Theory Of Nuclear Matter Research Articles

Effective interaction for 40Ca(p,p') at Ep=318 MeV.

Differential cross sections and analyzing powers have been measured for the excitation by 318 MeV protons of states of $^{40}\mathrm{Ca}$ below 7.2 MeV. The data for those normal-parity excitations for which transition densities are available from electroexcitation measurements are analyzed in terms of medium modifications to the nucleon-nucleon interaction. We find that the empirical effective interaction previously fitted to $^{16}\mathrm{O}$(p,p') data at the same energy predicts $^{40}\mathrm{Ca}$(p,p') very well. Density-dependent modifications of the effective interaction fitted to data for $^{40}\mathrm{Ca}$ or $^{16}\mathrm{O}$, either independently or simultaneously, are virtually identical. The density dependence of the empirical interaction is considerably stronger than that of interactions based upon nonrelativistic nuclear matter theory and persists to lower density. The most significant differences are that the empirical interaction has a stronger repulsive core and that absorption is enhanced at high density, contrary to expectations based upon Pauli blocking. We also find substantial suppression of the spin-orbit interaction at low density and enhancement at high density. Nevertheless, the independence of the effective interaction from the target supports the concept of local nuclear matter density. We also find that optical potentials based upon the empirical effective interaction are very similar to Schr\"odinger-equivalent potentials based upon a relativistic impulse approximation model, suggesting that the empirical density dependence is similar to the equivalent density dependence that arises from elimination of lower components from Dirac wave functions. Finally, the results are compared with global optical potentials from Dirac phenomenology.

Skyrme-Landau particle-particle interaction and application to 18O and 18F

Patterned after Landau's Fermi-liquid theory of nuclear matter, we develop an extension of the theory for finite nuclei. Since the particle-hole interaction V ph derived from the Skyrme-Landau HF ground state is antisymmetric and the exchange term of the phonon-induced interaction is added to V ph when the renormalization of the HF single-particles due to the particle-phonon coupling is included, the total effective particle-particle interaction is anti-symmetric. We use the newly developed Skyrme-Landau interaction SL1 to evaluate the particle-particle matrix elements in the s-, d-shells. Except for a few cases, the results agree well with those calculated from the G-matrix and those from the empirical study. The spectra of 18O and 18F are predicted which indicate that except for the 5 + state of 18F, the results are similar to those obtained from the Kuo-Brown G-matrix. These results represent great improvement from predictions of the other Skyrme-type interactions which are plagued with either the anti-pairing effect or the lack of anti-symmetry in the particle-particle matrix elements.

Scalar coupling in relativistic mean field theory and properties of nuclei and nuclear matter

We have considered various types of scalar couplings in relativistic mean-field theory, including the derivative scalar coupling proposed recently, and study the influence of these couplings on the properties of infinite nuclear matter and of finite nuclei. In addition, a comparison is made with the properties of the non-relativistic Skyrme interaction. The effective mass at saturation is found to play an important role in influencing all the properties of infinite nuclear matter and finite nuclei in the relativistic mean-field theory.

Covariant Feynman rules at finite temperature: Application to nuclear matter.

A unified treatment of relativistic many-body systems at finite temperature and density, incorporating both real- and imaginary-time formalisms, is applied to hadronic field theories of nuclear matter (quantum hadrodynamics). Covariant Feynman rules are given, which permit direct calculations in any convenient reference frame or in manifestly covariant form. The real-time rules are illustrated by the derivation of covariant expressions for the one-loop energy-momentum tensor. Next, the partition function is evaluated at one-loop order, which yields the thermodynamic potential and pressure in covariant form and verifies the virial theorem. Finally, covariant imaginary-time rules are shown to reproduce the real-time one-loop calculations.

Effective interactions and nuclear structure using 180 MeV protons. I. 16O(p,p').

Differential cross sections and analyzing powers for scattering of 180 MeV protons by $^{16}\mathrm{O}$ have been measured for all narrow states below 12.1 MeV of excitation. Medium modifications to the effective interaction for normal-parity isoscalar transitions were studied using transition densities determined by electron scattering to minimize nuclear structure uncertainties. An empirical effective interaction, guided by nuclear matter theory, was fitted to inelastic scattering data for six states simultaneously. Distorted waves were generated from self-consistent optical potentials computed from the same effective interaction. The isoscalar effective interaction determined by this procedure provides a good global fit to the inelastic scattering data and is consistent with elastic scattering data that were not included in the fit. The results are consistent with earlier results for 135 MeV and show that the effective interaction is suppressed at low density but is less density dependent than predicted by nuclear matter theory and the local density approximation. These comparisons suggest effects in finite nuclei beyond the local density approximation. Finally, we compare data for ${0}^{\mathrm{\ensuremath{-}}}$ and ${2}^{\mathrm{\ensuremath{-}}}$ states at both 135 and 180 MeV with representative calculations.

Effective interactions and nuclear structure using 180 MeV protons. II. 28Si(p,p').

Differential cross sections and analyzing powers for the scattering of 180 MeV protons have been measured for 14 states of $^{28}\mathrm{Si}$ for momentum transfers between about 0.4 and 2.1 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. Medium modifications to the effective interaction for normal-parity isoscalar transitions were studied using transition densities fitted to electroexcitation data to minimize uncertainties due to nuclear structure. An empirical effective interaction, guided by nuclear matter theory, was fitted to inelastic scattering data for five states of $^{28}\mathrm{Si}$ using self-consistent distorted waves. A good fit to the inelastic scattering data was achieved with an interaction similar to previous results for $^{16}\mathrm{O}$. The elastic data, which were not fitted, are also described well. In addition, we tested for mass dependence in the empirical effective interaction by repeating the analysis using data for both $^{16}\mathrm{O}$ and $^{28}\mathrm{Si}$ simultaneously. This global analysis produced an interaction intermediate between the two independent results without compromising the fit to either data set. Therefore, the effective interaction in finite nuclei appears to depend strongly upon local density but only weakly upon target.

Effect of isobar on nucleus-nucleus potential

An effective nucleon-nucleon interaction is constructed from the extended Reid soft-core potential using the lowest order Brueckner theory of nuclear matter with the continuous choice of the single particle spectrum. A nucleus-nucleus potential is derived from the effective two-nucleon interaction using the energy-density formalism. The effect of the Delta (1236) isobar on the effective interaction and the nucleus-nucleus potential is studied. It is observed that with the inclusion of the Delta -isobar the nucleus-nucleus potential gets diluted which is quite prominent in the high-density overlap region.

Empirical effective interaction for 135 MeV nucleons

A model for medium modifications to the two-nucleon effective interaction, based upon the results of nuclear matter theory, is proposed for the analysis of proton inelastic scattering to normal-parity isoscalar states of self-conjugate nuclei. An empirical effective interaction is fitted to cross section and analyzing power data for the excitation by 135 MeV protons of six states of $^{16}\mathrm{O}$ simultaneously. Transition densities determined by electron scattering minimize uncertainties due to nuclear structure. Distorted waves are generated from the self-consistent optical potential computed from the same effective interaction, corrected for rearrangement effects. We find that a unique effective interaction provides a good global fit to all inelastic scattering data and is consistent with data for elastic scattering, which were not included in the fit. The density dependence of the empirical interaction is similar to, but somewhat smaller than, that of the Paris-Hamburg G matrix. However, we also find that the interaction strength is reduced at zero density. These comparisons suggest effects due to nonlocal density dependence beyond the local density approximation.

Dileptons as a probe of pion, kaon, nucleon, and antinucleon dynamics in nuclear matter.

We continue our study of dilepton radiation from high-temperature nuclear matter by computing the rates for the annihilations ${K}^{+}$${K}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$ and NN\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\rightarrow}${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$. In general this radiation would yield information on the abundances of kaons and antinucleons in hot and dense nuclear matter. More specifically, the former may yield information on the approach to kaon condensation, and the latter may yield information on the nucleon-antinucleon dispersion relations as predicted by relativistic field theories of nuclear matter. However, these yields are mostly overshadowed by the processes np\ensuremath{\rightarrow}${\mathrm{npe}}^{+}$${e}^{\mathrm{\ensuremath{-}}}$ and ${\ensuremath{\pi}}^{+}$${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$, so that dilepton production remains essentially a probe of pion dynamics in the nuclear medium.

Complex microscopic optical potential between two nuclei based on Dirac-Brueckner theory for nuclear matter

The real and imaginary parts of the optical-model potential between two nuclei are calculated in the energy density formalism. The energy density is derived from the Dirac-Brueckner approach to nuclear matter. In this approach, both free NN scattering and the saturation properties of nuclear matter can be explained starting from a realistic NN interaction. The relativistic features incorporated in the Dirac-Brueckner approach make the real part of the optical potential less attractive than that obtained in a non-relativistic calculation while the imaginary part is enhanced. The comparison of the calculated differential cross section for elastic 12C- 12C scattering with the experimental data suggests that the enhancement of the imaginary part due to the relativistic treatment is favourable while its repulsive contribution to the real part is unfavourable.

Relativistic theory of nuclear matter

Relativistic theory of nuclear matter

Nuclear equation of state from the nonlinear relativistic mean field theory.

The properties of symmetric nuclear matter are investigated in the nonlinear relativistic mean field theory of nuclear matter. We consider the constraints imposed by four nuclear ground state properties on the coupling constants and on the equation of state at zero and at finite temperature. We find that the compression constant K(${\ensuremath{\rho}}_{0}$) as well as the temperature is irrelevant for the stiffness of the equation of state for ${m}^{\mathrm{*}}$(${\ensuremath{\rho}}_{0}$)\ensuremath{\le}0.7. The main point is that the relativistic mean field theory exhibits acausal and unphysical behavior for compressibilities below K(${\ensuremath{\rho}}_{0}$)=200 MeV. Every set of coupling constants with a negative quartic coupling constant c is unstable against small quantum fluctuations.

Nuclear matter problem in the relativistic Green's function approach.

In this paper we present the theory of nuclear matter in the framework of relativistic nuclear field theory utilizing the technique of relativistic many-body Green's functions. The analytic properties of the Green's functions and related quantities are given and used to obtain the final set of equations for the nuclear matter problem. In detail, we have investigated theoretically and numerically the so-called ..lambda../sup 00/ and ..lambda../sup 10/ approximations. For comparison we also calculated the relativistic Hartree-Fock and the Brueckner-Hartree-Fock approximation, respectively. For masses and coupling strengths we used (phenomenological) parameter sets given by the Bonn and Groningen group. The results of the ..lambda.. approximations are similar to the relativistic Brueckner treatment.

Instability in relativistic mean-field theories of nuclear matter

We investigate the stability of the nuclear matter ground state with respect to small perturbations of the meson fields in relativistic mean-field theories. The popular σ- ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion collisions are discussed briefly.

Isospin symmetry breaking in relativistic mean-field theories of nuclear matter

Taking into account σ-, ω- and ρ-mesons, an expression for the interaction function of quasiparticles in non-isoscalar nuclear matter is derived. This medium resembles a state of broken symmetry, which gives rise to a Goldstone boson. It obtains nonzero mass, if the electromagnetic interaction is included. Treating the electromagnetic field self-consistently, dressing factors for the single-particle current in non-isoscalar nuclear matter are determined. As an application, the effective angular momentum g-factor for a single nucleon added at the Fermi surface is calculated.

Effective interactions and elementary excitations in nuclear matter

We present a polarization potential theory for nuclear matter. Starting from a realistic two-nucleon interaction, position space Pseudopotentials which describe effective nucleon-nucleon interactions are constructed in a manner similar to that used by Aldrich and Pines in the helium liquids. Important modifications which result from tensor forces and three-body interactions are incorporated; exchange and screening effects are included. The resulting momentum-dependent quasiparticle interactions are used to calculate higher-order Fermi liquid parameters, dynamic and static structure functions, and static polarizabilities. Comparisons are made with recent microscopic calculations.

Relativistic theory of nuclear matter and finite nuclei

The relativistic theory of nuclear matter and finite nuclei is reviewed. Both, effective as well as microscopic approaches are discussed. In the latter approach one starts with a one-boson-exchange nucleon-nucleon interaction leading to the Dirac-Brueckner description. In the first method, one formulates the Hartree- (mean field) or Hartree-Fock approximation to some effective Lagrangian which is used to describe directly nuclear matter and finite nuclei. Both approaches are considered and derived in the same framework: the Martin-Schwinger hierarchy of Green's functions. We treat briefly the relativistic Fermi liquid theory, the influence of Δ-degrees of freedom and the situation regarding vacuum fluctuations. We present and discuss results for nuclear matter: saturation properties, equation of state and thermal properties, asymmetric nuclear matter and Landau parameters. In the case of finite nuclei we study optical potentials in nucleon-nucleus scattering and the relation to Dirac phenomenology. Finally, some selected nuclear structure results obtained in Hartree-(Fock) approximation are given.

Summation of ring diagrams of nuclear thermodynamic potential

Using an imaginary-time linked diagram expansion of the thermodynamic potential Ω, we derive methods by which the particle-particle (hole-hole) and the particle-hole ring diagrams of Ω can each be summed up to all orders in a rather convenient way. A model space P and a corresponding finite temperature reaction matrix K are introduced in order to take care of the strong short-range correlations between nucleons. Methods of the finite temperature Green functions are employed. The contribution from the particle-particle (hole-hole) ring diagrams to Ω is given in terms of simple integrals of the form ∝ 0 1d λ tr p { M( λ) K} where λ is a strength parameter, and M a thermal transition matrix which is calculated from a finite-temperature RPA-type secular equation. Solutions of this equation are derived, and their possible connections with phase transitions are discussed. The particle-hole ring diagrams are treated in a similar way. Applications of the present approach and prospects for formulating a Brueckner-type theory of nuclear matter at finite temperature are discussed.

A chirally invariant fermionic field theory for nuclear matter

We present a chiral field theory for nuclear matter purely based on fermionic degrees of freedom. The Nambu-Jona-Lasinio symmetry breaking mechanism is applied in order to obtain a nonvanishing density dependent effective mass of the nucleon. The equation of state is studied at zero temperature. It saturates only if a higher-order scalar-vector fermion self-interaction is included.

Infinite order summation of particle-particle ring diagrams in a model-space approach for nuclear matter

A ring diagram model-space nuclear matter theory is formulated and applied to the calculation of the binding energy per nucleon ( BE A ) , saturation Fermi momentum ( k F) and incompressibility coefficient ( K) of symmetric nuclear matter, using the Paris and Reid nucleon-nucleon potentials. A model space is introduced where all nucleons are restricted to have momentum k ⩽ k M, typical values of k M being ∼3.2 fm −. Using a model-space Hartree-Fock approach, self-consistent single particle spectra are derived for holes ( k ⩽ k F) and particles with momentum k F < k ⩽ k M. For particles with k > k M, we use a free particle spectrum. Within the model space we sum up the particle-particle ring diagrams (both forward- and backward-going) to all orders. A rather simple expression for the energy shift ΔE 0 pp is obtained, namely ΔE 0 pp is expressed as integrals involving the trace of Y( λ) Y +( λ) G M where G M is the model-space reaction matrix, the Y's are transition amplitudes obtained from solving RPA-type secular equations and λ is a strength parameter to be integrated from 0 to 1. We have used angle-average approximations in our calculations, and in this way different partial wave channels are decoupled. For the 3S 1- 3D 1 channel, the effect of the ring diagrams is found to be particularly important. The inclusion of the ring diagrams has largely increased the role of the tensor force in determining the nuclear matter saturation properties, and consequently we obtain saturation densities which are significantly lower than those given by most other calculations. For the Paris potential, our results for BE A , k F and K are respectively 17.38 MeV, 1.42 fm −1 and 96.3 MeV. For the Reid potential, the corresponding results are 15.15 MeV, 1.30 fm −1 and 110.7 MeV. Our calculated values for the binding energy per nucleon and saturation density are both in rather satisfactory agreement with the corresponding empirical values.