New articles on Nuclear Theory

[1] 2306.04036

Five-body calculation of $s$-wave $n$-$^4$He scattering at next-to-leading order pionless effective field theory

We present the first five-body calculations of $s$-wave $n$-$^4$He scattering within leading order and next-to-leading order (NLO) pionless effective field theory. Using an harmonic oscillator trap technique and pionless effective field theory fitted to just six well-established experimental parameters, we predict the $s$-wave $n$-$^4$He phase shifts, scattering length $a^{1/2}_{n ^4\text{He}}(\text{NLO})=2.47(4\ \text{num.})~(17\ \text{theor.})~{\rm fm}$, and effective range $r^{1/2}_{n ^4\text{He}}(\text{NLO})=1.384(3\ \text{num.})~(211\ \text{theor.})~{\rm fm}$ in agreement with experiment. The apparent cutoff independence of our results is used to estimate the theoretical errors coming as an integral part of our final results.

[2] 2306.04171

Nuclear mass predictions based on deep neural network and finite-range droplet model (2012)

A neural network with two hidden layers is developed for nuclear mass prediction, based on the finite-range droplet model (FRDM12). Different hyperparameters, including the number of hidden units, the choice of activation functions, the initializers, and the learning rates, are adjusted explicitly and systematically. The resulting mass predictions are achieved by averaging the predictions given by several different sets of hyperparameters with different regularizers and seed numbers. It can provide us not only the average values of mass predictions but also reliable estimations in the mass prediction uncertainties. The overall root-mean-square deviations of nuclear mass have been reduced from $0.603$ MeV for the FRDM12 model to $0.200$ MeV and $0.232$ MeV for the training set and validation set, respectively.

[3] 2306.04304

Momentum Shell in Quarkyonic Matter from Explicit Duality: A Solvable Model Analysis

We present a model of Quarkyonic matter that is explicitly dual between quarks and baryons. The baryon number and energy densities are expressed as functionals of either the baryon momentum distribution, $f_{\rm B}$, or the quark distribution, $f_{\rm Q}$, which are subject to the constraints on fermions, $0 \le f_{\rm B,Q} \le 1$. The theory is ideal in the sense that the confinement of quarks into baryons is reflected in the duality relation between $f_{\rm Q}$ and $f_{\rm B}$, while other possible interactions among quarks and baryons are all neglected. The variational problem with the duality constraints is formulated and we explicitly construct analytic solutions, finding two distinct regimes: A nuclear matter regime at low density and a Quarkyonic regime at high density. In the Quarkyonic regime, baryons underoccupy states at low momenta but form a momentum shell with $f_{\rm B}=1$ on top of a quark Fermi sea. Such a theory describes a rapid transition from a soft nuclear equation of state to a stiff Quarkyonic equation of state. At this transition, there is a rapid increase in the sound speed.

[4] 2306.04472

The magnetic dual chiral density wave phase in a rotating quark matter

The effect of rotation on the formation of the magnetic dual chiral density wave (MDCDW) in a dense and magnetized quark matter is studied. This phase is supposed to exist in the extreme conditions prevailing, e.g., in neutron star cores. These conditions are, apart from high densities and strong magnetic fields, a relatively large angular velocity. To answer the question of whether the rotation enhances or suppresses the formation of this phase, we first determine the effect of rotation on the energy dispersion relation of a fermionic system in the presence of a constant magnetic field, and then focus on the thermodynamic potential of the model at zero temperature and finite chemical potential. The thermodynamic potential consists, in particular, of an anomalous part leading to certain topological effects. We show that in comparison with the nonrotating case, a term proportional to the angular velocity appears in this anomalous potential. We then solve the corresponding gap equations to the chiral and spatial modulation condensates, and study the dependence of these dynamical variables on the chemical potential ($\mu$), magnetic field ($eB$), and angular velocity ($\Omega$). It turns out that the interplay between these parameters suppresses the formation of the MDCDW phase in relevant regimes for neutron stars. This is interpreted as the manifestation of the inverse magnetorotational catalysis, which is also reflected in the phase portraits $eB$-$\mu$, $eB$-$\Omega R$, and $\mu$-$\Omega R$, explored in this work.

[5] 2306.04500

Structure Factors for Hot Neutron Matter from Ab Initio Lattice Simulations with High-Fidelity Chiral Interactions

We present the first ab initio lattice calculations of spin and density correlations in hot neutron matter using high-fidelity interactions at next-to-next-to-next-to-leading order (N3LO) in chiral effective field theory. These correlations have a large impact on neutrino heating and shock revival in core-collapse supernovae and are encapsulated in functions called structure factors. Unfortunately, calculations of structure factors using high-fidelity chiral interactions were well out of reach using existing computational methods. In this work, we solve the problem using a computational approach called the rank-one operator (RO) method. The RO method is a general technique with broad applications to simulations of fermionic many-body systems. It uses the fact that the determinant of a matrix composed of rank-one operators is at most linear in each operator coefficient. Using the RO method, we compute the vector and axial static structure factors for hot neutron matter as a function of temperature and density. The ab initio lattice results are in good agreement with virial expansion calculations at low densities and can be used to calibrate random phase approximation codes commonly used to estimate many-body effects on the neutrino opacity in core-collapse supernovae.

[6] 2306.04478

Coupled-channel influence on the $a_0(1700/1800)$ line shape

Based on the assumption that the $a_0(1700/1800)$ meson is a state similar to the four-quark state from the MIT bag, belonging to either the $\underline{9}^*$ or the $\underline{36}^*$ $q^2\bar q^2$ multiplet, we analyze the influence of the strong $a_0(1700/1800)$ coupling to the vector channels $K^*\bar K^*$, $\rho\phi$, and $\rho \omega$ on its line shape in the decay channels into pseudoscalar mesons $K\bar K$, $\pi\eta$, and $\pi\eta'$. This effect depends on the location of the resonance mass $m_{a_0}$ relative to the nominal thresholds of vector channels. For example, if $m_{a_0}\approx 1700$ MeV, then the influence turns out to be hidden in a fairly wide range of coupling constants. In any case, to confirm the presence of the strong $a_0(1700/1800)$ coupling to vector channels, the direct detection of the decays $a_0(1700/1800)\to K^*\bar K^*$, $\rho\phi$, $\rho\omega$ is required. The appearance of even certain hints of the existence of these decays would make it possible to fundamentally advance in understanding the nature of the new $a_0$ state.

[7] 2306.04517

Binding energies of ground and isomeric states in neutron-rich Ru isotopes: measurements at JYFLTRAP and comparison to theory

We report on precision mass measurements of $^{113,115,117}$Ru performed with the JYFLTRAP double Penning trap mass spectrometer at the Accelerator Laboratory of University of Jyv\"askyl\"a. The phase-imaging ion-cyclotron-resonance technique was used to resolve the ground and isomeric states in $^{113,115}$Ru and enabled for the first time a measurement of the isomer excitation energies, $E_x(^{113}$Ru$^{m})=100.4(9)$ keV and $E_x(^{115}$Ru$^{m})=129(5)$ keV. The ground state of $^{117}$Ru was measured using the time-of-flight ion-cyclotron-resonance technique. The new mass-excess value for $^{117}$Ru is around 37 keV lower and 7 times more precise than the previous literature value. With the more precise ground-state mass values, the evolution of the two-neutron shell-gap energies is further constrained and a similar trend as predicted by the BSkG1 model is obtained up to the neutron number $N=71$.

[8] 2306.04626

Constraining nuclear parameters using f-modes from glitching pulsars

Gravitational waves (GW) emanating from unstable quasi-normal modes in Neutron Stars (NS) could be accessible with the improved sensitivity of the present gravitational wave (GW) detectors or with the next-generation GW detectors and therefore employed to study the NS interior. By taking into account potential GW candidates detectable by A+ and Einstein Telescope (ET) originating from f-modes excited by glitches in isolated pulsars, we demonstrate the inverse problem of NS asteroseismology in a Bayesian formalism to constrain the nuclear parameters within a relativistic mean field (RMF) description of NS interior. We find that for a single detected GW event from the Vela pulsar in A+ and ET, with the considered RMF model, the nucleon effective mass ($m^*$) can be restricted (within $90\%$ credible interval) within $10\%$ and $5\%$, respectively. With the considered RMF model, the incompressibility ($K$) and the slope of the symmetry energy ($L$) are only loosely constrained. With a single observed event in A+ and ET, the f-mode frequency of a $1.4M_{\odot}$ ($f_{1.4M_{\odot}}$) inside a 90\% symmetric credible interval (SCI) can be confined to 100 Hz and 50 Hz, respectively. Additionally, we consider multiple GW candidates in our analysis. For detecting multiple (ten) events with A+ and ET, $m^*$ can be constrained to $3\%$ and $2\%$, respectively. All the other nuclear saturation parameters get well constrained. In particular, $K$ and $L$ can be constrained within $10\%$ and $20\%$ (< $90\%$ SCI), respectively. Within the 90\% SCI, $f_{1.4M_{\odot}}$ can be estimated within 50 Hz and 20 Hz in A+ and ET, respectively. Uncertainty of other NS properties such as radius of a $1.4M_{\odot}$ ($R_{1.4M_{\odot}}$), f-mode damping time of a $1.4M_{\odot}$ ($\tau_{1.4M_{\odot}}$) and few equations of state (EOS) properties including squared speed of sound ($c_s^2$) are also estimated.