A reflection-asymmetric triaxial particle rotor model with three quasiparticles and a reflection-asymmetric triaxial rotor is developed, and applied to investigate the observed multiple chiral doublets (M\c{hi}D) candidates with octupole correlations in 131Ba, i.e., two pairs of positive-parity bands D3-D4 and D5-D6, as well as one pair of negative-parity bands D7-D8. The energy spectra, the energy staggering parameters, the B(M1)/B(E2) ratios, and the B(E1)/B(E2) ratios are reproduced well. The chiral geometries for these M\c{hi}D candidates are examined by the azimuthal plots, and the evolution of chiral geometry with spin is clearly demonstrated. The intrinsic structure for the positive-parity bands is analyzed and the possible pseudospin-chiral quartet bands are suggested.
The single-particle spectrum of deformed shell-model states in nuclei, is shown to exhibit a supersymmetric pattern. The latter involves deformed pseudospin doublets and intruder levels. The underlying supersymmetry is associated with the relativistic pseudospin symmetry of the nuclear mean-field Dirac Hamiltonian with scalar and vector potentials.
We investigate the spin and pseudospin symmetry in the single-particle resonant states by solving the Dirac equation containing a Woods-Saxon potential with Green's function method. Taking double-magic nucleus $^{208}$Pb as an example, three spin doublets $3d$, $2h$, and $1j$ and three pseudospin doublets $3\tilde{p}$, $1\tilde{i}$, and $1\tilde{j}$ are obtained for the single-neutron resonant states. By analyzing the energy splittings, we find that the threshold effect plays an important role in resonant pseudospin doubles. Besides, there is a reversed level structure of pseudospin doublets i…
The relevance of the pseudospin symmetry in nuclei is considered. New insight is obtained from looking at the continuous transition from a model satisfying the spin symmetry to another one satisfying the pseudospin symmetry. This study suggests that there are models allowing no missing single-particle states in this transition, contrary to what is usually advocated. It rather points out to an association of pseudospin partners different from the one usually assumed, together with a strong violation of the corresponding symmetry. A comparison with results obtained from some relativistic approac…
Relativistic symmetries of the Dirac Hamiltonian with a mixture of spherically symmetric Lorentz scalar and vector potentials, are examined from the point of view of supersymmetric quantum mechanics. The cases considered include the Coulomb, pseudospin and spin limits relevant, respectively, to atoms, nuclei and hadrons.
A reflection-asymmetric triaxial particle rotor model (RAT-PRM) with a quasi-proton and a quasi-neutron coupled with a reflection-asymmetric triaxial rotor is developed and applied to investigate the multiple chiral doublet (M$χ$D) bands candidates with octupole correlations in $^{78}$Br. The calculated excited energies, energy staggering parameters, and $B(M1)/B(E2)$ ratios are in a reasonable agreement with the data of the chiral doublet bands with positive- and negative-parity. The influence of the triaxial deformation $γ$ on the calculated $B(E1)$ is found to be significant. By changing $γ…
Recently it has been shown that pseudospin symmetry has its origins in a relativistic symmetry of the Dirac Hamiltonian. Using this symmetry we relate single - nucleon relativistic magnetic moments of states in a pseudospin doublet to the relativistic magnetic dipole transitions between the states in the doublet, and we relate single - nucleon relativistic Gamow - Teller transitions within states in the doublet. We apply these relationships to the Gamow - Teller transitions from $^{39}Ca$ to its mirror nucleus $^{39}K$.
We review the status of a quasi - degenerate doublets in nuclei, called pseudospin doublets, which were discovered about thirty years ago and the origins of which have remained a mystery, until recently. We show that pseudospin doublets originate from an SU(2) symmetry of the Dirac Hamiltonian which occurs when the scalar and vector potentials are opposite in sign but equal in magnitude. Furthermore, we survey the evidence that pseudospin symmetry is approximately conserved for a Dirac Hamiltonian with realistic scalar and vector potentials. We briefly discuss the relationship of pseudospin sy…
The identification of pseudospin symmetry as a relativistic symmetry of the Dirac Hamiltonian is used to explain the structure of radial nodes occurring in pseudospin doublets and to illuminate the special status of nodeless intruder states in nuclei.
The nearly degenerate triplet bands with the $πg_{9/2}^{-1}\otimes νh_{11/2} (g_{7/2},d_{5/2})$ configuration in $^{105}$Ag are studied via the relativistic mean-field (RMF) theory and the multiparticle plus rotor model (MPRM), which indicates that these bands are associated with chiral symmetry and pseudospin symmetry. The configuration-fixed constrained triaxial RMF calculations exhibit the pseudospin symmetry in single particle spectra and the triaxial shape coexistence. The experimental excitation energies and the electromagnetic transition probabilities for the triplet bands are reproduce…
We show that a natural explanation for characteristic features (angular momentum and radial quantum numbers) of pseudospin doublets and intruder levels in nuclei can be obtained by combining the relativistic attributes of pseudospin symmetry with known properties of Dirac bound states.
Dirac Hamiltonian is scaled in the atomic units $\hbar =m=1$, which allows us to take the non-relativistic limit by setting the Compton wavelength $% λ\rightarrow 0 $. The evolutions of the spin and pseudospin symmetries towards the non-relativistic limit are investigated by solving the Dirac equation with the parameter $λ$. With $λ$ transformation from the original Compton wavelength to 0, the spin splittings decrease monotonously in all spin doublets, and the pseudospin splittings increase in several pseudospin doublets, no change, or even reduce in several other pseudospin doublets. The var…
We review the status of quasi-degenerate doublets in nuclei, called pseudospin doublets, which were discovered about thirty years ago and the origins of which have remained a mystery, until recently. We show that pseudospin doublets originate from an SU(2) symmetry of the Dirac Hamiltonian which occurs when the sum of the scalar and vector potentials is a constant. Furthermore, we survey the evidence that pseudospin symmetry is approximately conserved in nuclear spectra and eigenfunctions and in nucleon-nucleus scattering for a Dirac Hamiltonian with realistic nuclear scalar and vector potenti…
Shell-model states involving several pseudospin doublets and ``intruder'' levels in nuclei, are combined into larger multiplets. The corresponding single-particle spectrum exhibits a supersymmetric pattern whose origin can be traced to the relativistic pseudospin symmetry of a nuclear mean-field Dirac Hamiltonian with scalar and vector potentials.
The model of coherent quadrupole and octupole motion (CQOM) is applied to describe non-yrast split parity-doublet spectra in odd-mass nuclei. The yrast levels are described as low-energy rotation-vibration modes coupled to the ground single-particle (s.p.) state, while the non-yrast parity-doublet structures are obtained as higher-energy rotation-vibration modes coupled to excited s.p. states. It is shown that the extended model scheme describes both the yrast and non-yrast quasi parity-doublet spectra and the related B(E1) and B(E2) transition rates in different regions of heavy odd-A nuclei.…
In the framework of the Relativistic Mean Field Approach a pseudospin dependence of the residual forces in nuclei is considered. It is shown that this dependence is relatively weak. As a consequence, a pseudospin dependence of the particle--core coupling is weak as well. This leads to a small splitting of the pseudospin doublets produced by a vector coupling of an odd particle pseudospin and a pseudo--orbital momentum of the core. Some possibilities for experimental investigations of the manifestations of the pseudospin symmetry in the spectra of odd nuclei with $Z\ge$ 100 are indicated.
The origin of pseudospin symmetry and its broken in real nuclei are discussed in the relativistic mean field theory. In the exact pseudospin symmetry, even the usual intruder orbits have degenerate partners. In real nuclei, pseudospin symmetry is approximate, and the partners of the usual intruder orbits will disappear. The difference is mainly due to the pseudo spin-orbit potential and the transition between them is discussed in details. The contribution of pseudospin-orbit potential for intruder orbits is quite large, compared with that for pseudospin doublets. The disappearance of the pseud…
The relativistic mean field theory in combination with the analytic continuation in the coupling constant method is used to determine the energies and widths of single-particle resonant states in Sn isotopes. It is shown that there exists clear shell structure in the resonant levels as appearing in the bound levels. In particular, the isospin dependence of pseudospin symmetry is clearly shown in the resonant states, is consistent with that in the bound states, where the splittings of energies and widths between pseudospin doublets are found in correlation with the quantum numbers of single-par…
Properties of excited states in $^{147}$Nd have been studied with multispectra and $γγ$ coincidence measurements. Twenty-four new $γ$-lines and three new levels have been introduced into the level scheme of $^{147}$Nd. Lifetimes of eight excited levels in $^{147}$Nd, populated in the $β$ decay of $^{147}$Pr, have been measured using the advanced time-delayed $βγγ$(t) method. Reduced transition probabilities have been determined for 30 $γ$-transitions in $^{147}$Nd. Potential energy surfaces on the ($β_{2}$,$β_{3}$) plane calculated for $^{147}$Nd using the Strutinsky method predict two single …
We report the first beyond-mean-field study of low-lying parity-doublet states in 224Ra by extending the multireference relativistic energy density functional method to include dynamical correlations related to symmetry restoration and quadrupole-octupole shape fluctuation with a generator coordinate method combined with parity, particle-number, and angular-momentum projections. We clarify full microscopically that the origin of spin-dependent parity splitting in low-spin states is related to the octupole shape stabilization of positive-parity states, the dominated shapes of which drift gradua…
Symmetry plays a fundamental role in physics. The quasi-degeneracy between single-particle orbitals $(n, l, j = l + 1/2)$ and $(n-1, l + 2, j = l + 3/2)$ indicates a hidden symmetry in atomic nuclei, the so-called pseudospin symmetry (PSS). Since the introduction of the concept of PSS in atomic nuclei, there have been comprehensive efforts to understand its origin. Both splittings of spin doublets and pseudospin doublets play critical roles in the evolution of magic numbers in exotic nuclei discovered by modern spectroscopic studies with radioactive ion beam facilities. Since the PSS was recog…
Low-spin states of 157Dy have been studied using the JUROGAM II array, following the 155Gd (α, 2n) reaction at a beam energy of 25 MeV. The level scheme of 157Dy has been expanded with four new bands. Rotational structures built on the [523]5/2- and [402]3/2+ neutron orbitals constitute new additions to the level scheme as do many of the inter- and intra-band transitions. This manuscript also reports the observation of cross I- to (I-1)- and I- to (I-1)+ E1 dipole transitions inter-linking structures built on the [523]5/2- (band 5) and [402]3/2+ (band 7) neutron orbitals. These interlacing ban…
Based on the reflection-asymmetric Nilsson potential, the parity-doublet rotational bands in odd-$A$ isotones \element{237}U and \element{239}Pu have been investigated by using the particle-number-conserving (PNC) method in the framework of the cranked shell model (CSM). The experimental kinematic moments of inertia (MOIs) and angular momentum alignments are reproduced very well by the PNC-CSM calculations. The significant differences of rotational properties between \element{237}U and \element{239}Pu are explained with the contribution of nucleons occupying proton octupole-correlation pairs o…
New transitions in neutron rich $^{100}$Y have been identified in a $^9$Be+$^{238}$U experiment with mass- and Z- gates to provide full fragment identification. These transitions and high spin levels of $^{100}$Y have been investigated by analyzing the high statistics $γ$-$γ$-$γ$ and $γ$-$γ$-$γ$-$γ$ coincidence data from the spontaneous fission of $^{252}$Cf at the Gammasphere detector array. Two new bands, 14 new levels and 23 new transitions have been identified. The $K^π=4^+$ new band decaying to an 1s isomeric state is assigned to be the high-$K$ Gallagher-Moszkowski (GM) partner of the kn…
Collective P- and T- odd moments produced by parity and time invariance violating forces in reflection asymmetric nuclei are considered. The enhanced collective Schiff, electric dipole and octupole moments appear due to the mixing of rotational levels of opposite parity. These moments can exceed single-particle moments by more than two orders of magnitude. The enhancement is due to the collective nature of the intrinsic moments and the small energy separation between members of parity doublets. In turn these nuclear moments induce enhanced T- and P- odd effects in atoms and molecules. First a …
