Nuclear Matter Calculations Research Articles

Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter based on improved approximation schemes

We present Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter which are based on improved approximations schemes. The potential matrix elements have been adapted for isospin asymmetric nuclear matter in order to account for the proton-neutron mass splitting in a more consistent way. The proton properties are particularly sensitive to this adaption and its consequences, whereas the neutron properties remains almost unaffected in neutron rich matter. Although at present full Brueckner calculations are still too complex to apply to finite nuclei, these relativistic Brueckner results can be used as a guidance to construct a density dependent relativistic mean field theory, which can be applied to finite nuclei. It is found that an accurate reproduction of the Dirac-Brueckner-Hartree-Fock equation of state requires a renormalization of these coupling functions.

Scales in nuclear matter: Chiral dynamics with pion nucleon form factors⋆

A systematic calculation of nuclear matter is performed which includes the long-range correlations between nucleons arising from one- and two-pion exchange. Three-body effects from 2π exchange with excitations of virtual Δ(1232)-isobars are also taken into account in our diagrammatic calculation of the energy per particle ¯(k f). In order to eliminate possible high-momentum components from the interactions we introduce at each pion-baryon vertex a form factor of monopole type. The empirical nuclear matter saturation point, ρ0 ≃ 0.16fm^-3, ¯0 ≃ - 16MeV, is well reproduced with a monopole mass of Λ ≃ 4πf π ≃ 1.16GeV. As in the recent approach based on the universal low-momentum NN potential V low-k, the inclusion of three-body effects is crucial in order to achieve saturation of nuclear matter. We demonstrate that the dependence of the pion exchange contributions to ¯(k f) on the “resolution” scale Λ can be compensated over a wide range of Λ by counterterms with two “running” contact couplings. As a further application we study the in-medium chiral condensate 〈¯q〉(ρ) beyond the linear density approximation. For ρ ⩽ 1.5ρ0 we find small corrections from the derivative d¯(k f)/dm π, which are stable against variations of the monopole regulator mass Λ.

Diagrammatic calculation of thermodynamical quantities in nuclear matter

In medium $T$-matrix calculations for symmetric nuclear matter at zero and finite temperatures are presented. The internal energy is calculated from the Galitskii-Koltun's sum rule and from the summation of the diagrams for the interaction energy. The pressure at finite temperature is obtained from the generating functional form of the thermodynamic potential. The entropy at high temperature is estimated and compared to expressions corresponding to a quasiparticle gas.

Correlations and effective interactions in nuclear matter

We performed Self-Consistent Greens Function (SCGF) calculations for symmetric nuclear matter using realistic nucleon-nucleon (NN) interactions and effective low-momentum interactions ($V_{low-k}$), which are derived from such realistic NN interactions. We compare the spectral distributions resulting from such calculations. We also introduce a density-dependent effective low-momentum interaction which accounts for the dispersive effects in the single-particle propagator in the medium.

Beyond the quasi-particle picture in nuclear matter calculations using Green's function techniques

Widths of low-lying states in nuclei are of the order of 30 MeV. These large widths are a consequence of the strong interactions leading to a strongly correlated many body system at the typical densities of nuclear matter. Nevertheless ’’traditional’’ Brueckner calculations treat these states as quasiparticles i.e. with spectral functions of zero widths. The width is related to the imaginary part of the selfenergy and is included selfconsistently in an extension of the Brueckner theory using T-matrix and Green's function (GF) techniques. A more general formulation applicable also to non-equilibrium systems is contained in the Kadanoff-Baym (KB) equations while still maintaining the basic many-body techniques of Brueckner theory. In the present work the two-time KB-equations are timestepped along the imaginary timeaxis to calculate the binding energy of nuclear matter as a function of density, including the spectral widths self-consistently. These zero temperature calculations are compared with quasiparticle calculations. The inclusion of the selfconsistent widths are found to add several MeV to the binding. The spectral widths are due to the long-ranged correlations. Short ranged correlations decrease rather than increase the binding. The method is easily extended to nonzero temperatures where the importance of the widths are expected to increase.

Spectral properties of nuclear matter

We review self-consistent spectral methods for nuclear matter calculations. The in-medium T-matrix approach is conserving and thermodynamically consistent. It gives both the global and the single-particle properties the system. The T-matrix approximation allows to address the pairing phenomenon in cold nuclear matter. A generalization of nuclear matter calculations to the super.uid phase is discussed and numerical results are presented for this case. The linear response of a correlated system going beyond the Hartree-Fock+ Random-Phase-Approximation (RPA) scheme is studied. The polarization is obtained by solving a consistent Bethe-Salpeter (BS) equation for the coupling of dressed nucleons to an external field. We find that multipair contributions are important for the spin(isospin) response when the interaction is spin(isospin) dependent.

The few scales of nuclei and nuclear matter

The well-known correlations of low-energy three and four-nucleon observables with a typical three-nucleon scale (e.g., the Tjon line) is extended to light nuclei and nuclear matter. Evidence for the scaling between light nuclei binding energies and the triton one are pointed out. We argue that the saturation energy and density of nuclear matter are correlated to the triton binding energy. The available systematic nuclear matter calculations indicate a possible band structure representing these correlations.

Isospin-dependent optical potentials in Dirac-Brueckner-Hartree-Fock approach

The relativistic microscopic optical potential (RMOP) is studied within the framework of the Dirac-Brueckner-Hartree-Fock (DBHF) approach. A new decomposition of the Dirac structure of nuclear self-energy in the DBHF is extended to asymmetric nuclear matter calculations. A nucleon effective interaction is introduced to reproduce the results of the G matrix. The real part of nucleon self-energy in asymmetric nuclear matter is calculated with the G matrix in the Hartree-Fock approach, while the imaginary part is obtained from the polarization diagram. Nuclear optical potentials in finite nuclei are derived from the self-energies in asymmetric matter through a local-density approximation. The differential cross sections and the analyzing powers in p+Ca-40 and p+Pb-208 elastic scattering at E-p<= 200 MeV are studied with these RMOPs. A satisfactory agreement with the experimental data is found. This is achieved without readjusting phenomenologically the RMOP derived from the DBHF plus polarization diagram.

Ground state of heavy closed shell nuclei: An effective interaction and local density approximation approach

We study the ground-state properties of heavy closed-shell nuclei such as {sup 48}Ca, {sup 90}Zr, {sup 120}Sn, and {sup 208}Pb as well as {sup 4}He, {sup 16}O, and {sup 40}Ca. Similar to our recent work, the local density approximation in the harmonic oscillator basis and different channel-dependent effective two-body interactions that are generated through the lowest-order constrained variational calculation for asymmetric nuclear matter with the Reid68Day, Reid68, and {delta}-Reid68 potentials are used. Unlike nuclear matter, it is shown that Reid68 potential gives ground-state binding energies closer to the experimental data with respect to the {delta}-Reid68 potential and there is not much difference between Reid68 and Reid68Day potentials, which have been define up to J=5. The different channel-dependent effective interactions (J>2) and one- and two-body density distribution functions are discussed and they are compared with the results of other approaches such as the Brueckner local density approximation, correlated basis function, variational fermion hypernetted chain, variational cluster Monte Carlo, Brueckner-Hartree-Fock, fermionic molecular dynamics, and coupled cluster. Finally it is concluded that the three-body force (isobar degrees of freedom) is very important for light (heavy) nuclei because in the most of recent many-body calculations, it is observed that the available two-body nuclear forcesmore » usually underbind light nuclei and overbind heavy nuclei and nuclear matter.« less

Folding model analysis of proton radioactivity of spherical proton emitters

Half-lives of the decays of spherical nuclei away from the proton drip line by proton emissions are estimated theoretically. The quantum mechanical tunneling probability is calculated within the WKB approximation. Microscopic proton-nucleus interaction potentials are obtained by single folding the densities of the daughter nuclei with M3Y effective interaction supplemented by a zero-range pseudopotential for exchange along with the density dependence. Parameters of the density dependence are obtained from the nuclear matter calculations. Spherical charge distributions are used for Coulomb interaction potentials. These calculations provide reasonable estimates for the observed proton-radioactivity lifetimes of proton-rich nuclei for proton emissions from 26 ground and isomeric states of spherical proton emitters.

Is nuclear matter perturbative with low-momentum interactions?

The nonperturbative nature of inter-nucleon interactions is explored by varying the momentum cutoff of a two-nucleon potential. Conventional force models, which have large cutoffs, are nonperturbative because of strong short-range repulsion, the iterated tensor interaction, and the presence of bound or nearly-bound states. But for low-momentum interactions with cutoffs around 2 fm −1 , the softened potential combined with Pauli blocking leads to corrections in nuclear matter in the particle-particle channel that are well converged at second order in the potential, suggesting that perturbation theory can be used in place of Brueckner resummations. Calculations of nuclear matter using the low-momentum two-nucleon force V low k with a corresponding leading-order three-nucleon (3N) force from chiral effective field theory (EFT) exhibit nuclear binding in the Hartree–Fock approximation, and become less cutoff dependent with the inclusion of the dominant second-order contributions. The role of the 3N force is essential to obtain saturation, and the contribution to the total potential energy is compatible with EFT power-counting estimates.

Effective potential and local density approximation approach to the binding energy of closed shell nuclei

The ground state binding energies of closed shell nuclei such as {sup 4}He,{sup 12}C,{sup 16}O,{sup 28}Si,{sup 32}S,{sup 40}Ca, and {sup 56}Ni are calculated by using the local density approximation in the harmonic oscillator basis. Different channel effective two-body interactions are generated from the lowest order constrained variational calculation for nuclear matter with the Reid68 and {delta}-Reid68 potentials. It is shown that the unlike nuclear matter, Reid68 potential gives ground state binding energies closer to the experimental data with respect to the {delta}-Reid68 interaction. The different channel effective interactions as well as one- and two-body density distribution functions are discussed and compared with the results of other approaches such as the correlated basis function, variational fermion hypernetted chain, variational cluster Monte Carlo, Brueckner-Hartree-Fock, fermionic molecular dynamics, and coupled cluster.

Asymmetrical nuclear matter calculations with the new charge-dependent Reid potential

We calculate the equation of state for asymmetric nuclear matter with the new charge-dependent Reid potential (Reid93) within the lowest order constrained variational method (LOCV) for the wide range of densities and proton to neutron ratio ( R ). Like our previous work on the symmetrical nuclear matter, it is found that the Reid93 potential over binds the asymmetrical nuclear matter with respect to other potentials at same density and R ratio. The symmetry energy of about 50 MeV is obtained at the saturation density. Various properties of the asymmetrical nuclear matter such as the symmetry energy, validity of α 2 law, etc., are examined and the results are compared with the others many-body calculations.

Isospin dependence ofHe6+poptical potential and the symmetry energy

A consistent folding analysis of the elastic p({sup 6}He,{sup 6}He)p scattering and charge exchange p({sup 6}He,{sup 6}Li{sup *})n reaction data measured at E{sub lab}=41.6A MeV has been performed within the coupled channels formalism. We have used the isovector coupling to link the isospin dependence of {sup 6}He+p optical potential to the cross section of p({sup 6}He,{sup 6}Li{sup *})n reaction exciting the 0{sup +} isobaric analog state (IAS) at 3.563 MeV in {sup 6}Li. Based on these results and the Hartree-Fock calculation of asymmetric nuclear matter using the same isospin-dependent effective nucleon-nucleon interaction, we were able to confirm that the most realistic value of the symmetry energy E{sub sym} is around 31 MeV. Our analysis has also shown that the measured charge exchange p({sup 6}He,{sup 6}Li{sup *})n data are quite sensitive to the halo tail of the {sup 6}He density used in the folding calculation and the IAS of {sup 6}Li is likely to have a halo structure similar to that established for the ground state of {sup 6}He.

Lambda Hypernuclei in a Chiral Hadronic Model

Nuclear matter calculations in a chiral hadronic model have beenperformed. It has been found that the scalar and the vector potentialsand binding energies per nucleon in the chiral hadronic model are veryclose to those of the microscopic relativistic Brueckner–Hartree–Fockcalculations. The good results for finite nuclei can be obtained in themean field approximation only if scalar mass ms and coupling constantgs have been improved with the fixed values of cs2≡gs2(M/ms)2 as those given by the original parameter sets of the chiralhadronic model. Then the chiral hadronic model is extended to lambdahypernuclei. Our results predicted by the chiral hadronic model arecompared with those by the nonlinear Walecka model. It has been shownthat the hadronic model can also be used to describe lambda hypernucleisuccessfully.

Chiral approach to nuclear matter: role of two-pion exchange with virtual delta-isobar excitation

We extend a recent three-loop calculation of nuclear matter by including the effects from two-pion exchange with single and double virtual Δ ( 1232 ) -isobar excitation. Regularization dependent short-range contributions from pion-loops are encoded in a few NN-contact coupling constants. The empirical saturation point of isospin-symmetric nuclear matter, E ¯ 0 = − 16 MeV , ρ 0 = 0.16 fm −3 , can be well reproduced by adjusting the strength of a two-body term linear in density (and tuning an emerging three-body term quadratic in density). The nuclear matter compressibility comes out as K = 304 MeV . The real single-particle potential U ( p , k f 0 ) is substantially improved by the inclusion of the chiral π N Δ -dynamics: it grows now monotonically with the nucleon momentum p. The effective nucleon mass at the Fermi surface takes on a realistic value of M ∗ ( k f 0 ) = 0.88 M . As a consequence of these features, the critical temperature of the liquid-gas phase transition gets lowered to the value T c ≃ 15 MeV . In this work we continue the complex-valued single-particle potential U ( p , k f ) + i W ( p , k f ) into the region above the Fermi surface p > k f . The effects of 2 π-exchange with virtual Δ-excitation on the nuclear energy density functional are also investigated. The effective nucleon mass associated with the kinetic energy density is M ˜ ∗ ( ρ 0 ) = 0.64 M . Furthermore, we find that the isospin properties of nuclear matter get significantly improved by including the chiral π N Δ -dynamics. Instead of bending downward above ρ 0 as in previous calculations, the energy per particle of pure neutron matter E ¯ n ( k n ) and the asymmetry energy A ( k f ) now grow monotonically with density. In the density regime ρ = 2 ρ n < 0.2 fm −3 relevant for conventional nuclear physics our results agree well with sophisticated many-body calculations and (semi)-empirical values.

Folding model analysis of proton scattering from mirror nuclei 18Ne and 18O

The elastic and inelastic scattering of protons from mirror nuclei 18Ne and 18O are studied in a folding model approach. For comparison, two different effective interactions are folded with Hartree–Fock densities to obtain the nuclear interaction potentials. Both of them provide equivalent descriptions to the data and the deformation parameters extracted from inelastic scattering are reasonable. The density dependence parameters obtained from nuclear matter calculations and used for present analysis also provide a good estimate for the nuclear mean free path. The present formalism unifies radioactivity, nuclear matter and nuclear scattering.

Hyperons in a relativistic mean-field approach to asymmetric nuclear matter

Relativistic mean-field theory with $\delta$ meson, nonlinear isoscalar self-interactions and isoscalar-isovector cross interaction terms with parametrizations obtained to reproduce Dirac-Brueckner-Hartree-Fock calculations for nuclear matter is used to study asymmetric nuclear matter properties in $\beta$-equilibrium, including hyperon degrees of freedom and (hidden) strange mesons. Influence of cross interaction on composition of hyperon matter and electron chemical potential is examined. Softening of nuclear equation of state by the cross interactions results in lowering of hyperonization, although simultaneously enhancing a hyperon-induced decrease of the electron chemical potential, thus indicating further shift of a kaon condensate occurence to higher densities.

Scattering of GeV electrons in the framework of the relativistic hartree approximation

The high momentum transfer electron-nucleus scattering cross section is evaluated within the plane wave impulse approximation (PWIA) supplemented by the relativistic Hartree approximation (RHA). Binding effects on the struck nucleon are introduced through the scalar and vector meson-exchange fields within the framework of quantum hadrodynamics. This model naturally satisfies the current conservation, with the off-shell nucleons behaving as being on the mass shell but having an effective mass. The nucleon inelastic response is included via different parameterizations of the structure function measured at SLAC, while the smearing of the Fermi surface is introduced through a momentum distribution obtained from a perturbative nuclear matter calculation. Recent CEBAF data on inclusive scattering of 4.05 GeV electrons on 56Fe are well reproduced for all measured geometries by the first time. Scaling effects are analyzed as well, and the scaling properties of the nuclear response in terms of the y variable associated to the PWIA within the RHA framework are discussed. The theoretical scaling function obtained in our approach also significantly improves previous PWIA calculations within the multi-GeV electron scattering regime, and describes properly the CEBAF scaling data.

Lowest Order Constrained Variational Calculation for Nuclear and Neutron Matter with a New Charge-Dependent Reid Potential

The lowest order constrained variational (LOCV) method is reformulated to calculate the equation of state of nuclear and neutron matter with a new charge-dependent Reid potential (Reid93). The state-dependent correlation functions are calculated by performing a full functional minimization for each JLSTM T -channel and the resulting Euler Lagrange equations are solved up to J = 9. The correlation functions are compared with those coming from LOCV calculation with the old Reid68 potential. It is shown that unlike ∆-Reid68 and AV18 interactions, the new Reid93 over binds nuclear matter at much larger saturation density than Reid68. Finally, the results are being compared with similar calculations with other potentials and many-body techniques.