Novel features of asymmetric nuclear matter from terrestrial experiments and astrophysical observations of neutron stars

Abstract

The accurate measurement of neutron skin thickness of ²⁰⁸Pb by the PREX Collaboration suggests a large value of the nuclear symmetry energy slope parameter, , whereas the smaller is preferred to account for the small neutron-star radii from NICER observations. To resolve this discrepancy between nuclear experiments and astrophysical observations, new effective interactions have been developed using relativistic mean-field models with the isoscalar- and isovector-meson mixing. We investigate the effects of -nucleon coupling and – mixing on the ground-state properties of finite nuclei, as well as the characteristics of isospin-asymmetric nuclear matter and neutron stars. Additionally, we explore the role of the quartic -meson self-interaction in dense nuclear matter to mitigate the stiff equation of state for neutron stars resulting from the large -nucleon coupling. It is found that the nuclear symmetry energy undergoes a sudden softening at approximately twice the saturation density of nuclear matter, taking into account the PREX-2 result, the recent NICER observation of PSR J04374715, and the binary neutron star merger, GW170817.

1 Introduction

The astrophysical phenomena concerning compact stars as well as the characteristics of finite nuclei and nuclear matter are determined by the nuclear equation of state (EoS), characterized by the relation between the energy density and pressure of the system [1, 2]. Many nuclear EoSs have been contemplated so far through realistic nuclear models in a non-relativistic or relativistic framework [3, 4]. Relativistic mean-field (RMF) calculations, based on the one-boson exchange potential for nuclear interactions [5, 6], have achieved great success in understanding of the properties of nuclear matter and finite nuclei [7]. To reproduce a reasonable nuclear incompressibility and properties of unstable nuclei, the RMF models have been developed by introducing the non-linear self-couplings of isoscalar, Lorentz-scalar and Lorentz-vector mesons [8, 9]. In addition, the isovector, Lorentz-vector meson and its non-linear couplings have been considered to describe a neutron skin thickness of heavy nuclei and characteristics of isospin-asymmetric nuclear matter [10, 11]. The RMF approach is, at present, one of the most powerful tools to study neutron star physics [12–14], as in the case of the Skyrme energy density functional [15–18].

The nuclear symmetry energy, , which is defined as the difference between the energies of pure neutron and symmetric nuclear matter, is recognized to be an important physical quantity to study the properties of isospin-asymmetric nuclear EoS [19, 20]. In addition, the slope parameter of nuclear symmetry energy, , gives a significant constraint on the density dependence of and is related to the neutron skin thickness of heavy nuclei [21]. Laboratory experiments have been also performed to investigate the properties of low-density nuclear matter and to impose constraints on and through the heavy-ion collisions (HICs) [22, 23]. Recently, the impacts of the higher-order coefficients—the curvature and skewness of nuclear symmetry energy, and —have been studied in light of some astrophysical observations, for instance the mass-radius relations of neutron stars and the cooling process of proto-neutron stars [24–26].

Owing to the precise observations of neutron stars, such as the Shapiro delay measurement of a binary millisecond pulsar J16142230 [27, 28] and the radius measurement of PSR J07406620 from Neutron Star Interior Composition Explorer (NICER) and from X-ray Multi-Mirror (XMM-Newton) Data [29–32], theoretical studies have been currently performed more than ever to elucidate neutron star physics through the nuclear EoS for dense matter. It has been found that the nuclear EoS should satisfy at least to support the high-mass PSR J07406620 event, and that the precise measurements of neutron-star radii provide the valuable information in determining the features of isospin-asymmetric nuclear matter. In addition, the direct detection of gravitational-wave (GW) signals from a binary neutron star merger, GW170817, observed by Advanced LIGO and Advanced Virgo detectors has placed stringent restrictions on the mass–radius relation of neutron stars [33–35]. In particular, the tidal deformability of a neutron star [36, 37] plays a critical role in constructing the EoS for neutron star matter [38–41]. It has been reported that there are the strong correlations of neutron-star radii with and , and the radius of a typical neutron star is determined by [42–45]. Using a Bayesian analysis based on constraints from NICER and GW170817 within chiral effective field theory calculations, is currently estimated as = (43.7–70.0) MeV [46].

The accurate measurement of neutron skin thickness of ²⁰⁸Pb, , by the PREX Collaboration, using the parity-violating electron scattering, has revealed a serious discrepancy between the measured and theoretical predictions [47]. The neutron skin thickness, , is defined here as the difference between the root-mean-square radii of point neutrons and protons, and , in a nucleus:

To explain the PREX-2 result, Reed et al. [48] have proposed the large value as MeV, by exploiting the strong correlation between and . In contrast, Reinhard et al. [49], using modern relativistic and non-relativistic energy density functionals, have predicted the smaller value, MeV, by carefully assessing theoretical uncertainty on the parity-violating asymmetry, , in ²⁰⁸Pb. Additionally, the CREX experiment, which provides a precise measurement of the neutron skin thickness of ⁴⁸Ca, , through the parity-violating electron scattering [50], complicates the understanding of isospin-asymmetric nuclear matter. This complexity arises from the difficulty of reconciling the PREX-2 and CREX results simultaneously. In addition, the measurements from polarized proton scattering off ²⁰⁸Pb indicate smaller , and consequently smaller , compared to those obtained from the PREX-2 experiment [51, 52]. As a result, and remain uncertain in theoretical calculations [53, 54]. At present, many species of neutron skin thickness have been reported from a combination of experimental and theoretical results [55].

Under these constraints, we examine the effects of the -nucleon coupling and – mixing on the ground-state properties of finite nuclei, and consider the PREX-2 and CREX results. Additionally, we investigate the impact of the quartic self-interactions of and mesons on the nuclear EoS to study the properties of neutron star matter.

This paper is organized as follows. A summary and analytical calculations concerning the RMF model with non-linear couplings are described in Section 2. Numerical results and detailed discussions are presented in Section 3. Finally, we give a summary in Section 4.

2 Theoretical framework

2.1 Lagrangian density

In quantum hydrodynamics [7], we employ the recently updated effective Lagrangian density including the isoscalar ( and ) and isovector ( and ) mesons as well as nucleons [57, 58]. The total Lagrangian density is then given bywhere is the iso-doublet, nucleon field, is its isospin matrix, , and . The meson-nucleon coupling constants are respectively denoted by , , , and . The photon- interaction, with , is also taken into account to describe the characteristics of finite nuclei [7, 66]. Additionally, a non-linear potential in Equation 1 is supplemented as follows:

The first and second terms in Equation 2 are introduced to obtain a quantitative description of ground-state properties for symmetric nuclear matter [8, 67]. The quartic self-interactions of , , and mesons are also introduced in Equation 2 [9, 10, 68, 69]. We also consider the isoscalar- and isovector-meson mixing, which only affects the characteristics of finite nuclei and isospin-asymmetric nuclear matter [56, 70, 71], while the scalar-vector mixing is not included in the present study [11, 72–75].

2.2 Field equations for finite nuclei in mean-field approximation

In mean-field approximation, the meson and photon fields are replaced by the mean-field values: , , , , and . Then, the effective nucleon mass in matter is simply expressed aswhere ( MeV) is the nucleon mass in free space. If we restrict consideration to spherical finite nuclei, the equation of motion for is given bywith being the nucleon single-particle energy. The meson and photon fields are then given byandwhere is the scalar (baryon) density for , which is computed self-consistently using nucleon wave functions in Equation 4 that are solutions to the Dirac equation in the spatially dependent meson and photon fields. The effective meson masses are defined by

The total energy of the system is thus written aswhere the sum runs over the occupied states of with the degeneracy [7].

2.3 Infinite nuclear matter

To study the bulk properties of nuclear and neutron star matter, it is necessary to compute the nuclear equation of state (EoS)—a relation between the energy density, , and pressure, . In infinite nuclear matter, the surface terms in Equations 5–9 have no influence on its characteristics as the gradient reads zero. The scalar and baryon density for are then obtained aswhere and are the Fermi momentum and energy for . With the self-consistent calculations of the meson fields, and are respectively given by and where the nucleon and meson parts are expressed asand

2.4 Nuclear bulk properties

In general, the bulk properties of infinite nuclear matter are identified by the expansion of isospin-asymmetric nuclear EoS with a power series in the isospin asymmetry, , and the total baryon density, [76, 77]. The binding energy per nucleon is then written aswhere is the binding energy per nucleon of symmetric nuclear matter (SNM) and is the nuclear symmetry energy (NSE),

Besides, and can be expanded around the nuclear saturation density, , aswith being the dimensionless variable characterizing the deviations of from . The incompressibility coefficient of SNM, , the slope and curvature parameters of NSE, and , and the third-order incompressibility coefficients of SNM and NSE, and , are respectively defined as

Taking into account the thermodynamic condition, the pressure of infinite nuclear matter, , is given bywith the binding energy per nucleon in Equation 14. The nuclear incompressibility, , is then expressed as

Hence, the incompressibility coefficient of SNM, , in Equation 16 is related with through . In the RMF calculation, we can obtain the analytical expression of using the following equation:where the density derivatives of meson fields are calculated through the relationwithand

We here use the following quantities:andwithwhere the effective meson masses, , , and , are given in Equations 10–13, and for reads

According to the Hugenholtz-Van Hove theorem in nuclear matter, defined in Equation 15 can be generally written aswhere is the single-particle energy for , which is determined self-consistently by solving the following transcendental equation [78, 79]:

The effective mass, (four) momentum, and energy for are here defined as [80, 81]with being the scalar (time) [space] component of nucleon self-energy. In addition, is divided into the kinetic and potential terms as

Based on the Lorentz-covariant decomposition of NSE [82], is expressed aswith the scalar , time (0), and space components. The is thus computed as follows:where the effective quantities at the Fermi surface in Equations 22–25 are then given by , , and at , namely, . In RMF approximation, are respectively given by

Using Equations 20, 21, can be finally expressed as

Note that and in RMF approximation.

The and given in Equation 17 are also expressed aswhere the kinetic, scalar, and time components are respectively given bywith

2.5 Stability of nuclear and neutron star matter

In order to move on the calculations of neutron stars in which the charge neutrality and equilibrium conditions are imposed, we introduce the degrees of freedom of leptons (electrons and muons) as well as nucleons and mesons in Equation 2.where is the lepton field and its mass is given by .

When we consider the stability of matter in cold neutron stars, the first principle of thermodynamics should be considered:with , , , , and being the total internal energy per nucleon, pressure, volume per nucleon, chemical potential, and charge fraction, respectively [83–86]. In neutron star matter, the charge neutrality and equilibrium conditions readwith the lepton density. The stability of neutron star matter are then expressed as the following two constraints on chemical potential and pressure:

The total internal energy per baryon, , can be decomposed into the baryon and lepton contributions aswith . At zero temperature, the equilibrium condition leads to the relation [87].where the isospin symmetry breaking (ISB) energy of infinite nuclear matter is given by

Considering the differentiation of , we findwhere and are respectively the Fermi momenta for electrons and muons . For simplicity, we here define the nuclear symmetry energy involving the isospin asymmetry, , as

Note that we explicitly keep to consider the stability of nuclear and neutron star matter, though the nuclear symmetry energy is in general calculated at , namely, , as shown in Equation 15. Hence the stability constraint on chemical potential, , can be satisfied by assuming that is positive at any .

As for the pressure stability, the differentiation of readswith the baryon and lepton contributions. Similar to Equation 27, the baryon contribution is given by

Using the thermodynamic definitions of pressure and incompressibility of infinite nuclear matter in Equations 18, 19, this equation can be simplified aswhere the slope of ISB energy, , is defined as

The lepton contribution is also given by the simple form under the equilibrium condition:

Therefore, the stability of neutron star matter under the charge neutrality and equilibrium conditions can be clarified by the thermodynamic constraints on chemical potential and pressure, namely, and

The thermodynamic stability is used in several calculations of nuclear and neutron star matter, for instance, the compressibility of -equilibrated matter [56, 88] and the phase transition between the crust and core regions in neutron stars [89–91].

3 Results and discussions

3.1 Nuclear models

We adopt the recently developed effective interactions labeled as the OMEG family, which are constructed to reproduce the characteristics of finite nuclei, nuclear matter, and neutron stars [58, 92]. In particular, the – coupling and – mixing in the OMEG family are determined so as to support the astrophysical constraints on the neutron-star radii from the NICER mission [29–32] and the tidal deformabilities from the binary merger events due to GW signals [34, 93]. Various theoretical calculations using the well-calibrated parameter sets based on the RMF models are also presented: BigApple [94], DINO [95], FSU- [59], FSUGarnet [96], FSUGold [97], FSUGold2 [98], Bayesian refinement of FSUGarnet and FSUGold2, FSUGarnet+R and FSUGold2+R [99, 100], HPNL0 and HPNL5 [101], IOPB-I [102], IU-FSU [103], NL3 [67], PD15 [104], TAMUC-FSUa [105, 106], and TM1 [9]. In Tables 1, 2, we summarize the model parameters and the properties of symmetric nuclear matter at for the effective interactions used in the present study.

In addition, we present the extended interactions based on the FSUGarnet, TAMUC-FSUa, and FSUGold2 models, in which the – coupling are introduced to investigate the effect of meson. Since the – coupling only influences the properties of finite nuclei and isospin-asymmetric nuclear matter, we adjust and to preserve the original model’s predictions for when the – coupling is included. Simultaneously, the other coupling constants related to the properties of finite nuclei and isospin-symmetric nuclear matter—, , , and —are readjusted to closely match the experimental data for the binding energy per nucleon and charge radius of several closed-shell nuclei, as well as to maintain the original value. The resultant coupling constants and nuclear properties for the FSUGarnet, TAMUC-FSUa, and FSUGold2 series are listed in Table 3. Furthermore, the parameter sets for the FSUGold2 with the – coupling and the quartic self-interaction of meson are also given in Table 4, where the quartic coupling constant, , is varied in the range of with the fixed parameters, and .

3.2 Finite nuclei

The theoretical predictions for the neutron skin thickness of ⁴⁰Ca and ²⁰⁸Pb, and , in the RMF models are presented in Figure 1, compared with the experimental data: the electric dipole polarizability of ⁴⁸Ca (RCNP; –0.20 fm) [107], the complete electric dipole response on ²⁰⁸Pb (RCNP; fm) [52], the coherent pion photoproduction cross sections measurement of ²⁰⁸Pb (MAMI; fm) [108], and the parity-violating electron scattering off ⁴⁸Ca (CREX; fm) [50] and off ²⁰⁸Pb (PREX-2; fm) [47].

FIGURE 1

As for the OMEG family, the OMEG0 and OMEG1 give the large values, fm and fm, respectively, which meet the PREX-2 result. The OMEG2 is selected so as to match the predicted result, fm, by the assessment of the theoretical uncertainty on parity-violating asymmetry in ²⁰⁸Pb [49]. Meanwhile, the OMEG3 exhibits the small value, fm, which satisfies the experimental result in RCNP and is near the range of CREX experiment, fm. We summarize the predictions for the charge radius, , neutron skin thickness, , and weak radius, , of ⁴⁸Ca and ²⁰⁸Pb in Table 5. We here consider the zero-point energy correction taken from the conventional Skyrme Hartree–Fock calculations [9, 109]. The is defined aswith being the point proton radius [98].

We see the linear correlation between and in the left panel of Figure 1. In general, the larger and are obtained by the models with the larger (see Table 2). To explain the results from RCNP, should be small such as the OMEG3, BigApple, FSUGarnet, and IU-FSU. In contrast, the DINO family is located far from the points calculated by the other RMF models. As explained in Reed et al. [95], the DINO family expresses the large by means of the huge – and – couplings. Although it is difficult to support the PREX-2 and CREX results simultaneously, only the DINOc successfully aligns with both data sets. We note that the - coupling and - mixing affect the charge radii of finite nuclei and hence while they have less influence on the binding energy because we focus on the finite, closed-shell nuclei, ¹⁶O, ^40,48Ca, ⁶⁸Ni, ⁹⁰Zr, ^100,116,132Sn, and ²⁰⁸Pb, in the present study [110].

To clarify the effect of meson on the characteristics of finite nuclei, we describe the correlation between and for the FSUGarnet, TAMUC-FSUa, and FSUGold2 series in the right panel of Figure 1. We also display the calculations based on the other RMF models including the meson as well as the , , and mesons. As shown in Table 3, becomes large as increases. Consequently, the TAMUC-FSUa, and FSUGold2 series draw the lines from the upper right to the bottom left. In particular, the FSUGold2 with the large – coupling supports both experimental data from the parity-violating electron scattering. On the other hand, the FSUGarnet series moves away from the PREX-2 and CREX results when the large is introduced.

The density profiles in ²⁰⁸Pb are displayed in Figure 2. We here present the baryon, charge, and weak charge densities, , , and , with the experimental results [47, 111]. The is approximately expressed aswith being the proton (neutron) weak charge and being the proton electric form factor [112–114]. The OMEG family is calibrated so as to reproduce and in ²⁰⁸Pb by the PREX-2 experiment.

FIGURE 2

In the left panel of Figure 2, we present the density profiles for the OMEG1, DINOc, FSUGarnet. The OMEG1 and FSUGarnet adequately satisfy the density distributions of from the elastic electron scattering [111]. On the other hand, the DINOc possesses the instability around the core of nuclei because of the strong – coupling constant [95]. As a result, the density profiles, , , and , show the large density fluctuations around the core.

The effect of – coupling on the density profiles for the FSUGold2 series is illustrated in the right panel of Figure 2. There is almost no difference up to . In the case of , and begin to show the instability around the core, but still matches the experimental data from PREX-2 [47]. When the larger value, , is taken, the unexpectedly large fluctuations of and emerge around the core, and the wave functions do not converge numerically. In the present study, we thus impose the limit on the – coupling as for the FSUGold2 series. We here comment that this defect can not be solved even if one considers the quartic self-interactions of and/or mesons in Equation 3, which less affect and .

3.3 Infinite nuclear matter

The -meson effect can be clearly seen in the effective nucleon mass, , in Equation 3. Displayed in Figure 3 is the density dependence of in pure neutron matter for the OMEG family and the FSUGold2 series. When the meson only is included, the RMF model gives the equal effective mass of proton and neutron. However, the iso-scalar meson is responsible for the mass splitting between protons and neutrons, where is much heavier than at high densities. Compared with the OMEG family, the FSUGold2 series shows the strong mass splitting, as increases, even at low densities. It is implied that the neutron distribution is more spread out than the proton one, because is lighter, and then, the large fluctuations of and appear around the core of ²⁰⁸Pb as shown in Figure 2. Due to the – coupling and the – mixing, and respectively reach the almost constant values at high densities in all the cases.

FIGURE 3

The density dependence of nuclear symmetry energy, , in Equation 26 is depicted in Figure 4. We here present the calculations using the OMEG, FSU-, and DINO families. Furthermore, we use the conventional ones (the NL3, FSUGold2, TAMUC-FSUa, IOPB-I, and FSUGarnet models). In addition, several experimental or theoretical constraints are presented. Figure 4 highlights significant differences in at high densities, that is, whereas the conventional calculations show a monotonic increase in , the models with the meson exhibit more complex behavior. In particular, the DINO family predicts a large above as the meson amplifies in dense nuclear matter [57]. The OMEG and FSU- families, on the other hand, display unusual trends depending on the strength of – coupling and – mixing. The – mixing has a weak influence on below , but, as discussed by Zabari et al. [56], it becomes substantial above . Specifically, the – mixing reduces at high densities, partially offsetting the increase from the – interaction. Furthermore, in the OMEG0 and FSU-, the inflection points appear above and the dip emerges around –. This behavior is similar to the cusp in in the skyrmion crystal approach [115, 116] and to the results from the Skyrme Hartree-Fock calculations [117]. We note that, as explained in Section 2.5, the thermodynamic constraint on chemical potential in isospin-asymmetric nuclear matter, , is satisfied over all densities, namely, .

FIGURE 4

Based on the Lorentz decomposition of nucleon self-energy in Section 2.4, is generally divided into the kinetic and potential terms, and , as . In RMF approximation, only the isovector mesons contribute to as , where the scalar and time (0) components, and , are respectively given by the and mesons. We show the Lorentz decomposition of for the OMEG family and the FSUGold2 series as a function of in Figure 5. The top panels are the density dependence of and . We see that the unique behavior of in the OMEG family is caused by because is almost the same as in both cases. The contents of are given in the middle and bottom panels of Figure 5. It is found that is negative while is positive, which is similar to the general understanding of – interaction described by the nuclear attractive and repulsive forces. Note that a similar description of has been reported using the RMF model with a contact interaction of isovector mesons, where the scalar contribution, , is positive while the vector one, , is negative [118, 119]. It is noticeable that, for the FSUGold2 series, is strongly influenced by the – coupling above , and the contribution of is small at high densities. Conversely, for the OMEG family, the – mixing shows less impact on below , but it strongly affects at high densities. When the absolute value of is larger than that of , has the rapid reduction, and then shows a dip around as in the cases for the OMEG0 and FSU- in Figure 4.

FIGURE 5

The EoSs for symmetric nuclear matter and pure neutron matter are displayed in Figure 6 with the constraints on the nuclear EoS extracted from the analyses of particle flow data in HICs [60–62]. In both panels, we show the various EoSs calculated by the OMEG, DINO, and FSU- families, and the FSUGarnet and FSUGold2 models. The meson does not affect in symmetric nuclear matter. All the cases except for the OMEG0 are well constructed to match the HIC data in symmetric nuclear matter because of the small . However, the stiffer EoS with MeV is still acceptable, taking into account the recent simulation of AuAu collisions [63]. In contrast, the meson has a large impact on in pure neutron matter. The DINOa and DINOc show the hard EoSs, which are far from the constraints from HICs, due to the large – coupling. Meanwhile, the strong – mixing softens the EoSs extremely for the OMEG and FSU- families in the density region from to , around which the characteristics of a canonical neutron star are generally determined.

FIGURE 6

We present the EoS for pure neutron matter for the FSUGold2 series in Figure 7. In the left panel, the EoS becomes hard with increasing the – coupling, and the EoS with exceeds the HIC results as in the cases for the DINO family in Figure 6. Hence, we find that, even if the large – coupling is introduced simply, it is not easy to explain simultaneously both properties of dense nuclear matter and characteristics of finite nuclei for and in Figure 1. In order to suppress such excessive stiffness of EoSs for pure neutron matter due to the – coupling, we additionally include the quartic self-interaction of meson in the FSUGold2 model with the upper limit of (see Table 4), given in the right panel of Figure 7. The EoS is soft and again reaches the upper edge of the constraint from HICs with increasing the quartic coupling, , whose effect is almost imperceptible below .

FIGURE 7

3.4 Neutron star physics

In studying neutron star physics, the EoS for non-uniform matter is additionally required as well as that for uniform nuclear matter since the radius of a neutron star is remarkably sensitive to the nuclear EoS at very low densities [120]. In the present study, to cover the crust region, we adopt the MYN13 EoS, in which nuclei are taken into consideration using the Thomas-Fermi calculation in non-uniform matter and the EoS for infinite nuclear matter is constructed with the relativistic Hartree-Fock calculation [80, 81, 121, 122]. We list in Table 6 the predicted stellar properties, which are calculated by solving the Tolman–Oppenheimer–Volkoff (TOV) equation [123, 124].

There are three methods used widely to determine the crust-core transition density, [125]: the thermo-dynamical method, the dynamical method, and the random-phase-approximation method. We employ the first method in the present study. As explained in Section 2.5, the stability of nuclear and neutron star matter is determined by the constraints on chemical potential and pressure, and , in the first law of thermodynamics. Since the proton fraction, , is supposed to be small in the crust region, the second-order Taylor series approximation of the nuclear EoS is generally adopted in the density derivative of baryon pressure, , in Equation 28 [83]. However, it has been reported that the parabolic approximation of isospin-asymmetric nuclear EoS may be misleading as regards the predictions for [89]. We thus employ the exact nuclear EoS to calculate defined in Equation 29.

We summarize the results of in the second column of Table 6. Compared with the results from the Taylor series expansion, the our results settle between the second-order and fourth-order calculations. For example, for the FSUGold, the exact value is while the second-order (fourth-order) result is (see Table 2 in Routray et al. [89]). In addition, the current results are almost the same as the transition density from the pasta phase to the homogeneous nuclear matter in the model calculation with Thomas-Fermi approximation [126]. The EoS for neutron star matter in the OMEG family is presented in Figure 8. The crust-core phase transition occurs at , which is also described in the left panel of Figure 9. As it is well known, the EoS with larger gives the smaller [127].

FIGURE 8

FIGURE 9

Since the large – mixing enhances the rapid reduction of around as shown in Figure 4, we have to investigate the stability of neutron star matter. Similar to the crust-core phase transition, we adopt the thermo-dynamical method. It is especially important to apply the exact nuclear EoS to because is by no means small and the Taylor series expansion is prohibited at high densities. It is found that the constraint on chemical potential, , is always satisfied as is positive at any densities. Hence, all we have to do is check the thermodynamic stability of pressure, . In Figure 9, we show in neutron star matter. In general, changes from negative to positive at , and the stable EoS possesses even at high densities. Despite the OMEG0 give a strong concavity in by the – mixing, it satisfies the thermodynamic stability. In the right panel of Figure 9, we show for the FSUGold2 series. The neutron star matter keeps when the – coupling only is included, whereas the large quartic self-interaction of meson, , makes the matter unstable. Though the quartic -meson self-interaction is useful to figure out the HIC data as mentioned in the right panel of Figure 7, the large value of is unfavorable to the neutron star physics.

We illustrate in Figure 10 the proton fraction, , in neutron star matter with the threshold for the direct URCA process. The direct URCA process is visible only when is large enough to conserve momentum in -equilibrated matter, in which the Fermi momenta of neutrons, protons, and electron must satisfy the relation: . Hence, can be estimated as , above which the direct URCA cooling occurs [118, 128, 129]. We find that as increases, the threshold of for the direct URCA process shifts toward the upper boundary where muons are present. The for the DINOa grows quickly with increasing due to the large – coupling, and then the direct URCA process is allowed sufficiently at , which corresponds to the core density of a canonical neutron star. Conversely, in the OMEG and FSU- families, the – mixing suppresses , and then delays the direct URCA process. Particularly, the direct URCA process never occurs for the OMEG0, OMEG2, and OMEG3 in the current density region, and thus the so-called modified URCA process, which is the standard model of neutron-star coolings, mainly takes place for the neutrino emission [130]. Alternatively, the possibility of exotic degrees of freedom in the core of a neutron star, such as hyperons, quarks, gluons and/or some unusual condensations of boson-like matter, should be taken into account to understand the rapid neutron star cooling.

FIGURE 10

The mass–radius relations of neutron stars are displayed in Figure 11. We here show the astrophysical constraints from the NICER observations: PSR J00300451 [29, 31], PSR J07406620 [32, 64, 65], and PSR J04374715 [131, 132]. According to the observation from PSR J07406620, the maximum mass of a neutron star, , should be larger than . Thus the EoS involving the large , such as the NL3, is ruled out. It is found that the large – coupling affects the large in the DINO family, whereas the – mixing makes small in the OMEG family. In particular, though the DINOa and OMEG0 have the same as MeV, their – relations are completely different and the difference of at canonical-mass point reads approximately 1.7 km (see also Table 6). The OMEG family can support not only the NICER constraint on from PSR J00300451 but also that from PSR J04374715, which is the latest result based on new chiral effective field theory inputs [131].

FIGURE 11

The dimensionless tidal deformability, , of neutron stars is displayed in Figure 12 as a function of . The is defined as with being the second Love number [36, 37]. The astrophysical constraints on at the canonical-mass point, , from the binary merger events detected by the Advanced LIGO and Advanced Virgo observatories are also presented as follows: for GW170817 [34] and for GW190814 [93]. As explained in Miyatsu et al. [57], the – coupling enlarges for the DINOa, and then lies far from the constraints on from GW190814. On the other hand, the – mixing has a promising effect on , and thus the OMEG family sufficiently matches the severe constraints from both GW170817 and GW190814.

FIGURE 12

4 Summary and conclusion

We have developed a new family of nuclear EoSs, referred to as the OMEG family, using the RMF model with non-linear couplings between the isoscalar and isovector mesons. In addition to the , , and mesons, we have also included the meson to examine the ground-state properties of finite, closed-shell nuclei as well as the characteristics of nuclear and neutron star matter. Specifically, we have investigated the effects of – coupling and – mixing on the EoS for both nuclear and neutron star matter. The model parameters for the OMEG family have been calibrated so as to satisfy the constraints from the particle flow data in HICs [60–62], the observed neutron-star mass of PSR J07406620 [32, 64, 65], and the dimensionless tidal deformability, , from the neutron star merger, GW170817 [34], as well as the results from the PREX-2 and CREX experiments [47, 50].

It has been found that the – coupling and the – mixing significantly influence the properties of isospin-asymmetric nuclear matter and finite nuclei, playing a crucial role in reconciling terrestrial experiments with astrophysical observations of neutron stars. The strong – coupling for the FSUGold2 series can simultaneously explain the large and the small measured by the PREX-2 and CREX experiments. However, it seems difficult that the FSUGold2 series satisfy the combined constraints from the particle flow data in HICs and astrophysical observations, such as the EoS for pure neutron matter and the of neutron stars. Even with the inclusion of quartic -meson self-interaction in the FSUGold2 series, both experimental and observational results can not be understood, because the large destabilizes neutron star matter. In contrast, the OMEG family can satisfy the recent measurement of km for PSR J04374715 from NICER [131] and the stringent constraint on from GW170817 [34]. This is attributed to the – mixing, which suppresses above , resulting in a softer nuclear EoS in the density region corresponding to the core density of the canonical neutron stars.

In a future work, we plan to extend the present study to global calculations of finite nuclei properties covered the periodic table, aiming to achieve well-calibrated parameter sets for the RMF models. Finally, we comment that the further theoretical studies are necessary to reconcile the measured by proton (in)elastic scattering with that obtained from parity-violating electron scattering. In particular, it is very significant to investigate the discrepancy between the PREX-2 data [47] and the results from RCNP [51, 52] and MAMI [108]. It is also essential to consider the effect of isospin symmetry breaking on asymmetric nuclear matter from the quark level [133–138].

References

• 1.

  BaymGBetheHAPethickC. Neutron star matter. Nucl Phys A (1971) 175:225–71. 10.1016/0375-9474(71)90281-8

  • CrossRef
  • Google Scholar

• 2.

  BetheHABrownGEApplegateJLattimerJM. Equation of state in the gravitational collapse of stars. Nucl Phys A (1979) 324:487–533. 10.1016/0375-9474(79)90596-7

  • CrossRef
  • Google Scholar

• 3.

  LattimerJMSwestyFD. A Generalized equation of state for hot, dense matter. Nucl Phys A (1991) 535:331–76. 10.1016/0375-9474(91)90452-C

  • CrossRef
  • Google Scholar

• 4.

  GlendenningNKMoszkowskiSA. Reconciliation of neutron star masses and binding of the lambda in hypernuclei. Phys Rev Lett (1991) 67:2414–7. 10.1103/PhysRevLett.67.2414

  • CrossRef
  • Google Scholar

• 5.

  MachleidtRHolindeKElsterC. The bonn meson exchange model for the nucleon nucleon interaction. Phys Rept (1987) 149:1–89. 10.1016/S0370-1573(87)80002-9

  • CrossRef
  • Google Scholar

• 6.

  MachleidtR. The Meson theory of nuclear forces and nuclear structure. Adv Nucl Phys (1989) 19:189–376. 10.1007/978-1-4613-9907-0_2

  • CrossRef
  • Google Scholar

• 7.

  SerotBDWaleckaJD. The relativistic nuclear many body problem. Adv Nucl Phys (1986) 16:1–327.

  • Google Scholar

• 8.

  BogutaJBodmerAR. Relativistic calculation of nuclear matter and the nuclear surface. Nucl Phys A (1977) 292:413–28. 10.1016/0375-9474(77)90626-1

  • CrossRef
  • Google Scholar

• 9.

  SugaharaYTokiH. Relativistic mean field theory for unstable nuclei with nonlinear sigma and omega terms. Nucl Phys A (1994) 579:557–72. 10.1016/0375-9474(94)90923-7

  • CrossRef
  • Google Scholar

• 10.

  MuellerHSerotBD. Relativistic mean field theory and the high density nuclear equation of state. Nucl Phys A (1996) 606:508–37. 10.1016/0375-9474(96)00187-X

  • CrossRef
  • Google Scholar

• 11.

  HorowitzCJPiekarewiczJ. The Neutron radii of Pb-208 and neutron stars. Phys Rev C (2001) 64:062802. 10.1103/PhysRevC.64.062802

  • CrossRef
  • Google Scholar

• 12.

  OertelMHempelMKlähnTTypelS. Equations of state for supernovae and compact stars. Rev Mod Phys (2017) 89:015007. 10.1103/RevModPhys.89.015007

  • CrossRef
  • Google Scholar

• 13.

  AlfordMGBrodieLHaberATewsI. Relativistic mean-field theories for neutron-star physics based on chiral effective field theory. Phys Rev C (2022) 106:055804. 10.1103/PhysRevC.106.055804

  • CrossRef
  • Google Scholar

• 14.

  PatraNKVennetiAImamSMAMukherjeeAAgrawalBK. Systematic analysis of the impacts of symmetry energy parameters on neutron star properties. Phys Rev C (2023) 107:055804. 10.1103/PhysRevC.107.055804

  • CrossRef
  • Google Scholar

• 15.

  StoneJR. Nuclear physics and astrophysics constraints on the high density matter equation of state. Universe (2021) 7:257. 10.3390/universe7080257

  • CrossRef
  • Google Scholar

• 16.

  StoneJR. Nuclear symmetry energy in strongly interacting matter: past, present and future. Symmetry (2024) 16:1038. 10.3390/sym16081038

  • CrossRef
  • Google Scholar

• 17.

  ZhouJXuJPapakonstantinouP. Bayesian inference of neutron-star observables based on effective nuclear interactions. Phys Rev C (2023) 107:055803. 10.1103/PhysRevC.107.055803

  • CrossRef
  • Google Scholar

• 18.

  SunBBhattiproluSLattimerJM. Compiled properties of nucleonic matter and nuclear and neutron star models from nonrelativistic and relativistic interactions. Phys Rev C (2024) 109:055801. 10.1103/PhysRevC.109.055801

  • CrossRef
  • Google Scholar

• 19.

  LiB-AChenL-WKoCM. Recent progress and new challenges in isospin physics with heavy-ion reactions. Phys Rept (2008) 464:113–281. 10.1016/j.physrep.2008.04.005

  • CrossRef
  • Google Scholar

• 20.

  LattimerJM. Symmetry energy in nuclei and neutron stars. Nucl Phys A (2014) 928:276–95. 10.1016/j.nuclphysa.2014.04.008

  • CrossRef
  • Google Scholar

• 21.

  TypelSBrownBA. Neutron radii and the neutron equation of state in relativistic models. Phys Rev C (2001) 64:027302. 10.1103/PhysRevC.64.027302

  • CrossRef
  • Google Scholar

• 22.

  TsangMBZhangYDanielewiczPFamianoMLiZLynchWGet alConstraints on the density dependence of the symmetry energy. Phys Rev Lett (2009) 102:122701. 10.1103/PhysRevLett.102.122701

  • CrossRef
  • Google Scholar

• 23.

  TsangMBStoneJRCameraFDanielewiczPGandolfiSHebelerKet alConstraints on the symmetry energy and neutron skins from experiments and theory. Phys Rev C (2012) 86:015803. 10.1103/PhysRevC.86.015803

  • CrossRef
  • Google Scholar

• 24.

  ZhangN-BLiB-A. Impact of NICER’s radius measurement of PSR J0740+6620 on nuclear symmetry energy at suprasaturation densities. Astrophys J (2021) 921:111. 10.3847/1538-4357/ac1e8c

  • CrossRef
  • Google Scholar

• 25.

  RichterJLiB-A. Empirical radius formulas for canonical neutron stars from bidirectionally selecting features of equations of state in extended Bayesian analyses of observational data. Phys Rev C (2023) 108:055803. 10.1103/PhysRevC.108.055803

  • CrossRef
  • Google Scholar

• 26.

  XieW-JLiB-AZhangN-B. Impact of the newly revised gravitational redshift of x-ray burster GS 1826-24 on the equation of state of supradense neutron-rich matter. Phys Rev D (2024) 110:043025. 10.1103/PhysRevD.110.043025

  • CrossRef
  • Google Scholar

• 27.

  DemorestPPennucciTRansomSRobertsMHesselsJ. Shapiro delay measurement of A two solar mass neutron star. Nature (2010) 467:1081–3. 10.1038/nature09466

  • CrossRef
  • Google Scholar

• 28.

  ArzoumanianZBrazierABurke-SpolaorSChamberlinSChatterjeeSChristyBet alThe NANOGrav 11-year data set: high-precision timing of 45 millisecond pulsars. Astrophys J Suppl (2018) 235:37. 10.3847/1538-4365/aab5b0

  • CrossRef
  • Google Scholar

• 29.

  MillerMCLambFKDittmannAJBogdanovSArzoumanianZGendreauKCet alPSR J0030+0451 mass and radius from NICER data and implications for the properties of neutron star matter. Astrophys J Lett (2019) 887:L24. 10.3847/2041-8213/ab50c5

  • CrossRef
  • Google Scholar

• 30.

  MillerMCLambFKDittmannAJBogdanovSArzoumanianZGendreauKCet alThe radius of PSR J0740+6620 from NICER and XMM-Newton data. Astrophys J Lett (2021) 918:L28. 10.3847/2041-8213/ac089b

  • CrossRef
  • Google Scholar

• 31.

  RileyTEWattsALBogdanovSRayPSLudlamRMGuillotSet alA NICER view of PSR J0030+0451: millisecond pulsar parameter estimation. Astrophys J Lett (2019) 887:L21. 10.3847/2041-8213/ab481c

  • CrossRef
  • Google Scholar

• 32.

  RileyTEWattsALRayPSBogdanovSGuillotSMorsinkSMet alA NICER view of the massive pulsar PSR J0740+6620 informed by radio timing and XMM-Newton spectroscopy. Astrophys J Lett (2021) 918:L27. 10.3847/2041-8213/ac0a81

  • CrossRef
  • Google Scholar

• 33.

  AbbottBPAbbottRAbbottTDAcerneseFAckleyKAdamsCet alGW170817: observation of gravitational waves from a binary neutron star inspiral. Phys Rev Lett (2017) 119:161101. 10.1103/PhysRevLett.119.161101

  • CrossRef
  • Google Scholar

• 34.

  AbbottBPAbbottRAbbottTDAcerneseFAckleyKAdamsCet alGW170817: measurements of neutron star radii and equation of state. Phys Rev Lett (2018) 121:161101. 10.1103/PhysRevLett.121.161101

  • CrossRef
  • Google Scholar

• 35.

  AbbottBPAbbottRAbbottTDAcerneseFAckleyKAdamsCet alProperties of the binary neutron star merger GW170817. Phys Rev X (2019) 9:011001. 10.1103/PhysRevX.9.011001

  • CrossRef
  • Google Scholar

• 36.

  HindererT. Tidal Love numbers of neutron stars. Astrophys J (2008) 677:1216–20. Erratum: Astrophys.J. 697, 964 (2009)10.1086/533487

  • CrossRef
  • Google Scholar

• 37.

  HindererTLackeyBDLangRNReadJS. Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral. Phys Rev D (2010) 81:123016. 10.1103/PhysRevD.81.123016

  • CrossRef
  • Google Scholar

• 38.

  AnnalaEGordaTKurkelaAVuorinenA. Gravitational-wave constraints on the neutron-star-matter equation of state. Phys Rev Lett (2018) 120:172703. 10.1103/PhysRevLett.120.172703

  • CrossRef
  • Google Scholar

• 39.

  LimYHoltJW. Neutron star tidal deformabilities constrained by nuclear theory and experiment. Phys Rev Lett (2018) 121:062701. 10.1103/PhysRevLett.121.062701

  • CrossRef
  • Google Scholar

• 40.

  MostERWeihLRRezzollaLSchaffner-BielichJ. New constraints on radii and tidal deformabilities of neutron stars from GW170817. Phys Rev Lett (2018) 120:261103. 10.1103/PhysRevLett.120.261103

  • CrossRef
  • Google Scholar

• 41.

  RaithelCÖzelFPsaltisD. Tidal deformability from GW170817 as a direct probe of the neutron star radius. Astrophys J Lett (2018) 857:L23. 10.3847/2041-8213/aabcbf

  • CrossRef
  • Google Scholar

• 42.

  AlamNAgrawalBKFortinMPaisHProvidênciaCRadutaARet alStrong correlations of neutron star radii with the slopes of nuclear matter incompressibility and symmetry energy at saturation. Phys Rev C (2016) 94:052801. 10.1103/PhysRevC.94.052801

  • CrossRef
  • Google Scholar

• 43.

  HuJBaoSZhangYNakazatoKSumiyoshiKShenH. Effects of symmetry energy on the radius and tidal deformability of neutron stars in the relativistic mean-field model. PTEP (2020) 2020:043D01. 10.1093/ptep/ptaa016

  • CrossRef
  • Google Scholar

• 44.

  LiB-AMagnoM. Curvature-slope correlation of nuclear symmetry energy and its imprints on the crust-core transition, radius and tidal deformability of canonical neutron stars. Phys Rev C (2020) 102:045807. 10.1103/PhysRevC.102.045807

  • CrossRef
  • Google Scholar

• 45.

  LopesLL. Role of the symmetry energy slope in neutron stars: exploring the model dependency. Phys Rev C (2024) 110:015805. 10.1103/PhysRevC.110.015805

  • CrossRef
  • Google Scholar

• 46.

  LimYSchwenkA. Symmetry energy and neutron star properties constrained by chiral effective field theory calculations. Phys Rev C (2024) 109:035801. 10.1103/PhysRevC.109.035801

  • CrossRef
  • Google Scholar

• 47.

  AdhikariDAlbatainehHAndroicDAniolKArmstrongDAverettTet alAccurate determination of the neutron skin thickness of ²⁰⁸Pb through parity-violation in electron scattering. Phys Rev Lett (2021) 126:172502. 10.1103/PhysRevLett.126.172502

  • CrossRef
  • Google Scholar

• 48.

  ReedBTFattoyevFJHorowitzCJPiekarewiczJ. Implications of PREX-2 on the equation of state of neutron-rich matter. Phys Rev Lett (2021) 126:172503. 10.1103/PhysRevLett.126.172503

  • CrossRef
  • Google Scholar

• 49.

  ReinhardP-GRoca-MazaXNazarewiczW. Information content of the parity-violating asymmetry in Pb208. Phys Rev Lett (2021) 127:232501. 10.1103/PhysRevLett.127.232501

  • CrossRef
  • Google Scholar

• 50.

  AdhikariDAlbatainehHAndroicDAniolKArmstrongDAverettTet alPrecision determination of the neutral weak form factor of ⁴⁸Ca. Phys Rev Lett (2022) 129:042501. 10.1103/PhysRevLett.129.042501

  • CrossRef
  • Google Scholar

• 51.

  ZenihiroJSakaguchiHMurakamiTYosoiMYasudaYTerashimaSet alNeutron density distributions of Pb-204, Pb-206, Pb-208 deduced via proton elastic scattering at Ep=295 MeV. Phys Rev C (2010) 82:044611. 10.1103/PhysRevC.82.044611

  • CrossRef
  • Google Scholar

• 52.

  TamiiAPoltoratskaIvon Neumann-CoselPFujitaYAdachiTBertulaniCAet alComplete electric dipole response and the neutron skin in 208Pb. Phys Rev Lett (2011) 107:062502. 10.1103/PhysRevLett.107.062502

  • CrossRef
  • Google Scholar

• 53.

  CentellesMRoca-MazaXVinasXWardaM. Nuclear symmetry energy probed by neutron skin thickness of nuclei. Phys Rev Lett (2009) 102:122502. 10.1103/PhysRevLett.102.122502

  • CrossRef
  • Google Scholar

• 54.

  DutraMLourençoOAvanciniSSCarlsonBVDelfinoAMenezesDPet alRelativistic mean-field hadronic models under nuclear matter constraints. Phys Rev C (2014) 90:055203. 10.1103/PhysRevC.90.055203

  • CrossRef
  • Google Scholar

• 55.

  TrzcinskaAJastrzebskiJLubinskiPHartmannFJSchmidtRvon EgidyTet alNeutron density distributions deduced from anti-protonic atoms. Phys Rev Lett (2001) 87:082501. 10.1103/PhysRevLett.87.082501

  • CrossRef
  • Google Scholar

• 56.

  ZabariNKubisSWójcikW. Influence of the interactions of scalar mesons on the behavior of the symmetry energy. Phys Rev C (2019) 99:035209. 10.1103/PhysRevC.99.035209

  • CrossRef
  • Google Scholar

• 57.

  MiyatsuTCheounM-KSaitoK. Asymmetric nuclear matter in relativistic mean-field models with isoscalar- and isovector-meson mixing. Astrophys J (2022) 929:82. 10.3847/1538-4357/ac5f40

  • CrossRef
  • Google Scholar

• 58.

  MiyatsuTCheounM-KKimKSaitoK. Can the PREX-2 and CREX results be understood by relativistic mean-field models with the astrophysical constraints?Phys Lett B (2023) 843:138013. 10.1016/j.physletb.2023.138013

  • CrossRef
  • Google Scholar

• 59.

  LiFCaiB-JZhouYJiangW-ZChenL-W. Effects of isoscalar- and isovector-scalar meson mixing on neutron star structure. Astrophys J (2022) 929:183. 10.3847/1538-4357/ac5e2a

  • CrossRef
  • Google Scholar

• 60.

  DanielewiczPLaceyRLynchWG. Determination of the equation of state of dense matter. Science (2002) 298:1592–6. 10.1126/science.1078070

  • CrossRef
  • Google Scholar

• 61.

  FuchsC. Kaon production in heavy ion reactions at intermediate energies. Prog Part Nucl Phys (2006) 56:1–103. 10.1016/j.ppnp.2005.07.004

  • CrossRef
  • Google Scholar

• 62.

  LynchWGTsangMBZhangYDanielewiczPFamianoMLiZet alProbing the symmetry energy with heavy ions. Prog Part Nucl Phys (2009) 62:427–32. 10.1016/j.ppnp.2009.01.001

  • CrossRef
  • Google Scholar

• 63.

  OliinychenkoDSorensenAKochVMcLerranL. Sensitivity of Au+Au collisions to the symmetric nuclear matter equation of state at 2–5 nuclear saturation densities. Phys Rev C (2023) 108:034908. 10.1103/PhysRevC.108.034908

  • CrossRef
  • Google Scholar

• 64.

  CromartieHTFonsecaERansomSMDemorestPBArzoumanianZBlumerHet alRelativistic Shapiro delay measurements of an extremely massive millisecond pulsar. Nat Astron (2019) 4:72–6. 10.1038/s41550-019-0880-2

  • CrossRef
  • Google Scholar

• 65.

  FonsecaECromartieHTPennucciTTRayPSKirichenkoAYRansomSMet alRefined mass and geometric measurements of the high-mass PSR J0740+6620. Astrophys J Lett (2021) 915:L12. 10.3847/2041-8213/ac03b8

  • CrossRef
  • Google Scholar

• 66.

  RingP. Relativistic mean field theory in finite nuclei. Prog Part Nucl Phys (1996) 37:193–263. 10.1016/0146-6410(96)00054-3

  • CrossRef
  • Google Scholar

• 67.

  LalazissisGAKonigJRingP. A New parametrization for the Lagrangian density of relativistic mean field theory. Phys Rev C (1997) 55:540–3. 10.1103/PhysRevC.55.540

  • CrossRef
  • Google Scholar

• 68.

  PradhanBKChatterjeeDGandhiRSchaffner-BielichJ. Role of vector self-interaction in neutron star properties. Nucl Phys A (2023) 1030:122578. 10.1016/j.nuclphysa.2022.122578

  • CrossRef
  • Google Scholar

• 69.

  MalikTDexheimerVProvidênciaC. Astrophysics and nuclear physics informed interactions in dense matter: inclusion of PSR J0437-4715. Phys Rev D (2024) 110:043042. 10.1103/PhysRevD.110.043042

  • CrossRef
  • Google Scholar

• 70.

  Todd-RutelBGPiekarewiczJ. Neutron-Rich nuclei and neutron stars: a new accurately calibrated interaction for the study of neutron-rich matter. Phys Rev Lett (2005) 95:122501. 10.1103/PhysRevLett.95.122501

  • CrossRef
  • Google Scholar

• 71.

  MiyatsuTCheounM-KSaitoK. Equation of state for neutron stars in SU(3) flavor symmetry. Phys Rev C (2013) 88:015802. 10.1103/PhysRevC.88.015802

  • CrossRef
  • Google Scholar

• 72.

  HorowitzCJPiekarewiczJ. Neutron star structure and the neutron radius of Pb-208. Phys Rev Lett (2001) 86:5647–50. 10.1103/PhysRevLett.86.5647

  • CrossRef
  • Google Scholar

• 73.

  HaidariMMSharmaMM. Sigma-omega meson coupling and properties of nuclei and nuclear matter. Nucl Phys A (2008) 803:159–72. 10.1016/j.nuclphysa.2008.02.296

  • CrossRef
  • Google Scholar

• 74.

  SharmaMM. Scalar-vector Lagrangian without nonlinear self-interactions of bosonic fields in the relativistic mean-field theory. Phys Lett B (2008) 666:140–4. 10.1016/j.physletb.2008.07.005

  • CrossRef
  • Google Scholar

• 75.

  KubisSWójcikWCastilloDAZabariN. Relativistic mean-field model for the ultracompact low-mass neutron star HESS J1731-347. Phys Rev C (2023) 108:045803. 10.1103/PhysRevC.108.045803

  • CrossRef
  • Google Scholar

• 76.

  ChenL-WKoCMLiB-A. Isospin-dependent properties of asymmetric nuclear matter in relativistic mean-field models. Phys Rev C (2007) 76:054316. 10.1103/PhysRevC.76.054316

  • CrossRef
  • Google Scholar

• 77.

  ChenL-WCaiB-JKoCMLiB-AShenCXuJ. Higher-order effects on the incompressibility of isospin asymmetric nuclear matter. Phys Rev C (2009) 80:014322. 10.1103/PhysRevC.80.014322

  • CrossRef
  • Google Scholar

• 78.

  CzerskiPDe PaceAMolinariA. Revisiting the Hugenholtz-Van Hove theorem in nuclear matter. Phys Rev C (2002) 65:044317. 10.1103/PhysRevC.65.044317

  • CrossRef
  • Google Scholar

• 79.

  CaiB-JChenL-W. Lorentz covariant nucleon self-energy decomposition of the nuclear symmetry energy. Phys Lett B (2012) 711:104–8. 10.1016/j.physletb.2012.03.058

  • CrossRef
  • Google Scholar

• 80.

  MiyatsuTKatayamaTSaitoK. Effects of Fock term, tensor coupling and baryon structure variation on a neutron star. Phys Lett B (2012) 709:242–6. 10.1016/j.physletb.2012.02.009

  • CrossRef
  • Google Scholar

• 81.

  KatayamaTMiyatsuTSaitoK. EoS for massive neutron stars. Astrophys J Suppl (2012) 203:22. 10.1088/0067-0049/203/2/22

  • CrossRef
  • Google Scholar

• 82.

  MiyatsuTCheounM-KIshizukaCKimKSMaruyamaTSaitoK. Decomposition of nuclear symmetry energy based on Lorentz-covariant nucleon self-energies in relativistic Hartree-Fock approximation. Phys Lett B (2020) 803:135282. 10.1016/j.physletb.2020.135282

  • CrossRef
  • Google Scholar

• 83.

  KubisS. Nuclear symmetry energy and stability of matter in neutron stars. Phys Rev C (2007) 76:025801. 10.1103/PhysRevC.76.025801

  • CrossRef
  • Google Scholar

• 84.

  LattimerJMPrakashM. Neutron star observations: prognosis for equation of state constraints. Phys Rept (2007) 442:109–65. 10.1016/j.physrep.2007.02.003

  • CrossRef
  • Google Scholar

• 85.

  XuJChenL-WLiB-AMaH-R. Nuclear constraints on properties of neutron star crusts. Astrophys J (2009) 697:1549–68. 10.1088/0004-637X/697/2/1549

  • CrossRef
  • Google Scholar

• 86.

  MoustakidisCCNiksicTLalazissisGAVretenarDRingP. Constraints on the inner edge of neutron star crusts from relativistic nuclear energy density functionals. Phys Rev C (2010) 81:065803. 10.1103/PhysRevC.81.065803

  • CrossRef
  • Google Scholar

• 87.

  PsonisVPMoustakidisCCMassenSE. Nuclear symmetry energy effects on neutron stars properties. Mod Phys Lett A (2007) 22:1233–53. 10.1142/S0217732307023572

  • CrossRef
  • Google Scholar

• 88.

  KubisSWójcikWZabariN. Multilayer neutron stars with scalar mesons crossing term. Phys Rev C (2020) 102:065803. 10.1103/PhysRevC.102.065803

  • CrossRef
  • Google Scholar

• 89.

  RoutrayTRViñasXBasuDNPattnaikSPCentellesMRobledoLet alExact versus Taylor-expanded energy density in the study of the neutron star crust–core transition. J Phys G (2016) 43:105101. 10.1088/0954-3899/43/10/105101

  • CrossRef
  • Google Scholar

• 90.

  ZhangN-BLiB-AXuJ. Combined constraints on the equation of state of dense neutron-rich matter from terrestrial nuclear experiments and observations of neutron stars. Astrophys J (2018) 859:90. 10.3847/1538-4357/aac027

  • CrossRef
  • Google Scholar

• 91.

  XieW-JLiB-A. Bayesian inference of high-density nuclear symmetry energy from radii of canonical neutron stars. Astrophys J (2019) 883:174. 10.3847/1538-4357/ab3f37

  • CrossRef
  • Google Scholar

• 92.

  MiyatsuTCheounM-KKimKSaitoK. Massive neutron stars with small radii in relativistic mean-field models optimized to nuclear ground states. Preprint arXiv:2209.02861 (2022) [nucl–th]. 10.48550/arXiv.2209.02861

  • CrossRef
  • Google Scholar

• 93.

  AbbottRAbbottTDAbrahamSAcerneseFAckleyKAdamsCet alGW190814: gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object. Astrophys J Lett (2020) 896:L44. 10.3847/2041-8213/ab960f

  • CrossRef
  • Google Scholar

• 94.

  FattoyevFJHorowitzCJPiekarewiczJReedB. GW190814: impact of a 2.6 solar mass neutron star on the nucleonic equations of state. Phys Rev C (2020) 102:065805. 10.1103/PhysRevC.102.065805

  • CrossRef
  • Google Scholar

• 95.

  ReedBTFattoyevFJHorowitzCJPiekarewiczJ. Density dependence of the symmetry energy in the post–PREX-CREX era. Phys Rev C (2024) 109:035803. 10.1103/PhysRevC.109.035803

  • CrossRef
  • Google Scholar

• 96.

  ChenW-CPiekarewiczJ. Searching for isovector signatures in the neutron-rich oxygen and calcium isotopes. Phys Lett B (2015) 748:284–8. 10.1016/j.physletb.2015.07.020

  • CrossRef
  • Google Scholar

• 97.

  FattoyevFJPiekarewiczJ. Sensitivity of the moment of inertia of neutron stars to the equation of state of neutron-rich matter. Phys Rev C (2010) 82:025810. 10.1103/PhysRevC.82.025810

  • CrossRef
  • Google Scholar

• 98.

  ChenW-CPiekarewiczJ. Building relativistic mean field models for finite nuclei and neutron stars. Phys Rev C (2014) 90:044305. 10.1103/PhysRevC.90.044305

  • CrossRef
  • Google Scholar

• 99.

  SalinasMPiekarewiczJ. Bayesian refinement of covariant energy density functionals. Phys Rev C (2023) 107:045802. 10.1103/PhysRevC.107.045802

  • CrossRef
  • Google Scholar

• 100.

  SalinasMPiekarewiczJ. Building an equation of state density ladder. Symmetry (2023) 15:994. 10.3390/sym15050994

  • CrossRef
  • Google Scholar

• 101.

  KumarSKumarMKumarRDhimanSK. Implications of isoscalar and isovector scalar meson mixed interaction on nuclear and neutron star properties. Phys Rev C (2023) 108:055802. 10.1103/PhysRevC.108.055802

  • CrossRef
  • Google Scholar

• 102.

  KumarBAgrawalBKPatraSK. New relativistic effective interaction for finite nuclei, infinite nuclear matter and neutron stars. Phys Rev C (2018) 97:045806. 10.1103/PhysRevC.97.045806

  • CrossRef
  • Google Scholar

• 103.

  FattoyevFJHorowitzCJPiekarewiczJShenG. Relativistic effective interaction for nuclei, giant resonances, and neutron stars. Phys Rev C (2010) 82:055803. 10.1103/PhysRevC.82.055803

  • CrossRef
  • Google Scholar

• 104.

  LilianiNDiningrumJPSulaksonoA. Tensor and Coulomb-exchange terms in the relativistic mean-field model with δ-meson and isoscalar-isovector coupling. Phys Rev C (2021) 104:015804. 10.1103/PhysRevC.104.015804

  • CrossRef
  • Google Scholar

• 105.

  FattoyevFJPiekarewiczJ. Has a thick neutron skin in ²⁰⁸Pb been ruled out?Phys Rev Lett (2013) 111:162501. 10.1103/PhysRevLett.111.162501

  • CrossRef
  • Google Scholar

• 106.

  PiekarewiczJ. Symmetry energy constraints from giant resonances: a theoretical overview. Eur Phys J (2014) A 50:25. 10.1140/epja/i2014-14025-x

  • CrossRef
  • Google Scholar

• 107.

  BirkhanJMiorelliMBaccaSBassauerSBertulaniCHagenGet alElectric dipole polarizability of ⁴⁸Ca and implications for the neutron skin. Phys Rev Lett (2017) 118:252501. 10.1103/PhysRevLett.118.252501

  • CrossRef
  • Google Scholar

• 108.

  TarbertCMWattsDGlazierDAguarPAhrensJAnnandJet alNeutron skin of ²⁰⁸Pb from coherent pion photoproduction. Phys Rev Lett (2014) 112:242502. 10.1103/PhysRevLett.112.242502

  • CrossRef
  • Google Scholar

• 109.

  ReinhardPGRufaMMaruhnJGreinerWFriedrichJ. Nuclear ground state properties in a relativistic meson field theory. Z Phys A (1986) 323:13–25. 10.1007/bf01294551

  • CrossRef
  • Google Scholar

• 110.

  LilianiNNugrahaAMDiningrumJPSulaksonoA. Tensor and isovector–isoscalar terms of relativistic mean field model: impacts on neutron-skin thickness, charge radius, and nuclear matter. Nucl Phys A (2024) 1042:122812. 10.1016/j.nuclphysa.2023.122812

  • CrossRef
  • Google Scholar

• 111.

  De VriesHDe JagerCWDe VriesC. Nuclear charge-density-distribution parameters from elastic electron scattering. Atom Data Nucl Data Tabl (1987) 36:495–536. 10.1016/0092-640X(87)90013-1

  • CrossRef
  • Google Scholar

• 112.

  HorowitzCJPollockSJSouderPAMichaelsR. Parity violating measurements of neutron densities. Phys Rev C (2001) 63:025501. 10.1103/PhysRevC.63.025501

  • CrossRef
  • Google Scholar

• 113.

  HorowitzCJAhmedZJenCMRakhmanASouderPADaltonMMet alWeak charge form factor and radius of 208Pb through parity violation in electron scattering. Phys Rev C (2012) 85:032501. 10.1103/PhysRevC.85.032501

  • CrossRef
  • Google Scholar

• 114.

  NiksicTVretenarDFinelliPRingP. Relativistic Hartree-Bogoliubov model with density-dependent meson-nucleon couplings. Phys Rev C (2002) 66:024306. 10.1103/PhysRevC.66.024306

  • CrossRef
  • Google Scholar

• 115.

  MaY-LRhoM. Topology change, emergent symmetries and compact star matter. AAPPS Bull (2021) 31:16. 10.1007/s43673-021-00016-1

  • CrossRef
  • Google Scholar

• 116.

  LeeHKMaY-LPaengW-GRhoM. Cusp in the symmetry energy, speed of sound in neutron stars and emergent pseudo-conformal symmetry. Mod Phys Lett A (2022) 37:2230003. 10.1142/S0217732322300038

  • CrossRef
  • Google Scholar

• 117.

  ChenL-WKoCMLiB-A. Nuclear matter symmetry energy and the neutron skin thickness of heavy nuclei. Phys Rev C (2005) 72:064309. 10.1103/PhysRevC.72.064309

  • CrossRef
  • Google Scholar

• 118.

  MaruyamaTChibaS. Equation of state of neutron star matter and the isovector nucleon optical model potential. J Phys G (1999) 25:2361–9. 10.1088/0954-3899/25/12/306

  • CrossRef
  • Google Scholar

• 119.

  MaruyamaTBalantekinABCheounM-KKajinoTKusakabeMMathewsGJ. A relativistic quantum approach to neutrino and antineutrino emission via the direct Urca process in strongly magnetized neutron-star matter. Phys Lett B (2022) 824:136813. 10.1016/j.physletb.2021.136813

  • CrossRef
  • Google Scholar

• 120.

  GlendenningNK (1997) Compact stars: nuclear physics, particle physics, and general relativity

  • Google Scholar

• 121.

  MiyatsuTYamamuroSNakazatoK. A new equation of state for neutron star matter with nuclei in the crust and hyperons in the core. Astrophys J (2013) 777:4. 10.1088/0004-637X/777/1/4

  • CrossRef
  • Google Scholar

• 122.

  MiyatsuTCheounM-KSaitoK. Equation of state for neutron stars with hyperons and quarks in the relativistic Hartree–Fock approximation. Astrophys J (2015) 813:135. 10.1088/0004-637X/813/2/135

  • CrossRef
  • Google Scholar

• 123.

  TolmanRC. Static solutions of Einstein’s field equations for spheres of fluid. Phys Rev (1939) 55:364–73. 10.1103/PhysRev.55.364

  • CrossRef
  • Google Scholar

• 124.

  OppenheimerJRVolkoffGM. On massive neutron cores. Phys Rev (1939) 55:374–81. 10.1103/PhysRev.55.374

  • CrossRef
  • Google Scholar

• 125.

  SulaksonoAAlamNAgrawalBK. Core–crust transition properties of neutron stars within systematically varied extended relativistic mean-field model. Int J Mod Phys E (2014) 23:1450072. 10.1142/S0218301314500724

  • CrossRef
  • Google Scholar

• 126.

  ProvidênciaCAvanciniSSCavagnoliRChiacchieraSDucoinCGrillFet alImprint of the symmetry energy on the inner crust and strangeness content of neutron stars. Eur Phys J (2014) A 50:44. 10.1140/epja/i2014-14044-7

  • CrossRef
  • Google Scholar

• 127.

  LiB-AKrastevPGWenD-HZhangN-B. Towards understanding astrophysical effects of nuclear symmetry energy. Eur Phys J (2019) A 55:117. 10.1140/epja/i2019-12780-8

  • CrossRef
  • Google Scholar

• 128.

  HorowitzCJPiekarewiczJ. Constraining URCA cooling of neutron stars from the neutron radius of Pb-208. Phys Rev C (2002) 66:055803. 10.1103/PhysRevC.66.055803

  • CrossRef
  • Google Scholar

• 129.

  PageDGeppertUWeberF. The Cooling of compact stars. Nucl Phys A (2006) 777:497–530. 10.1016/j.nuclphysa.2005.09.019

  • CrossRef
  • Google Scholar

• 130.

  LattimerJMPrakashMPethickCJHaenselP. Direct URCA process in neutron stars. Phys Rev Lett (1991) 66:2701–4. 10.1103/PhysRevLett.66.2701

  • CrossRef
  • Google Scholar

• 131.

  RutherfordNMendesMSvenssonISchwenkAWattsALHebelerKet alConstraining the dense matter equation of state with new NICER mass–radius measurements and new chiral effective field theory inputs. Astrophys J Lett (2024) 971:L19. 10.3847/2041-8213/ad5f02

  • CrossRef
  • Google Scholar

• 132.

  ChoudhuryDSalmiTVinciguerraSRileyTEKiniYWattsALet alA NICER view of the nearest and brightest millisecond pulsar: PSR J0437–4715. Astrophys J Lett (2024) 971:L20. 10.3847/2041-8213/ad5a6f

  • CrossRef
  • Google Scholar

• 133.

  GuichonPAM. A possible quark mechanism for the saturation of nuclear matter. Phys Lett B (1988) 200:235–40. 10.1016/0370-2693(88)90762-9

  • CrossRef
  • Google Scholar

• 134.

  SaitoKThomasAW. A Quark - meson coupling model for nuclear and neutron matter. Phys Lett B (1994) 327:9–16. 10.1016/0370-2693(94)91520-2

  • CrossRef
  • Google Scholar

• 135.

  SaitoKThomasAW. The Nolen-Schiffer anomaly and isospin symmetry breaking in nuclear matter. Phys Lett B (1994) 335:17–23. 10.1016/0370-2693(94)91551-2

  • CrossRef
  • Google Scholar

• 136.

  SaitoKTsushimaKThomasAW. Nucleon and hadron structure changes in the nuclear medium and the impact on observables. Prog Part Nucl Phys (2007) 58:1–167. 10.1016/j.ppnp.2005.07.003

  • CrossRef
  • Google Scholar

• 137.

  SaitoKMiyatsuTCheounM-K. Effect of isoscalar and isovector scalar fields on baryon semileptonic decays in nuclear matter. Phys Rev D (2024) 110:113001. 10.1103/PhysRevD.110.113001

  • CrossRef
  • Google Scholar

• 138.

  NagaiSMiyatsuTSaitoKTsushimaK. Quark-meson coupling model with the cloudy bag. Phys Lett B (2008) 666:239–44. 10.1016/j.physletb.2008.07.065

  • CrossRef
  • Google Scholar

• 139.

  ChenL-WKoCMLiB-A. Determination of the stiffness of the nuclear symmetry energy from isospin diffusion. Phys Rev Lett (2005) 94:032701. 10.1103/PhysRevLett.94.032701

  • CrossRef
  • Google Scholar

• 140.

  LiB-AChenL-W. Nucleon-nucleon cross sections in neutron-rich matter and isospin transport in heavy-ion reactions at intermediate energies. Phys Rev C (2005) 72:064611. 10.1103/PhysRevC.72.064611

  • CrossRef
  • Google Scholar

• 141.

  EsteeJLynchWTsangCBarneyJJhangGTsangMet alProbing the symmetry energy with the spectral pion ratio. Phys Rev Lett (2021) 126:162701. 10.1103/PhysRevLett.126.162701

  • CrossRef
  • Google Scholar

• 142.

  LynchWGTsangMB. Decoding the density dependence of the nuclear symmetry energy. Phys Lett B (2022) 830:137098. 10.1016/j.physletb.2022.137098

  • CrossRef
  • Google Scholar

• 143.

  TsangCYTsangMBLynchWGKumarRHorowitzCJ. Determination of the equation of state from nuclear experiments and neutron star observations. Nat Astron (2024) 8:328–36. 10.1038/s41550-023-02161-z

  • CrossRef
  • Google Scholar

• 144.

  ChenL-W. Symmetry energy systematics and its high density behavior. EPJ Web Conf (2015) 88:00017. 10.1051/epjconf/20158800017

  • CrossRef
  • Google Scholar

• 145.

  LiB-ACaiB-JXieW-JZhangN-B. Progress in constraining nuclear symmetry energy using neutron star observables since GW170817. Universe (2021) 7:182. 10.3390/universe7060182

  • CrossRef
  • Google Scholar

• 146.

  NegeleJWVautherinD. Neutron star matter at subnuclear densities. Nucl Phys A (1973) 207:298–320. 10.1016/0375-9474(73)90349-7

  • CrossRef
  • Google Scholar

• 147.

  SotaniHOtaS. Neutron star mass formula with nuclear saturation parameters for asymmetric nuclear matter. Phys Rev D (2022) 106:103005. 10.1103/PhysRevD.106.103005

  • CrossRef
  • Google Scholar

• 148.

  LattimerJM. Constraints on nuclear symmetry energy parameters. Particles (2023) 6:30–56. 10.3390/particles6010003

  • CrossRef
  • Google Scholar