Parity Projection Research Articles

Variation after parity projection calculation with the Skyrme interaction for light nuclei

A self-consistent calculation with variation after parity projection is proposed to study both ground and excited states of light nuclei. This procedure provides description of the ground state incorporating some correlation effects, and self-consistent solutions for the excited states of negative parity. For flexible description of nuclear shapes, single particle orbitals are represented on a uniform grid in the three-dimensional Cartesian coordinates. The angular momentum projection is performed after variation to calculate rotational spectra. To demonstrate the usefulness of the method, results are shown for two $N=Z$ nuclei, $^{20}\mathrm{Ne}$ and $^{12}\mathrm{C}$, for which clustering correlations are known to be important. In the $^{20}\mathrm{Ne}$ nucleus, both cluster-like and shell-model-like states are described simultaneously in the present framework. For $^{12}\mathrm{C}$ nucleus, the appearance of three-alpha clustering correlation in the ground state is investigated in relation to the strength of the two-body spin-orbit interaction.

Charge- and parity-projected Hartree–Fock study with the tensor force of light nuclei

We propose a mean field framework in which the charge and the parity symmetries of a single-particle state are broken. We break these symmetries to incorporate the correlation induced by the tensor force into a nuclear mean field model. We perform the charge- and the parity projections before variation and obtain a Hartree-Fock-like equation (charge- and parity-projected Hartree-Fock equation), which is solved self-consistently. We apply the Hartree-Fock-like equation to the alpha particle and find that, by breaking the parity and the charge symmetries, the correlation induced by the tensor force is obtained.

Charge- and parity-projected Hartree–Fock method for the strong tensor correlation and its application to the alpha particle

We propose a new mean-field-type framework which can treat the strong correlation induced by the tensor force. To treat the tensor correlation we break the charge and parity symmetries of a single-particle state and restore these symmetries of the total system by the projection method. We perform the charge and parity projections before variation and obtain a Hartree–Fock-like equation, which is solved self-consistently. We apply the Hartree–Fock-like equation to the alpha particle and find that by breaking the parity and charge symmetries, the correlation induced by the tensor force is obtained in the projected mean-field framework. We emphasize that the projection before the variation is important to pick up the tensor correlation in the present framework.

Charge- and parity-projected Hartree?Fock method for the strong tensor correlation and its application to the alpha particle

We propose a new mean-field-type framework which can treat the strong correlation induced by the tensor force. To treat the tensor correlation we break the charge and parity symmetries of a single-particle state and restore these symmetries of the total system by the projection method. We perform the charge and parity projections before variation and obtain a Hartree–Fock-like equation, which is solved self-consistently. We apply the Hartree–Fock-like equation to the alpha particle and find that by breaking the parity and charge symmetries, the correlation induced by the tensor force is obtained in the projected mean-field framework. We emphasize that the projection before the variation is important to pick up the tensor correlation in the present framework.

Negative-parity baryon spectrum in quenched anisotropic lattice QCD

We investigate the negative-parity baryon spectra in quenched lattice QCD. We employ the anisotropic lattice with standard Wilson gauge and O(a) improved Wilson quark actions at three values of lattice spacings with renormalized anisotropy xi=a_sigma/a_tau=4, where a_sigma and a_tau are spatial and temporal lattice spacings, respectively. The negative-parity baryons are measured with the parity projection. In particular, we pay much attention to the lowest SU(3) flavor-singlet negative-parity baryon, which is assigned as the Lambda(1405) in the quark model. For the flavor octet and decuplet negative-parity baryons, the calculated masses are close to the experimental values of corresponding lowest-lying negative-parity baryons. In contrast, the flavor-singlet baryon is found to be about 1.7 GeV, which is much heavier than the Lambda(1405). Therefore, it is difficult to identify the Lambda(1405) to be the flavor-singlet three-quark state, which seems to support an interesting picture of the penta-quark (uds qbar q) state or the N-Kbar molecule for the Lambda(1405).

Spin-3/2 nucleon andΔbaryons in lattice QCD

We present the first results for masses of spin-$\frac{3}{2}$ N and $\ensuremath{\Delta}$ baryons in lattice QCD using fat-link irrelevant clover fermions. Spin-$\frac{3}{2}$ interpolating fields, providing overlap with both spin-$\frac{3}{2}$ and spin-$\frac{1}{2}$ states, are considered. In the isospin-$\frac{1}{2}$ sector we observe, after appropriate spin and parity projection, a strong signal for the ${J}^{P}={\frac{3}{2}}^{\ensuremath{-}}$ state together with a weak but discernible signal for the ${\frac{3}{2}}^{+}$ state with a mass splitting near that observed experimentally. We also find good agreement between the ${\frac{1}{2}}^{\ifmmode\pm\else\textpm\fi{}}$ masses and earlier nucleon mass simulations with the standard spin-$\frac{1}{2}$ interpolating field. For the isospin-$\frac{3}{2}$ $\ensuremath{\Delta}$ states, clear mass splittings are observed between the various ${\frac{1}{2}}^{\ifmmode\pm\else\textpm\fi{}}$ and ${\frac{3}{2}}^{\ifmmode\pm\else\textpm\fi{}}$ channels, with the calculated level orderings in good agreement with those observed empirically.

Spin-3/2 baryons in lattice QCD

We present first results for masses ofspin-3/2 baryons in lattice QCD, using a novel fat-link clover fermion action in which only the irrelevant operators are constructed using fat links. In theisospin-1/2 sector; we observe, after appropriate spin and parity projection, a strong signal for the J P =3/2 − state, and find good agreement between the½ + mass and earlier nucleon mass simulations with aspin-½ interpolating field. For theisospin-3/2 Δ states, clear mass splittings are observed between the various½ ±and3/2 ± channels, with the calculated level orderings in good agreement with those observed empirically.

Counting Color: Ambivalence and Contradiction in the American Society of Newspaper Editors’ Discourse of Diversity

Of particular interest to any inquiry into the post-Kerner failure of newspapers to remedy past racial exclusion is why the industry’s seemingly progressive affirmative action efforts have fallen so far short of their goals. This article analyzes the discourse surrounding a moment of crisis in the American Society of Newspaper Editors’ diversity initiative to show that the organization’s demographic parity project in fact continually resecures white domination and marginalizes the non-white journalists it invites to work in its newsrooms.

Parity effect in a tiny SQUID

A tiny superconducting quantum interference device (SQUID) with a fixed electron number is studied based on the BCS theory with parity projection. It is shown that, especially when the Josephson junction comprises a single electronic channel, the Josephson coupling is significantly suppressed in the odd-parity state as compared to the even-parity state. The case of a multichannel junction and the possibility of experimental observation are also discussed.

N* masses from an anisotropic lattice QCD action

We report N* masses in the spin- 3 2 sector from a highly-improved anisotropic action. States with both positive and negative parity are isolated via a parity projection method. The extent to which spin projection is needed is examined. The gross features of the splittings from the nucleon ground state show a trend consistent with experimental results at the quark masses explored.

Study of Even-Z Nuclei Up to Mg with the Gogny Force Using AMD

Employing the Gogny force as an effective force, we study the ground state properties of light nuclei using antisymmetrized molecular dynamics (AMD). In this study, we are mainly concerned with the binding energies and radii of light even-Z isotopes, namely He, Be, C, O, Ne and Mg. Using a new technique to calculate the density dependent term of the effective force, we have realized fast and accurate calculations. From a comparison with Skyrme SIII results within the same AMD framework, we find that the Gogny and SIII forces well reproduce the experimental binding energies of stable nuclei. The two forces give almost equal radii, except in the case of 7 Be and 9 Be. For both forces, approximate treatment of the center-of-mass kinetic energy causes overestimation of the binding energy compared with the exact treatment. It also causes a decrease of the nuclear deformation compared with the exact treatment. We also carry out an energy variation after the parity projection. With regard to the binding energies and radii, parity-projected calculations do not exhibit a large difference compared to non-projected results, although the density distribution and clustering features are often significantly changed by the parity projection.

Deformation and Clustering in Even-Z Nuclei Up to Mg Studied Using AMD with the Gogny Force

Employing the Gogny force as an effective force, we study the ground state properties of light nuclei using antisymmetrized molecular dynamics (AMD). In a previous paper, we discussed the nuclear binding energies and nuclear radii of He, Be, C, O, Ne and Mg isotopes. In this paper, we mainly consider the deformation properties and the clustering nature of these isotopes. By comparing the calculated results with the AMD results by use of the Skyrme-III (SIII) force, we investigated the differences and similarities between the SIII force and the Gogny force. We find that the Gogny force yields rather better binding energy and larger deformation than the SIII force. We carry out the parity-projected calculations. Parity projection enhances the parity-violating deformation and the cluster structure of certain nuclei. Shape of the deformation energy surface is also changed by parity projection. This causes a competition between the mean-field-like structure and the cluster-like structure. A modified version of AMD, which employs deformed Gaussian wave packets instead of spherical ones, is shown to give large quadrupole moments in the case of Mg isotopes.

Paramagnetic breakdown of superconductivity in nanoscale particles at finite temperature

The effects of temperature and fluctuations on the paramagnetic breakdown of superconductivity in nanometer-scale systems are investigated using the static path plus random phase approximation to the partition function, implemented with number parity projection. The dependence with size and parity of the BCS critical fields is examined, but as size diminishes the ensuing transitions become strongly attenuated by gap fluctuations, which lead to non-negligible pairing effects in the magnetization and the odd-even free energy difference beyond the critical fields. The stepwise decrease of pairing correlations with increasing fields is also discussed. Comparison with exact results for a very small system confirms the predictions of the present method.

Shape-phase transitions in mixed parity systems and the onset of octupole deformation

Shape-phase transitions in mixed parity boson systems are studied using mean field theory. It is shown that without parity projection, shape transitions in mixed parity systems are very similar to those in positive parity systems, both requiring a finite interaction strength for the onset of deformation. The shape-phase diagram in mixed parity systems, however, changes significantly after parity projection, with the critical point for the onset of octupole deformation moving to zero strength. Shape transitions in the Lipkin model are shown to exhibit the same features, indicating that this is a direct consequence of parity projection in finite, mixed parity systems independent of the nature of interacting particles.

Structure of excited states of10Bestudied with antisymmetrized molecular dynamics

We study structure of excited states of 10Be with the method of variation after spin parity projection in the framework of antisymmetrized molecular dynamics. Present calculations describe many excited states and reproduce the experimental data of E2 and E1 transitions and the new data of the $\beta$ transition strength successfully. We make systematic discussions on the molecule-like structures of light unstable nuclei and the important role of the valence neutrons based on the results obtained with the framework which is free from such model assumptions as the existence of inert cores and clusters.

Theoretical description of the octupole phase transition in lanthanide nuclei at high spin

The phase transition to reflection asymmetric intrinsic nuclear shapes at high angular momentum is analyzed in the framework of the cranked Hartree-Fock-Bogoliubov approximation, with the Gogny interaction, using approximate parity projection before variation. The N = 88 isotones are studied and good agreement is found for the energy splitting and dipole moments before and after the transition.

Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics

In order to study the structure of excited states we perform a variational calculation after spin parity projection (VAP) within the framework of Antisymmetrized Molecular Dynamics (AMD). The framework is proven to be a new powerful approach for the study of the various structures of excited states because it is free from model assumptions such as inert cores, existence of clusters, and the axial symmetry. By using finite range interactions with a density dependent term we reproduce well all the energy levels below 15 MeV in $^{12}$C. This is the first theoretical model that reproduces many $E2$ transition rates and $\beta$ decays to $^{12}$C successfully.

Structure of excited states of unstable nuclei studied with antisymmetrized molecular dynamics

We study the structure of the excited states of unstable nuclei with variational calculations after spin parity projection in the framework of antisymmetrized molecular dynamics (AMD). The theoretical results reproduce energy levels of the excited states of , and . In the results of excited states both shell-model-like and clustering aspects appear. The valence neutrons play important roles for the development of the clustering structure in Be isotopes.

Fingerprints of Reflection Asymmetry at High Angular Momentum in Atomic Nuclei

The reflection asymmetric phase transition in nuclei at high angular momentum is analyzed in the framework of the cranked Hartree-Fock-Bogoliubov approximation, with the Gogny interaction, using approximate parity projection before variation. The $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}88$ isotones are studied and our results compared with experimental data. Good agreement is found for the energy splitting of the even and odd parity states and $B(E1)$ transition probabilities. Differences on intrinsic deformations, dipole moments, and pairing energies between odd and even parity states found at low spin disappear with increasing angular momentum.

Thermal and Quantal Fluctuations for Fixed Particle Number in Finite Superfluid Systems

We investigate fluctuations and even-odd effects in small superfluid systems at finite temperature by means of the static path approximation (SPA) plus random-phase approximation (RPA) treatment, where exact number parity projection is introduced. The RPA correction to the SPA is evaluated exactly. Results are given first for a schematic 20-level pairing model, where an excellent agreement with the exact canonical results is obtained both for even and odd systems, and then for a heavy nucleus, where the smoothing of the BCS transition and the even-odd effects in the pairing energy and specific heat are examined.