arXiv subjects

J. Piekarewicz

Publications and source records attributed to J. Piekarewicz.

At least 127 records · Page 7Linked to original sources

arXiv2002

Quasifree processes from nuclei: Meson photoproduction and electron scattering

We have developed a relativistic formalism for studying quasi-free processes from nuclei. The formalism can be applied with ease to a variety of processes and renders transparent analytical expressions for all observables. We have applied it to kaon photoproduction and to electron scattering. For the case of the kaon, we compute the recoil polarization of the lambda-hyperon and the photon asymmetry. Our results indicate that polarization observables are insensitive to relativistic, nuclear target, and distortion effects. Yet, they are sensitive to the reactive content, making them ideal tools for the study of modifications to the elementary amplitude -- such as in the production, propagation, and decay of nucleon resonances -- in the nuclear medium. For the case of the electron, we have calculated the spectral function of He-4. An observable is identified for the clean and model-independent extraction of the spectral function. Our calculations provide baseline predictions for the recently measured, but not yet fully analyzed, momentum distribution of He-4 by the A1-collaboration from Mainz. Our approach predicts momentum distributions for He-4 that rival some of the best non-relativistic calculations to date.

nucl-th↗

arXiv2002

Covariant RPA in Effective Hadronic Field Theory

In an effective hadronic theory constructed to describe long-range nuclear physics, the dynamics of the vacuum can be expanded in terms with zero or a finite number of derivatives acting on the fields. Thus vacuum dynamics can always be absorbed in the (infinite number of) counterterm parameters necessarily present in the effective lagrangian. These finite parameters, which at present must be fitted to data, encode the empirical vacuum physics as well as other short-range dynamics into the effective lagrangian; in practice, only a small number of parameters must be fitted. The strength of the effective field theory (EFT) framework is that there is no need to make a concrete picture of the vacuum dynamics, as one does in a renormalizable hadronic theory. At the one-loop level, the most convenient renormalization scheme requires explicit sums over long-range (``valence'') nucleon orbitals only, thus explaining the so-called ``no-sea approximation'' used in successful covariant mean-field theory (MFT) calculations of static ground states. When excited states are studied in the random-phase approximation (RPA), the same EFT scheme dictates the inclusion of both familiar particle-hole pairs and contributions that mix valence and negative-energy single-particle Dirac wave functions. The modern EFT strategy therefore justifies and explains the omission of some explicit contributions from the negative-energy Dirac sea of nucleons, as was done to maintain conservation laws in earlier pragmatic calculations of the nuclear linear response.

nucl-th↗

arXiv2002

The long journey from the giant-monopole resonance to the nuclear-matter incompressibility

Differences in the density dependence of the symmetry energy predicted by nonrelativistic and relativistic models are suggested, at least in part, as the culprit for the discrepancy in the values of the compression modulus of symmetric nuclear matter extracted from the energy of the giant monopole resonance in 208Pb. ``Best-fit'' relativistic models, with stiffer symmetry energies than Skyrme interactions, consistently predict higher compression moduli than nonrelativistic approaches. Relativistic models with compression moduli in the physically acceptable range of K=200-300 MeV are used to compute the distribution of isoscalar monopole strength in 208Pb. When the symmetry energy is artificially softened in one of these models, in an attempt to simulate the symmetry energy of Skyrme interactions, a lower value for the compression modulus is indeed obtained. It is concluded that the proposed measurement of the neutron skin in 208Pb, aimed at constraining the density dependence of the symmetry energy and recently correlated to the structure of neutron stars, will also become instrumental in the determination of the compression modulus of nuclear matter.

nucl-th↗

arXiv2002

Parity Violating Measurements of Neutron Densities: Implications for Neutron Stars

Parity violating electron scattering can measure the neutron density of a heavy nucleus accurately and model independently. This is because the weak charge of the neutron is much larger then that of the proton. The Parity Radius Experiment (PREX) at Jefferson Laboratory aims to measure the root mean square neutron radius of $^{208}$Pb with an absolute accuracy of 1% ($\pm 0.05$ Fm). This is more accurate then past measurements with hadronic probes, which all suffer from controversial strong interaction uncertainties. PREX should clearly resolve the neutron-rich skin. Furthermore, this benchmark value for $^{208}$Pb will provide a calibration for hadronic probes, such as proton scattering, which can then be used to measure neutron densities of many exotic nuclei. The PREX result will also have many implications for neutron stars. The neutron radius of Pb depends on the pressure of neutron-rich matter: the greater the pressure, the larger the radius as neutrons are pushed out against surface tension. The same pressure supports a neutron star against gravity. The Pb radius is sensitive to the equation of state at normal densities while the radius of a 1.4 solar mass neutron star also depends on the equation of state at higher densities. Measurements of the radii of a number of isolated neutron stars such as Geminga and RX J185635-3754 should soon improve significantly. By comparing the equation of state information from the radii of both Pb and neutron stars one can search for a softening of the high density equation of state from a phase transition to an exotic state. Possibilities include kaon condensates, strange quark matter or color superconductors.

astro-ph↗

arXiv2001

Novel Methods for Determining Effective Interactions for the Nuclear Shell Model

The Contractor Renormalization (CORE) method is applied in combination with modern effective-theory techniques to the nuclear many-body problem. A one-dimensional--yet ``realistic''--nucleon-nucleon potential is introduced to test these novel ideas. It is found that the magnitude of ``model-space'' (CORE) corrections diminishes considerably when an effective potential that eliminates the hard-momentum components of the potential is first introduced. As a result, accurate predictions for the ground-state energy of the there-body system are made with relatively little computational effort when both techniques are used in a complementary fashion.

nucl-th↗

arXiv2001

Modeling the strangeness content of hadronic matter

The strangeness content of hadronic matter is studied in a string-flip model that reproduces various aspects of the QCD-inspired phenomenology, such as quark clustering at low density and color deconfinement at high density, while avoiding long range van der Waals forces. Hadronic matter is modeled in terms of its quark constituents by taking into account its internal flavor (u,d,s) and color (red, blue, green) degrees of freedom. Variational Monte-Carlo simulations in three spatial dimensions are performed for the ground-state energy of the system. The onset of the transition to strange matter is found to be influenced by weak, yet not negligible, clustering correlations. The phase diagram of the system displays an interesting structure containing both continuous and discontinuous phase transitions. Strange matter is found to be absolutely stable in the model.

nucl-th↗

arXiv2001

Extracting the spectral function of He-4 from a relativistic plane-wave treatment

The spectral function of He-4 is extracted from a plane-wave approximation to the (e,e'p) reaction using a fully relativistic formalism. We take advantage of both an algebraic ``trick'' and a general relativistic formalism for quasifree processes developed earlier to arrive at transparent, analytical expressions for all quasifree (e,e'p) observables. An observable is identified for the clean and model-independent extraction of the spectral function. Our simple relativistic plane-wave calculations provide baseline predictions for the recently measured, but not yet fully analyzed, momentum distribution of He-4 by the A1-collaboration from Mainz. Yet in spite of its simplicity, our approach predicts momentum distributions for He-4 that rival some of the best nonrelativistic calculations to date. Finally, we highlight some of the challenges and opportunities that remain, both theoretically and experimentally, in the extraction of quasifree observables.

nucl-th↗

arXiv2001

Neutron Star Structure and the Neutron Radius of 208Pb

We study relationships between the neutron-rich skin of a heavy nucleus and the properties of neutron-star crusts. Relativistic effective field theories with a thicker neutron skin in $^{208}$Pb have a larger electron fraction and a lower liquid-to-solid transition density for neutron-rich matter. These properties are determined by the density dependence of the symmetry energy which we vary by adding nonlinear couplings between isoscalar and isovector mesons. An accurate measurement of the neutron radius in $^{208}$Pb---via parity violating electron scattering---may have important implications for the structure of neutron stars.

astro-ph↗

arXiv2000

Relativistic Approach to Isoscalar Giant Resonances in 208Pb

We calculate the longitudinal response of 208Pb using a relativistic random-phase approximation to three different parameterizations of the Walecka model with scalar self-interactions. From a nonspectral calculation of the response-that automatically includes the mixing between positive- and negative-energy states-we extract the distribution of strength for the isoscalar monopole, dipole, and high-energy octupole resonances. We employ a consistent formalism that uses the same interaction in the calculation of the ground state as in the calculation of the response. As a result, the conservation of the vector current is strictly maintained throughout the calculation. Further, at small momentum transfers the spurious dipole strength-associated with the uniform translation of the center-of-mass-gets shifted to zero excitation energy and is cleanly separated from the sole remaining physical fragment located at an excitation energy of about 24 MeV; no additional dipole strength is observed. The best description of the collective modes is obtained using a ``soft'' parameterization having a compression modulus of K=224 MeV.

nucl-th↗

arXiv2000

Quark Coulomb Interactions and the Mass Difference of Mirror Nuclei

We study the Okamoto-Nolen-Schiffer (ONS) anomaly in the binding energy of mirror nuclei at high density by adding a single neutron or proton to a quark gluon plasma. In this high-density limit we find an anomaly equal to two-thirds of the Coulomb exchange energy of a proton. This effect is dominated by quark electromagnetic interactions---rather than by the up-down quark mass difference. At normal density we calculate the Coulomb energy of neutron matter using a string-flip quark model. We find a nonzero Coulomb energy because of the neutron's charged constituents. This effect could make a significant contribution to the ONS anomaly.

nucl-th↗

arXiv1999

Strange matter in the string-flip model

We employ variational Monte Carlo methods to study the transition to strange matter in a simple one-dimensional string-flip model with two flavors and two colors of quarks. The dynamics of the system are described in terms of a many-body potential that confines quarks within hadrons, yet enables the hadrons to separate without generating unphysical long-range van der Waals forces. The model has ``natural'' low- and high-density limits: it behaves as a system of isolated hadrons at low density and as a Fermi gas of quarks at high density. We show that the system exhibits a transition to strange matter characterized by an increase in the length-scale for confinement. Yet the small increase at the transition region --- of only ten percent --- suggests that clustering correlations remain strong well into the strange-matter domain. Our results put into question descriptions of strange matter in terms of noninteracting, or weakly interacting, quarks.

nucl-th↗

arXiv1999

Quasifree kaon-photoproduction from nuclei in a relativistic approach

We compute the recoil polarization of the lambda-hyperon and the photon asymmetry for the quasifree photoproduction of kaons in a relativistic impulse-approximation approach. Our motivation for studying polarization observables is threefold. First, polarization observables are more effective discriminators of subtle dynamics than the unpolarized cross section. Second, earlier nonrelativistic calculations suggest an almost complete insensitivity of polarization observables to distortions effects. Finally, this insensitivity entails an enormous simplification in the theoretical treatment. Indeed, by introducing the notion of a ``bound-nucleon propagator'' we exploit Feynman's trace techniques to develop closed-form, analytic expressions for all photoproduction observables. Moreover, our results indicate that polarization observables are also insensitive to relativistic effects and to the nuclear target. Yet, they are sensitive to the model parameters, making them ideal tools for the study of modifications to the elementary amplitude --- such as in the production, propagation, and decay of nucleon resonances --- in the nuclear medium.

nucl-th↗

arXiv1999

Relativistic Treatment of Hypernuclear Decay

We compute for the first time the decay width of lambda-hypernuclei in a relativistic mean-field approximation to the Walecka model. Due to the small mass difference between the lambda-hyperon and its decay products---a nucleon and a pion---the mesonic component of the decay is strongly Pauli blocked in the nuclear medium. Thus, the in-medium decay becomes dominated by the non-mesonic, or two-body, component of the decay. For this mode, the lambda-hyperon decays into a nucleon and a spacelike nuclear excitation. In this work we concentrate exclusively on the pion-like modes. By relying on the analytic structure of the nucleon and pion propagators, we express the non-mesonic component of the decay in terms of the spin-longitudinal response function. This response has been constrained from precise quasielastic (p,n) measurements done at LAMPF. We compute the spin-longitudinal response in a relativistic random-phase-approximation model that reproduces accurately the quasielastic data. By doing so, we obtain hypernuclear decay widths that are considerably smaller---by factors of two or three---relative to existing nonrelativistic calculations.

nucl-th↗

arXiv1998

Lessons to be learned from the coherent photoproduction of pseudoscalar mesons

We study the coherent photoproduction of pseudoscalar mesons---particularly of neutral pions---placing special emphasis on the various sources that put into question earlier nonrelativistic-impulse-approximation calculations. These include: final-state interactions, relativistic effects, off-shell ambiguities, and violations to the impulse approximation. We establish that, while distortions play an essential role in the modification of the coherent cross section, the uncertainty in our results due to the various choices of optical-potential models is relatively small (of at most 30%). By far the largest uncertainty emerges from the ambiguity in extending the many on-shell-equivalent representations of the elementary amplitude off the mass shell. Indeed, relativistic impulse-approximation calculations that include the same pionic distortions, the same nuclear-structure model, and two sets of elementary amplitudes that are identical on-shell, lead to variations in the magnitude of the coherent cross section by up to factors of five. Finally, we address qualitatively the assumption of locality implicit in most impulse-approximation treatments, and suggest that the coherent reaction probes---in addition to the nuclear density---the polarization structure of the nucleus.

nucl-th↗

arXiv1998

Mean-Field Theory for Spin Ladders Using Angular-Momentum Coupled Bases

We study properties of two-leg Heisenberg spin ladders in a mean-field approximation using a variety of angular-momentum coupled bases. The mean-field theory proposed by Gopalan, Rice, and Sigrist, which uses a rung basis, assumes that the mean-field ground state consists of a condensate of spin-singlets along the rungs of the ladder. We generalize this approach to larger angular-momentum coupled bases which incorporate---by their mere definition---a substantial fraction of the important short-range structure of these materials. In these bases the mean-field ground-state remains a condensate of spin singlet---but now with each involving a larger fraction of the spins in the ladder. As expected, the ``purity'' of the ground-state, as judged by the condensate fraction, increases with the size of the elementary block defining the basis. Moreover, the coupling to quasiparticle excitations becomes weaker as the size of the elementary block increases. Thus, the weak-coupling limit of the theory becomes an accurate representation of the underlying mean-field dynamics. We illustrate the method by computing static and dynamic properties of two-leg ladders in the various angular-momentum coupled bases.

cond-mat.str-el↗

arXiv1998

Perturbation Theory for Spin Ladders Using Angular-Momentum Coupled Bases

We compute bulk properties of Heisenberg spin-1/2 ladders using Rayleigh-Schrödinger perturbation theory in the rung and plaquette bases. We formulate a method to extract high-order perturbative coefficients in the bulk limit from solutions for relatively small finite clusters. For example, a perturbative calculation for an isotropic $2\times 12$ ladder yields an eleventh-order estimate of the ground-state energy per site that is within 0.02% of the density-matrix-renormalization-group (DMRG) value. Moreover, the method also enables a reliable estimate of the radius of convergence of the perturbative expansion. We find that for the rung basis the radius of convergence is $λ_c\simeq 0.8$, with $λ$ defining the ratio between the coupling along the chain relative to the coupling across the chain. In contrast, for the plaquette basis we estimate a radius of convergence of $λ_c\simeq 1.25$. Thus, we conclude that the plaquette basis offers the only currently available perturbative approach which can provide a reliable treatment of the physically interesting case of isotropic $(λ=1)$ spin ladders. We illustrate our methods by computing perturbative coefficients for the ground-state energy per site, the gap, and the one-magnon dispersion relation.

cond-mat.str-el↗

arXiv1997

Nuclear dependence of the coherent eta photoproduction reaction in a relativistic approach

We study the nuclear (or A) dependence of the coherent eta photoproduction reaction in a relativistic impulse approximation approach. We use a standard relativistic parameterization of the elementary amplitude, based on a set of four Lorentz- and gauge-invariant amplitudes, to calculate the coherent production cross section from He-4, C-12, and Ca-40. In contrast to nonrelativistic treatments, our approach maintains the full relativistic structure of the process. The nuclear structure affects the process through the ground-state tensor density. This density is sensitive to relativistic effects and depends on A in a different manner than the vector density used in nonrelativistic approaches. This peculiar dependence results in He-4 having a cross section significantly smaller than that of C-12---in contrast to existent nonrelativistic calculations. Distortion effects are incorporated through an eta-nucleus optical potential that is computed in a simple ``t rho'' approximation.

nucl-th↗

arXiv1997

Dynamic Spin Response for Heisenberg Ladders

We employ the recently proposed plaquette basis to investigate static and dynamic properties of isotropic 2-leg Heisenberg spin ladders. Simple non-interacting multi-plaquette states provide a remarkably accurate picture of the energy/site and dynamic spin response of these systems. Insights afforded by this simple picture suggest a very efficient truncation scheme for more precise calculations. When the small truncation errors are accounted for using recently developed Contractor Renormalization techniques, very accurate results requiring a small fraction of the computational effort of exact calculations are obtained. These methods allow us to determine the energy/site, gap, and spin response of 2x16 ladders. The former two values are in good agreement with density matrix renormalization group results. The spin response calculations show that nearly all the strength is concentrated in the lowest triplet level and that coherent many-body effects enhance the response/site by nearly a factor of 1.6 over that found for 2x2 systems.

cond-mat.str-el↗