Chiral Bands Research Articles

Coupling Parameter in the Single-j Shell Model

We propose a modified formula which is used to determine the coupling parameter C in the Hamiltonian of the single-j shell. In comparison with the previously known formula, the new formula improves the agreement between the intruder single-j levels and the Nilsson ones. For studies of chiral bands within the particle rotor model, the new coupling parameter will considerably influence the energy splitting between the doublet bands.

Chirality in odd-A nucleus 135Nd in particle rotor model

A particle rotor model is developed which couples several valence protons and neutrons to a rigid triaxial rotor core. It is applied to investigating the chirality in odd-A nucleus 135Nd with πh11/22⊗νh11/2−1 configuration for the first time in a fully quantal approach. For the two chiral sister bands, the observed energies and the B(M1) and B(E2) values for the in-band as well as interband transitions are reproduced excellently. Root mean square values of the angular momentum components and their probability distributions are used for discussing in detail the chiral geometry of the aplanar rotation and its evolution with angular momentum. Chirality is found to change from a soft chiral vibration to nearly static chirality at spin I=39/2 and back to another type of chiral vibration at higher spin.

Chiral doublet bands and energy-level crossing

Different definitions for chiral doublet bands based on excitation energies, B(E2) and B(M1) respectively are discussed in the triaxial particle rotor model. For the ideal chiral geometry, the selection rules of the electromagnetic transitions in different band definitions are illustrated. It is also shown that the energy-level crossings between chiral doublet bands may occur.

Search for chiral bands in A ∼ 110 neutron-rich nuclei

High spin states in A ∼ 110 neutron-rich 106Mo, 110Ru and 112Ru nuclei have been reinvestigated by measuring the prompt γ-rays from the spontaneous fission of 252Cf. Two similar sets of bands are observed to high spins in each of three nuclei. Through analyzing of characters of the band structures, the chiral doublet bands are suggested in 106Mo, 110Ru and 112Ru.

πg9/2 ⊗vh11/2 doublet bands in A ∼ 100 mass region

Using the model with one particle and one hole coupled with a triaxial rotor, the πg9/2−1 ⊗vh11/2 doublet bands in the A ∼ 100 mass region are studied, and compared with the πh11/2−1 ⊗vh11/2 doublet bands. It is found that the calculated results for the configuration of πg9/2−1 ⊗vh11/2 are very similar the results for a pure h11/2 proton particle and a neutron quasiparticle with λn = ∊5. After including the pair correlation, the model describes the candidate chiral doublet bands in 106Rh successfully, which supports the interpretation of chirality geometry.

Triaxial deformation in 104Rh of the chiral doublet bands

Triaxial relativistic mean field (RMF) approaches are used to study the properties of 104Rh. The existence of multiple chiral doublets is suggested for 104Rh based on the triaxial deformations and their corresponding proton and neutron configurations.

CHIRAL SYMMETRY IN ATOMIC NUCLEI

The significant progresses of the chirality in atomic nuclei are briefly reviewed for both experimental and theoretical sides. Chiral doublet bands beyond one-particle and one-hole coupled with a triaxial rotor as well as the possibilities of new phenomenon MχD are discussed.

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.

Possible chirality in the doubly-oddTl198nucleus: Residual interaction at play

A candidate for chiral bands was found in $^{198}\mathrm{Tl}$ for the first time in a mass region of oblate (or nonaxial with $\ensuremath{\gamma}\ensuremath{\geqslant}{30}^{\ifmmode^\circ\else\textdegree\fi{}}$) deformed nuclei. Two bands show very similar quasiparticle alignments, moments of inertia, and $B(M1)/B(E2)$ ratios. They have a relative excitation energy of about 500 keV and different patterns of energy staggering. Calculations using the two-quasiparticle-plus-triaxial-rotor model with residual proton-neutron interaction included show that a triaxial deformation with $\ensuremath{\gamma}~{44}^{\ifmmode^\circ\else\textdegree\fi{}}$ agrees very well with all the experimental observations. Furthermore, considerable energy staggering for both partner bands was calculated for this $\ensuremath{\pi}{h}_{9/2}\ensuremath{\bigotimes}\ensuremath{\nu}{i}_{13/2}^{\ensuremath{-}1}$ configuration at $\ensuremath{\gamma}~{30}^{\ifmmode^\circ\else\textdegree\fi{}}$, suggesting that chiral bands may have substantial energy staggering.

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

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.

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.

Effect ofγSoftness on the Stability of Chiral Geometry: Spectroscopy ofAg106

A study of the nucleus 106Ag has revealed the presence of two strongly coupled negative-parity rotational bands up to the 19- and 20- states, respectively, which cross each other at spin I approximately 14. The data suggest that near the crossover point the bands correspond to different shapes, which is different to the behavior expected from a pair of chiral bands. Inspection of the properties of these bands indicates a triaxial and a planar nature of rotation for the two structures. Possible causes for this may be understood in terms of a shape transformation resulting from the large degree of gamma softness of 106Ag. These data, along with the systematics of the odd-odd structures in the mass 100 region, suggest that gamma softness has marked implications for the phenomenon of nuclear chirality.

Doublet bands inCs126in the triaxial rotor model coupled with two quasiparticles

The positive-parity doublet bands based on the $\ensuremath{\pi}{h}_{11/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ configuration in $^{126}\mathrm{Cs}$ were investigated in the two quasiparticles coupled with a triaxial rotor model. The energy spectra $E(I)$, energy staggering parameter $S(I)=[E(I)\ensuremath{-}E(I\ensuremath{-}1)]/2I,B(M1)$ and $B(E2)$ values, intraband $B(M1)/B(E2)$ ratios, $B(M1){}_{\mathrm{in}}/B(M1){}_{\mathrm{out}}$ ratios, and orientation of the angular momentum for the rotor as well as the valence proton and neutron are calculated. After including the pairing correlation, good agreement has been obtained between the calculated results and the data available, which supports the interpretation of this positive-parity doublet bands as chiral bands.

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.

CHIRALITY IN NUCLEAR STRUCTURE: AN EXPERIMENTAL VIEW INTO UNDERLYING SYMMETRIES

The experimental information on the observed nearly degenerate bands in the N = 75 isotones, in particular 134 Pr , which is considered as the best candidate for chiral bands, if critically analyzed, shows that most properties of the bands, in particular the recently measured branching ratios and lifetimes, are in clear disagreement with the interpretation of the two bands as chiral bands. For I = 14 - 18 in 134 Pr , where the observed energies are almost degenerate, a value of 2.0(4) for the ratio of the transition quadrupole moments of the two bands was obtained, which implies a considerable difference in the nuclear shape associated with the two bands. The insufficiency of the near-degeneracy criterion to trace nuclear chirality is clearly emphasized.

Charge and Spin Hall Conductivity in Metallic Graphene

Graphene has an unusual low-energy band structure with four chiral bands and half-quantized and quantized Hall effects that have recently attracted theoretical and experimental attention. We study the Fermi energy and disorder dependence of its spin Hall conductivity sigma(xy)(SH). In the metallic regime we find that vertex corrections enhance the intrinsic spin Hall conductivity and that skew scattering can lead to sigma(xy)(SH) values that exceed the quantized ones expected when the chemical potential is inside the spin-orbit induced energy gap. We predict that large spin Hall conductivities will be observable in graphene even when the spin-orbit gap does not survive disorder.

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.