Parity Doublet Research Articles

Triangular D3h Symmetry in the Rotation-Vibration Spectrum of 12C

Our recent measurements of new states in 12C including the second 2+ at 10 MeV and the high spin 5− state at 22.4 MeV allow us to study the Rotation-Vibration spectrum of 12C from which evidence for a new (D3h) geometrical symmetry emerges. The data fit very well to the predicted (ground state) rotational band of an oblate equilateral triangular spinning top with a D3h symmetry characterized by the sequence of states: 0+, 2+, 3−, 4±, 5− with almost degenerate 4+ and 4− (parity doublet) states. Such a D3h symmetry was observed in triatomic molecules, and it is observed in 12C for the first time in nuclear physics. The triatomic like structure in nuclei is reminiscent of the discovery of diatomic α+14C structure in 18O. We discuss a classification of other rotation-vibration bands in 12C such as the (0+) Hoyle band and the (1−) bending mode band and suggest measurements in search of the predicted ("missing") states that may shed new light on clustering in 12C and light nuclei. In particular, the observation (or non observation) of the predicted ("missing") states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.654 MeV in 12C.

Separation of the [formula omitted] parity doublet in 20Ne

The (J,T)=(1,1) parity doublet in 20Ne at 11.26 MeV is a good candidate to study parity violation in nuclei. However, its energy splitting is known with insufficient accuracy for quantitative estimates of parity violating effects. To improve on this unsatisfactory situation, nuclear resonance fluorescence experiments using linearly and circularly polarized γ-ray beams were used to determine the energy difference of the parity doublet ΔE=E(1−)−E(1+)=−3.2(±0.7)stat(−1.2+0.6)sys keV and the ratio of their integrated cross sections Is,0(+)/Is,0(−)=29(±3)stat(−7+14)sys. Shell-model calculations predict a parity-violating matrix element having a value in the range 0.46–0.83 eV for the parity doublet. The small energy difference of the parity doublet makes 20Ne an excellent candidate to study parity violation in nuclear excitations.

The Rotation-Vibration Structure of 12C

The newly measured high spin Jπ = 5− state at 22.4(2) MeV in 12C reported in this conference, fits very well to the predicted (ground state) rotational band of an oblate equilateral triangular spinning top with a D3h symmetry characterized by the sequence of states: 0+, 2+, 3− 4±, 5− with almost degenerate 4+ and 4− (parity doublet) states. Such a D3h symmetry was observed in triatomic molecules, and it is observed here for the first time in nuclear physics. We discuss a classification of other rotation-vibration bands in 12C such as the (0+) Hoyle band and the (1−) bending mode band and suggest measurements in search of the predicted ("missing") states that may shed new light on clustering in 12C and light nuclei. In particular, the observation (or non observation) of the predicted ("missing") states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.654 MeV in 12 C.

Study of cluster structure in 13C with AMD+HON-constraint method

The 3α + n cluster states of 13C are discussed on the basis of antisymmetrized molecular dynamics with the constraint on the harmonic oscillator quanta. We predict two different kinds of the cluster states, the hoyle analogue state and the linear-chain state. The former is understood as the 0+2 state (Hoyle state) of 12C accompanied by a valence neutron occupying the s-wave. The latter constitute the parity doublet bands of Kπ = 1/2± owing to its parity asymmetric intrinsic structure.

Chiral density wave in nuclear matter

Inspired by recent work on inhomogeneous chiral condensation in cold, dense quark matter within models featuring quark degrees of freedom, we investigate the chiral density-wave solution in nu- clear matter at zero temperature and nonvanishing baryon number density in the framework of the so-called extended linear sigma model (eLSM). The eLSM is an effective model for the strong interaction based on the global chiral symmetry of quantum chromodynamics (QCD). It contains scalar, pseudoscalar, vector, and axial-vector mesons as well as baryons. In the latter sector, the nucleon and its chiral partner are introduced as parity doublets in the mirror assignment. The eLSM simultaneously provides a good description of hadrons in vacuum as well as nuclear matter ground-state properties. We find that an inhomogeneous phase in the form of a chiral density wave is realized, but only for densities larger than 2.4 {\rho}0, where {\rho}0 is the nuclear matter ground-state density.

Evidence for triangular D3h symmetry in 12C.

We report a measurement of a new high spin Jπ=5- state at 22.4(2) MeV in 12C which fits very well to the predicted (ground state) rotational band of an oblate equilateral triangular spinning top with a D3h symmetry characterized by the sequence 0+, 2+, 3-, 4±, 5- with almost degenerate 4+ and 4- (parity doublet) states. Such a D3h symmetry was observed in triatomic molecules, and it is observed here for the first time in nuclear physics. We discuss a classification of other rotation-vibration bands in 12C such as the (0+) Hoyle band and the (1-) bending mode band and suggest measurements in search of the predicted ("missing") states that may shed new light on clustering in 12C and light nuclei. In particular, the observation (or nonobservation) of the predicted ("missing") states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.654 MeV in 12C.

Superdeformed structures and low Ω parity doublet in Ne-S nuclei near neutron drip-line

AbstractThe structures of Ne, Na, Mg, Al, Si, P and S nuclei near the neutron drip-line region are investigated in the frame-work of relativistic mean field theory and non-relativistic Skyrme Hartree-Fock formalism. The recently discovered nuclei 40Mg and 42Al, which are beyond the drip-line predicted by various mass formulae are located within these models. We find many largely deformed neutron-rich nuclei, whose structures are analyzed. From the structure anatomy, we find that at large deformation low orbits of opposite parities (e.g. $$\frac{1} {2}^ +$$ and $$\frac{1} {2}^ -$$) occur close to each other in energy.

Superdeformation andα-cluster structure in35Cl

A superdeformed (SD) band has been identified in a non - alpha - conjugate nucleus 35Cl. It crosses the negative parity ground band above 11/2- and becomes the yrast at 15/2-. Lifetimes of all relevant states have been measured to follow the evolution of collectivity. Enhanced B(E2), B(E1) values as well as energetics provide evidences for superdeformation and existence of parity doublet cluster structure in an odd-A nucleus for the first time in A = 40 region. Large scale shell model calculations assign (sd)16(pf)3 as the origin of these states. Calculated spectroscopic factors correlate the SD states in 35Cl to those in 36Ar.

Compton scattering off massive fundamental bosons of pure spin 1

Relativistic particles with spins $J>0$ are described by means of multicomponent wave functions which transform covariantly according to Lorentz-group representations that contain at rest the spin of interest. The symmetry group of space-time provides not one but an infinity of such representations which are equivalent for free particles but yield different electromagnetic couplings upon gauging; thus the challenge is to develop criteria which allow us to select those of them which relate to physically detectable particles. We here take the position that the unitarity of the Compton scattering cross sections in the ultrarelativistic limit, when predicted by a consistent method for a spin-$1$ description, could provide such a criterion. We analyze the properties of massive fundamental spin-$1$ bosons transforming as antisymmetric tensors of second rank, $(1,0)\oplus(0,1)$. For this purpose, we employ the Poincar\'e covariant projector method, which provides consistent, causal, and representation specific Lagrangians. This formalism yields a twofold extension of the Proca Lagrangian for the description of spin-$1$ bosons, first from an in-built $g=1$ value of the gyromagnetic ratio to an unspecified $g\not=1$, and from, single-parity, to parity-doublet degrees of freedom. We find different results for Compton scattering in these theories and track the differences to the lack of universality of the vector-antisymmetric-tensor equivalence theorem which is specific only to Proca's framework, and valid for $g=1$, while it is violated within the covariant projector formalism. Our main result is that a finite Compton scattering differential cross section in the ultrarelativistic limit requires us to consider the contributions of both parities in $(1,0)\oplus(0,1)$. On that basis, we conclude that massive spin-$1$ bosons transforming as antisymmetric tensors are physical parity doublets.

Formation and local symmetry of the Holstein polaron in the t–J model

The formation and local symmetry of a spin–lattice polaron has been investigated semiclassically in planar Holstein t–J-like models within the exact diagonalization method. Due to the interplay of strong correlations and electron–lattice interaction, the doped hole may either move freely or lead to the localized spin–lattice distortion and form a Holstein polaron. The formation of a polaron breaks the translational symmetry by suppression of antiferromagnetic correlations and inducement of ferromagnetic correlations locally. Moreover, the breaking of local rotational symmetry around the polaron has been shown. The ground state is generically a parity singlet and the first excited state may be a parity doublet. Further consequences of the density of states spectra for comparison with scanning tunneling microscopy experiments are discussed.

Evolution of octupole collectivity in221Th

Reflection-asymmetric octupole structures are studied in the transitional nucleus ${}^{221}$Th. There are several modifications at intermediate spins to the previously reported yrast structure. The level scheme is considerably extended with yrast states up to (39/2)$\ensuremath{\hbar}$ established. A nonyrast octupole structure is identified which does not constitute a parity doublet with the yrast states, unlike those observed in some of the heavier odd-$A$ Th isotopes. This is attributed to the low $\mathit{K}$ value of the ground-state configuration. The strength of octupole correlations and quadrupole collectivity is found to vary with spin. The role of nucleon alignments in influencing collective properties is explored through cranking calculations incorporating octupole deformation.

Unexpected5/2−spin of the ground state in147Ba: No octupole deformation in ground states of odd-ABa isotopes

The ${}^{147}$Ba nucleus has been studied in prompt $\ensuremath{\gamma}$-ray spectroscopy using the EUROGAM2 Ge array. Spin and parity of the ground state has been determined to be $5/{2}^{\ensuremath{-}}$. The unexpected, $5/{2}^{\ensuremath{-}}$ ground state results from interaction with other negative-parity configurations. A new ground-state band has been established in ${}^{147}$Ba and some previously reported levels have been arranged into a $3/{2}^{\ensuremath{-}}$ band, which may correspond to the $3/{2}^{\ensuremath{-}}$[532] configuration. The new spin assignments in ${}^{147}$Ba suggest that the theoretical predictions of static octupole deformation in the ground state of ${}^{147}$Ba may not be be valid. No candidates for parity doublets have been found in ${}^{147}$Ba. Instead, an octupole band built on the ground state has been proposed.

Hybrid stars in an SU(3) parity doublet model

We apply an extended version of the SU(3) parity model, containing quark degrees of freedom, to study neutron stars. The model successfully reproduces the main thermodynamic features of QCD which allows us to describe the composition of dense matter. Chiral symmetry restoration is realized inside the star and the chiral partners of the baryons appear, their masses becoming degenerate. Furthermore, quark degrees of freedom appear in a transition to a deconfined state. Performing an investigation of the macroscopic properties of neutron stars, we show that observational constraints, like mass and thermal evolution, are satisfied and new predictions can be made.

Reflection symmetry of the near-yrast excitations in145Ba

Excited states in ${}^{145}$Ba, populated in spontaneous fission of ${}^{248}$Cm, have been studied by means of $\ensuremath{\gamma}$ spectroscopy, using high-fold $\ensuremath{\gamma}$ coincidences measured with the EUROGAM2 array of Ge detectors. The 507.7-keV level, which has been assigned in this work spin and parity 9/2${}^{+}$, belongs to the ${i}_{13/2}$ intruder band. We have identified in ${}^{145}$Ba a new 9/2${}_{2}^{\ensuremath{-}}$ level at 346.3 keV and a band on top of it. The negative parity indicates that it is not due to an octupole excitation. The position of the 5/2${}^{\ensuremath{-}}$ ground state, relative to the positive-parity band, could be reproduced by calculations with a reflection-symmetric potential and we do not observe a parity doublet to the ground state. Therefore we conclude that octupole excitations in ${}^{145}$Ba are most likely due to octupole vibrations coupled either to the reflection-symmetric ground state or to the ${i}_{13/2}$, decoupled neutron configuration.

Band structure of149Ce

The ${}^{149}$Ce nucleus has been studied via prompt $\ensuremath{\gamma}$-ray spectroscopy using the EUROGAM2 Ge array. The 3/2${}^{\ensuremath{-}}$ ground-state band has been extended to medium spins and the 3/2${}^{+}$ band has been connected to low-spin excitations established previously in ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay. No evidence for parity doublets in ${}^{149}$Ce was found.

Energy separation of the 1+/1− parity doublet in 20Ne

The parity doublet of 1+/1− states of Ne-20 at 11.26 MeV excitation energy is one of the best known test cases to study the weak part of the nuclear Hamiltonian. The feasibility of parity violation experiments depend on the effective nuclear enhancement factor (RN/|E(1+) − E(l−)|) which amplifies the impact of the matrix element of the weak interaction on observables indicating parity mixing. An extreme large value of Rn/|E(1+) − E(l−)| = (670 ± 7000) MeV−1 was reported for the doublet in 20Ne. The large uncertainty depends amongst others on the large uncertainty of |E(1+) − E(l−)| = 7.7±5.5 keV of the parity doublet. Nuclear resonance fluorescence (NRF) experiments with linearly and circularly polarized photon beams were performed at the High Intensity Gamma-Ray Source at Duke University, Durham, NC, USA, to determine the energy difference of the parity doublet with higher precision. The different angular distributions for 0+ → 1− → 0+ and 0+ → 1+ → 0+ NRF cascades in polarized γ-ray beams were used to determine the energy difference of the parity doublet to 2.9(13) keV.

Chiral thermodynamics of dense hadronic matter

We discuss phases of hot and dense hadronic matter using chiral Lagrangians. A two-flavored parity doublet model constrained by the nuclear matter ground state predicts chiral symmetry restoration. The model thermodynamics is shown within the mean-field approximation. A field-theoretical constraint on possible phases from the anomaly matching is also discussed.

Evidence for a negative-parity spin-doublet of nucleon resonances at 1.88 GeV

Evidence is reported for two nucleon resonances with spin-parity JP=1/2− and JP=3/2− at a mass just below 1.9 GeV. The evidence is derived from a coupled-channel analysis of a large number of pion and photo-produced reactions. The two resonances are nearly degenerate in mass with two resonances of the same spin but positive parity. Such parity doublets are predicted in models claiming restoration of chiral symmetry in high-mass excitations of the nucleon. Further examples of spin parity doublets are found in addition. Alternatively, the spin doublet can be interpreted as member of the 56-plet expected in the third excitation band of the nucleon. Implications for the problem of the missing resonances are discussed.

Dilaton-limit fixed point in hidden local symmetric parity doublet model

We study nucleon structure with positive and negative parities using a parity doublet model endowed with hidden local symmetry (HLS) with the objective to probe dense baryonic matter. The model -- that we shall refer to as "PDHLS model" for short -- allows a chiral-invariant mass of the nucleons unconnected to spontaneously broken chiral symmetry which comes out to be m_0 ~ 200 MeV at tree level from fitting to the decay width of the parity doubler, N(1535), to nucleon-pion and nucleon axial coupling g_A=1.267. The presence of a substantial m_0 that remains non-vanishing at chiral restoration presents a deep issue for the origin of the nucleon mass as well as will affect nontrivially the equation of state for dense baryonic matter relevant for compact stars. We construct a chiral perturbation theory at one-loop order and explore the phase structure of the model using renormalization group equations. We find a fixed point that corresponds exactly to the "dilaton limit" at which the HLS vector mesons decouple from the nucleons before reaching the vector manifestation fixed point. We suggest that cold baryonic system will flow to this limit as density increases toward that of chiral restoration.

Hyperons Analogous to the Λ(1405)

The low mass of the $\Lambda(1405)$ hyperon with $j^P = 1/2^-$, which is higher than the ground state $\Lambda(1116)$ mass by 290 MeV, is difficult to understand in quark models. We analyze the hyperon spectrum in the bound state approach of the Skyrme model that successfully describes both the $\Lambda(1116)$ and the $\Lambda(1405)$. This model predicts that several hyperon resonances of the same spin but with opposite parity form parity doublets that have a mass difference of around 300 MeV, which is indeed realized in the observed hyperon spectrum. Furthermore, the existence of the $\Xi(1620)$ and the $\Xi(1690)$ of $j^P=1/2^-$ is predicted by this model. Comments on the $\Omega$ baryons and heavy quark baryons are made as well.