arXiv subjects

E. Khan

Publications and source records attributed to E. Khan.

At least 19 recordsLinked to original sources

arXiv2026

Nuclear structure within a relativistic mean field approach including chiral symmetry and confinement-inspired nucleon response

The relativistic mean field approach, within a theoretical framework known as the chiral confining model incorporating chiral symmetry breaking and confinement-inspired nucleon response, is applied for the first time to finite nuclei. Model parameters are calibrated through a Bayesian approach using nuclear empirical properties and doubly magic nuclei. The model provides a satisfactory description of binding energies and charge radii for medium and heavy nuclei, while larger discrepancies are observed in light nuclei. This behavior is linked to the constrained form of the chiral potential, which reduces flexibility away from saturation density. Charge radii are reproduced with very good accuracy, although density profiles remain slightly more diffuse than experimental ones. The extension to open-shell nuclei with a separable Gogny pairing interaction reveals enhanced pairing correlations associated with the large Dirac and non-relativistic effective masses, reduced spin-orbit splittings, and increased single-particle level density around the Fermi surface. Finally, departures from the linear sigma model potential motivated by the Nambu-Jona-Lasinio framework are explored. Allowing additional flexibility in the chiral potential improves the description of light nuclei and reduces the effective masses, which in turn suppresses the anomalous pairing. These results highlight the sensitivity of finite nuclei properties to the structure of the chiral potential and the associated single-particle spectrum.

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arXiv2026

How well known is the compressibility of nuclear matter?

The most accurate approach to determine the compressibility of nuclear matter remains the one based on microscopic Energy Density Functionals (EDFs). Recent analyses yield a value for nuclear incompressibility modulus $K_\sat=240\pm 20$~MeV, defined in nuclear matter as the second derivative of the energy per particle at saturation density. However, we demonstrate that the compressibility modulus can be reduced to values shifted by four times the suggested uncertainty, i.e., $K_\sat\approx 160$~MeV, by providing examples based on models where the second derivative ($K_\sat$) and third derivative ($Q_\sat$) of the energy per particle at saturation density can be independently varied, while the experimental binding energies, charge radii, and ISGMR data in $^{120}$Sn and $^{208}$Pb are enforced. The present work suggests a new methodology to access the compressibility of nuclear matter from nuclear experiments, still based on microscopic models, but using EDFs containing more flexibility than the ones employed up to now. Consequences of our results for nuclear matter at supra-saturation density are also discussed by exploring the quarkyonic cross-over. We predict that, for our models with low values for $K_\sat$, the quark onset density has to be low for neutron stars to exist.

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arXiv2026

Role of the symmetry energy on hybrid stars

The impact of the symmetry energy on the properties of compact stars is analyzed considering constraints from nuclear physics and astrophysics. A compact star can be a neutron star composed only of nuclear matter or a hybrid star with a quark core. Two typical models (soft and stiff) are considered for the nuclear equation of state, and for the hybrid one, a parameterized first-order phase transition approach, completed with a linear quark matter equation of state, is implemented. We show that the phase transition reduces the tension between GW170817 and NICER observations, and we illustrate the impact of the symmetry energy for the understanding of the nature of the binary system in GW170817. We also confirm our previous findings that the GW170817 waveform is best described as a binary HS with a low-density onset of stiff quark matter. This could also be interpreted as a quarkyonic cross-over.

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arXiv2025

Modeling Ultra-High-Energy Cosmic Rays propagation using the input from Configuration Interaction Shell Model

The dipole response of a nuclear system, characterized by its photon strength function (PSF), is a key ingredient of many applications of nuclear structure, ranging from nuclear reactor design and nuclear waste transmutation to astrophysical models of nucleosynthesis and stellar evolution. While the majority of those applications require the knowledge of PSF of mid-mass and heavy nuclei, there is now renewed interest in $E1$ strength distributions of light nuclei in the framework of the PANDORA project, which aims at an understanding of the mass distribution of ultrahigh-energy cosmic radiation (UHECR).UHECR is of extragalactic origin and its interaction along the travel path is dominated by photoabsorption of cosmic background radiation boosted to the Giant Dipole Resonance (GDR) energy region in the center-of-mass system. Thus, systematic knowledge of the photoabsorption cross sections in light nuclei and of their subsequent particle decay is required. The purpose of this work is to enhance the database of available theoretical evaluations of PSF of light nuclei that are necessary in the studies of UHECR propagation. We employ the Configuration Interaction Shell Model (CI-SM) approach to provide predictions of $E1$ dipole response for $p$ and $sd$-shell nuclei, with mass number $A$ between 7 and 40. Theoretical predictions are compared to available data and to existing predictions from phenomenological and microscopic models. Finally, the impact of using of CI-SM PSF on the predicted propagation of a $^{40}$Ca UHECR source is studied.

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arXiv2025

The $\alpha$-particle condensation in diluted $^{16}\text{O}$ at finite temperature

We investigate the effect of temperature on $\alpha$-particle clustering in the diluted nucleus $^{16}\text{O}$ using the multi-constrained finite-temperature relativistic Hartree-Bogoliubov model with the DD-ME2 interaction. At a critical density the nucleus undergoes a Mott-like transition from a homogeneous to a localised configuration characterised by $\alpha$-particle clustering and the emergence of a finite non-axial octupole deformation. We study the interplay between the onset of localisation under nuclear dilution and the suppression of deformation and $\alpha$-particle clustering due to increasing temperature. Investigating the temperature-density plane, our findings indicate that temperature delays the formation of non-axial octupole deformation and $\alpha$-particle clustering in dilute environments. Following the transition from homogeneous to clustered configurations, the non-axial octupole deformation continues to increase with further dilution of the system and becomes nearly independent of temperature. We found that $\alpha$-particle clusters appear at temperatures up to $T = 4.10$ MeV and at a corresponding normalised density $\rho_{\text{Mott}}/\rho_0 \approx 0.09$.

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arXiv2025

Patterns of spin and pseudo-spin symmetries in nuclear relativistic mean-field approaches

The behavior of spin doublets is known to play a major role in nuclear structure and shell effects. Pseudo-spin doublets are also known to impact the single-particle spectrum. The covariant framework, having these two effects encoded in its approach, is an excellent tool to understand the main mechanism driving theses spin and pseudo-spin symmetries and their breaking. A perturbative expansion of the degeneracy raising related to spin and pseudo-spin effects is proposed, up to second order. It allows to understand the main behavior of spin and pseudo-spin energy doublets, such as their A dependence, as well as their common footing and differences. In the case of the spin symmetry, only the lower component of the Dirac bi-spinor is involved, whereas in the case of the pseudo-spin one, both the upper and lower components are involved. Their interplay with the covariant potentials is also analyzed.

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arXiv2024

A unified mechanism for the origin and evolution of nuclear magicity

A simple pattern of organization, the nuclear shell structure, emerges from the complex interactions between nucleons in nuclei and determines, to some significant degree, nuclear structure properties. Recent experimental investigations of exotic nuclei revealed a shortfall in our current understanding of nuclear shell evolution and nuclear magicity. We introduce a novel perspective in the Energy Density Functional framework, where the Dirac mass kinetic term, which stems from the singular participation of a spin-0 boson in the nuclear strong force, plays a pivotal role in generating the nuclear shell structure. Namely, the combination of the Dirac mass kinetic term with the spin-orbit term redefines magic numbers both in stable and exotic nuclei. The identification of this mechanism allows to provide a broad understanding of the origin and evolution of nuclear magic numbers.

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arXiv2024

Large quadrupole deformation in $^{20}$Ne challenges rotor model and modern theory: urging for $\alpha$ clusters in nuclei

The spectroscopic quadrupole moment of the first excited state, $Q_{_S}(2^{+}_{1})$, at 1.634 MeV in $^{20}$Ne was determined from sensitive reorientation-effect Coulomb-excitation measurements using a heavy target and safe energies well below the Coulomb barrier. Particle-$\gamma$ coincidence measurements were collected at iThemba LABS with a digital data-acquisition system using the {\sc AFRODITE} array coupled to an annular, doubled-sided silicon detector. A precise value of $Q_{_S}(2^{+}_{1})=-0.22(2)$ eb was determined at backward angles in agreement with the only safe-energy measurement prior to this work, $Q_{_S}(2^{+}_{1})=-0.23(8)$ eb. This result adopts 1$\hbar\omega$ shell-model calculations of the nuclear dipole polarizability of the 2$^+_1$ state that contributes to the effective quadrupole interaction and determination of $Q_{_S}(2^{+}_{1})$. It disagrees, however, with the ideal rotor model for axially-symmetric nuclei by almost $3\sigma$. Larger discrepancies are computed by modern state-of-the-art calculations performed in this and prior work, including {\it ab initio} shell model with chiral effective interactions and the multi-reference relativistic energy density functional ({\sc MR-EDF}) model. The intrinsic nucleon density of the 2$^+_1$ state in $^{20}$Ne calculated with the {\sc MR-EDF} model illustrates the presence of $\alpha$ clustering, which explains the largest discrepancy with the rotor model found in the nuclear chart and motivates the explicit inclusion of $\alpha$ clustering for full convergence of $E2$ collective properties.

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arXiv2024

Use of quantality in nuclei and many-body systems

The use of quantality is discussed in the case of nuclei and other many-body systems such as atomic electrons. This dimensionless quantity is known to indicate when a many-body system behaves like a crystal or a quantum liquid. Its role is further analyzed by showing its relation to the scattering length. The emergence of a fundamental lengthscale, the limit radius, is also shown. It corresponds to the hard-core of the nucleon-nucleon interaction in the case of nucleons, and to a value close to the Bohr radius in the case of atomic electrons. The occurrence of a cluster phase in nuclei is analyzed using the quantality through its relation to the localization parameter, allowing for the identification of both the number of nucleons and the density as control parameters for the occurrence of this phase. The relation of the quantality to the magnitude of the interaction also exhibits a third dimensionless parameter, monitoring the magnitude of the spin-orbit effect in finite systems, through the realization of the pseudo-spin symmetry. The impact of quantality on the spin-orbit effect is compared in various many-body systems. The role of quantality in the relative effect of the binding energy and the shell one is also analyzed in nuclei. Finally, additional dimensionless quantities are proposed from the generalization of the quantality. Nuclei are found to be exceptional systems because all their dimensionless quantities are close to the order of unity, at variance with other many-body systems.

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arXiv2023

On the nature of compact stars determined by gravitational waves, radio-astronomy, x-ray emission and nuclear physics

We investigate the question of the nature of compact stars, considering they may be neutron stars or hybrid stars containing a quark core, within the present constraints given by gravitational waves, radio-astronomy, X-ray emissions from millisecond pulsars and nuclear physics. A Bayesian framework is used to combine together all these constraints and to predict tidal deformabilities and radii for a 1.4~M$_\odot$ compact star. We find that present gravitation wave and radio-astronomy data favors stiff nucleonic EoS compatible with nuclear physics and that GW170817 waveform is best described for binary hybrid stars. Binary neutron stars with soft EoS could however not be totally excluded. In all cases, these %In addition, this data favor stiff quark matter, independently of the nuclear EoS, with a low value for the transition density ($n_\mathrm{tr}\in[0.18,0.35]~\mathrm{fm}^{-3}$). Combining these results with constraints from X-ray observation supports the existence $1.4$~M$_\odot$ mass hybrid star, with a radius predicted to be about $R_{1.4}=12.22(45)$~km.

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arXiv2022

Microscopic description of $\alpha$, $2\alpha$, and cluster decays of $^{216-220}$Rn and $^{220-224}$Ra

Alpha and cluster decays are analyzed for heavy nuclei located above $^{208}$Pb on the chart of nuclides: $^{216-220}$Rn and $^{220-224}$Ra, that are also candidates for observing the $2 \alpha$ decay mode. A microscopic theoretical approach based on relativistic Energy Density Functionals (EDF), is used to compute axially-symmetric deformation energy surfaces as functions of quadrupole, octupole and hexadecupole collective coordinates. Dynamical least-action paths for specific decay modes are calculated on the corresponding potential energy surfaces. The effective collective inertia is determined using the perturbative cranking approximation, and zero-point and rotational energy corrections are included in the model. The predicted half-lives for $\alpha$-decay are within one order of magnitude of the experimental values. In the case of single $\alpha$ emission, the nuclei considered in the present study exhibit least-action paths that differ significantly up to the scission point. The differences in alpha-decay lifetimes are not only driven by Q values, but also by variances of the least-action paths prior to scission. In contrast, the $2 \alpha$ decay mode presents very similar paths from equilibrium to scission, and the differences in lifetimes are mainly driven by the corresponding Q values. The predicted $^{14}$C cluster decay half-lives are within three orders of magnitudes of the empirical values, and point to a much more complex pattern compared to the alpha-decay mode.

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arXiv2022

PANDORA project: photo-nuclear reactions below $A=60$

Photo-nuclear reactions of light nuclei below a mass of $A=60$ are studied experimentally and theoretically by the PANDORA (Photo-Absorption of Nuclei and Decay Observation for Reactions in Astrophysics) project. Two experimental methods, virtual-photon excitation by proton scattering and real-photo absorption by a high-brilliance gamma-ray beam produced by laser Compton scattering, will be applied to measure the photo-absorption cross sections and the decay branching ratio of each decay channel as a function of the photon energy. Several nuclear models, e.g. anti-symmetrized molecular dynamics, mean-field type models, a large-scale shell model, and ab initio models, will be employed to predict the photo-nuclear reactions. The uncertainty in the model predictions will be evaluated from the discrepancies between the model predictions and the experimental data. The data and the predictions will be implemented in a general reaction calculation code TALYS . The results will be applied to the simulation of the photo-disintegration process of ultra-high-energy cosmic rays in inter-galactic propagation.

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arXiv2022

Covariant energy density functionals with and without tensor couplings at the Hartree-Bogoliubov level

Background: The study of additional terms in functionals is relevant to better describe nuclear structure phenomenology. Among these terms, the tensor one is known to impact nuclear structure properties, especially in neutron-rich nuclei. However, its effect has not been studied on the whole nuclear chart yet. Purpose: The impact of terms corresponding to the tensor at the Hartree level, is studied for infinite nuclear matter as well as deformed nuclei, by developing new density-dependent functionals including these terms. In particular, we study in details the improvement such a term can bring to the description of specific nuclear observables. Methods: The framework of covariant energy density functional is used at the Hartree-Bogoliubov level. The free parameters of covariant functionals are optimized by combining Markov-Chain-Monte-Carlo and simplex algorithms. Results: An improvement of the RMS binding energies, spin-orbit splittings and gaps is obtained over the nuclear chart, including axially deformed ones, when including tensors terms. Small modifications of the potential energy surface and densities are also found. In infinite matter, the Dirac mass is shifted to a larger value, in better agreement with experiments. Conclusions: Taking into account additional terms corresponding to the tensor terms in the vector-isoscalar channel at the Hartree level, improves the description of nuclear properties, both in nuclei and in nuclear matter.

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arXiv2022

Alpha-particle formation and clustering in nuclei

The nucleonic localization function has been used for a decade to study the formation of alpha-particles in nuclei, by providing a measure of having nucleons of a given spin in a single place. However, differences in interpretation remain, compared to the nucleonic density of the nucleus. In order to better understand the respective role of the nucleonic localization function and the densities in the alpha-particle formation in cluster states or in alpha-decay mechanism, both an analytic approximation and microscopic calculations, using energy density functionals, are undertaken. The nucleonic localization function is shown to measure the anti-centrifugal effect, and is not sensitive to the level of compactness of the alpha-particle itself. It probes the purity of the spatial overlap of four nucleons in the four possible (spin, isospin) states. The density provides, in addition, information on the compactness of an alpha-particle cluster. The respective roles of the nucleonic localization function and the density are also analyzed in the case of alpha-particle emission. More generally, criteria to assess the prediction of alpha-cluster in nuclear states are provided.

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arXiv2021

Derivation of the M$_n$/M$_p$ ratio in exotic nuclei

A generalized formula is provided, to calculate the M$_n$/M$_p$ ratio of the multipole transition matrix elements, in the framework of the so-called phenomenological analysis. It takes into account the possible difference between the neutron and proton radii and diffuseness, which can occur, especially in exotic nuclei. The validity domain of the original Bernstein formula is discussed, in the case of the proton scattering probe at few tens of MeV. The largest discrepancies are obtained for very neutron-rich nuclei (N/Z$\gtrsim$1.6) or when the electromagnetic deformation parameter is larger than the proton scattering one. The reduction of the statistical error bars, and the study of very neutron-rich nuclei at facilities of exotic beams of new generation, should favor the use of the generalized Bernstein formula.

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arXiv2021

Systematical studies of the E1 photon strength functions combining Skyrme-HFB+QRPA model and experimental giant dipole resonance properties

Valuable theoretical predictions of nuclear dipole excitations in the whole nuclear chart are of great interest for different applications, including in particular nuclear astrophysics. We present here the systematic study of the electric dipole (E1) photon strength functions (PSFs) combining the microscopic Hartree-Fock-Bogoliubov plus Quasiparticle Random Phase Approximation (HFB+QRPA) model and the parametrizations constrained by the available experimental giant dipole resonance (GDR) data. For about 10000 nuclei with 8<Z<124 lying between the proton and the neutron drip-lines on nuclear chart, the particle-hole strength distributions are computed using the HFB+QRPA model under the assumption of spherical symmetry and making use of the BSk27 Skyrme effective interaction derived from the most accurate HFB mass model (HFB-27) so far achieved. Large-scale calculations of the BSk27+QRPA E1 PSFs are performed in the framework of a specific folding procedure, in which three phenomenological improvements are considered. First, two interference factors are introduced and adjusted to reproduce at best the available experimental GDR data. Second, an empirical expression accounting for the deformation effect is applied to describe the peak splitting of the strength function. Third, the width of the strength function is corrected by a temperature-dependent term, which effectively increases the de-excitation photon strength function at low-energy. The E1 PSFs as well as the extracted GDR peaks and widths are compared with available experimental data. A relatively good agreement with data indicates the reliability of the calculations. Eventually, the astrophysical (n,g) rates for all the 10000 nuclei with 8<Z<124 are estimated using the present E1 PSFs. The resulting reaction rates are compared with previous BSk7+QRPA results and Gogny-HFB+QRPA predictions based on the D1M interaction.

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arXiv2021

Low-energy monopole strength in spherical and deformed nuclei : cluster and soft modes

Background : Several recent experiments report significant low-energy isoscalar monopole strength, below the giant resonance, in various nuclei. In light $α$-conjugate nuclei, these low-energy resonances were recently interpreted as cluster vibration modes. However, the nature of these excitations in neutron-rich nuclei remain elusive. Purpose : The present work provides a systematic analysis of the low-energy monopole strength in isotopic chains, from Neon to Germanium, in order to monitor and understand its nature and conditions of emergence. Methods : We perform covariant quasiparticle random phase approximation (QRPA) calculations, formulated within the finite amplitude method (FAM), on top of constrained relativistic Hartree-Bogoliubov (RHB) reference states. Results : Neutron excess leads to the appearance of low-energy excitations according to a systematic pattern reflecting the single-particle features of the underlying RHB reference state. With the onset of deformation, these low-energy resonances get split and give rise to more complex patterns, with possible mixing with the giant resonance. At lower energy, cluster-like excitations found in $N=Z$ systems survive in neutron-rich nuclei, with valence neutrons arranging in molecular-like orbitals. Finally, at very low energy, pair excitations are also found in superfluid nuclei, but remain negligible in most of the cases. Conclusions : The low-energy part of the monopole strength exhibits various modes, from cluster vibrations ($\sim$ 5-10 MeV) to components of the giant resonance downshifted by the onset of deformation, including soft modes ($\sim$ 10-15 MeV) as well as pair excitation ($<$ 5 MeV), with possible mixing, depending on neutron-excess, deformation, and pairing energy.

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arXiv2021

Ground State Properties of Charmed Hypernuclei with Mean Field Approach

Closed shell charmed hypernuclei $^5_{Λ_c}$Li, $^{17}_{Λ_c}$F, $^{41}_{Λ_c}$Sc, $^{57}_{Λ_c}$Cu, $^{133}_{Λ_c}$Sb and $^{209}_{Λ_c}$Bi are calculated within Hartree-Fock approach by using three different force sets derived from microscopic Brueckner-Hartree-Fock calculations of $Λ$ hypernuclei. Ground state properties (binding energies, $Λ_c$ separation energies, $Λ_c$ single particle energies and $Λ_c$ densities) of charmed nuclei are examined. Due to the Coulomb repulsion between protons and the $Λ_c$ baryon, charmed hypernuclei are most bound for $16\leq$A$\leq 41$, where $^{17}_{Λ_c}$F can be considered as an excellent candidate to measure charmed hypernuclei. The competition between the attractive nucleon-$Λ_c$ interaction and the Coulomb repulsion is discussed, and we compare $Λ$ and $Λ_c$ hypernuclei properties.

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