^{18}$Ne and $^{20}$Mg nuclei, to discuss the isospin impurity in the $2^+_1$ excitation of the $A=18,T=1$ and $A=20,T=2$ isobars.

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arXiv2008

Probing the isoscalar excitations of 12C with inelastic alpha scattering

The robust (spin and isospin zero) $α$-particle remains one of the best projectiles to probe the nuclear isoscalar excitations. In the present work, a microscopic folding model analysis of the \ac inelastic scattering to the 2$^+$ (4.44 MeV), 0$^+$ (7.65 MeV), 3$^-$ (9.64 MeV), 0$^+$ (10.3 MeV) and 1$^-$ (10.84 MeV) states in $^{12}$C has been performed using the 3-$α$ resonating group method wave functions. The isoscalar transition strengths of these states were carefully studied based on the coupled-channel analysis using the microscopic folded form factors. A correlation between the weak binding and/or short lifetime of the excited state and absorption in the exit channel of inelastic scattering has been established.

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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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