Low-momentum interactions with Brown-Rho-Ericson scalings and the density dependence of the nuclear symmetry energy

We have calculated the nuclear symmetry energy $E_{sym}(\rho)$ up to densities of $4 \sim 5 \rho_0$ with the effects from the Brown-Rho (BR) and Ericson scalings for the in-medium mesons included. Using the $V_{low-k}$ low-momentum interaction with and without such scalings, the equations of state (EOS) of symmetric and asymmetric nuclear matter have been calculated using a ring-diagarm formalism where the particle-particle-hole-hole ring diagrams are included to all orders. The EOS for symmetric nuclear matter and neutron matter obtained with linear BR scaling are both overly stiff compared with the empirical constraints of Danielewicz {\it et al.} \cite{daniel02}. In contrast, satisfactory results are obtained by either using the nonlinear Ericson scaling or by adding a Skyrme-type three-nucleon force (TNF) to the unscaled $V_{low-k}$ interaction. Our results for $E_{sym}(\rho)$ obtained with the nonlinear Ericson scaling are in good agreement with the empirical values of Tsang {\it et al.} \cite{tsang09} and Li {\it et al.} \cite{li05}, while those with TNF are slightly below these values. For densities below the nuclear saturation density $\rho_0$, the results of the above calculations are nearly equivalent to each other and all in satisfactory agreement with the empirical values.Comment: 7 pages, 6 figure

Shell model description of the 14C dating beta decay with Brown-Rho-scaled NN interactions

We present shell model calculations for the beta-decay of the 14C ground state to the 14N ground state, treating the states of the A=14 multiplet as two 0p holes in an 16O core. We employ low-momentum nucleon-nucleon (NN) interactions derived from the realistic Bonn-B potential and find that the Gamow-Teller matrix element is too large to describe the known lifetime. By using a modified version of this potential that incorporates the effects of Brown-Rho scaling medium modifications, we find that the GT matrix element vanishes for a nuclear density around 85% that of nuclear matter. We find that the splitting between the (J,T)=(1+,0) and (J,T)=(0+,1) states in 14N is improved using the medium-modified Bonn-B potential and that the transition strengths from excited states of 14C to the 14N ground state are compatible with recent experiments.Comment: 4 pages, 5 figures Updated to include referee comments/suggestion

Neutron star, β\beta-stable ring-diagram equation of state and Brown-Rho scaling

Neutron star properties, such as its mass, radius, and moment of inertia, are calculated by solving the Tolman-Oppenheimer-Volkov (TOV) equations using the ring-diagram equation of state (EOS) obtained from realistic low-momentum NN interactions $V_{low-k}$. Several NN potentials (CDBonn, Nijmegen, Argonne V18 and BonnA) have been employed to calculate the ring-diagram EOS where the particle-particle hole-hole ring diagrams are summed to all orders. The proton fractions for different radial regions of a $\beta$-stable neutron star are determined from the chemical potential conditions $\mu_n-\mu_p = \mu_e = \mu_\mu$. The neutron star masses, radii and moments of inertia given by the above potentials all tend to be too small compared with the accepted values. Our results are largely improved with the inclusion of medium corrections based on Brown-Rho scaling where the in-medium meson masses, particularly those of $\omega$, $\rho$ and $\sigma$, are slightly decreased compared with their in-vacuum values. Representative results using such medium corrected interactions are neutron star mass $M\sim 1.8 M_{\odot}$, radius $R\sim 9$ km and moment of inertia $\sim 60 M_{\odot}km^2$. The mass-radius trajectories given by the above four realistic NN potentials are by and large overlapping.Comment: 12.7 pages, 13 figures, 3 table

Half-Skyrmions and the Equation of State for Compact-Star Matter

The half-skyrmions that appear in dense baryonic matter when skyrmions are put on crystals modify drastically hadron properties in dense medium and affect strongly the nuclear tensor forces, thereby influencing the equation of state (EoS) of dense nuclear and asymmetric nuclear matter. The matter comprised of half skyrmions has vanishing quark condensate but non-vanishing pion decay constant and could be interpreted as a hadronic dual of strong-coupled quark matter. We infer from this observation combined with certain predictions of hidden local symmetry in low-energy hadronic interactionsa a set of new scaling laws -- called "new-BR" -- for the parameters in nuclear effective field theory controlled by renormalization-group flow. They are subjected to the EoS of symmetric and asymmetric nuclear matter, and are then applied to nuclear symmetry energies and properties of compact stars. The changeover from the skyrmion matter to a half-skyrmion matter that takes place after the cross-over density $n_{1/2}$ provides a simple and natural field theoretic explanation for the change of the EoS from soft to stiff at a density above that of nuclear matter required for compact stars as massive as $\sim 2.4M_\odot$. Cross-over density in the range 1.5n_0 \lsim n_{1/2} \lsim 2.0 n_0 has been employed, and the possible skyrmion half-skyrmion coexistence {or cross-over} near $n_{1/2}$ is discussed. The novel structure of {the tensor forces and} the EoS obtained with the new-BR scaling is relevant for neutron-rich nuclei and compact star matter and could be studied in RIB (rare isotope beam) machines.Comment: 12 pages, 7 figures, slightly revised for PRC, in pres

Unitarity potentials and neutron matter at the unitary limit

We study the equation of state of neutron matter using a family of unitarity potentials all of which are constructed to have infinite $^1S_0$ scattering lengths $a_s$. For such system, a quantity of much interest is the ratio $\xi=E_0/E_0^{free}$ where $E_0$ is the true ground-state energy of the system, and $E_0^{free}$ is that for the non-interacting system. In the limit of $a_s\to \pm \infty$, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely $\xi\sim 0.44(1)$. In the present work we calculate this ratio $\xi$ using a family of hard-core square-well potentials whose $a_s$ can be exactly obtained, thus enabling us to have many potentials of different ranges and strengths, all with infinite $a_s$. We have also calculated $\xi$ using a unitarity CDBonn potential obtained by slightly scaling its meson parameters. The ratios $\xi$ given by these different unitarity potentials are all close to each other and also remarkably close to 0.44, suggesting that the above ratio $\xi$ is indifferent to the details of the underlying interactions as long as they have infinite scattering length. A sum-rule and scaling constraint for the renormalized low-momentum interaction in neutron matter at the unitary limit is discussed.Comment: 7.5 pages, 7 figure

Matrix Elements and Few-Body Calculations within the Unitary Correlation Operator Method

We employ the Unitary Correlation Operator Method (UCOM) to construct correlated, low-momentum matrix elements of realistic nucleon-nucleon interactions. The dominant short-range central and tensor correlations induced by the interaction are included explicitly by an unitary transformation. Using correlated momentum-space matrix elements of the Argonne V18 potential, we show that the unitary transformation eliminates the strong off-diagonal contributions caused by the short-range repulsion and the tensor interaction, and leaves a correlated interaction dominated by low-momentum contributions. We use correlated harmonic oscillator matrix elements as input for no-core shell model calculations for few-nucleon systems. Compared to the bare interaction, the convergence properties are dramatically improved. The bulk of the binding energy can already be obtained in very small model spaces or even with a single Slater determinant. Residual long-range correlations, not treated explicitly by the unitary transformation, can easily be described in model spaces of moderate size allowing for fast convergence. By varying the range of the tensor correlator we are able to map out the Tjon line and can in turn constrain the optimal correlator ranges.Comment: 16 pages, 9 figures, using REVTEX

A nonlinear approach to NN interactions using self-interacting meson fields

Motivated by the success of models based on chiral symmetry in NN interactions we investigate self-interacting scalar, pseudoscalar and vector meson fields and their impact for NN forces. We parametrize the corresponding nonlinear field equations and get analytic wavelike solutions. A probability amplitude for the propagation of particle states is calculated and applied in the framework of a boson-exchange NN potential. Using a proper normalization of the meson fields makes all self-scattering amplitudes finite. The same normalization is able to substitute for the phenomenological form factors used in conventional boson exchange potentials and thus yields an phenomenological understanding of this part of the NN interaction. We find an empirical scaling law which relates the meson self-interaction couplings to the pion mass and self-interaction coupling constant. Our model yields np phase shifts comparable to the Bonn B potential results and deuteron properties, in excellent agreement with experimental data.Comment: Reviewed version, 25 pages REVTeX, more info at http://i04ktha.desy.d

Taming the Pion Cloud of the Nucleon

We present a light-front determination of the pionic contribution to the nucleon self-energy, $\Sigma_\pi$, to second-order in pion-baryon coupling constants that allows the pion-nucleon vertex function to be treated in a model-independent manner constrained by experiment. The pion mass $\mu$ dependence of $\Sigma_\pi$ is consistent with chiral perturbation theory results for small values of $\mu$ and is also linearly dependent on $\mu$ for larger values, in accord with the results of lattice QCD calculations. The derivative of $\Sigma_\pi$ with respect to $\mu^2$ yields the dominant contribution to the pion content, which is consistent with the $\bar{d}-\bar{u}$ difference observed experimentally in the violation of the Gottfried sum rule.Comment: 11 pages, 3 figure

Nucleon Resonances with Hidden Charm in Coupled-Channel Models

The model dependence of the predictions of nucleon resonances with hidden charm is investigated. We consider several coupled-channel models which are derived from relativistic quantum field theory by using (1) a unitary transformation method, and (2) the three-dimensional reductions of Bethe-Salpeter Equation. With the same vector meson exchange mechanism, we find that all models give very narrow molecular-like nucleon resonances with hidden charm in the mass range of 4.3 GeV $< M_R <$ 4.5 GeV, in consistent with the previous predictions.Comment: 17 pages, 3 figure