Martine Jaminon

Single-particle potential in a relativistic Hartree-Fock mean field approximation

Abstract A relativistic Hartree-Fock mean field approximation is investigated in a model in which the nucleon field interacts with scalar and vector meson fields. The Hartree-Fock potential felt by individual nucleons enters in a relativistic Dirac single-particle equation. It is shown that in the case of symmetric nuclear matter one can always find a potential which is fully equivalent to the most general mean field and which is only the sum of a Lorentz scalar, of one component of a Lorentz tensor and of the fourth component of a Lorentz vector. A non-relativistic potential is derived which yields exactly the same single-particle energies and elastic scattering phase shifts as the relativistic Hartree-Fock potential. Analytical results are presented in the case of nuclear matter. A local density approximation is constructed which enables one to consider finite nuclei. The input parameters of the model can be chosen in such a way that the empirical saturation properties of nuclear matter are well reproduced. Good agreement is obtained between the calculated non-relativistic potential and the empirical value of the real part of the optical-model potential at low and at intermediate energy. At intermediate energy, the wine-bottle bottom shape which had previously been found for the potential in the framework of the relativistic Hartree approximation is maintained when the Fock contribution is included.

Chiral theory of mesons in dense baryonic matter (I)

Abstract Chiral symmetry restoration at finite baryonic density is studied in a quark model involving both scalar and vector interactions. The presence of vector interactions makes the vacuum stiffer against chiral symmetry restoration. On-shell masses and coupling constants are calculated for the π, ω, ϱ and a 1 mesons. An attempt is made to relate the quark-meson interactions to the observed nucleon-meson coupling constants.

The coupling of quark and gluon condensates in dense systems

Two lagrangians, which implement the QCD (quantum chromodynamics) scale anomaly, are used to study the coupling of quark and gluon condensates in dense baryonic matter. It is shown both numerically and analytically that the behaviour of the system depends crucially on the assumed value of the vacuum quark condensate. For a low value, compatible with the bag constant, the gluon condensate [open quotes]feels[close quotes] the chiral phase transition. With a higher value, deduced from QCD sum rules, the gluon condensate decouples from the quark condensate and does not change appreciably across the chiral phase transition. In one of the lagrangians, the pion mass drops gradually to zero as the phase transition is approached. 25 refs., 12 figs., 2 tabs.

Chiral mesons in dense nuclear matter

Abstract Chiral symmetry restoration together with the σ- and π-meson propagators are calculated in dense baryonic matter. The vacuum is described by a Nambu-Jona-Lasinio model of quarks. Nuclear matter is described by a Fermi sea of either quarks or nucleons. The two descriptions are found to give different results for chiral symmetry restoration at high densities.

Dependence of the density distribution of 208Pb on the occupation probabilities of shell-model orbits

Abstract An independent-particle model for the proton density distribution of 208 Pb is constructed; it closely approximates the Hartree-Fock calculation of Decharge and Gogny. We investigate the modifications which arise when one introduces a depletion of the Fermi sea of the amount suggested by analyses of recent electron scattering data and by nuclear-matter calculations. The main effect of the depletion is to flatten the density distribution in the nuclear interior. The calculated density is in good agreement with the empirical one near the nuclear centre but is too small in the vicinity of 5 fm. The main consequences of the depletion are shown to be largely independent of the details of the model. It is concluded that Hartree-Fock single-particle wave functions which yield good agreement with empirical density distributions are rather different from the natural orbitals. Accordingly they should not be expected to yield a good approximation to the off-diagonal elements of the one-body density matrix, e.g. to the momentum distribution.

Inability of any Hartree-Fock approximation to reproduce simultaneously the density and momentum distributions of nuclei

Abstract We evaluate the effect of a large depletion of the Fermi sea on the charge largeness of this depletion makes it impossible to construct an independent particle model which would simultaneously reproduce both the diagonal and the off-diagonal elements of the nuclear one-body density matrix.

Mean square deviation from a slater determinant and scaling effects in models of the correlated ground state of nuclear matter and of 208Pb

Abstract It is proposed to characterize the deviation of the one-body density matrix, ϱ , of the correlated nuclear ground state from that, ϱ 0 , of an uncorrelated system by the following quantity σ = A −1 tr ( ϱ − ϱ 0 ) 2 , where A is the number of nucleons. This “mean square deviation per nucleon” σ has a lower bound, σ min , which is reached when the uncorrelated many-body wave function is constructed with the natural orbitals. It is shown that in the case of nuclear matter this minimum can be expressed in terms of the momentum probability distribution. In a nucleus the expression of σ min involves the occupation probabilities of the natural orbitals; it is argued that σ min ≈ 0.02–0.03 for realistic nucleon-nucleon interactions. The value of σ min is evaluated in the case of various models which have recently been introduced in order to study the effect of correlations on the density and momentum distributions of protons in 208 Pb. We investigate how the latter quantities are modified when previous approximations for the natural orbitals are modified by performing either a scaling transformation or by changing the Woods-Saxon potential from which these natural orbitals are generated. Two sets of single-particle orbitals are found which yield good agreement with the experimental values of both the charge and momentum density distributions of 208 Pb when realistic occupation probabilities are introduced; the latter correspond to a 11.6% depletion of the Fermi sea, of which only 3.6% arise from long-range correlations as described by the random phase approximation.

Effect of correlations on the momentum distribution of protons in 208Pb

Abstract The momentum distribution of protons in 208 Pb is investigated in the framework of a model in which the ground-state wave function is specified by the occupation probabilities of shell-model orbits. Three main cases are considered: (i) the Hartree-Fock approximation (uncorrelated case), (ii) the random-phase approximation associated with long-range correlations, (iii) the case including short-, medium- and long-range as well as tensor correlations. The three cases yield similar results for momenta smaller than 1.6 fm −1 , but the medium- and short-range and tensor correlations increase by several orders of magnitude the probability of finding a proton with momentum larger than 1.6 fm −1 in the nuclear ground state. These features are in semi-quantitative agreement with those previously found in lighter nuclei by using the Brueckner-Hartree-Fock, the Jastrow and the exp( S ) approaches, and also with results obtained in the limit of nuclear matter. They considerably differ from those derived from two simple local-density approximations. The calculated momentum distributions are compared with empirical results.

Anomalous pion decay in effective QCD at finite temperature

Abstract The width of the process π 0 → γγ is calculated within effective QCD at finite temperature. We use two different effective models which describe chiral symmetry breaking and its restoration at finite temperature in SU(2) ƒ : (i) an effective lagrangian with a nonlocal separable interaction kernel, (ii) A- and B-scaledNJL lagrangians which implement the scale anomaly of QCD. We calculate the temperature dependences of the quark and pion masses as well as of the pion-park-antiquark coupling strength below and above the double quark mass threshold. At zero temperature we obtain a fairly good agreement with the experimental value for the decay width. The temperature dependence of the decay width is related to that of the pion mass. Γ π 0 → γγ is enhanced in the vicinity of the Mott temperature ( M π = 2 m q ) for the nonlocal as well as for the A-scaled model and suppressed for the B-scaled model. We compare our results with the SU(2) Nambu-Jona-Lasinio model which is contained as a limiting case in our approach.

The current quark mass and the regularisation of the Nambu-Jona-Lasinio action

We show that the Nambu-Jona-Lasinio model can distinguish observables, such as the meson masses, the pion decay constant and the constituent quark mass, which have logarithmic divergences, from quadratically divergent quantities such as the quark condensate 〈yψ〉 or the current quark mass. The latter can be eliminated from the lagrangian which can then be regularized with a single subtraction involving a cut-off mass. The range of possible cut-offs is considerably enlarged when it is realized that the quadratically divergent current quark mass requires two subtractions and therefore two cut-off parameters.