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Register a new userNuclear pairing from microscopic forces: singlet channels and higher-partial waves
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Background: An accurate description of nuclear pairing gaps is extremely important for understanding static and dynamic properties of the inner crusts of neutron stars and to explain their cooling process. Purpose: We plan to study the behavior of the pairing gaps $Delta_F$ as a function of the Fermi momentum $k_F$ for neutron and nuclear matter in all relevant angular momentum channels where superfluidity is believed to naturally emerge. The calculations will employ realistic chiral nucleon-nucleon potentials with the inclusion of three-body forces and self-energy effects. Methods: The superfluid states of neutron and nuclear matter are studied by solving the BCS gap equation for chiral nuclear potentials using the method suggested by Khodel et al., where the original gap equation is replaced by a coupled set of equations for the dimensionless gap function $chi(p)$ defined by $Delta(p) = Delta_F chi(p)$ and a non-linear algebraic equation for the gap magnitude $Delta_F = Delta(p_F)$ at the Fermi surface. This method is numerically stable even for small pairing gaps, such as that encountered in the coupled $^3PF_2$ partial wave. Results: We have successfully applied Khodels method to singlet ($S$) and coupled channel ($SD$ and $PF$) cases in neutron and nuclear matter. Our calculations agree with other ab-initio approaches, where available, and provide crucial inputs for future applications in superfluid systems.
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The energy- and density-dependent single-particle potential for nucleons is constructed in a medium of infinite isospin-symmetric nuclear matter starting from realistic nuclear interactions derived within the framework of chiral effective field theory. The leading-order terms from both two- and three-nucleon forces give rise to real, energy-independent contributions to the nucleon self-energy. The Hartree-Fock contribution from the two-nucleon force is attractive and strongly momentum dependent, in contrast to the contribution from the three-nucleon force which provides a nearly constant repulsive mean field that grows approximately linearly with the nuclear density. Together, the leading-order perturbative contributions yield an attractive single-particle potential that is however too weak compared to phenomenology. Second-order contributions from two- and three-body forces then provide the additional attraction required to reach the phenomenological depth. The imaginary part of the optical potential, which is positive (negative) for momenta below (above) the Fermi momentum, arises at second-order and is nearly inversion-symmetric about the Fermi surface when two-nucleon interactions alone are present. The imaginary part is strongly absorptive and requires the inclusion of an effective mass correction as well as self-consistent single-particle energies to attain qualitative agreement with phenomenology.
We study the cooling of isolated neutron stars with particular regard to the importance of nuclear pairing gaps. A microscopic nuclear equation of state derived in the Brueckner-Hartree-Fock approach is used together with compatible neutron and proton pairing gaps. We then study the effect of modifying the gaps on the final deduced neutron star mass distributions. We find that a consistent description of all current cooling data can be achieved and a reasonable neutron star mass distribution can be predicted employing the (slightly reduced by about 40%) proton 1S0 Bardeen-Cooper-Schrieffer (BCS) gaps and no neutron 3P2 pairing.
The recent direct detection of gravitational waves (GWs) from binary black hole mergers (2016, Phys. Rev. Lett. 116, no. 6, 061102; no. 24, 241103) opens up an entirely new non-electromagnetic window into the Universe making it possible to probe physics that has been hidden or dark to electromagnetic observations. In addition to cataclysmic events involving black holes, GWs can be triggered by physical processes and systems involving neutron stars. Properties of neutron stars are largely determined by the equation of state (EOS) of neutron-rich matter, which is the major ingredient in calculating the stellar structure and properties of related phenomena, such as gravitational wave emission from elliptically deformed pulsars and neutron star binaries. Although the EOS of neutron-rich matter is still rather uncertain mainly due to the poorly known density dependence of nuclear symmetry energy at high densities, significant progress has been made recently in constraining the symmetry energy using data from terrestrial nuclear laboratories. These constraints could provide useful information on the limits of GWs expected from neutron stars. Here after briefly reviewing our previous work on constraining gravitational radiation from elliptically deformed pulsars with terrestrial nuclear laboratory data in light of the recent gravitational wave detection, we estimate the maximum gravitational wave strain amplitude, using an optimistic value for the breaking strain of the neutron star crust, for 15 pulsars at distances 0.16 kpc to 0.91 kpc from Earth, and find it to be in the range of $sim[0.2-31.1]times 10^{-24}$, depending on the details of the EOS used to compute the neutron star properties. Implications are discussed.
We present microscopic valence-shell calculations of pairing gaps in the calcium isotopes, focusing on the role of three-nucleon (3N) forces and many-body processes. In most cases, we find a reduction in pairing strength when the leading chiral 3N forces are included, compared to results with low-momentum two-nucleon (NN) interactions only. This is in agreement with a recent energy density functional study. At the NN level, calculations that include particle-particle and hole-hole ladder contributions lead to smaller pairing gaps compared with experiment. When particle-hole contributions as well as the normal-ordered one- and two-body parts of 3N forces are consistently included to third order, we find reasonable agreement with experimental three-point mass differences. This highlights the important role of 3N forces and many-body processes for pairing in nuclei. Finally, we relate pairing gaps to the evolution of nuclear structure in neutron-rich calcium isotopes and study the predictions for the 2+ excitation energies, in particular for 54Ca.
A new implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the Luescher formalism is described. The method includes higher partial waves and multiple decay channels, and the fitting procedure properly includes all covariances and statistical uncertainties. The method is also simpler than previously used procedures. Formulas and software for handling total spins up to $S=2$ and orbital angular momenta up to $L=6$ are presented.
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