Antimagnetic Rotation Research Articles

Progress on microcosmic investigation for magnetic and antimagnetic rotation

Magnetic rotation and antimagnetic rotation are exotic rotational phenomena observed in weakly deformed or near-spherical nuclei, which are respectively interpreted in terms of the shears mechanism and two shearslike mechanism. Since their observations, magnetic rotation and antimagnetic rotation phenomena have been mainly investigated in the framework of tilted axis cranking based on the pairing plus quadrupole model. For the last decades, the covariant density functional theory and its extension have been proved to be successful in describing the properties of nuclei and many nuclear phenomena. Recently, the self-consistent tilted axis cranking covariant density functional theories based on the non-linear meson-exchange models and a point-coupling interaction were established, and applied successfully to investigate the magnetic and antimagnetic rotations. This paper mainly reviews the application of the tilted axis cranking covariant density functional theory in the magnetic rotation and antimagnetic rotation phenomena. Take $^{60}$Ni, $^{105}$Cd and $^{110}$Cd as examples, we will introduce the description on the energy spectra, the relation between the spin and the rotational frequency, the reduced $M1$ and $E2$ transition probabilities. By investigating the orientation of the neutron and proton angular momenta, the shears mechanism for the magnetic rotation and the two-shears-like mechanism for the antimagnetic rotation are examined.

Lifetime measurement for the possible antimagnetic rotation band inPd101

Lifetime measurements were made for the $\ensuremath{\nu}{h}_{11/2}$ band in $^{101}\mathrm{Pd}$, which had been interpreted as a possible antimagnetic rotation band based on the comparison of $I\ensuremath{-}\ensuremath{\omega}$ behavior with the calculation of a semiclassical particle-rotor model in our previous study. Doppler broadened line shapes were analyzed for the decaying $\ensuremath{\gamma}$ rays in the band following the reaction $^{68}\mathrm{Zn}(^{37}\mathrm{Cl},\phantom{\rule{0.16em}{0ex}}\text{1p3n})^{101}\mathrm{Pd}$. The semiclassical particle-rotor model was modified to reproduce both the $I\ensuremath{-}\ensuremath{\omega}$ plot and the $B(E2)$ behavior simultaneously for the antimagnetic rotation bands in Pd and Cd nuclei, for which $B(E2)$ values had been measured so far. Reasonable agreements between the experiment and the calculation were obtained. It is concluded that the lower part of the $\ensuremath{\nu}{h}_{11/2}$ band in $^{101}\mathrm{Pd}$ can be interpreted as an antimagnetic rotor.

Antimagnetic rotation and sudden change of electric quadrupole transition strength in 143Eu

Lifetimes of the states in the quadrupole structure in 143Eu have been measured using the Doppler shift attenuation method and the parity of the states in the sequence has been firmly identified from polarization measurements using the Indian National Gamma Array. The decreasing trends of the deduced quadrupole transition strength B(E2) with spin, along with increasing J(2)/B(E2) values before the band crossing, conclusively establish the origin of these states as arising from antimagnetic rotation. The abrupt increase in the B(E2) values after the band crossing in the quadrupole band, a novel feature observed in the present experiment, may possibly indicate the crossing of different shears configurations resulting in the re-opening of a shears structure. The results are reproduced well by numerical calculations within the framework of a semi-classical geometric model.

Magnetic and antimagnetic rotation inCd110within tilted axis cranking relativistic mean-field theory

The self-consistent tilted axis cranking relativistic mean-field (TAC-RMF) theory based on a point-coupling interaction is applied to investigate the observed magnetic and antimagnetic rotations in the nucleus $^{110}\mathrm{Cd}$. The energy spectra, the relation between the spin and the rotational frequency, the deformation parameters, and the reduced $M1$ and $E2$ transition probabilities are studied with the various configurations. It is found that the configuration has to be changed to reproduce the energy spectra and the relations between the spin and the rotational frequency for both the magnetic and antimagnetic rotational bands. The shears mechanism for the magnetic rotation and the two-shears-like mechanism for the antimagnetic rotation are examined by investigating the orientation of the neutron and proton angular momenta. The calculated electromagnetic transitions $B(M1)$ and $B(E2)$ are in reasonable agreement with the data, and their tendencies are coincident with the typical characteristics of the magnetic and antimagnetic rotations.

Role of neutrons in the coexistence of magnetic and antimagnetic rotation bands inCd107

Negative parity high-spin states of $^{107}\mathrm{Cd}$ have been investigated using the reaction $^{94}\mathrm{Zr}({}^{18}\mathrm{O}$,5n), from the $\ensuremath{\gamma}$-ray coincidence events recorded by the Indian National Gamma Array. A magnetic dipole ($M1$) band structure was established for the first time in this nucleus decaying to the low-spin states via several paths. Lifetimes of five in-band levels in this band have been measured using the Doppler shift attenuation method. The experimentally deduced $B(M1)$ values are found to decrease with increasing spin. The experimental observations, interpreted by the tilted axis cranking calculations, suggest that the $M1$ band is developed from the shears mechanism based on the 5qp configuration $\ensuremath{\pi}({g}_{9/2}^{\ensuremath{-}2})\ensuremath{\bigotimes}\ensuremath{\nu}({h}_{11/2}{g}_{7/2}^{2})$, which is then crossed by another 5qp configuration $\ensuremath{\pi}({g}_{9/2}^{\ensuremath{-}2})\ensuremath{\bigotimes}\ensuremath{\nu}({h}_{11/2}^{3})$. The semiclassical model of the shears mechanism also reasonably reproduces the decreasing trend of the observed $B(M1)$ values as a function of spin, supporting the above interpretation. The present work highlights the unique coexistence of both magnetic and antimagnetic (observed by us earlier) rotation bands in one nucleus arising from the same proton configuration, but different neutron configurations.

Antimagnetic rotation in104Pd

The electric quadrupole transition rates for the high-spin yrast states of ${}^{104}$Pd have been measured by using the Doppler-shift attenuation method. These values decrease with the increase of angular momentum, which can be associated with the phenomenon of antimagnetic rotation. In the present work, a numerical calculation based on the semiclassical particle plus rotor model for antimagnetic rotation has been employed, giving a good description of the experimental Routhian and the transition rates and providing conclusive evidence of antimagnetic rotation in a nucleus other than cadmium.

Competition between antimagnetic and core rotation in109Cdwithin covariant density functional theory

The tilted axis cranking model based on covariant density functional theory is used to investigate the negative-parity yrast sequence in ${}^{109}\mathrm{Cd}$. The energy spectra, the relation between spin and rotational frequency, deformation parameters, and reduced $E2$ transition probabilities are calculated, which are in good agreement with available data. The orientation of angular momentum is also extracted and discussed in detail. By investigating microscopically the orientation of angular momentum and the contributions of antimagnetic rotation and core rotation to the total angular momentum, we find that ${}^{109}\mathrm{Cd}$ should be a critical transitional nucleus between the antimagnetic and core rotations.

Tilted axis cranking covariant density functional theory and its applications

Recent progress on tilted axis cranking covariant density functional theory and its applications to nuclear magnetic and antimagnetic rotation are briefly presented. In particular, the magnetic rotation band in 198 Pb and the antimagnetic rotational band in 105 Cd are discussed.

Nuclear superfluidity for antimagnetic rotation in105Cd and106Cd

The effects of nuclear superfluidity on antimagnetic rotation bands in ${}^{105}$Cd and ${}^{106}$Cd are investigated by the cranked shell model with the pairing correlations and blocking effects treated by a particle-number-conserving method. The experimental moments of inertia and the reduced $B(E2)$ transition values are excellently reproduced. Nuclear superfluidity is essential to reproduce the experimental moments of inertia. The two-shears-like mechanism for the antimagnetic rotation is investigated by examining the shears angle, i.e., the closing of the two-proton-hole angular momenta, and its sensitive dependence on nuclear superfluidity is revealed.

Comment on “Evidence of antimagnetic rotation in odd-A105Cd”

Comment on “Evidence of antimagnetic rotation in odd-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow /><mml:mn>105</mml:mn></mml:msup></mml:math>Cd”

Multiple antimagnetic rotation bands in odd-A107Cd

Lifetimes of the excited states of a pair of positive-parity $\ensuremath{\Delta}I=2$ bands of ${}^{107}$Cd have been measured by using the Doppler-shift attenuation method. The obtained $B(E2)$ transition rates significantly decrease with increasing spin, a behavior typical of antimagnetic rotation (AMR). The observed results, interpreted by the semiclassical model (SCM) calculations, confirm these bands to be AMR bands resulting from the coupling of a pair of high-$\ensuremath{\Omega}$ ${g}_{9/2}$ proton holes to aligned ${g}_{7/2}{({h}_{11/2})}^{2}$ neutron particles. This is the first evidence for two AMR bands in a single nucleus.

Progress on tilted axis cranking covariant density functional theory for nuclear magnetic and antimagnetic rotation

Magnetic rotation and antimagnetic rotation are exotic rotational phenomena observed in weakly deformed or near-spherical nuclei, which are respectively interpreted in terms of the shears mechanism and two shearslike mechanism. Since their observations, magnetic rotation and antimagnetic rotation phenomena have been mainly investigated in the framework of tilted axis cranking based on the pairing plus quadrupole model. For the last decades, the covariant density functional theory and its extension have been proved to be successful in describing series of nuclear ground-states and excited states properties, including the binding energies, radii, single-particle spectra, resonance states, halo phenomena, magnetic moments, magnetic rotation, low-lying excitations, shape phase transitions, collective rotation and vibrations, etc. This review will mainly focus on the tilted axis cranking covariant density functional theory and its application for the magnetic rotation and antimagnetic rotation phenomena.

Nuclear current and antimagnetic rotation in 105Cd

The effects of the nuclear current in the antimagnetic rotation band of 105Cd have been investigated in a fully self-consistent and microscopic way by using the tilted axis cranking relativistic mean-field model. It was found that the inclusion of nuclear current leads to a higher angular momentum and thus a larger kinetic moment of inertia at a given rotational frequency. As a consequence, the B(E2) values with current are always smaller than those without current.

Candidate antimagnetic rotational band in112In

High spin states of ${}^{112}$In were investigated using the reaction ${}^{110}$Pd(${}^{7}$Li,5$n$)${}^{112}$In at a beam energy of 50 MeV. A new level sequence has been found in this nucleus and the configuration $\ensuremath{\pi}{g}_{9/2}^{\ensuremath{-}2}{g}_{7/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ before the alignment and the configuation $\ensuremath{\pi}{g}_{9/2}^{\ensuremath{-}2}{g}_{7/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}^{3}$ after the alignment are assigned. The self-consistent titled axis cranking relativistic mean-field model calculations are performed to interpret the rotational structure and the characteristic features of antimagnetic rotation have been presented for the band after backbend.

Possible antimagnetic rotational band and neutron alignment in101Pd

High-spin states of ${}^{101}$Pd were studied through in-beam $\ensuremath{\gamma}$-ray spectroscopy by using the reaction ${}^{68}$Zn(${}^{37}$Cl, $1p3n$). The band based on the ${h}_{11/2}$ neutron orbital was extended up to (${\frac{51}{2}}^{\ensuremath{-}}$), and the band based on the ${d}_{5/2}$ neutron orbital was revised. Various transitions decaying to these bands were observed, and consequently several side bands were established. Electric dipole transitions from the $\ensuremath{\nu}{h}_{11/2}$ band to the $\ensuremath{\nu}{d}_{5/2}$ band were also observed. The structure of the $\ensuremath{\nu}{h}_{11/2}$ band is discussed from the viewpoint of antimagnetic rotation based on a semiclassical particle-rotor model by taking neutron alignments into account. The possible existence of octupole correlations is also discussed on the basis of $B(E1)/B(E2)$ ratios for the decays of the $\ensuremath{\nu}{h}_{11/2}$ band.

Covariant density functional theory for antimagnetic rotation

Following the previous letter on the first microscopic description of the antimagnetic rotation (AMR) in 105Cd, a systematic investigation and detailed analysis for the AMR band in the frame-work of tilted axis cranking (TAC) model based on covariant density functional theory are carried out. After performing the microscopic and self-consistentTAC calculations with an given density functional, the configuration for the observed AMR band in 105Cd is obtained from the single-particle Routhians. With the configuration thus obtained, the tilt angle for a given rotational frequency is determined self-consistently by minimizing the total Routhian with respect to the tilt angle. In such a way, the energy spectrum, total angular momenta, kinetic and dynamic moments of inertia, and the B(E2) values for the AMR band in 105Cd are calculated. Good agreement with the data is found. By investigating microscopically the contributions from neutrons and protons to the total angular momentum, the "two-shears-like" mechanism in the AMR band is clearly illus-trated. Finally, the currents leading to time-odd mean fields in the Dirac equation are presented and discussed in detail. It is found that they are essentially determined by the valence particles and/or holes. Their spatial distribution and size depend onthe specific single-particle orbitals and the rotational frequency.

Antimagnetic Rotation Band in Nuclei: A Microscopic Description

Covariant density functional theory and the tilted axis cranking method are used to investigate antimagnetic rotation (AMR) in nuclei for the first time in a fully self-consistent and microscopic way. The experimental spectrum as well as the B(E2) values of the recently observed AMR band in (105)Cd are reproduced very well. This gives a further strong hint that AMR is realized in specific bands in nuclei.

Possibility of antimagnetic rotation in odd-ACd isotopes

The classical particle plus rotor model for antimagnetic rotation (AMR) has been used to investigate the possibility of observation of AMR in the high spin levels of $^{105,\,107,\,109}$Cd. The calculated I($\omega$) plot and B(E2) values have been compared with the available experimental data.

Evidence of antimagnetic rotation in odd-ACd105

The lifetimes of the levels above spin $23/{2}^{\ensuremath{-}}$ in the negative-parity yrast band of $^{105}\mathrm{Cd}$ have been measured using the Doppler shift attenuation method. The obtained $B(E2)$ values are small and show a decrease with an increase in spin. This establishes, for the first time, antimagnetic rotation (AMR) in an odd-$A$ nucleus. An excellent agreement between the theoretical (semiclassical model) and experimental results along with a large ${\mathcal{I}}^{(2)}/B(E2)$ ratio for the states strongly suggests that the structure of the levels beyond spin $23/{2}^{\ensuremath{-}}$ has the character of a twin-shears type AMR band resulting from the coupling of a pair of ${g}_{9/2}$ proton holes with aligned ${h}_{11/2}$ and $({g}_{7/2}){}^{2}$ neutron particles, along with a small contribution from the core rotation.

Possible magnetic and antimagnetic rotations inDy144

High spin states of $^{144}\mathrm{Dy}$ have been studied through in-beam $\ensuremath{\gamma}$-ray spectroscopy by using the reaction $^{92}\mathrm{Mo}(^{56}\mathrm{Fe},2p2n)$. It has been found that the continuation of the ground-state band forks into three $\ensuremath{\Delta}I=2$ bands above the ${8}^{+}$ state. This forking has been attributed to the alignments of $\ensuremath{\pi}{h}_{11/2}^{2}$ or $\ensuremath{\nu}{h}_{11/2}^{\ensuremath{-}2}$ configurations with the help of the systematics in neighboring nuclei. Additionally a negative-parity sideband of $\ensuremath{\Delta}I=2$ cascades has been observed to start from the ${5}^{(\ensuremath{-})}$ state and continue to a dipole band above the (${13}^{\ensuremath{-}}$) state through another negative-parity sideband of $\ensuremath{\Delta}I=2$ cascades in between. These structures have been discussed from the viewpoint of a competition between ``Magnetic Rotation'' and ``Anti-magnetic Rotation'' based on a classical particles-plus-rotor model.