Multiple chirality in nuclear rotation: A microscopic view

Abstract

Covariant density functional theory and three-dimensional tilted axis cranking are used to investigate multiple chirality in nuclear rotation for the first time in a fully self-consistent and microscopic way. Two distinct sets of chiral solutions with negative and positive parities, respectively, are found in the nucleus 106 Rh. The negative-parity solutions reproduce well the corresponding experimental spectrum as well as the B(M 1)/B(E2) ratios of the transition strengths. This indicates that a predicted positive-parity chiral band should also exist. Therefore, it provides a further strong hint that multiple chirality is realized in nuclei. two chiral systems differ from each other by their intrinsic chirality, and are thus related by the chiral operator T R(π) that combines time reversal T and spatial rotation by π.The broken chiral symmetry in the body-fixed frame should be restored in the laboratory frame. This gives rise to the so-called chiral doublet bands, which consist of a pair of nearly-degenerate ∆I = 1 sequences with the same parity (for reviews see Refs. [2,3]).The chiral geometry of a rotating triaxial nucleus requires substantial angular momentum components along all of the three principal axes. For actual nuclear systems, this relates to configurations where high-j valence particles and holes align along the short and long axes, respectively, and the collective core rotates around the intermediate axis.Based on such configurations, so far, many candidates for chiral doublet bands have been reported experimentally in the A ∼ 80, 100, 130, and 190 mass regions of the nuclear chart; see e.g.Figure 1: (color online). A schematic picture for the aplanar rotation of a triaxial nucleus. The arrow J denotes the total angular momentum vector, and the short, intermediate, and long axes are denoted by x, y, and z, respectively.These observations indicate that chirality is not restricted to a specific configuration in a certain mass region. In particular, two pairs of chiral bands with different configurations were discussed respectively in Refs. [8,9] for 105 Rh. The resultant possibility of having more than one pair of chiral bands in a single nucleus was demonstrated by searching for triaxial chiral configurations in Rh isotopes using constrained relativistic mean-field calculations in Ref. [19], which introduced the acronym MχD for multiple chiral doublet bands. Further studies were carried out in Refs. [20,21,22]. Strong

Ground state properties and potential energy surfaces of 270Hs from multidimensionally-constrained relativistic mean field model

“…As reviewed in Ref. [78], this empirical functional has been very successful in describing nuclear ground state properties, e.g., the Coulomb displacement energies between mirror nuclei [79], nuclear binding energies [80][81][82] and quadrupole moments [83][84][85] and phase transitions in the nuclear shape [86], and low-energy excited states including nuclear chiral rotations [87] and magnetic and antimagnetic rotations [88][89][90][91][92]. PC-PK1 has also been used to study properties of SHN [93][94][95].…”

Microscopic resolution of the nuclear chiral conundrum with crossing twin bands in Ag106

“…To examine the possible presence of chiral vibration, it is crucial to check the calculated orientation angles θ and φ of the total angular momentum J in the intrinsic frame. Here, θ is the angle between the angular momentum and the long axis, and φ the angle between the angular momentum projection onto the intermediate-short plane and the short axis [30]. In the present calculations with the four-quasiparticle configuration, the polar angle θ varies from 46 • to 69 • driven by the increasing rotational frequency, while the azimuth angle φ vanishes at all rotational frequencies.…”

“…Covariant DFT starts from a Lagrangian, and the corresponding Kohn-Sham equations have the form of a Dirac equation with effective fields S(r) and V µ (r) derived from this Lagrangian [37][38][39][40][41]. In the 3DTAC method [30], these fields are triaxially deformed, and the calculations are carried out in the intrinsic frame rotating with a constant angular velocity vector ω, pointing in an arbitrary direction in space:…”

“…It provides a consistent treatment of the spin degrees of freedom, includes the complex interplay between the large Lorentz scalar and vector self-energies induced at the QCD level [25], and naturally provides the nuclear currents induced by the spatial parts of the vector self-energies, which play an essential role in rotating nuclei. To describe nuclear rotation, covariant DFT has been extended with the cranking method [26][27][28][29][30], and this has provided a satisfactory description of rotational excited states all over the periodic table and has demonstrated high predictive power [31][32][33][34][35][36]. For nuclear chirality, in particular, the recently developed three-dimensional tilted axis cranking (3DTAC) approach based on covariant DFT has been successfully applied for describing the multiple chirality in 106 Rh [30].…”

Behavior of the collective rotor in nuclear chiral motion

“…With the prediction [9] and confirmation [10] of multiple chiral doublets (MχD) in a single nucleus, the investigation of nuclear chirality continues to be one of the hottest topic in modern nuclear physics [11-33].By now it is well-known that chiral rotations (aplanar rotations of the total angular momentum) can exist only above a critical spin I, see Refs. [23,32,[34][35][36]. Actually, at low spins a chiral vibration, understood as an oscillation of the total angular momentum between the left-and the right-handed configuration, happens.…”