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 Schr\"odinger 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 ($2 \le A \le 4$, internal quantum state $\nu$) are treated as quasiparticles with energies $E_{A,\nu}(P; T, n_n,n_p)$ that depend on the center of mass momentum $\vec P$, the temperature $T$, and the total densities $n_n,n_p$ 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.Comment: 5 pages, 1 figure, 2 table

The Nucleon Spectral Function at Finite Temperature and the Onset of Superfluidity in Nuclear Matter

Nucleon selfenergies and spectral functions are calculated at the saturation density of symmetric nuclear matter at finite temperatures. In particular, the behaviour of these quantities at temperatures above and close to the critical temperature for the superfluid phase transition in nuclear matter is discussed. It is shown how the singularity in the thermodynamic T-matrix at the critical temperature for superfluidity (Thouless criterion) reflects in the selfenergy and correspondingly in the spectral function. The real part of the on-shell selfenergy (optical potential) shows an anomalous behaviour for momenta near the Fermi momentum and temperatures close to the critical temperature related to the pairing singularity in the imaginary part. For comparison the selfenergy derived from the K-matrix of Brueckner theory is also calculated. It is found, that there is no pairing singularity in the imaginary part of the selfenergy in this case, which is due to the neglect of hole-hole scattering in the K-matrix. From the selfenergy the spectral function and the occupation numbers for finite temperatures are calculated.Comment: LaTex, 23 pages, 21 PostScript figures included (uuencoded), uses prc.sty, aps.sty, revtex.sty, psfig.sty (last included

Critical Enhancement of the In-medium Nucleon-Nucleon Cross Section at low Temperatures

The in-medium nucleon-nucleon cross section is calculated starting from the thermodynamic T-matrix at finite temperatures. The corresponding Bethe-Salpeter-equation is solved using a separable representation of the Paris nucleon-nucleon-potential. The energy-dependent in-medium N-N cross section at a given density shows a strong temperature dependence. Especially at low temperatures and low total momenta, the in-medium cross section is strongly modified by in-medium effects. In particular, with decreasing temperature an enhancement near the Fermi energy is observed. This enhancement can be discussed as a precursor of the superfluid phase transition in nuclear matter.Comment: 10 pages with 4 figures (available on request from the authors), MPG-VT-UR 34/94 accepted for publication in Phys. Rev.

Spontaneous breaking of rotational symmetry in superconductors

We show that homogeneous superconductors with broken spin/isospin symmetry lower their energy via a transition to a novel superconducting state where the Fermi-surfaces are deformed to a quasi-ellipsoidal form at zero total momentum of Cooper pairs. In this state, the gain in the condensation energy of the pairs dominates over the loss in the kinetic energy caused by the lowest order (quadrupole) deformation of Fermi-surfaces from the spherically symmetric form. There are two energy minima in general, corresponding to the deformations of the Fermi-spheres into either prolate or oblate forms. The phase transition from spherically symmetric state to the superconducting state with broken rotational symmetry is of the first order.Comment: 5 pages, including 3 figures, published versio

Pairing properties of nucleonic matter employing dressed nucleons

A survey of pairing properties of nucleonic matter is presented that includes the off-shell propagation associated with short-range and tensor correlations. For this purpose, the gap equation has been solved in its most general form employing the complete energy and momentum dependence of the normal self-energy contributions. The latter correlations include the self-consistent calculation of the nucleon self-energy that is generated by the summation of ladder diagrams. This treatment preserves the conservation of particle number unlike approaches in which the self-energy is based on the Brueckner-Hartree-Fock approximation. A huge reduction in the strength as well as temperature and density range of ${}^3S_1$-${}^3D_1$ pairing is obtained for nuclear matter as compared to the standard BCS treatment. Similar dramatic results pertain to ${}^1S_0$ pairing of neutrons in neutron matter.Comment: 15 pages, 10 figure

Spatially inhomogeneous condensate in asymmetric nuclear matter

We study the isospin singlet pairing in asymmetric nuclear matter with nonzero total momentum of the condensate Cooper pairs. The quasiparticle excitation spectrum is fourfold split compared to the usual BCS spectrum of the symmetric, homogeneous matter. A twofold splitting of the spectrum into separate branches is due to the finite momentum of the condensate, the isospin asymmetry, or the finite quasiparticle lifetime. The coupling of the isospin singlet and triplet paired states leads to further twofold splitting of each of these branches. We solve the gap equation numerically in the isospin singlet channel in the case where the pairing in the isospin triplet channel is neglected and find nontrivial solutions with finite total momentum of the pairs. The corresponding phase assumes a periodic spatial structure which carries a isospin density wave at constant total number of particles. The phase transition from the BCS to the inhomogeneous superconducting phase is found to be first order and occurs when the density asymmetry is increased above 0.25. The transition from the inhomogeneous superconducting to the unpaired normal state is second order. The maximal values of the critical total momentum (in units of the Fermi momentum) and the critical density asymmetry at which condensate disappears are $P_c/p_F = 0.3$ and $\alpha_c = 0.41$. The possible spatial forms of the ground state of the inhomogeneous superconducting phase are briefly discussed.Comment: 13 pages, including 3 figues, uses RevTeX; minor corrections, PRC in pres

A Self-Consistent Solution to the Nuclear Many-Body Problem at Finite Temperature

The properties of symmetric nuclear matter are investigated within the Green's functions approach. We have implemented an iterative procedure allowing for a self-consistent evaluation of the single-particle and two-particle propagators. The in-medium scattering equation is solved for a realistic (non-separable) nucleon-nucleon interaction including both particle-particle and hole-hole propagation. The corresponding two-particle propagator is constructed explicitely from the single-particle spectral functions. Results are obtained for finite temperatures and an extrapolation to T=0 is presented.Comment: 11 pages 5 figure

Corrections to Tribimaximal Mixing from Nondegenerate Phases

We propose a seesaw scenario that possible corrections to the tribimaximal pattern of lepton mixing are due to the small phase splitting of the right-handed neutrino mass matrix. we show that the small deviations can be expressed analytically in terms of two splitting parameters($\delta_1$ and $\delta_2$) in the leading order. The solar mixing angle $\theta_{12}$ favors a relatively smaller value compared to zero order value ($35.3^\circ$), and the Dirac type CP phase $\delta$ chooses a nearly maximal one. The two Majorana type CP phases $\rho$ and $\sigma$ turn out to be a nearly linear dependence. Also a normal hierarchy neutrino mass spectrum is favored due to the stability of perturbation calculations.Comment: 19 pages 6 figures, Accepted by Mod. Phy. Lett.

Four-particle condensate in strongly coupled fermion systems

Four-particle correlations in fermion systems at finite temperatures are investigated with special attention to the formation of a condensate. Instead of the instability of the normal state with respect to the onset of pairing described by the Gorkov equation, a new equation is obtained which describes the onset of quartetting. Within a model calculation for symmetric nuclear matter, we find that below a critical density, the four-particle condensation (alpha-like quartetting) is favored over deuteron condensation (triplet pairing). This pairing-quartetting competition is expected to be a general feature of interacting fermion systems, such as the excition-biexciton system in excited semiconductors. Possible experimental consequences are pointed out.Comment: LaTeX, 11 pages, 2 figures, uses psfig.sty (included), to be published in Phys. Rev. Lett., tentatively scheduled for 13 April 1998 (Volume 80, Number 15