Nuclear Matter Calculations Research Articles

Neutron Star Matter as a Dilute Solution of Protons in Neutrons.

Neutron stars contain neutron-rich matter with around 5% protons at nuclear saturation density. In this Letter, we consider equilibrium between bulk phases of matter based on asymmetric nuclear matter calculations using chiral effective field theory interactions rather than, as has been done in the past, by interpolation between the properties of symmetric nuclear matter and pure neutron matter. Neutron drip (coexistence of nuclear matter with pure neutrons) is well established, but from earlier work it is unclear whether proton drip (equilibrium between two phases, both of which contain protons and neutrons) is possible. We find that proton drip is a robust prediction of any physically reasonable equation of state, but that it occurs over a limited region of densities and proton fractions. An analytical model based on expanding the energy in powers of the proton density, rather than the neutron excess, is able to account for these features of the phase diagram.

Systematic investigation of nucleon optical model potentials in (p, d) transfer reactions* *Supported by the National Natural Science Foundation of China (U2067205, 12205098), and the National Key Research and Development Program of China (2022YFA1602403)

The consistent three-body model reaction methodology (TBMRM) proposed by J. Lee et al. [ Phys. Rev. C 69, 064313 (2004); Phys. Rev. C 73, 044608 (2006); Phys. Rev. C 75, 064320 (2007)], which includes adopting the simple zero-range adiabatic wave approximation, constraining the single-particle potentials using modern Hartree–Fock calculations, and using global nucleon optical model potential (OMP) geometries, are widely applied in systematic studies of transfer reactions. In this study, we investigate the influence of different nucleon OMPs in extracting spectroscopic factors (SFs) from ( ) reactions. Our study covers 32 sets of angular distribution data of ( ) reactions on four targets and a large range of incident energies (20-200 MeV/nucleon). This study uses two semi-microscopic nucleon OMPs, i.e., Jeukenne, Lejeune, and Mahaux (JLM) [Phys. Rev. C 16, 80 (1977); Phys. Rev. C 58, 1118 (1998)] and CTOM [Phys. Rev. C 94, 034606 (2016)], and a pure microscopic nucleon potential, i.e., WLH [Phys. Rev. Lett. 127, 182502 (2021)]. The results are compared with those using the phenomenological global optical potential KD02 [Nucl. Phys. A 713, 231 (2003)]. We find that the incident energy dependence of spectroscopic factors extracted from ( ) reactions is evidently suppressed when microscopic OMPs are employed for 12C, 28Si, and 40Ca. In addition, spectroscopic factors extracted using the systematic microscopic optical potential CTOM based on the Dirac-Brueckner-Hartree-Fock theory are more in line with the results obtained from ( ) measurements, except for 16O and 40Ca at high energies (> 100 MeV), necessitating an exact treatment of double-magic nuclei. The results obtained by using the pure microscopic optical potential, WLH, based on the EFT theory show the same trend as those of CTOM but are generally higher. The JLM potential, which relies on simplified nuclear matter calculations with old-fashioned bare interactions, produces results that are very similar to those of the phenomenological potential KD02. Our results indicate that modern microscopic OMPs are reliable tools for probing the nuclear structure using transfer reactions across a wide energy range.

Asymmetric nuclear matter and neutron star properties in relativistic ab initio theory in the full Dirac space

The long-standing controversy about the isospin dependence of the effective Dirac mass in ab initio calculations of asymmetric nuclear matter is clarified by solving the relativistic Brueckner-Hartree-Fock equations in the full Dirac space. The symmetry energy and its slope parameter at the saturation density are $E_{\text{sym}}(\rho_0)=33.1$ MeV and $L=65.2$ MeV, in agreement with empirical and experimental values. Further applications predict the neutron star radius $R_{1.4M_\odot}\approx 12$ km and the maximum mass of a neutron star $M_{\text{max}}\leq 2.4M_\odot$.

Calculations for nuclear matter and finite nuclei within and beyond energy-density-functional theories through interactions guided by effective field theory

We propose a novel idea to construct an effective interaction under energy-density-functional (EDF) theories which is adaptive to the enlargement of the model space. Guided by effective field theory principles, iterations of interactions as well as enlargements of the model space through particle-hole excitations are carried out for infinite nuclear matter and selected closed-shell nuclei ($^{4}\mathrm{He}, ^{16}\mathrm{O}, ^{40}\mathrm{Ca}, ^{56}\mathrm{Ni}$, and $^{100}\mathrm{Sn}$) up to next-to-leading order. Our approach provides a new way for handling the nuclear matter and finite nuclei within the same scheme, with advantages from both EDF and ab initio approaches.

Implications of NICER for Neutron Star Matter: The QHC21 Equation of State

The recent NICER measurement of the radius of the neutron star PSR J0740+6620, and the inferred small variation of radii from 1.4 to 2.1 M ⊙, reveal key features of the equation of state of neutron star matter. The pressure rises rapidly in the regime of baryon density n ∼ 2–4 times nuclear saturation density, n 0—the region where we expect hadronic matter to be undergoing transformation into quark matter—and the pressure in the nuclear regime is greater than predicted by microscopic many-body variational calculations of nuclear matter. To incorporate these insights into the microscopic physics from the nuclear to the quark matter regimes, we construct an equation of state, QHC21, within the framework of quark–hadron crossover. We include nuclear matter results primarily based on the state-of-the-art chiral effective field theory, but also note results of using nuclear matter variational calculations based on empirical nuclear forces. We employ explicit nuclear degrees of freedom only up to n ∼ 1.5 n 0, in order to explore the possibility of further physical degrees of freedom than nucleonic here. The resulting QHC21, which has a peak in sound velocity in ∼2–4 n 0, is stiffer than the earlier QHC19 below 2 n 0, predicting larger radii in substantial agreement with the NICER data.

Nuclear matter calculations with the phenomenological three-nucleon interaction

Employing the concept of three-body radial distribution function and using the two-body correlation functions, calculated based on the lowest order constrained variational method, we investigated the effect of the three-body force (TBF) on the nuclear matter properties, for Argonne and Urbana v14 potentials. As such, the results for nuclear matter density, incompressibility, energy per nucleon, and symmetry energy are presented at the saturation point. The inclusion of a phenomenological TBF resulted in closer values of the saturation density, incompressibility, and symmetry energy to the empirical ones for the symmetric nuclear matter. This is especially the case for the Urbana v14 potential. In addition, an empirically-verified parabolic approximation of the interaction energy was utilized to perform an approximate study of the nuclear matter with neutron excess. Hence, at densities higher than about 0.3 fm−3 and for proton-to-neutron density ratios close to the symmetric nuclear matter, the inclusion of TBF resulted in an extra attraction for the Argonne as compared to the Urbana v14 potential.

Low-rank matrix decompositions for ab initio nuclear structure

The extension of ab initio quantum many-body theory to higher accuracy and larger systems is intrinsically limited by the handling of large data objects in form of wave-function expansions and/or many-body operators. In this work we present matrix factorization techniques as a systematically improvable and robust tool to significantly reduce the computational cost in many-body applications at the price of introducing a moderate decomposition error. We demonstrate the power of this approach for the nuclear two-body systems, for many-body perturbation theory calculations of symmetric nuclear matter, and for non-perturbative in-medium similarity renormalization group simulations of finite nuclei. Establishing low-rank expansions of chiral nuclear interactions offers possibilities to reformulate many-body methods in ways that take advantage of tensor factorization strategies.

Nuclear pasta and symmetry energy in the relativistic point-coupling model

Nonuniform structure of low-density nuclear matter, known as nuclear pasta, is expected to appear not only in the inner crust of neutron stars but also in core-collapse supernova explosions and neutron-star mergers. We perform fully three-dimensional calculations of inhomogeneous nuclear matter and neutron-star matter in the low-density region using the Thomas-Fermi approximation. The nuclear interaction is described in the relativistic mean-field approach with the point-coupling interaction, where the meson exchange in each channel is replaced by the contact interaction between nucleons. We investigate the influence of nuclear symmetry energy and its density dependence on pasta structures by introducing a coupling term between the isoscalar-vector and isovector-vector interactions. It is found that the properties of pasta phases in the neutron-rich matter are strongly dependent on the symmetry energy and its slope. In addition to typical shapes like droplets, rods, slabs, tubes, and bubbles, some intermediate pasta structures are also observed in cold stellar matter with a relatively large proton fraction. We find that nonspherical shapes are unlikely to be formed in neutron-star crusts, since the proton fraction obtained in $\beta$ equilibrium is rather small. The inner crust properties may lead to a visible difference in the neutron-star radius.

Constraints on the nuclear symmetry energy from asymmetric-matter calculations with chiral NN and 3N interactions

The nuclear symmetry energy is a key quantity in nuclear (astro)physics. It describes the isospin dependence of the nuclear equation of state (EOS), which is commonly assumed to be almost quadratic. In this work, we confront this standard quadratic expansion of the EOS with explicit asymmetric nuclear-matter calculations based on a set of commonly used Hamiltonians including two- and three-nucleon forces derived from chiral effective field theory. We study, in particular, the importance of non-quadratic contributions to the symmetry energy, including the non-analytic logarithmic term introduced by Kaiser [Phys.~Rev.~C \textbf{91}, 065201 (2015)]. Our results suggest that the quartic contribution to the symmetry energy can be robustly determined from the various Hamiltonians employed, and we obtain 1.00(8) MeV (or 0.55(8) MeV for the potential part) at saturation density, while the logarithmic contribution to the symmetry energy is relatively small and model-dependent. We finally employ the meta-model approach to study the impact of the higher-order contributions on the neutron-star crust-core transition density, and find a small 5\% correction.

New equations of state constrained by nuclear physics, observations, and QCD calculations of high-density nuclear matter

We present new equations of state for applications in core-collapse supernova and neutron star merger simulations. We start by introducing an effective mass parametrization that is fit to recent microscopic calculations up to twice saturation density. This is important to capture the predicted thermal effects, which have been shown to determine the proto--neutron star contraction in supernova simulations. The parameter range of the energy-density functional underlying the equation of state is constrained by chiral effective field theory results at nuclear densities as well as by functional renormalization group computations at high densities based on QCD. We further implement observational constraints from measurements of heavy neutron stars, the gravitational wave signal of GW170817, and from the recent NICER results. Finally, we study the resulting allowed ranges for the equation of state and for properties of neutron stars, including the predicted ranges for the neutron star radius and maximum mass.

Isospin-density-dependent pairing from infinite nuclear matter to finite nuclei

The effective isospin-density dependent pairing interaction (P1) [S. S. Zhang, U. Lombardo and E. G. Zhao, Sci. Chin. Phys. Mech. Astro. {\bf 54}, 236 (2011)] extracted from neutron pairing gaps for $^1$S$_0$ in asymmetric nuclear matter calculations [S. S. Zhang, L. G. Cao, U. Lombardo, et al. Phys. Rev. C {\bf 81}, 044313 (2010)] is employed to study the bulk properties of Ca, Ni, Zr and Sn isotopes. The odd-even mass (OEM) staggering is calculated by the Skyrme Hartree-Fock plus BCS method (SHF + BCS) with the SkP interaction. For comparison, we study two other types of isovector effective pairing interactions. One is also extracted from pairing gaps of infinite nuclear matter by the Brueckner-Hartree-Fock (BHF) method but for free spectrum (P2). The other is obtained by fitting the empirical OEM (P3). An isoscalar effective pairing interaction (P4) is also adopted which is determined by fitting the empirical OEM. We find that interaction P1 can better describe the OEM staggering of Ni, Zr and Sn isotopes by $14.3 \%, 41 \%, 30.4 \%$ compared with interaction P2, in terms of root mean square deviations to the empirical OEM, respectively. On the other hand, the performance of P1 and P2 is comparable for Ca isotopes. For Ca and Ni isotopes, P1 behaves similarly as P3, but for Zr isotopes P1 is better than P3 by $\sim 34 \%$. Among the four pairing interactions studied, P4 performs the worst. Therefore, one may conclude that for neutron pairings in finite nuclei, the isovector pairings are preferred than the isoscalar one. It is quite interesting to note that the pairing interaction P1 extracted from nuclear matter calculations can describe pairing gaps of finite nuclei as well as or even better than the interaction P3 directly fitted to finite nuclei.

Surface Localization of the Dineutron in ^{11}Li.

The formation of a dineutron in the ^{11}Li nucleus is found to be localized to the surface region. The experiment measured the intrinsic momentum of the struck neutron in ^{11}Li via the (p,pn) knockout reaction at 246 MeV/nucleon. The correlation angle between the two neutrons is, for the first time, measured as a function of the intrinsic neutron momentum. A comparison with reaction calculations reveals the localization of the dineutron at r∼3.6 fm. The results also support the density dependence of dineutron formation as deduced from Hartree-Fock-Bogoliubov calculations for nuclear matter.

Surface energy of nuclear matter above and below neutron drip with the Skyrme-type effective interactions

Neutron star crust consists of highly neutron excess nuclei, which are inaccessible for laboratory experiments. In the deepest region of the crust (so-called inner crust, located after the neutron drip) atomic nuclei are immersed into the sea of degenerate unbound neutrons. Study of the crust structure and equation of state in such conditions relies on the theoretical nuclear mass models. In particular, it is convenient to use the compressible liquid drop model, which contains the surface tension term. A thermodynamically consistent description must take into account adsorption of neutrons on the nucleus surface (neutron skin) and dependence of surface tension on matter properties in two-phase equilibrium. We calculate the surface tension of nuclear matter by the extended Thomas-Fermi approach. For this aim, we parametrize the number density profile of the two-phase system by Fermi-Dirac type functions, totally containing 5 parameters, and minimize the thermodynamic potential Ω to obtain equilibrium configuration. We use Skyrme-type nuclear interactions SLy4 and BSk24, fulfilling experimental data of atomic nuclei, observational constraints on the maximal neutron star mass and theoretical calculations of high-density nuclear matter. The results are presented as a function of neutron chemical potential, which is useful for compressible liquid drop models in the inner crust of a neutron star.

Symmetry energy properties of neutron-rich nuclei from the coherent density fluctuation model applied to nuclear matter calculations with Bonn potentials

We derive the values of nuclear symmetry energy, its components, as well as pressure in finite nuclei at saturation density from their corresponding values in nuclear matter obtained in non-relativistic Brueckner-Hartree-Fock calculations with the realistic Bonn B and Bonn CD potentials using the coherent density fluctuation model in the framework of a self-consistent Skyrme-Hartree-Fock plus BCS method. We focus on three isotopic chains of spherical nuclei (Ni, Sn, and Pb) and compare our results with those obtained with an effective Brueckner density-dependent potential. The role of the three-body forces on the considered quantities is also studied and discussed.

LOCV calculation for nuclear and neutron matter with the Nijmegen potential

The lowest order constrained variational (LOCV) formalism is formulated for the Nijmegen soft-core potential, which is fitted by the proton-proton (pp) scattering phase shift. The calculations are performed for the equation of state (EOS) of both nuclear and neutron matter. The state-dependent correlation functions are calculated by the minimization of two-body cluster energy, and the resulting Euler Lagrange equations are solved for this kind of potential. It is shown that LOCV calculations can work with this kind of interaction as well as other interactions in configuration space. The state-dependent correlation functions are calculated by minimization of two-body cluster energy for each channel with various JLSTMT, by using Nijmegen interaction. The correlation functions are compared with those coming from UV14 interaction in LOCV formalism. It is shown that unlike UV14, AV14, and AV18 potentials, the binding energy obtained from Nijmegen in the LOCV framework is −16.81 MeV that is close to the experimental value. Finally, it is recognized our LOCV results with Nijmegen interaction are similar to calculations with different interactions and different many-body methods.

Non-Linear Derivative Interactions in Relativistic Hadrodynamics

The Lagrangian of Relativistic Hadrodynamics (RHD) is extended by introducing non-linear derivative (NLD) operators into the interactions between the nucleon with the meson elds. As the novel feature of the NLD model, the nucleon selfenergy depends on both, on energy and density. Our approach contains a single cut-o parameter, which determines the density dependence of the nuclear equation of state (EoS) and the energy dependence of the nucleon-nucleus optical potential. The NLD formalism is compatible with results from microscopic nuclear matter calculations as well as with Dirac phenomenology.

A nuclear matter calculation with the tensor-optimized Fermi sphere method with central interaction

Abstract The tensor-optimized Fermi sphere (TOFS) theory is applied first for the study of the property of nuclear matter using the Argonne V4$^\prime$$NN$ potential. In the TOFS theory, the correlated nuclear matter wave function is taken to be a power-series type of the correlation function $F$, where $F$ can induce central, spin–isospin, tensor, etc. correlations. This expression has been ensured by a linked cluster expansion theorem established in the TOFS theory. We take into account the contributions from all the many-body terms arising from the product of the nuclear matter Hamiltonian $\mathcal{H}$ and $F$. The correlation function is optimally determined in the variation of the total energy of nuclear matter. It is found that the density dependence of the energy per particle in nuclear matter is reasonably reproduced up to the nuclear matter density $\rho \simeq 0.20$ fm$^{-3}$ in the present numerical calculation, in comparison with other methods such as the Brueckner–Hartree–Fock approach.

Consistent nuclear matter calculations with local three-nucleon interactions

I calculate the energy per particle of symmetric nuclear matter and pure neutron matter in the framework of the microscopic Brueckner-Hartree-Fock approach using some recent interactions derived in chiral perturbation theory at next-to-next-to-next-to-leading order (N3LO) for the nucleon-nucleon ($NN$) force, and next-to-next-to-leading order (N2LO) for the nucleon-nucleon-nucleon ($NNN$) one. The interactions considered in the present work have been adjusted to properties of light nuclei with $A=3$, adopting local regulators for the $NNN$ interaction. I performed several calculations using an effective density dependent two-body force obtained from the original $NNN$ one keeping the same parameters and the same regularization scheme employed in finite light nuclei calculations; I then compared these results with other calculations obtained, retaining the same parameters of the $NNN$ force fixed on light nuclei but using a nonlocal regulator. This second strategy has been often used in the literature due to the easier derivation of the effective $NN$ force in this case. I found that in pure neutron matter the use of local or nonlocal regulators does not sensibly affect the calculation of the energy per particle while in symmetric nuclear matter the use of local or nonlocal regulators produces appreciable differences. Saturation properties of nuclear matter are discussed for the various models considered; the uncertainties on the reported calculations are also estimated.

The calculation of Binding Energy and Incompressibility, Pressure, and Velocity of Sound of Infinite Nuclear matter Using New One Boson Interaction.

The use of effective nucleon – nucleon (N N) interactions for the determination of nuclear matter properties such as, binding energy per nucleon, incompressibility,K of infinite nuclear matter, pressure 0 and velocity of sound of nuclear matter has been a subject of great interest to nuclear physicists for many decades. The effective interaction usually involved in these calculations has been the Michigan three Yukawa (M3Y) effective interactions whose origin is from G- matrix approach. In this research work however, we have used a newly developed interaction known as new one boson (NOB) effective interaction to carry out similar calculations. This new interaction is based on the Lowest Order Constrained Variational (LOCV) technique. The interaction reproduces the saturation energy of spin and isospin infinite nuclear matter of approximately -16MeV at the normal nuclear matter saturation density consistent with the best available density-dependent interaction derived from the G-matrix approach. The results of the incompressibility obtained using the NOB interaction ranges from 304 to 309 MeV. These values are in good agreement with the values of incompressibility obtained for similar calculations using the M3Y – Reid effective interaction, in which values for K range from 304 to 310 MeV. The results of 0 pressure and velocity of sound of infinite nuclear matter obtained in the present calculations are also in excellent agreement with results of other workers. The results of our present calculations indicate that, the NOB interaction has passed the basic test for an effective interaction. The NOB may therefore be applied to other nuclear matter and optical model calculations to ascertain its reliability.

Non-Linear Derivative Interactions in Relativistic Hadrodynamics

The Lagrangian of Relativistic Hadrodynamics (RHD) is extended by introducing non- linear derivative (NLD) operators into the interactions between the nucleon with the meson fields. As the novel feature of the NLD model, the nucleon selfenergy depends on both, on energy and density. Our approach contains a single cut-off parameter, which determines the density dependence of the nuclear equation of state (EoS) and the energy dependence of the nucleon-nucleus optical potential. The NLD formalism is compatible with results from microscopic nuclear matter calculations as well as with Dirac phenomenology.