FIG 5 - uploaded by Jerzy Dudek
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Evolution of the angular frequency vector in the intrinsic frame along the HF planar (circles) and chiral (triangles) bands. Solid lines show the analogous bands obtained in the classical model. Scales are given in units of MeV/¯ h.
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Self-consistent solutions for the so-called planar and chiral rotational bands in 132La are obtained for the first time within the Skyrme-Hartree-Fock cranking approach. It is suggested that the chiral rotation cannot exist below a certain critical frequency which under the approximations used is estimated as Planck's omega(crit) approximately 0.5-...
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Citations
... In studying the evolution of the chiral mode with rotation, the critical frequency (hω c ) is an essential concept. It was first introduced within the self-consistent Skyrme-Hartree-Fock cranking approach [33,34] and represents the minimum rotational frequency needed for stable chiral solutions. Below thehω c , the angular momentum lies in the sl plane. ...
... One realizes that in the cranking model, the rotational frequencyhω serves as the variable characterizing the velocity of nuclear rotation. The critical frequencyhω c is proposed in this model to describe the transition from planar to aplanar rotation [33,34,40,41]. However, in the PRM, the total spin I is a conserved quantum number and serves as the variable to characterize the nuclear rotation. ...
... As the spin reaches I = 13h, a noticeable kink appears in the plot of the yrast band, indicating the onset of aplanar rotation, consistent with the observation in Fig. 3 for P(θ , ϕ). This kink represents the critical frequencyhω c where the transition from planar to aplanar rotation occurs [33,34,40,41] and is delineated with a shadow for emphasis. Furthermore, the right panel of Fig. 5 demonstrates clearly that an increase in the ∆ n corresponds to a decrease in the value ofhω c . ...
... Several theoretical approaches have been employed to explain the observed doublet bands. For example, the particle rotor model (PRM) [1][2][3][4][5], the tilted axis cranking (TAC) model [6][7][8][9][10], the TAC plus random-phase approximation (RPA) [11], the collective Hamiltonian method [12,13], the interacting boson-fermion fermion model [14], and the angular momentum projection (AMP) method [15][16][17]. The most successful approach has been made in terms of chirality in nuclear rotation by Dimitrov et al. [10]. ...
... Several theoretical approaches have been employed to explain the observed doublet bands. For example, the particle rotor model (PRM) [1][2][3][4][5], the tilted axis cranking (TAC) model [6][7][8][9][10], the TAC plus random-phase approximation (RPA) [11], the collective Hamiltonian method [12,13], the interacting boson-fermion fermion model [14], and the angular momentum projection (AMP) method [15][16][17]. The most successful approach has been made in terms of chirality in nuclear rotation by Dimitrov et al. [10]. ...
Large-scale shell model calculations are performed within the model spaces sd, zbme and psdpf, to study the positive- and negative-parity energy levels and electromagnetic transitions in the exotic 20-23Mg isotopes. Core-polarization effects on reduced transition probability are introduced through first order perturbation theory, which allows for higher energy configurations through excitations of nucleons from core orbits to that outside model space up to 9 ℏω . The core-polarization effects have been improved the agreement of B(E2) with their corresponding experimental data, and have ignorable effect on B(M1) and B(E1).
... Several theoretical approaches have been employed to explain the observed doublet bands. For example, the particle rotor model (PRM) [1][2][3][4][5], the tilted axis cranking (TAC) model [6][7][8][9][10], the TAC plus random-phase approximation (RPA) [11], the collective Hamiltonian method [12,13], the interacting boson-fermion fermion model [14], and the angular momentum projection (AMP) method [15][16][17]. The most successful approach has been made in terms of chirality in nuclear rotation by Dimitrov et al. [10]. ...
... The nuclear chirality has been extensively investigated with many theoretical approaches, including the triaxial particle rotor model (PRM) [1,10,11,12,13,14,15,16], the three-dimensional (3D) cranking model [17,1,18,19,20,21], the 3D cranking model with the random phase approximation [22,23], the 3D cranking model with the collective Hamiltonian [24,25,26], the interacting bosonfermion-fermion model [27], the generalized coherent state model [28], and the projected shell model [29,30,31,32,33]. Among them, the 3D cranking relativistic [20,21] and nonrelativistic [19] density functional theories can describe the nuclear chirality in a microscopic and self-consistent way, predict new chiral nuclei, and include important effects such as the core polarizations and nuclear currents [34,19,35]. ...
... The nuclear chirality has been extensively investigated with many theoretical approaches, including the triaxial particle rotor model (PRM) [1,10,11,12,13,14,15,16], the three-dimensional (3D) cranking model [17,1,18,19,20,21], the 3D cranking model with the random phase approximation [22,23], the 3D cranking model with the collective Hamiltonian [24,25,26], the interacting bosonfermion-fermion model [27], the generalized coherent state model [28], and the projected shell model [29,30,31,32,33]. Among them, the 3D cranking relativistic [20,21] and nonrelativistic [19] density functional theories can describe the nuclear chirality in a microscopic and self-consistent way, predict new chiral nuclei, and include important effects such as the core polarizations and nuclear currents [34,19,35]. ...
... The nuclear chirality has been extensively investigated with many theoretical approaches, including the triaxial particle rotor model (PRM) [1,10,11,12,13,14,15,16], the three-dimensional (3D) cranking model [17,1,18,19,20,21], the 3D cranking model with the random phase approximation [22,23], the 3D cranking model with the collective Hamiltonian [24,25,26], the interacting bosonfermion-fermion model [27], the generalized coherent state model [28], and the projected shell model [29,30,31,32,33]. Among them, the 3D cranking relativistic [20,21] and nonrelativistic [19] density functional theories can describe the nuclear chirality in a microscopic and self-consistent way, predict new chiral nuclei, and include important effects such as the core polarizations and nuclear currents [34,19,35]. ...
The microscopic understanding on the influence of the pairing correlations or the superfluidity on the nuclear chiral rotation has been a longstanding and challenging problem. Based on the three-dimensional cranking covariant density functional theory, a shell-model-like approach with exact particle number conservation is implemented to take into account the pairing correlations and applied for the chiral doublet bands in Nd135. The data available are well reproduced. It is found that the superfluidity can reduce the critical frequency and make the chiral rotation easier. The mechanism is that the particle/hole alignments along the short/long axis are reduced by the pairing correlations, resulting in the enhanced preference of the collective rotation along the intermediate axis, and inducing the early appearance of the chiral rotation.
... Conversely, the values located in the middle of the plot which are close to unity correspond to the ideal chiral configurations |L and |R , where the three spins are perpendicular to each other. According to Ref. [19], the existence of the chiral critical frequency would result in the planar orientation of the three angular momentum vectors for the I = 9h isomeric bandhead. From the two opposite planar geometries, the one with proton angular momentum j p tending towards the momentum of the core j R is energy favored by Coriolis interaction. ...
... The nuclear state of a definite spin, |JM , can be expressed as a product of the states of proton | j p , neutron | j n , and core | j R coupled to the total angular momentum as follows: j p , j n coupled to a vector j pn = j p + j n , which, in turn, is coupled with j R to J = j pn + j R , |( j p j n ) j pn j R ; JM = m p ,m n ,m pn ,m R j p m p j n m n | j pn m pn j pn m pn j R m R |JM | j p m p | j n m n | j R m R . (19) There are several possible j pn quantum numbers, indicating that the total spin state |JM may be formed in several ways, here called coupling schemes. A single coupling scheme given by Eq. (19) defines a unique set of expected mutual angles between each pair of the angular momentum vectors. ...
The g factor of the isomeric I=9+ bandhead of the yrast states in Cs128 is obtained from the time differential perturbed angular distribution measurement performed with the electromagnet at IPN Orsay. An external magnetic field of 2.146 T at the target position was attained with GAMIPE reaction chamber surrounded by four high-purity germanium detectors, of which two were low-energy photon spectrometer type. The results are in accordance with πh11/2⊗νh11/2−1I=9+ bandhead assignment and are discussed in the context of chiral interpretation of the Cs128 nucleus as a composition of the odd proton, odd neutron, and even-even core with their angular momentum vectors. The obtained g-factor value was compared with predictions of the particle-rotor model. The experimental g factor corresponds to the nonchiral geometry of the isomeric bandhead. This observation indicates the existence of the chiral critical frequency in Cs128 and may explain the absence of the chiral doublet members for I<13ℏ.
... For the description of spectra with higher excitation energies, the cranking model [19] based on nonrelativistic [20,21] and relativistic [22,23] DFTs have been demonstrated as powerful tools. Moreover, the two-dimensional and the three-dimensional tilted axis cranking DFTs have been successfully applied to many novel rotational phenomena [24][25][26][27][28]. However, the band crossing phenomena cannot be properly described by the cranking approach [29] because the cranking states are obtained at the constant rotational frequency rather than the constant angular momentum. ...
The effects of four-quasiparticle configurations and time-odd interactions are investigated in the framework of configuration-interaction projected density functional theory by taking the yrast states of Fe60 as examples. Based on the universal PC-PK1 density functional, the energies of the yrast states with spin up to 20ℏ and the available B(E2) transition probabilities are well reproduced. The yrast states are predicted to be of four-quasiparticle structure above spin I=16ℏ. The inclusion of the time-odd interactions increases the kinetic moments of inertia and delays the appearance of the first band crossing, and, thus, improves the description of the data.
... [20,21] and relativistic [22,23] DFTs have been demonstrated as powerful tools. Moreover, two-and three-dimensional tilted axis cranking DFTs have been successfully applied to many novel rotational phenomena [24][25][26][27][28]. However, the band crossing phenomena cannot be properly described by the cranking approach [29] because the cranking states are obtained at a constant rotational frequency rather than a constant angular momentum. ...
The effects of four-quasiparticle configurations and time-odd interactions are investigated in the framework of configuration interaction projected density functional theory by taking the yrast states of 60Fe as examples. Based on the universal PC-PK1 density functional, the energies of the yrast states with spin up to 20\hbar and the available B(E2) transition probabilities are well reproduced. The yrast states are predicted to be of four-quasiparticle structure above spin I = 16\hbar. The inclusion of the time-odd interactions increases the kinetic moments of inertia and delays the appearance of the first band crossing, and, thus, improves the description of the data.
... [43,46] for details. Both relativistic and nonrelativistic DFTs have been extended with the TAC method to investigate nuclear chirality [47,48]. In particular, the recent TAC-CDFT has been widely used to investigate the chirality in nuclei 106 Rh [48], 135 Nd [49], 136 Nd [19], and 106 Ag [50]. ...
The dynamics of chiral nuclei is investigated for the first time with the time-dependent and tilted axis cranking covariant density functional theories on a three-dimensional space lattice in a microscopic and self-consistent way. The experimental energies of the two pairs of the chiral doublet bands in $^{135}$Nd are well reproduced without any adjustable parameters beyond the well-defined density functional. A novel mechanism, i.e., chiral precession, is revealed from the microscopic dynamics of the total angular momentum in the body-fixed frame, whose harmonicity is associated with a transition from the planar into aplanar rotations with the increasing spin. This provides a fully microscopic and dynamical view to understand the chiral excitations in nuclei.
... [43,46] for details. Both relativistic and nonrelativistic DFTs have been extended with the TAC method to investigate nuclear chirality [47,48]. In particular, the recent TAC-CDFT has been widely used to investigate 2469-9985/2022/105(1)/L011301 (6) ...
... [43,46] for details. Both relativistic and nonrelativistic DFTs have been extended with the TAC method to investigate nuclear chirality [47,48]. In particular, the recent TAC-CDFT has been widely used to investigate the chirality in nuclei 106 Rh [48], 135 Nd [49], 136 Nd [19], and 106 Ag [50]. ...
The dynamics of chiral nuclei is investigated for the first time with the time-dependent and tilted axis cranking covariant density functional theories on a three-dimensional space lattice in a microscopic and self-consistent way. The experimental energies of the two pairs of the chiral doublet bands in Nd135 are well reproduced without any adjustable parameters beyond the well-defined density functional. A novel mechanism, i.e., chiral precession, is revealed from the microscopic dynamics of the total angular momentum in the body-fixed frame, whose harmonicity is associated with a transition from the planar into aplanar rotations with the increasing spin. This provides a fully microscopic and dynamical view to understand the chiral excitations in nuclei.
