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Register a new userLow-density homogeneous symmetric nuclear matter: disclosing dinucleons in coexisting phases
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The effect of in-medium dinucleon bound states on self-consistent single-particle fields in Brueckner, Bethe and Goldstone theory is investigated in symmetric nuclear matter at zero temperature. To this end, dinucleon bound state occurences in the $^1S_0$ and ${}^3SD_1$ channels are explicitly accounted for -within the continuous choice for the auxiliary fields- while imposing self-consistency in Brueckner-Hartree-Fock approximation calculations. Searches are carried out at Fermi momenta in the range $0<k_Fleq1.75$~fm$^{-1}$, using the Argonne $v_{18}$ bare nucleon-nucleon potential without resorting to the effective mass approximation. As a result, two distinct solutions meeting the self-consistency requirement are found with overlapping domains in the interval $0.130;textrm{fm}^{-1} leq k_F leq 0.285;textrm{fm}^{-1}$, corresponding to mass densities between $10^{11.4}$ and $10^{12.4}$ g cm$^{-3}$. Effective masses as high as three times the nucleon mass are found in the coexistence domain. The emergence of superfluidity in relationship with BCS pairing gap solutions is discussed.
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We study the equation of state of symmetric nuclear matter at zero temperature over a wide range of densities using two complementary theoretical approaches. At low densities up to twice nuclear saturation density, we compute the energy per particle based on modern nucleon-nucleon and three-nucleon interactions derived within chiral effective field theory. For higher densities we derive for the first time constraints in a Fierz-complete setting directly based on quantum chromodynamics using functional renormalization group techniques. We find remarkable consistency of the results obtained from both approaches as they come together in density and the natural emergence of a maximum in the speed of sound $c_S$ at supranuclear densities with a value beyond the asymptotic $c_S^2 = 1/3$. The presence of a maximum appears tightly connected to the formation of a diquark gap.
We study the equation of state for symmetric nuclear matter using a ring-diagram approach in which the particle-particle hole-hole ($pphh$) ring diagrams within a momentum model space of decimation scale $Lambda$ are summed to all orders. The calculation is carried out using the renormalized low-momentum nucleon-nucleon (NN) interaction $V_{low-k}$, which is obtained from a bare NN potential by integrating out the high-momentum components beyond $Lambda$. The bare NN potentials of CD-Bonn, Nijmegen and Idaho have been employed. The choice of $Lambda$ and its influence on the single particle spectrum are discussed. Ring-diagram correlations at intermediate momenta ($ksimeq$ 2 fm$^{-1}$) are found to be particularly important for nuclear saturation, suggesting the necessity of using a sufficiently large decimation scale so that the above momentum region is not integrated out. Using $V_{low-k}$ with $Lambda sim 3$ fm$^{-1}$, we perform a ring-diagram computation with the above potentials, which all yield saturation energies $E/A$ and Fermi momenta $k_F^{(0)}$ considerably larger than the empirical values. On the other hand, similar computations with the medium-dependent Brown-Rho scaled NN potentials give satisfactory results of $E/A simeq -15$ MeV and $k_F^{(0)}simeq 1.4$ fm$^{-1}$. The effect of this medium dependence is well reproduced by an empirical 3-body force of the Skyrme type.
The phase diagram of isospin-asymmetrical nuclear matter may feature a number of unconventional phases, which include the translationally and rotationally symmetric, but isospin-asymmetrical BCS condensate, the current-carrying Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase, and the heterogeneous phase-separated phase. Because the Cooper pairs of the condensate carry a single unit of charge, these phases are charged superconductors and respond to electromagnetic gauge fields by either forming domains (type-I superconductivity) or quantum vortices (type-II superconductivity). We evaluate the Ginzburg-Landau (GL) parameter across the phase diagram and find that the unconventional phases of isospin-asymmetrical nuclear matter are good type-II superconductors and should form Abrikosov vortices with twice the quantum of magnetic flux. We also find that the LOFF phase at the boundary of the transition to the type-I state, with the GL parameter being close to the critical value $1/sqrt{2}$.
Changes in the meson-nucleon coupling constant and the vertex form factor in nuclear matter are studied in a modified Skyrme Lagrangian including the sigma-meson field that satisfies the scale invariance. Renormalization of the axial-vector coupling constant, and the nucleon mass are studied in a consistent model. The results are consistent with the empirical evidence. A calculation of pi N commutator, sigma-term, indicates that the medium changes its magnitude considerably.
Yields of equatorially emitted light isotopes, $1le Zle 14$, observed in ternary fission in the reaction $^{241}$Pu($n_{rm th}$,f) are employed to determine apparent chemical equilibrium constants for low-temperature and low-density nuclear matter. The degree of liberation and role of medium modifications are probed through a comparison of experimentally derived reaction quotients with equilibrium constants calculated using a relativistic mean-field model employing a universal medium modification correction for the attractive $sigma$ meson coupling. The results of these comparisons indicate that equilibrium is achieved for the lighter ternary fission isotopes. For the heavier isotopes experimental reaction quotients are well below calculated equilibrium constants. This is attributed to a dynamical limitation reflecting insufficient time for full equilibrium to develop. The role of medium effects leading to yield reductions is discussed as is the apparent enhancement of yields for $^8$He and other very neutron rich exotic nuclei.
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