Pion Condensation In Nuclear Matter Research Articles

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.

Hole-hole contact interaction in the t-J model.

Using an analytical variational approach we calculate the hole-hole contact interaction on the N\'{e}el background. Solution of the Bethe-Salpeter equation with this interaction gives bound states in $d$- and p-waves with binding energies close to those obtained by numerical methods. At $t/J \ge 2-3$ the bound state disappears. In conclusion we discuss the relation between short range and long range interactions and analogy with the problem of pion condensation in nuclear matter.

Application of the functional integration method to the theory of pion condensation in nuclear matter

The possibility of applying the functional integration method to the description of pion condensation in nuclear matter is examined. A perturbation theory for the thermodynamical potential with respect to the meson field is constructed, which describes the fluctuations of the condensate.

Possible Charged Pion Condensation in Neutron Matter with Small Proton Admixture

Since Migdal!) and Sawyer-Scalapino ) pointed out the possibility of pion condensation in nuclear matter, it has intensively studied not only on the pionic instability but also on the structure of pion condensed state. ) Possible spin, isospin and space structures of pion condensate were also considered in detail in both pure neutron matter and isosymmetric nuclear matter. 3 ).4) In a realistic neutron star. there exists an admixture of protons, equilibrating with electrons. These protons give rise to the characteristic pion condensate, so-called Jr, +-condensate, above some critical density. Its possibility has originally been suggested by Migdal, Markin and Mishustin in pure neutron matter though much qualitative as follows: even in pure neutron matter (Z = 0) there exists the energy branch of sound (w~+)<o) with the same quantum number as the positive pion. Iw~+)1 increases as the nucleon density P (=Pn, the neutron density in the case) to lead to overcome the neutron Fermi energy, that is w~+) +EW)=O. Then there occurs the instability of Jr, + in a sense of the Landau 2nd order phase transition. More rigorous statements will be done later. The critical density is estimated as Pc(Jr,+)/Po~O.4, where po is the normal density (Po' 0.5*»). The purpose of this paper is to study the Jr, +-condensate in a realistic iso-asymmetric nuclear matter (N;p.Z*O). In the case, the *) We take the natural unit as h= c= m~=l. critical density of this mode is considered to be the lowest as compared with the other kind of pion condensates. *) The energy gain of the system, the structure of the nucleon system and the relation with the so-called Jr±pair condensation leading from the instability of spontaneous production of Jr, +-sound excitation and Jr--pion one are the main subjects. On the transition mechanism from Jr, +-condensate to Jr±-pair one, it has been pointed oue) that the instability corresponding to Jr±-pair condensation does not arise, if the existence of Jr. +-condensate is taken into account. And the transition from Jr, +-condens ate to Jr±-pair one was suggested ) in the system with Z*O. On this subject we consider in detail. In order to get the qualitative understandings, we take only p-wave Jr-N interaction. First, we consider the behavior of the total energy of the system near the critical point in terms of the Landau formalism. The effective Hamiltonian is given as

The quasiparticle interaction, a shield of nuclear matter against pion condensation

A microscopic calculation is presented for the quasiparticle interaction in nuclear matter. As a starting point a Brueckener G-matrix is used, which is derived from realistic potentials (Reid soft core, HM2Δ). Keeping the full complexity of this interaction, the excitation modes for the different spin-isospin channels are evaluated. The effects of isobar excitation [Δ(3, 3)] are also taken into account. The exchange of the corresponding phonons is added to the bare G-matrix and the influence of this so-called crossed channel renormalization on the interaction of quasiparticles at the Fermi surface is discussed. This renormalization of the particle-hole interaction increases drastically the critical density for pion condensation in nuclear matter.

Axial Currents in Nuclei: The Gamow-Teller Matrix Element

We propose that the quenching of Gamow-Teller matrix elements in light nuclei can be effectively described by a mechanism that governs the $p$-wave pion-nucleus scattering. This may be providing a solution to the long-standing problem. The resulting Landau-Migdal parameter ${g}^{\ensuremath{'}}$ turns out to be quite consistent with the values extracted from the spectra of pionlike excitations and places a stringent constraint on pion condensation in nuclear matter.

Role of the effective nucleon mass for pion condensation in nuclear matter

The dependence of the threshold for pion condensation in symmetric nuclear matter on the effective nucleon mass M ∗ is investigated, using extrapolations of M ∗(ϱ) to high densities ϱ, based on boson exchange mechanisms. It is found that if M ∗(ϱ) decreases below the standard value M ∗=0.8M as the density increases beyond the nuclear matter density ϱ 0, the critical density is raised considerably beyond ϱ 0 once short-range repulsive correlations are included.

Death to pion condensates in nuclear matter

We first note that if the coupling of spin-, isospin-modes in nuclei to pions were of anywhere near the strength required to produce pion condensation in nuclear matter, then there would be strong effects in nuclear spectra, which are not seen. We then work through a model proposed by Migdal [1] and show that addition of a strong short-range repulsion in the nucleon-nuclear interaction modifies the effective interaction in such a way as to remove the main spin-isospin interaction which originally gave rise to the pion condensate. We believe that short-range repulsion also strongly modify the work of Sawyer and Scalapino [2], but have not yet shown that they destroy the condensate in neutron stars. Our conclusion is that the off-shell p-wave attraction of pions and nucleons lies, at least in the region of low momenta, completely in the domain of the Δ-isobars. Effects from these would be incapable of producing pion condensates, except at high densities, equal to several times normal nuclear density.