Condensate In Nuclear Matter Research Articles

ϕ meson properties in nuclear matter from QCD sum rules with chirally separated four-quark condensates

The modification of the $\ensuremath{\phi}$ meson spectrum in nuclear matter is studied in an updated QCD sum rule analysis, taking into account recent improvements in properly treating the chiral invariant and breaking components of four-quark condensates. Allowing both mass and decay width to change at finite density, the QCD sum rule analysis determines certain combinations of changes for these parameters that satisfy the sum rules equally well. A comprehensive error analysis, including uncertainties related to the behavior of various condensates at linear order in density, the employed renormalization scale and perturbative corrections of the Wilson coefficients, is used to compute the allowed ranges of these parameter combinations. We find that the $\ensuremath{\phi}$ meson mass shift in nuclear matter is especially sensitive to the strange sigma term ${\ensuremath{\sigma}}_{sN}$, which determines the decrease of the strange quark condensate in nuclear matter. Specifically, we obtain a linear relation between the width ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\phi}}$ and mass shift $\mathrm{\ensuremath{\Delta}}{m}_{\ensuremath{\phi}}$ given as ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\phi}}=a\mathrm{\ensuremath{\Delta}}{m}_{\ensuremath{\phi}}+b{\ensuremath{\sigma}}_{sN}+c$ with $a=({3.947}_{\ensuremath{-}0.130}^{+0.139})$, $b=({0.936}_{\ensuremath{-}0.177}^{+0.180})$ and $c=\ensuremath{-}({7.707}_{\ensuremath{-}5.679}^{+4.791})\text{ }\text{ }\mathrm{MeV}$.

Extraction of the Landau-Migdal Parameter from the Gamow-Teller Giant Resonance in ^{132}Sn.

The key parameter to discuss the possibility of the pion condensation in nuclear matter, i.e., the so-called Landau-Migdal parameter g^{'}, was extracted by measuring the double-differential cross sections for the (p,n) reaction at 216 MeV/u on a neutron-rich doubly magic unstable nucleus, ^{132}Sn with the quality comparable to data taken with stable nuclei. The extracted strengths for Gamow-Teller (GT) transitions from ^{132}Sn leading to ^{132}Sb exhibit the GT giant resonance (GTR) at the excitation energy of 16.3±0.4(stat)±0.4(syst) MeV with the width of Γ=4.7±0.8 MeV. The integrated GT strength up to E_{x}=25 MeV is S_{GT}^{-}=53±5(stat)_{-10}^{+11}(syst), corresponding to 56% of Ikeda's sum rule of 3(N-Z)=96. The present result accurately constrains the Landau-Migdal parameter as g^{'}=0.68±0.07, thanks to the high sensitivity of the GTR energy to g^{'}. In combination with previous studies on the GTR for ^{90}Zr and ^{208}Pb, the result of this work shows the constancy of this parameter in the nuclear chart region with (N-Z)/A=0.11 to 0.24 and A=90 to 208.

Mass shift of charmonium states in [formula omitted] collision

The masses of the low lying charmonium states, namely, the J/Ψ, Ψ(3686), and Ψ(3770) are shifted downwards due to the second order Stark effect. In p¯+Au collisions at 6–10 GeV we study their in-medium propagation. The time evolution of the spectral functions of these charmonium states is studied with a Boltzmann–Uehling–Uhlenbeck (BUU) type transport model. We show that their in-medium mass shift can be observed in the dilepton spectrum. Therefore, by observing the dileptonic decay channel of these low lying charmonium states, especially for Ψ(3686), we can gain information about the magnitude of the gluon condensate in nuclear matter. This measurement could be performed at the upcoming PANDA experiment at FAIR.

Phi meson spectral moments and QCD condensates in nuclear matter

A detailed analysis of the lowest two moments of the ϕ meson spectral function in vacuum and nuclear matter is performed. The consistency is examined between the constraints derived from finite energy QCD sum rules and the spectra computed within an improved vector dominance model, incorporating the coupling of kaonic degrees of freedom with the bare ϕ meson. In the vacuum, recent accurate measurements of the e+e−→K+K− cross section allow us to determine the spectral function with high precision. In nuclear matter, the modification of the spectral function can be described by the interactions of the kaons from ϕ→KK‾ with the surrounding nuclear medium. This leads primarily to a strong broadening and an asymmetric deformation of the ϕ meson peak structure. We confirm that, both in vacuum and nuclear matter, the zeroth and first moments of the corresponding spectral functions satisfy the requirements of the finite energy sum rules to a remarkable degree of accuracy. Limits on the strangeness sigma term of the nucleon are examined in this context. Applying our results to the second moment of the spectrum, we furthermore discuss constraints on four-quark condensates and the validity of the commonly used ground state saturation approximation.

Theory for Quartet Condensation in Fermi Systems with Applications to Nuclear Matter

α clustering and α condensation in lighter nuclei is presently strongly and increasingly discussed in the literature both from the experimental side as from the theoretical one. In proto-neutron stars a macroscopic condensate of α particles may occur. A discussion of the present status of the theory' for quartet condensation in general and for α particle condensation in nuclear matter in particular will be presented.

Antiferrosmectic ground state of two-component dipolar Fermi gases: An analog of meson condensation in nuclear matter

We show that an antiferrosmectic-$C$ phase has lower energy at high densities than the nonmagnetized Fermi gas and ferronematic phases in an ultracold gas of fermionic atoms, or molecules, with large magnetic dipole moments. This phase, which is analogous to meson condensation in dense nuclear matter, is a one-dimensional periodic structure in which the fermions localize in layers with their pseudospin direction aligned parallel to the layers and staggered layer by layer.

Chiral condensate in nuclear matter beyond linear density using chiral Ward identity

We discuss density corrections of the chiral condensate up to a NLO order us- ing the chiral Ward identity and an in-medium chiral perturbation theory. The in-medium chiral condensate is calculated by a correlation function of the axial current and pseu- doscalar density in the nuclear matter as a consequence of the chiral Ward identity. The correlation function is evaluated using the chiral perturbation theory with the hadronic quantities of pion-nucleon dynamics. We assume that the in-vacuum interaction vertices are known, which means that the in-vacuum loop corrections are renormalized to the tree chiral couplings by taking the values of the couplings in chiral Lagrangian as the physical values. We focus on density order in the physical quantities in our perturbative calcula- tion. This study shows that the medium effects to the chiral condensate beyond the linear density come from density corrections to theN sigma term. It implies that calculating the density dependence of the chiral condensate in nuclear matter is essentially equivalent to describe nuclear matter in chiral effective theory.

Many body approach to quartet condensation in nuclear matter

A self-consistent theory for quartet condensation in homogeneous infinite nuclear matter is proposed. It goes along similar lines as Gorkov theory for pairing. However, details and physical consequences are very different. For example in the quartet case no sharp quasi-particle pole develops in the single particle propagator. Also quartet condensation only exists in the BEC phase and no extended coherence length develops in weak coupling. The critical temperature for quartet condensation is also investigated in analogy to the Thouless criterion for pairing.

Quasiparticle light elements and quantum condensates in nuclear matter

Nuclei in dense matter are influenced by the medium. In the cluster mean field approximation, an effective Schrodinger equation for the A-particle cluster is obtained accounting for the effects of the surrounding medium, such as self-energy and Pauli blocking. Similar to the single-baryon states (free neutrons and protons), the light elements (2 ≤ A ≤ 4, internal quantum state ν) are treated as quasiparticles with energies EA,ν(P; T, nn, np) that depend on the center of mass momentum P⃗, the temperature T, and the total densities nn, np of neutrons and protons, respectively. We consider the composition and thermodynamic properties of nuclear matter at low densities. At low temperatures, quartetting is expected to occur. Consequences for different physical properties of nuclear matter and finite nuclei are discussed.

Non-Abelian behavior ofαbosons in cold symmetric nuclear matter

The ground-state energy of infinite symmetric nuclear matter is usually described by strongly interacting nucleons obeying the Pauli exclusion principle. We can imagine a unitary transformation which groups four nonidentical nucleons (i.e., with different spin and isospin) close in coordinate space. Those nucleons, being nonidentical, do not obey the Pauli principle, thus their relative momenta are negligibly small (just to fulfill the Heisenberg principle). Such a cluster can be identified with an $\ensuremath{\alpha}$ boson. But in dense nuclear matter, those $\ensuremath{\alpha}$ particles still obey the Pauli principle since are constituted of fermions. The ground state energy of nuclear matter $\ensuremath{\alpha}$ clusters is the same as for nucleons, thus it is degenerate. We could think of $\ensuremath{\alpha}$ particles as vortices which can now braid, for instance making $^{8}\mathrm{Be}$ which leave the ground state energy unchanged. Further braiding to heavier clusters ($^{12}\mathrm{C}$, $^{16}\mathrm{O}$$,\dots{}$) could give a different representation of the ground state at no energy cost. In contrast $d$-like clusters (i.e., $N=Z$ odd-odd nuclei, where $N$ and $Z$ are the neutron and proton number, respectively) cannot describe the ground state of nuclear matter and can be formed at high excitation energies (or temperatures) only. We show that even-even, $N=Z$, clusters could be classified as non-Abelian states of matter. As a consequence an $\ensuremath{\alpha}$ condensate in nuclear matter might be hindered by the Fermi motion, while it could be possible a condensate of $^{8}\mathrm{Be}$ or heavier clusters.

CRITICAL TEMPERATURE FOR α-CONDENSATION IN ASYMMETRIC NUCLEAR MATTER: THE ASTROPHYSICAL CONTEXT

The critical temperature for α-particle condensation in nuclear matter with Fermi surface imbalance between protons and neutrons is determined. The in-medium four-body Schrödinger equation, generalizing the Thouless criterion of the BCS transition, is applied using a Hartree-Fock wave function for the quartet projected onto zero total momentum in matter with different chemical potentials for protons and neutrons.

Pseudoscalar Mesons in Nuclei and Partial Restoration of Chiral Symmetry

Recent theoretical developments of hadrons in nuclei are briefly reviewed in the aspect of chiral symmetry in nuclei. We show a general sum rule connecting in-medium hadronic quantities and quark condensate, emphasizing that both pionic mode and particle-hole excitations in the nuclear medium are responsible for reduction of the chiral condensate in nuclear matter. We also discuss that few-body nuclear systems with kaons are good objects to investigate basic features of kaon-nucleus interactions, showing recent understandings of the structure of Lambda(1405) and possible bound states of KbarNN and KKbarN. We also mention eta mesonic nuclei in connection with chiral symmetry of baryons.

Critical temperature forα-particle condensation in asymmetric nuclear matter

The critical temperature for $\ensuremath{\alpha}$-particle condensation in nuclear matter with Fermi surface imbalance between protons and neutrons is determined. The in-medium four-body Schr\"odinger equation, generalizing the Thouless criterion of the BCS transition, is applied using a Hartree-Fock wave function for the quartet projected onto zero total momentum in matter with different chemical potentials for protons and neutrons.

Critical temperature of antikaon condensation in nuclear matter

We investigate the critical temperature of Bose-Einstein condensation of ${K}^{\ensuremath{-}}$ mesons in neutron star matter. This is studied within the framework of relativistic field theoretical models at finite temperature where nucleon-nucleon and (anti)kaon-nucleon interactions are mediated by the exchange of mesons. The melting of the antikaon condensate is studied for different values of antikaon optical potential depths. We find that the critical temperature of antikaon condensation increases with baryon number density. Further it is noted that the critical temperature is lowered as antikaon optical potential becomes less attractive. We also construct the phase diagram of neutron star matter with ${K}^{\ensuremath{-}}$ condensate.

Quantum condensates in nuclear matter

Nonrelativistic nuclear matter is considered as a special example of a many-particle system. Quantum statistical methods are applied to treat the formation and dissolution of bound states in dense matter. The formation of quantum condensates is investigated. Special aspects are the transition from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) pairing as well as the occurrence of quartetting. Consequences for the structure of nuclei are compared with experimental data. Exercises to illustrate the main features of in-medium effects in nuclear matter are given.

Density-induced suppression of the α-particle condensate in nuclear matter and the structure of α-cluster states in nuclei

At low densities, with decreasing temperatures, in symmetric nuclear matter \ensuremath{\alpha} particles are formed, which eventually give raise to a quantum condensate with four-nucleon \ensuremath{\alpha}-like correlations (quartetting). Starting with a model of \ensuremath{\alpha} matter, where undistorted \ensuremath{\alpha} particles interact via an effective interaction such as the Ali-Bodmer potential, the suppression of the condensate fraction at zero temperature with increasing density is considered. Using a Jastrow-Feenberg approach, it is found that the condensate fraction vanishes near saturation density. Additionally, the modification of the internal state of the \ensuremath{\alpha} particle due to medium effects will further reduce the condensate. In finite systems, an enhancement of the $S$-state wave function of the center-of-mass orbital of \ensuremath{\alpha}-particle motion is considered as the correspondence to the condensate. Wave functions have been constructed for self-conjugate $4n$ nuclei that describe the condensate state but are fully antisymmetrized on the nucleonic level. These condensate-like cluster wave functions have been successfully applied to describe properties of low-density states near the $n\ensuremath{\alpha}$ threshold. Comparison with orthogonality condition model calculations in $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ shows strong enhancement of the occupation of the $S$-state center-of-mass orbital of the \ensuremath{\alpha} particles. This enhancement is decreasing if the baryon density increases, similar to the density-induced suppression of the condensate fraction in \ensuremath{\alpha} matter. The ground states of $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ show no enhancement at all, thus a quartetting condensate cannot be formed at saturation densities.

Nucleon sigma term and quark condensate in nuclear matter

We study the bound nucleon sigma term and the quark condensate in nuclear matter. In the quark-meson coupling (QMC) model the nuclear correction to the sigma term is small and negative, i.e., it decelerates the decrease of the quark condensate in nuclear matter. However, the quark condensate in nuclear matter is controlled primarily by the scalar-isoscalar $\sigma$ field. Compared to the leading term, it moderates the decrease more than that of the nuclear sigma term alone at densities around and larger than the normal nuclear matter density.

Quartetting in Fermionic Matter and Alpha-Particle Condensation in Nuclear Systems

Quantum condensates in nuclear matter are treated beyond the mean-field approximation, with the inclusion of cluster formation. The occurrence of a separate binding pole in the four-particle propagator in nuclear matter is investigated with respect to the formation of a condensate of α-like particles (quartetting), which is dependent on temperature and density. Due to Pauli blocking, the formation of an α-like condensate is limited to the low-density region. Consequences for finite nuclei are considered. In particular, excitations of self-conjugate 2n-Z–2n-N nuclei near the n-α-breakup threshold are candidates for quartetting. We review some results and discuss their consequences. Exploratory calculations are performed for the density dependence of the α condensate fraction at zero temperature to address the suppression of the four-particle condensate below nuclear-matter density.

Gluon condensation and deconfinement critical density in nuclear matter

An upper limit to the critical density for the transition to the deconfined phase, at zero temperature, has been evaluated by analyzing the behavior of the gluon condensate in nuclear matter. Due to the non-linear baryon density effects, the upper limit to the critical density, ρ c turns out about nine times the saturation density, ρ 0 for the value of the gluon condensate in vacuum 〈 ( α s / π ) G 2 〉 = 0.012 GeV 4 . For neutron matter ρ c ≃ 8.5 ρ 0 . The dependence of the critical density on the value of the gluon condensate in vacuum is studied.

Quark condensates in nuclear matter in the global color symmetry model of QCD

With the global color symmetry model being extended to finite chemical potential, we study the density dependence of the local and nonlocal scalar quark condensates in nuclear matter. The calculated results indicate that the quark condensates increase smoothly with the increasing of nuclear matter density before the critical value (about 12$\rho_0$) is reached. It also manifests that the chiral symmetry is restored suddenly as the density of nuclear matter reaches its critical value. Meanwhile, the nonlocal quark condensate in nuclear matter changes nonmonotonously against the space-time distance among the quarks.