Chiral Doublet Research Articles

THE STRUCTURE OF N(1535) IN THE ASPECT OF CHIRAL SYMMETRY

The structure of N(1535) is discussed in dynamical and symmetry aspects based on chiral symmetry. We find that the N(1535) in chiral unitary model has implicitly some components other than meson-baryon one. We also discuss the N(1535) in the chiral doublet picture.

Lifetime measurement of candidate chiral doublet bands in theRh103,104isotopes with the recoil-distance Doppler-shift method in inverse kinematics

Lifetimes of chiral candidate structures in $^{103,104}\mathrm{Rh}$ were measured using the recoil distance Doppler-shift method. The Gammasphere detector array was used in conjunction with the Cologne plunger device. Excited states of $^{103,104}\mathrm{Rh}$ were populated by the ${}^{11}\mathrm{B}({}^{96}\mathrm{Zr},4n){}^{103}\mathrm{Rh}$ and ${}^{11}\mathrm{B}({}^{96}\mathrm{Zr},3n){}^{104}$Rh fusion-evaporation reactions in inverse kinematics. Three and five lifetimes of levels belonging to the proposed chiral doublet bands are measured in $^{103}\mathrm{Rh}$ and $^{104}\mathrm{Rh}$, respectively. The previously observed even-odd spin dependence of the $B(M1)/B(E2)$ values is caused by the variation in the $B(E2)$ values, whereas the $B(M1)$ values decrease as a function of spin.

Search for multiple chiral doublets in rhodium isotopes

The deformation in rhodium isotopes is investigated using adiabatic and configuration-fixed constrained triaxial relativistic mean field (RMF) approaches. The triaxial deformations are found in the ground states of (102,104,106,108,110)Rh, which is consistent with triaxial Skyrme Hartree-Fock calculations. Several minima with triaxial deformation in (104,106,108,110)Rh are obtained by the configuration-fixed constrained calculations. The corresponding configurations are characterized by the quantum numbers vertical bar nljm > obtained by transforming wave functions from a Cartesian basis to a spherical basis. The possible existence of multiple chiral doublets (M chi D) is demonstrated in (104,106,108,110)Rh isotopes, based on different particle-hole configurations and triaxial deformations.

Electronic Structure of Multilayer Graphene

We study the electronic structure of multilayer graphene using a $\pi$-orbital continuum model with nearest-neighbor intralayer and interlayer tunneling. Using degenerate state perturbation theory, we show that the low-energy electronic structure of arbitrarily stacked graphene multilayers consists of chiral pseudospin doublets with a conserved chirality sum.

Lifetime measurement of candidate chiral doublet bands in the Rh103,104 isotopes with the recoil-distance Doppler-shift method in inverse kinematics

Lifetime measurement of candidate chiral doublet bands in the Rh103,104 isotopes with the recoil-distance Doppler-shift method in inverse kinematics

Alternative Experimental Evidence for Chiral Restoration in Excited Baryons

It has been suggested that chiral symmetry is approximately restored in excited hadrons at zero temperature and density (effective symmetry restoration). Using very general chiral symmetry arguments, it is shown that those excited nucleons that are assumed from the spectroscopic patterns to be in approximate chiral multiplets must only weakly decay into the Npi channel, (fN*Npi}/fNNpi)(2) << 1. However, those baryons that have no chiral partner must decay strongly with a decay constant comparable with fNNpi. It turns out that for all those well-established excited nucleons which can be classified into chiral doublets the ratio is (fN*Npi}/fNNpi)(2) approximately 0.1 or much smaller for the high-spin states. In contrast, the only well-established excited nucleon for which the chiral partner cannot be identified from the spectroscopic data, N(1520), has a decay constant into the Npi channel that is comparable with fNNpi.

High-spin structure ofAg105: Search for chiral doublet bands

The high-spin structure of the $^{105}\mathrm{Ag}$ nucleus has been studied by using the $^{100}\mathrm{Mo}$($^{10}\mathrm{B}$, $5n)$$^{105}\mathrm{Ag}$ reaction to search for chiral doublet bands based on the three-quasiparticle $\ensuremath{\pi}{g}_{9/2}\ensuremath{\nu}({h}_{11/2}){}^{2}$ configuration. The level scheme of $^{105}\mathrm{Ag}$ has been extended. New bands were found and the placement of the yrast $\ensuremath{\pi}{g}_{9/2}\ensuremath{\nu}({h}_{11/2}){}^{2}$ band was corrected. No side band to the yrast $\ensuremath{\pi}{g}_{9/2}\ensuremath{\nu}({h}_{11/2}){}^{2}$ band could be found in the present experiment. This observation indicates that the \ensuremath{\gamma}-soft shape in the $^{106}\mathrm{Ag}$ changed to a more \ensuremath{\gamma}-rigid axially symmetric shape in the yrast $^{105}\mathrm{Ag}$ configuration. However, a new pair of bands was observed to show the expected properties of a chiral doublet structure.

A canonical [formula omitted

It is shown that quark mass dependence induced by one-loop corrections to the Breit–Fermi spin-dependent one-gluon-exchange potential permits an accurate determination of heavy–light meson masses. Thus the Ds(2317) is a canonical cs¯ meson in this scenario. The multiplet splitting relationship of chiral doublet models, M(1+)−M(1−)=M(0+)−M(0−), holds to good accuracy in the D and Ds systems, but is accidental. Radiative transitions and bottom flavoured meson masses are discussed.

FIFTY YEARS OF DISCOVERIES IN NUCLEAR STRUCTURE

The complementary nature of the Vanderbilt experimental work and the theoretical work of the Frankfurt group on the rotation-vibration model, the generalized collective model, shape coexistence and cluster radioactivity is described. Recent discoveries in neutron-rich nuclei γ-vibrational bands compared with RVM and GCM are presented. Ultimate examples of cluster radioactivity in cold binary and ternary fission are discussed. Finally, we present evidence for the evolution from axial symmetry in 101 Y to maximum triaxialilty in 113 Rh and for chiral doublet bands in neutron-rich triaxial even-even nuclei between A =106 - 112.

Chiral bands for a quasi-proton and quasi-neutron coupled with a triaxial rotor

A particle rotor model (PRM) with a quasi-proton and a quasi-neutron coupled with a triaxial rotor is developed and applied to study chiral doublet bands with configurations of an ${h}_{11/2}$ proton and an ${h}_{11/2}$ quasi-neutron. With pairing treated by the BCS approximation, the present quasiparticle PRM is aimed at simulating one proton and many neutron holes coupled with a triaxial rotor. After a detailed analysis of the angular momentum orientations, energy separation between the partner bands, and behavior of electromagnetic transitions, for the first time we find aplanar rotation or equivalently chiral geometry beyond the usual one proton and one neutron hole coupled with a triaxial rotor.

Examining the Chiral Geometry in 104Rh and 106Rh

The criteria for chiral doublet bands based on one particle and one holecoupled to a triaxial rotor have been summarized. Two representativecases in A~100 odd–odd nuclei, nearly degenerate ΔI = 1doublet bands in 104Rh and 106Rh, are checked against thesechiral criteria. It is shown that 106Rh possesses better chiralgeometry than 104Rh, although the energy near degeneracy isachieved in 104Rh in comparison with the constant energy separationof doublet bands in 106Rh.

Triaxiality, chiral bands and gamma vibrations in [formula omitted] nuclei

Prompt γ – γ – γ coincidence measurements of A = 99 –114 neutron-rich nuclei populated in the spontaneous fission of 252Cf were made with Gammasphere. The high statistics data, 5.7×10 11 triples and higher folds, opened up discoveries of new band structures and significant extensions of previously known bands. The new data for ground bands in 99,101Y, 101,105Nb, 105,107,109,111Tc and 111,113Rh when compared with one quasi-particle plus triaxial rotor calculation, revealed a smooth transition from axial symmetry in 99,101Y to maximize triaxiality in 111,113Rh. In 106Mo, 110,112Ru, pairs of Δ I = 1 doublet bands are established to high spins. Their constant and equal kinetic moments of inertia, small energy differences between states of the same spin and very similar B(E2)/B(M1) ratios for each band in these nuclei suggest that these are chiral doublet bands. If they are not chiral, then a new symmetry is indicted. Extended one- and new two-phonon γ -vibrational bands are observed in 110,112Ru. The extended one-phonon bands in 104-108Mo, and 108-112Ru exhibit an unexpected reversal in the energy level staggering pattern with spin. The first one- and two-phonon γ -bands in an odd- A nucleus are seen in 105Mo with level energies almost identical to these same bands known in 104Mo.

Candidate chiral doublet bands in the odd-odd nucleusCs126

The candidate chiral doublet bands recently observed in $^{126}\mathrm{Cs}$ have been extended to higher spins, several new linking transitions between the two partner members of the chiral doublet bands are observed, and \ensuremath{\gamma}-intensities related to the chiral doublet bands are presented by analyzing the $\ensuremath{\gamma}$-$\ensuremath{\gamma}$ coincidence data collected earlier at the NORDBALL through the $^{116}\mathrm{Cd}$($^{14}\mathrm{N}$, $4n$)$^{126}\mathrm{Cs}$ reaction at a beam energy of 65 MeV. The intraband $B(M1)/B(E2)$ and interband $B(M1){}_{\mathrm{in}}/B(M1){}_{\mathrm{out}}$ ratios and the energy staggering parameter, S(I), have been deduced for these doublet bands. The results are found to be consistent with the chiral interpretation for the two structures. Furthermore, the observation of chiral doublet bands in $^{126}\mathrm{Cs}$ together with those in $^{124}\mathrm{Cs}$, $^{128}\mathrm{Cs}$, $^{130}\mathrm{Cs}$, and $^{132}\mathrm{Cs}$ also indicates that the chiral conditions do not change rapidly with decreasing neutron number in these odd-odd Cesium isotopes.

Collective bands in 104,106,108Mo

We have used our analysis of γ-γ-γ data (5.7 × 1011 triples and higher folds) taken with Gammasphere from prompt γ rays emitted in the spontaneous fission of 252Cf to study the collective bands in 104,106,108Mo. The one-phonon and two-phonon γ-vibrational bands and known two-quasiparticle bands in neutron-rich 104,106Mo were extended to higher spins. The one-and two-phonon γ-vibrational bands have remarkably close energies for transitions from the same spin states and identical moments of inertia. Several new bands are observed and are proposed as quasiparticle bands in 104,106Mo, along with the first β-type vibrational band in 106Mo. The quasiparticle bands have essentially constant moments of inertia near the rigid-body value that indicate blocking of the pairing interaction. Candidates for chiral doublet bands in 106Mo are strong. These are the first reported chiral vibrational bands in an even-even nucleus.

Conjugacy classes and chiral doublets in the Hénon Hamiltonian repeller

Conjugacy classes hidden behind orbital symmetries under reflection are brought to light through the recognition of the fundamental role played by certain algebraic clusters underlying orbital equations of the area-preserving Hénon map, a discrete proxy of open Hamiltonian systems that exhibit chaotic scattering and transport. Specific number-fields ruling orbital coordinates are shown to slave large sets of orbits into being necessarily nonlinearly coupled. Particularly remarkable is the conjugacy class characterized by non-self-symmetric chiral doublets which completely dominates at higher periods.

Possible existence of multiple chiral doublets inRh106

Adiabatic and configuration-fixed constraint triaxial relativistic mean field (RMF) approaches are developed for the first time and a new phenomenon, the existence of multi chiral-doublets (M$\chi$D), i.e., more than one pairs of chiral doublets bands in one single nucleus, is suggested for nuclei in A~100 region, typically for $^{106}$Rh, based on the triaxial deformations together with their corresponding proton and neutron configurations.

Soft chiral vibrations in 106Mo

High-spin states in neutron-rich 106Mo were investigated by detecting the prompt γ-rays in the spontaneous fission of 252Cf with Gammasphere. Several new bands are observed. Two sets of ΔI = 1 bands in 106Mo are found to have all the characteristics of a new class of chiral vibrational doublets. Tilted axis cranking calculations support the chiral assignment and indicate that the chirality is generated by neutron h11/2 particle and mixed d5/2, g7/2 hole coupled to the short and long axis, repectively.

Nuclear Data Sheets for [formula omitted

Nuclear spectroscopic information for known nuclides of mass number 132 (Cd,In,Sn,Sb,Te,I,Xe,Cs,Ba,La, Ce,Pr,Nd,Pm,Sm,Eu) with Z = 48 to 63 and N = 84 to 69 have been evaluated and presented together with adopted energies and Jπ of levels in these nuclei. No excited state data are yet available for 132Cd. The identification of the 132Eu nuclide remains uncertain. Fairly rich structures are known in all the other A = 132 nuclides. Superdeformed structures are known in 132Pr (four SD bands and a highly-deformed structure) and in 132Nd (four SD or highly-deformed bands). Possible chiral doublet bands of π h 11 / 2 ν h 11 / 2 configuration have recently been identified in 132Pr, 132La and 132Cs. The decay scheme of 132La to 132Ba has been studied in several works, including some recent papers, but in the opinion of the evaluators, this decay scheme still suffers from incompleteness, especially from the point-of-view of separate level schemes from the ground state and the isomeric activities. The separate level schemes from two activities of 132Sb decay to 132Te are also not well established, although, the combined activity has recently been studied by the Yale group. This evaluation represents a complete update of previous evaluations of A = 132 : by Yu.V. Sergeenkov (1992Se04); and by H.R. Hiddleston and C.P. Browne (1976Hi02).

Search for the chiral doublet bands in 122Cs

High spin states in the odd–odd nucleus 122Cs have been studied by in-beam γ-ray spectroscopy with a 107Ag(19F,1p3n) fusion-evaporation reaction at a beam energy of 85 MeV. A previously known πh11/2 ⊗ νh11/2 yrast band was confirmed and its spin I was re-examined. A ΔI = 2 band was identified, which together with another known ΔI = 2 band forms a side band of the πh11/2 ⊗ νh11/2 yrast band. The two observed πh11/2 ⊗ νh11/2 bands are proposed as a pair of chiral doublet bands in 122Cs based on a systematic comparison with those in the neighbouring odd–odd Cs isotopes, as well as the relativistic mean field and the triaxial particle-rotor-model calculations.

Possible assignment of chiral twin bands inI188r

High-spin states in the doubly-odd $Z=77$ nucleus $^{188}\mathrm{I}\mathrm{r}$ were populated in the $^{186}\mathrm{W}(^{7}\mathrm{L}\mathrm{i},5n)$ reaction at $52\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$. Two nearly degenerate $\ensuremath{\Delta}I=1$ sequences with the same parity were established. Both bands have been assigned the $\ensuremath{\pi}{h}_{9∕2}\ensuremath{\bigotimes}\ensuremath{\nu}{i}_{13∕2}$ configuration, based on the systematic behavior of these excitations in the $\mathrm{Ir}$ nuclei and on the measured values for the $B(M1)∕B(E2)$ ratios, and they are suggested as candidates for a chiral doublet.