arXiv subjects

J. Piekarewicz

Publications and source records attributed to J. Piekarewicz.

At least 145 records · Page 8Linked to original sources

arXiv1997

Coherent eta-photoproduction from nuclei in a relativistic impulse approximation approach

We study coherent eta-photoproduction from nuclei in a relativistic impulse approximation approach. For the elementary production amplitude we use a standard relativistic parameterization based on a set of four Lorentz- and gauge-invariant amplitudes. The photonuclear amplitude is evaluated without recourse to a nonrelativistic reduction; the full relativistic structure of the amplitude is maintained. On general arguments we show that the coherent process is sensitive to only one of the elementary amplitudes. Moreover, we show that the nuclear structure information is fully contained in the ground-state tensor density. The tensor density is evaluated in a mean-field approximation to the Walecka model and it is shown to be sensitive to relativistic effects. Distortion effects are incorporated through an eta-nucleus optical potential that is computed in a simple t-rho approximation.

nucl-th↗

arXiv1997

Macroscopic Parity Violation and Supernova Asymmetries

Core collapse supernovae are dominated by weakly interacting neutrinos. This provides a unique opportunity for macroscopic parity violation. We speculate that parity violation in a strong magnetic field can lead to an asymmetry in the explosion and a recoil of the newly formed neutron star. We estimate the asymmetry from neutrino-polarized-neutron elastic scattering, polarized electron capture and neutrino-nucleus elastic scattering in a (partially) polarized electron gas.

hep-ph↗

arXiv1996

A Plaquette Basis for the Study of Heisenberg Ladders

We employ a plaquette basis-generated by coupling the four spins in a $2\times2$ lattice to a well-defined total angular momentum-for the study of Heisenberg ladders with antiferromagnetic coupling. Matrix elements of the Hamiltonian in this basis are evaluated using standard techniques in angular-momentum (Racah) algebra. We show by exact diagonalization of small ($2\times4$ and $2\times6$) systems that in excess of 90% of the ground-state probability is contained in a very small number of basis states. These few basis states can be used to define a severely truncated basis which we use to approximate low-lying exact eigenstates. We show how, in this low-energy basis, the isotropic spin-1/2 Heisenberg ladder can be mapped onto an anisotropic spin-1 ladder for which the coupling along the rungs is much stronger than the coupling between the rungs. The mapping thereby generates two distinct energy scales which greatly facilitates understanding the dynamics of the original spin-1/2 ladder. Moreover, we use these insights to define an effective low-energy Hamiltonian in accordance to the newly developed COntractor REnormalization group (CORE) method. We show how a simple range-2 CORE approximation to the effective Hamiltonian to be used with our truncated basis reproduces the low-energy spectrum of the exact $2\times6$ theory at the $\alt 1%$ level.

cond-mat↗

arXiv1995

Stability Analysis of the Instantaneous Bethe-Salpeter Equation and the Consequences for Meson Spectroscopy

We investigate the light and heavy meson spectra in the context of the instantaneous approximation to the Bethe-Salpeter equation (Salpeter's equation). We use a static kernel consisting of a one-gluon-exchange component and a confining contribution. Salpeter's equation is known to be formally equivalent to a random-phase-approximation equation; as such, it can develop imaginary eigenvalues. Thus, our study can not be complete without first discussing the stability of Salpeter's equation. The stability analysis limits the form of the kernel and reveals that, contrary to the usual assumption, the confining component can not transform as a Lorentz scalar; it must transform as the timelike component of a vector. Moreover, the stability analysis sets an upper limit on the size of the one-gluon-exchange component; the value for the critical coupling is determined through a solution of the ``semirelativistic'' Coulomb problem. These limits place important constraints on the interaction and suggest that a more sophisticated model is needed to describe the light and heavy quarkonia.

nucl-th↗

arXiv1995

Isospin-Violating Meson-Nucleon Vertices as an Alternate Mechanism of Charge-Symmetry Breaking

We compute isospin-violating meson-nucleon coupling constants and their consequent charge-symmetry-breaking nucleon-nucleon potentials. The couplings result from evaluating matrix elements of quark currents between nucleon states in a nonrelativistic constituent quark model; the isospin violations arise from the difference in the up and down constituent quark masses. We find, in particular, that isospin violation in the omega-meson--nucleon vertex dominates the class IV CSB potential obtained from these considerations. We evaluate the resulting spin-singlet--triplet mixing angles, the quantities germane to the difference of neutron and proton analyzing powers measured in elastic $\vec{n}-\vec{p}$ scattering, and find them commensurate to those computed originally using the on-shell value of the $ρ$-$ω$ mixing amplitude. The use of the on-shell $ρ$-$ω$ mixing amplitude at $q^2=0$ has been called into question; rather, the amplitude is zero in a wide class of models. Our model possesses no contribution from $ρ$-$ω$ mixing at $q^2=0$, and we find that omega-meson exchange suffices to explain the measured $n-p$ analyzing power difference~at~183 MeV.

nucl-th↗

arXiv1995

Charge-Symmetry-Breaking Potentials from Isospin-Violating Meson-Baryon Coupling Constants

We consider charge-symmetry violations in the nucleon-nucleon force which result from isospin-violating meson-baryon coupling constants. The vector mesons are assumed to couple to the nucleon's electromagnetic current, which we decompose into isoscalar and isovector quark components. We compute these currents in the context of a constituent quark model. The isospin violations in the meson-baryon couplings arise from the difference in the up and down constituent quark masses. We show that class IV charge-symmetry-breaking potentials arise in the resulting $ω$ and $ρ$ exchange contributions to the $NN$ force. The magnitude of these contributions is consistent with that phenomenologically required by the measured difference of $n$ and $p$ analyzing powers in elastic $\vec{n}-\vec{p}$ scattering at 183 MeV.

nucl-th↗

arXiv1995

Relativistic treatment of the charged-current reaction ${}^{12}{\rm C}(ν_μ,μ^{-})$ near threshold

We compute the cross section for the charged-current reaction ${}^{12}{\rm C}(ν_μ,μ^{-})$ near threshold using a relativistic mean-field formalism. A reduced value of the nucleon mass in the medium --- coupled to the finite muon mass --- leads to a 30\% reduction in the cross section relative to a free Fermi-gas estimate. Isovector RPA correlations, which are strongly repulsive at these momentum transfers, reduce the cross section by an additional 15-30\%. Hence, relativistic nuclear-structure effects can account for the more than a factor-of-two reduction in the cross section recently reported by the LSND collaboration.

nucl-th↗

arXiv1994

Relativistic nuclear structure effects in quasielastic neutrino scattering

Charged-current cross sections are calculated for quasielastic neutrino and antineutrino scattering using a relativistic meson-nucleon model. We examine how nuclear-structure effects, such as relativistic random-phase-approximation (RPA) corrections and momentum-dependent nucleon self-energies, influence the extraction of the axial form factor of the nucleon. RPA corrections are important only at low-momentum transfers. In contrast, the momentum dependence of the relativistic self-energies changes appreciably the value of the axial-mass parameter, $M_A$, extracted from dipole fits to the axial form factor. Using Brookhaven's experimental neutrino spectrum we estimate the sensitivity of M$_A$ to various relativistic nuclear-structure effects.

nucl-th↗

arXiv1994

Comparison of $K^+$ and $e^-$ Quasielastic Scattering

We formulate $K^+$-nucleus quasielastic scattering in a manner which closely parallels standard treatments of $e^-$-nucleus quasielastic scattering. For $K^+$ scattering, new responses involving scalar contributions appear in addition to the Coulomb (or longitudinal) and transverse $(e,e')$ responses which are of vector character. We compute these responses using both nuclear matter and finite nucleus versions of the Relativistic Hartree Approximation to Quantum Hadrodynamics including RPA correlations. Overall agreement with measured $(e,e')$ responses and new $K^+$ quasielastic scattering data for $^{40}$Ca at $|\qs|=500$ MeV/c is good. Strong RPA quenching is essential for agreement with the Coulomb response. This quenching is notably less for the $K^+$ cross section even though the new scalar contributions are even more strongly quenched than the vector contributions. We show that this ``differential quenching'' alters sensitive cancellations in the expression for the $K^+$ cross section so that it is reduced much less than the individual responses. We emphasize the role of the purely relativistic distinction between vector and scalar contributions in obtaining an accurate and consistent description of the $(e,e')$ and $K^+$ data within the framework of our nuclear structure model.

nucl-th↗

arXiv1994

Relativistic treatment of spin-transfer observables in quasielastic $(\vec{\bf p},\vec{\bf n})$ scattering

We calculate all spin-transfer observables for the quasielastic $(\vec{p},\vec{n})$ reaction in a relativistic plane-wave impulse approximation. The nuclear-structure information is contained in a large set of nuclear-response functions that are computed in nuclear matter using a relativistic random-phase approximation to the Walecka model. A reduced value of the nucleon mass in the medium induces important dynamical changes in the residual isovector interaction relative to its nonrelativistic counterpart. As a result, good agreement is found for all spin observables --- including the spin-longitudinal to spin-transverse ratio --- when compared to the original ($q=1.72$~fm$^{-1}$) NTOF experiment. In contrast, the spin-longitudinal to spin-transverse ratio is underpredicted at $q=1.2$~fm$^{-1}$ and overpredicted at $q=2.5$~fm$^{-1}$. We comment on the role of distortions as a possible solution to this discrepancy.

nucl-th↗

arXiv1994

On the Lorentz structure of the confinement potential

We investigate the Lorentz structure of the confinement potential through a study of the meson spectrum using Salpeter's instantaneous approximation to the Bethe-Salpeter equation. The equivalence between Salpeter's and a random-phase-approximation (RPA) equation enables one to employ the same techniques developed by Thouless, in his study of nuclear collective excitations, to test the stability of the solutions. The stablity analysis reveals the existence of imaginary eigenvalues for a confining potential that transforms as a Lorentz scalar. Moreover, we argue that the instability persists even for very large values of the constituent quark mass. In contrast, we find no evidence of imaginary eigenvalues for a timelike vector potential --- even for very small values of the constituent mass.

nucl-th↗

arXiv1994

Relativistically generated asymmetry in the missing momentum distribution from the $(e,e'p)$ reaction

We calculate the asymmetry in the missing-momentum distribution from the $(e,e'p)$ reaction in a relativistic formalism. Longitudinal and transverse response functions are evaluated in parallel kinematics as a function of the three-momentum transfer to the nucleus. Analytic expressions for the responses are obtained in a relativistic plane-wave impulse approximation. These expressions reveal a large asymmetry in the momentum distribution, at the plane-wave level, induced by the lower components of the bound-state wave functions. These relativistic effects contaminate any attempt to infer color transparency from a measurement of the asymmetry in the $(e,e'p)$ reaction.

nucl-th↗

arXiv1993

Dynamical Color Correlations in a $SU(2)_c$ Quark Exchange Model of Nuclear Matter

The quark exchange model is a simple realization of an adiabatic approximation to the strong-coupling limit of Quantum Chromodynamics (QCD): the quarks always coalesce into the lowest energy set of flux tubes. Nuclear matter is thus modeled in terms of its quarks. We wish to study the correlations imposed by total wavefunction antisymmetry when color degrees of freedom are included. To begin with, we have considered one-dimensional matter with a $SU(2)$ color internal degree of freedom only. We proceed by constructing a totally antisymmetric, color singlet {\it Ansatz} characterized by a variational parameter $λ$ (which describes the length scale over which two quarks in the system are clustered into hadrons) and by performing a variational Monte Carlo calculation of the energy to optimize $λ$ for a fixed density. We calculate the $q-q$ correlation function as well, and discuss the qualitative differences between the system at low and high density.

nucl-th↗

arXiv1993

Medium Modification to the $Ω$-Meson Mass in the Walecka Model

We calculate the effective mass of the $ω$ meson in nuclear matter in a relativistic random-phase approximation to the Walecka model. The dressing of the meson propagator is driven by its coupling to particle-hole pairs and nucleon-antinucleon ($N\bar{N}$) excitations. We report a reduction in the $ω$-meson mass of about 170~MeV at nuclear-matter saturation density. This reduction arises from a competition between the density-dependent (particle-hole) dressing of the propagator and vacuum polarization ($N\bar{N}$ pairs). While density-dependent effects lead to an increase in the mass proportional to the classical plasma frequency, vacuum polarization leads to an even larger reduction caused by the reduced effective nucleon mass in the medium.

nucl-th↗

arXiv1993

K$^+$-nucleus quasielastic scattering

K$^+$--nucleus quasielastic cross sections measured for a laboratory kaon beam momentum of 705 MeV/$c$ are presented for 3--momentum transfers of 300 and 500 MeV/$c$. The measured differential cross sections for C, Ca and Pb at 500 MeV/$c$ are used to deduce the effective number of nucleons participating in the scattering, which are compared with estimates based on the eikonal approximation. The long mean free path expected for K$^+$ mesons in nuclei is found. Double differential cross sections for C and Ca are compared to relativistic nuclear structure calculations.

nucl-th↗

arXiv1993

Levinson's Theorem for Dirac Particles

Levinson's theorem for Dirac particles constraints the sum of the phase shifts at threshold by the total number of bound states of the Dirac equation. Recently, a stronger version of Levinson's theorem has been proven in which the value of the positive- and negative-energy phase shifts are separately constrained by the number of bound states of an appropriate set of Schrödinger-like equations. In this work we elaborate on these ideas and show that the stronger form of Levinson's theorem relates the individual phase shifts directly to the number of bound states of the Dirac equation having an even or odd number of nodes. We use a mean-field approximation to Walecka's scalar-vector model to illustrate this stronger form of Levinson's theorem. We show that the assignment of bound states to a particular phase shift should be done, not on the basis of the sign of the bound-state energy, but rather, in terms of the nodal structure (even/odd number of nodes) of the bound state.

nucl-th↗

arXiv1993

Quark-based Description of Nuclear Matter with Simulated Annealing

We calculate ground-state properties of a many-quark system in the string-flip model using variational Monte Carlo methods. The many-body potential energy of the system is determined by finding the optimal grouping of quarks into hadrons. This (optimal) assignment problem is solved by using the stochastic optimization technique of simulated annealing. Results are presented for the energy and length-scale for confinement as a function of density. These results show how quarks clustering decreases with density and characterize the nuclear- to quark-matter transition. We compare our results to a previously published work with a similar model which uses, instead, a pairing approach to the optimization problem.

nucl-th↗

arXiv1993

Off-shell Behavior of the $π\!-\!η$ Mixing Amplitude

We extend a recent calculation of the momentum dependence of the $ρ-ω$ mixing amplitude to the pseudoscalar sector. The $π\!-\!η$ mixing amplitude is calculated in a hadronic model where the mixing is driven by the neutron-proton mass difference. Closed-form analytic expressions are presented in terms of a few nucleon-meson parameters. The observed momentum dependence of the mixing amplitude is strong enough as to question earlier calculations of charge-symmetry-breaking observables based on the on-shell assumption. The momentum dependence of the $π\!-\!η$ amplitude is, however, practically identical to the one recently predicted for $ρ-ω$ mixing. Hence, in this model, the ratio of pseudoscalar to vector mixing amplitudes is, to a good approximation, a constant solely determined from nucleon-meson coupling constants. Furthermore, by selecting these parameters in accordance with charge-symmetry-conserving data and SU(3)-flavor symmetry, we reproduce the momentum dependence of the $π\!-\!η$ mixing amplitude predicted from chiral perturbation theory. Alternatively, one can use chiral-perturbation-theory results to set stringent limits on the value of the $NNη$ coupling constant.

nucl-th↗