The short-range correlation (SRC) induced by the tensor force in the isosinglet neutron-proton interaction channel leads to a high-momentum tail (HMT) in the single-nucleon momentum distributions n(k) in nuclei. Owing to the remaining uncertainties a
bout the tensor force, the shape of the nucleon HMT may be significantly different from the dilute interacting Fermi gas model prediction $n(k) sim1/k^4$ similar to the HMT in cold atoms near the unitary limit. Within an isospin- and momentum-dependent Boltzmann-Uehling-Uhlenbeck transport model incorporating approximately the nucleon HMT, we investigate hard photon emissions in $^{14}$N+$^{12}$C and $^{48}$Ca+$^{124}$Sn reactions at beam energies around the Fermi energy. Imprints of different shapes of the HMT on the energy spectrum, angular distribution and transverse momentum spectrum of hard photons are studied. While the angular distribution does not carry any information about the shape of the nucleon HMT, the energy spectra and especially the mid-rapidity transverse momentum spectra of hard photons are found to bare strong imprints of the shapes of nucleon HMTs in the two colliding nuclei.
By directly inverting several neutron star observables in the three-dimensional parameter space for the Equation of State of super-dense neutron-rich nuclear matter, we show that the lower radius limit for PSR J0740+6620 of mass $2.08pm 0.07~M_{odot}
$ from Neutron Star Interior Composition Explorer (NICER)s very recent observation sets a much tighter lower boundary than previously known for nuclear symmetry energy in the density range of $(1.0sim 3.0)$ times the saturation density $rho_0$ of nuclear matter. The super-soft symmetry energy leading to the formation of proton polarons in this density region of neutron stars is clearly disfavoured by the first radius measurement for the most massive neutron star observed reliably so far.
New observational data of neutron stars since GW170817 have helped improve our knowledge about nuclear symmetry energy especially at high densities. We have learned particularly: (1) The slope parameter $L$ of nuclear symmetry energy at saturation de
nsity $rho_0$ of nuclear matter from 24 new analyses is about $Lapprox 57.7pm 19$ MeV at 68% confidence level consistent with its fiducial value, (2) The curvature $K_{rm{sym}}$ from 16 new analyses is about $K_{rm{sym}}approx -107pm 88$ MeV, (3) The magnitude of nuclear symmetry energy at $2rho_0$, i.e. $E_{rm{sym}}(2rho_0)approx 51pm 13$ MeV at 68% confidence level, has been extracted from 9 new analyses of neutron star observables consistent with results from earlier analyses of heavy-ion reactions and the latest predictions of the state-of-the-art nuclear many-body theories, (4) while the available data from canonical neutron stars do not provide tight constraints on nuclear symmetry energy at densities above about $2rho_0$, the lower radius boundary $R_{2.01}=12.2$ km from NICERs very recent observation of PSR J0740+6620 of mass $2.08pm 0.07$ $M_{odot}$ and radius $R=12.2-16.3$ km at 68% confidence level sets a tight lower limit for nuclear symmetry energy at densities above $2rho_0$, (5) Bayesian inferences of nuclear symmetry energy using models encapsulating a first-order hadron-quark phase transition from observables of canonical neutron stars indicate that the phase transition shift appreciably both the $L$ and $K_{rm{sym}}$ to higher values but with larger uncertaintie , (6) The high-density behavior of nuclear symmetry energy affects significantly the minimum frequency necessary to rotationally support GW190814s secondary component of mass (2.50-2.67) $M_{odot}$ as the fastest and most massive pulsar discovered so far.
Nuclear symmetry energy $E_{rm{sym}}(rho)$ at density $rho$ is normally expanded or simply parameterized as a function of $chi=(rho-rho_0)/3rho_0$ in the form of $E_{rm{sym}}(rho)approx S+Lchi+2^{-1}K_{rm{sym}}chi^2+6^{-1}J_{rm{sym}}chi^3+cdots$ usin
g its magnitude $S$, slope $L $, curvature $K_{rm{sym}}$ and skewness $J_{rm{sym}}$ at the saturation density $rho_0$ of nuclear matter. Much progress has been made in recent years in constraining especially the $S$ and $L$ parameters using various terrestrial experiments and astrophysical observations. However, such kind of expansions/parameterizations do not converge at supra-saturation densities where $chi$ is not small enough, hindering an accurate determination of high-density $E_{rm{sym}}(rho)$ even if its characteristic parameters at $rho_0$ are all well determined by experiments/observations. By expanding the $E_{rm{sym}}(rho)$ in terms of a properly chosen auxiliary function $Pi_{rm{sym}}(chi,Theta_{rm{sym}})$ with a parameter $Theta_{rm{sym}}$ fixed accurately by an experimental $E_{rm{sym}}(rho_{rm{r}})$ value at a reference density $rho_{rm{r}}$, we show that the shortcomings of the $chi$-expansion can be completely removed or significantly reduced in determining the high-density behavior of $E_{rm{sym}}(rho)$. In particular, using two significantly different auxiliary functions, we show that the new approach effectively incorporates higher $chi$-order contributions and converges to the same $E_{rm{sym}}(rho)$ much faster than the conventional $chi$-expansion at densities $lesssim3rho_0$. Several quantitative demonstrations using Monte Carlo simulations are given.
Both the incompressibility Ka of a finite nucleus of mass A and that ($K_{infty}$) of infinite nuclear matter are fundamentally important for many critical issues in nuclear physics and astrophysics. While some consensus has been reached about the $K
_{infty}$, accurate theoretical predictions and experimental extractions of $K_{tau}$ characterizing the isospin dependence of Ka have been very difficult. We propose a differential approach to extract the Kt and Ki independently from the Ka data of any two nuclei in a given isotope chain. Applying this new method to the Ka data from isoscalar giant monopole resonances (ISGMR) in even-even Pb, Sn, Cd and Ca isotopes taken by U. Garg {it et al.} at the Research Center for Nuclear Physics (RCNP), Osaka University, Japan, we find that the $^{106}$Cd-$^{116}$Cd and $^{112}$Sn-$^{124}$Sn pairs having the largest differences in isospin asymmetries in their respective isotope chains measured so far provide consistently the most accurate up-to-date Kt value of $K_{tau}=-616pm 59$ MeV and $K_{tau}=-623pm 86$ MeV, respectively, largely independent of the remaining uncertainties of the surface and Coulomb terms in expanding the $K_{rm A}$, while the $K_{infty}$ values extracted from different isotopes chains are all well within the current uncertainty range of the community consensus for $K_{infty}$. Moreover, the size and origin of the Soft Sn Puzzle is studied with respect to the Stiff Pb Phenomenon. It is found that the latter is favored due to a much larger (by $sim 380$ MeV) Kt for Pb isotopes than for Sn isotopes, while the Ki from analyzing the Ka data of Sn isotopes is only about 5 MeV less than that from analyzing the Pb data.
Nuclear clusters or voids in the inner crust of neutron stars were predicted to have various shapes collectively nicknamed nuclear pasta. The recent review in Ref. cite{Lopez1} by Lopez, Dorso and Frank summarized their systematic investigations into
properties especially the morphological and thermodynamical phase transitions of the nuclear pasta within a Classical Molecular Dynamics model, providing further stimuli to find more observational evidences of the predicted nuclear pasta in neutron stars.
[Purpose:] We infer the posterior probability distribution functions (PDFs) and correlations of nine parameters characterizing the EOS of dense neutron-rich matter encapsulating a first-order hadron-quark phase transition from the radius data of cano
nical NSs reported by LIGO/VIRGO, NICER and Chandra Collaborations. We also infer the quark matter (QM) mass fraction and its radius in a 1.4 M$_{odot}$ NS and predict their values in more massive NSs. [Method:] Meta-modelings are used to generate both hadronic and QM EOSs in the Markov-Chain Monte Carlo sampling process within the Bayesian statistical framework. An explicitly isospin-dependent parametric EOS for the $npemu$ matter in NSs at $beta$ equilibrium is connected through the Maxwell construction to the QM EOS described by the constant speed of sound (CSS) model of Alford, Han and Prakash. [Results:] (1) The most probable values of the hadron-quark transition density $rho_t/rho_0$ and the relative energy density jump there $Deep/ep_t$ are $rho_t/rho_0=1.6^{+1.2}_{-0.4}$ and $Deep/ep_t=0.4^{+0.20}_{-0.15}$ at 68% confidence level, respectively. The corresponding probability distribution of QM fraction in a 1.4 M$_{odot}$ NS peaks around 0.9 in a 10 km sphere. Strongly correlated to the PDFs of $rho_t$ and $Deep/ep_t$, the PDF of the QM speed of sound squared $cQMsq/c^2$ peaks at $0.95^{+0.05}_{-0.35}$, and the total probability of being less than 1/3 is very small. (2) The correlations between PDFs of hadronic and QM EOS parameters are very weak. [Conclusions:] The available astrophysical data considered together with all known EOS constraints from theories and terrestrial nuclear experiments prefer the formation of a large volume of QM even in canonical NSs.
Background: The nuclear symmetry energy $E_{sym}(rho)$ encodes information about the energy necessary to make nuclear systems more neutron-rich. While its slope parameter L at the saturation density $rho_0$ of nuclear matter has been relatively well
constrained by recent astrophysical observations and terrestrial nuclear experiments, its curvature $K_{rm{sym}}$ characterizing the $E_{sym}(rho)$ around $2rho_0$ remains largely unconstrained. Over 520 calculations for $E_{sym}(rho)$ using various nuclear theories and interactions in the literature have predicted several significantly different $K_{rm{sym}}-L$ correlations. Purpose: If a unique $K_{rm{sym}}-L$ correlation of $E_{sym}(rho)$ can be firmly established, it will enable us to progressively better constrain the high-density behavior of $E_{sym}(rho)$ using the available constraints on its slope parameter L. We investigate if and by how much the different $K_{rm{sym}}-L$ correlations may affect neutron star observables. Method: A meta-model of nuclear Equation of States (EOSs) with three representative $K_{rm{sym}}-L$ correlation functions is used to generate multiple EOSs for neutron stars. We then examine effects of the $K_{rm{sym}}-L$ correlation on the crust-core transition density and pressure as well as the radius and tidal deformation of canonical neutron stars. Results:The $K_{rm{sym}}-L$ correlation affects significantly both the crust-core transition density and pressure. It also has strong imprints on the radius and tidal deformability of canonical neutron stars especially at small L values. The available data from LIGO/VIRGO and NICER set some useful limits for the slope L but can not distinguish the three representative $K_{rm{sym}}-L$ correlations considered.
Using Stergioulass RNS code for investigating fast pulsars with Equation of States (EOSs) on the causality surface (where the speed of sound equals that of light) of the high-density EOS parameter space satisfying all known constraints from both nucl
ear physics and astrophysics, we show that one possible explanation for the GW190814s secondary component of mass $(2.50-2.67)$ M$_{odot}$ is that it is a super-fast pulsar spinning faster than 971 Hz about 42% below its Kepler frequency. If confirmed, it would be the fastest pulsar with the highest mass observed presently. There is a large and physically allowed EOS parameter space below the causality surface where pulsars heavier than 2.50 M$_{odot}$ are supported if they can rotate even faster with critical frequencies depending strongly on the high-density behavior of nuclear symmetry energy.
Using an explicitly isospin-dependent parametric Equation of State (EOS) for the core of neutron stars (NSs) within the Bayesian statistical approach, we infer the EOS parameters of super-dense neutron-rich nuclear matter from three sets of imagined
mass-radius correlation data representing typical predictions by various nuclear many-body theories, i.e, the radius stays the same, decreases or increases with increasing NS mass within $pm 15%$ between 1.4 M$_{odot}$ and 2.0 M$_{odot}$. The corresponding average density increases quickly, slowly or slightly decreases as the NS mass increases from 1.4 M$_{odot}$ to 2.0 M$_{odot}$. Using the posterior probability distribution functions (PDFs) of EOS parameters inferred from GW170817 and NICER radius data for canonical NSs as references, we investigate how future radius measurements of massive NS will improve our knowledge about the EOS of super-dense neutron-rich nuclear matter, especially its symmetry energy term, compared to what people have already learned from analyzing the GW170817 and NICER data. While the EOS of symmetric nuclear matter (SNM) inferred from the three data sets are approximately the same, the corresponding high-density symmetry energies at densities above about $2rho_0$ are very different, indicating that the radii of massive NSs carry reliable information about the high-density behavior of nuclear symmetry energy with little influence from the remaining uncertainties of the SNM EOS.
