Dynamic Moment Of Inertia Research Articles

Band head spin assignment of superdeformed bands in A ∼60−80 mass region through nuclear softness formula

The nuclear softness formula has been applied to obtain the band head spin ([Formula: see text]) of 7 superdeformed rotational bands ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]) in A[Formula: see text]60−80 mass region. To obtain the band head spin ([Formula: see text]) of 7 superdeformed rotational bands in A[Formula: see text]60−80 mass region least square fitting method is used. The parameters are extracted by fitting the intraband transition energies in the nuclear softness formula from where the root mean deviation (RMD) between the calculated and the observed transition energies are obtained. The calculated transition energies are in good agreement with the experimental transition energies whenever exact band head spin ([Formula: see text]) is assigned. The calculated values of dynamic moment of inertia and its variation with rotational frequency for seven superdeformed rotational bands in A[Formula: see text]60−80 mass region are also studied. Hence, it is suggested that the nuclear softness formula works very well in A[Formula: see text]60−80 mass region.

Interplay between antimagnetic and collective rotation in 58Fe

The self-consistent tilted axis cranking covariant density functional theory based on the point-coupling interaction PC-PK1 is applied to investigate the possible existence of antimagnetic rotation in the nucleus [Formula: see text]Fe. The observed data for Bands 3 and 4 are reproduced well with two assigned configurations. It is found that the interplay between antimagnetic rotation and collective motion plays an essential role in both bands due to the presence of considerable deformation. In particular, for Band 4, collective rotation is dominant in the competition with antimagnetic rotation. Moreover, it is shown that the behavior of the ratios between the dynamic moments of inertia and the [Formula: see text] values reflects the interplay between antimagnetic and collective rotation.

Spins of superdeformed rotational bands in Tl isotopes

The two-parameter model defined for even-even nuclei viz. soft-rotor formula is used to assign the band-head spin of the 17 rotational bands in Tl isotopes. The least-squares fitting method is employed to obtain the spins of these bands in the \(A\sim 190\) mass region. The calculated transition energies are found to depend sensitively on the proposed spin. Whenever a correct spin assignment is made, the calculated and experimental transition energies coincide very well. The dynamic moment of inertia is also calculated and its variation with rotational frequency is explored.

Systematics of a vibrational effect on the dynamic moments of inertia in superdeformed bands in the mass ≈150 region

Systematics of a vibrational effect on the dynamic moments of inertia in superdeformed bands in the mass <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>≈</mml:mo><mml:mn>150</mml:mn></mml:math> region

Identical high- K three-quasiparticle rotational bands

A comprehensive study of high-K three-quasiparticle rotational bands in odd-A nuclei indicates the similarity in $\gamma$ -ray energies and dynamic moment of inertia $\Im^{(2)}$ . The extent of the identicality between the rotational bands is evaluated by using the energy factor method. For nuclei pairs exhibiting identical bands, the average relative change in the dynamic moment of inertia $\Im^{(2)}$ is also determined. The identical behaviour shown by these bands is attributed to the interplay of nuclear structure parameters: deformation and the pairing correlations. Also, experimental trend of the $ I(\hbar)$ vs. $\hbar \omega$ (MeV) plot for these nuclei pairs is shown to be in agreement with Tilted-Axis Cranking (TAC) model calculations.

Band head spin assignment of superdeformed bands in 86Zr

Two parameter expressions for rotational spectra viz. variable moment of inertia (VMI), ab formula and three parameter Harris ω2 expansion are used to assign the band head spins (I0) of four rotational superdeformed bands in 86Zr. The least-squares fitting method is employed to obtain the band head spins of these four bands in the A ∼ 80 mass region. Model parameters are extracted by fitting of intraband γ-ray energies, so as to obtain a minimum root-mean-square (rms) deviation between the calculated and the observed transition energies. The calculated transition energies are found to depend sensitively on the assigned spins. Whenever an accurate band head spin is assigned, the calculated transition energies are in agreement with the experimental transition energies. The dynamic moment of inertia is also extracted and its variation with rotational frequency is investigated. Since a better agreement of band head spin with experimental results is found using the VMI model, it is a more powerful tool than the ab formula and Harris ω2 expansion.

Antimagnetic rotation in 108,110In with tilted axis cranking relativistic mean-field approach**Supported by National Natural Science Foundation of China (11205068, 11205069, 11405072, 11475072, 11547308) and China Postdoctoral Science Foundation (2012M520667)

Based on tilted axis cranking relativistic mean-field theory within point-coupling interaction PC-PK1, the rotational structure and the characteristic features of antimagnetic rotation for ΔI = 2 bands in 108,110In are studied. Tilted axis cranking relativistic mean-field calculations reproduce the experimental energy spectrum well and are in agreement with the experimental I ∼ ω plot, although the calculated spin overestimates the experimental values. In addition, the two-shears-like mechanism in candidate antimagnetic rotation bands is clearly illustrated and the contributions from two-shears-like orbits, neutron (gd) orbits above Z = 50 shell and Z = 50, N = 50 core are investigated microscopically. The predicted B(E2), dynamic moment of inertia ℑ(2), deformation parameters β and γ, and ℑ(2)/B(E2) ratios in tilted axis cranking relativistic mean-field calculations are discussed and the characteristic features of antimagnetic rotation for the bands before and after alignment are shown.

Band structure inSn113

The structure of collective bands in $^{113}\mathrm{Sn}$, populated in the reaction $^{100}\mathrm{Mo}(^{19}\mathrm{F},\phantom{\rule{0.16em}{0ex}}p5n)$ at a beam energy of 105 MeV, has been studied. A new positive-parity sequence of eight states extending up to 7764.9 keV and spin $(39/{2}^{+})$ has been observed. The band is explained as arising from the coupling of the odd valence neutron in the ${g}_{7/2}$ or the ${d}_{5/2}$ orbital to the deformed 2p-2h proton configuration of the neighboring even-$A$ Sn isotope. Lifetimes of six states up to an excitation energy of 9934.9 keV and spin $47/{2}^{\ensuremath{-}}\mathrm{belonging}$ to a $\mathrm{\ensuremath{\Delta}}I=2$ intruder band have been measured for the first time, including an upper limit for the last state, from Doppler-shift-attenuation data. A moderate average quadrupole deformation ${\ensuremath{\beta}}_{2}=0.22\ifmmode\pm\else\textpm\fi{}0.02$ is deduced from these results for the five states up to spin $43/{2}^{\ensuremath{-}}$. The transition quadrupole moments decrease with increase in rotational frequency, indicating a reduction of collectivity with spin, a feature common for terminating bands. The behavior of the kinematic and dynamic moments of inertia as a function of rotational frequency has been studied and total Routhian surface calculations have been performed in an attempt to obtain an insight into the nature of the states near termination.

From superdeformation to extreme deformation and clusterization in theN≈Znuclei of theA≈40mass region

A systematic search for extremely deformed structures in the N~Z nuclei of the A~40 mass region has been performed for the first time in the framework of covariant density functional theory. At spin zero such structures are located at high excitation energies which prevents their experimental observation. The rotation acts as a tool to bring these exotic shapes to the yrast line or its vicinity so that their observation could become possible with future generation of $\gamma-$tracking (or similar) detectors such as GRETA and AGATA. The major physical observables of such structures (such as transition quadrupole moments as well as kinematic and dynamic moments of inertia), the underlying single-particle structure and the spins at which they become yrast or near yrast are defined. The search for the fingerprints of clusterization and molecular structures is performed and the configurations with such features are discussed. The best candidates for observation of extremely deformed structures are identified. For several nuclei in this study (such as $^{36}$Ar), the addition of several spin units above currently measured maximum spin of $16\hbar$ will inevitably trigger the transition to hyper- and megadeformed nuclear shapes.

Rotational properties of the odd-Z transfermium nucleus 255Lr by a particle-number-conserving method in the cranked shell model

Experimentally observed ground state band based on the $1/2^{-}[521]$ Nilsson state and the first exited band based on the $7/2^{-}[514]$ Nilsson state in the odd-$Z$ nucleus $^{255}$Lr are studied by the cranked shell model (CSM) with the paring correlations treated by the particle-number-conserving (PNC) method. This is the first time the detailed theoretical investigations being performed on these rotational bands. Both the experimental kinematic and dynamic moment of inertia ($\mathcal{J}^{(1)}$ and $\mathcal{J}^{(2)}$) versus rotational frequency are reproduced quite well by the PNC-CSM calculations. By comparing the theoretical kinematic moment of inertia $\mathcal{J}^{(1)}$ with the experimental ones extracted from different spin assignments, the spin $17/2^{-}\rightarrow13/2^{-}$ is assigned to the lowest-lying $196.6(5)$ keV transition of the $1/2^{-}[521]$ band, and $15/2^{-}\rightarrow11/2^{-}$ to the $189(1)$ keV transition of the $7/2^{-}[514]$ band, respectively. The proton $N=7$ major shell is included in the calculations. The intruder of the high$-j$ low$-\Omega$ orbitals $1j_{15/2}$ $ (1/2^{-}[770])$ at the high spin leads to the band-crossing at $\hbar\omega\approx0.20$ ($\hbar\omega\approx0.25$) MeV for the $7/2^{-}[514]$ $\alpha=-1/2$ ($\alpha=+1/2$) band, and at $\hbar\omega\approx0.175$ MeV for the $1/2^{-}[521]$ $\alpha=-1/2$ band, respectively. Further investigations show that the band-crossing frequencies are quadrupole deformation dependent.

Theoretical Determination of Level Spins of Superdeformed Bands for Nuclei in the Mass Region A = 80 – 104

The bandhead spins of seventeen superdefomed bands in A = 80 – 104 region (38Sr, 39Y, 40Zr, 41Nb,42Mo, 43Tc, 46Pd) have assigned by an indirect method. The dynamical moment of inertia J(2) as a function of rotational frequency ђω are extracted from Harris expansion and fitted to the experimental values by using a computer simulated search program. The calculated dynamic moment of inertia with the best optimized parameters are integrated to give the spins. The intrinsic aligned angular momentum (the integration constant) is assumed to be zero. The values of the spins resulting from our approach are consistent with all spin assignments of other approaches, and have been used to determine the kinematic moment of inertia J(1). The systematic variation of J (2) and J (1) with rotational frequency ђω is investigated, which turns out to be helpful in the spin prediction. Most SD bands in this mass region exhibits decreasing in J(1) and J(2) with increasing ђω. The bandhead moment of inertia J0 which occur at J(2) = J (1) has been sensitive guideline parameter to spin proposition. The relationship between the Harris expansion three parameter model and the four parameter Bohr-Mottelson formula is derived.

Identicity in high-K three quasiparticle rotational bands: a theoretical approach

The systematics are studied for the identical band phenomenon in high-K three quasiparticle rotational bands. The identical rotational bands based on the same bandhead spin are analyzed on the basis of similarities in γ-ray energies, dynamic moment of inertia and kinematic moment of inertia in particular, which is a function of deformation degrees of freedom, pairing strengths and Nilsson orbitals in nuclei. It is established that a combined effect of all these parameters decides the identicity of the moment of inertia in high-K three quasiparticle rotational bands as the systematics are backed by the Tilted Axis Cranking model calculations.

Description of rotational properties of the superheavy nucleus 256,258,260Rf by projected shell model

Band structure of the Z = 104 nucleus 256Rf has been a recent research focus in nuclear physics. We performed projected shell model calculations for this and some other neighboring Rf isotopes. Specifically, we studied rotational properties of these nuclei and showed that variations in dynamic moment of inertia were sensitive to single-particle structures, which may be useful information for locating the anticipated island of stability. Electromagnetic transition properties were also calculated, and measurable quantities were predicted for further experimental test.

Projected shell model description for rotational bands in the proton emitter141Ho

Rotational bands of the deformed proton emitter ${}^{141}$Ho are studied by using the projected shell model. The known experimental states are well reproduced. Strongly suppressed $\ensuremath{\gamma}$ transition from the low-lying ${I}^{\ensuremath{\pi}}=3/{2}^{+}$ state makes this state isomeric, in favor of the suggestion that a proton emission could become the favorite decay mode for this state. Variations in the dynamical moment of inertia are found due to band crossings and a detailed structure in the crossing region is suggested. The role of hexadecapole deformation for this nucleus is emphasized.

IDENTICAL BANDS AND STAGGERING IN SUPERDEFORMED ROTATIONAL BANDS FOR 193,194,195TL NUCLEI

A simple collective rotational model has been constructed to investigate the identical bands in odd-odd nucleus 194Tl and its neighbor odd-A nuclei 193Tl and 195Tl, to describe the ∆I = 1 staggering effect in signature partner pairs of odd-A superdeformed bands 193Tl (SD1, SD2) and 195Tl (SD1, SD2) and to describe also the ∆I = 2 staggering observed in 194Tl (SD3). The model parameters and the bandhead spin ware obtained by adopted best fit method. The systematic variation of the kinematic and dynamic moments of inertia are studied as a function of the rotational frequency, it is found that the blocking effect of the high-j intruder orbital plays an important role. To describe the ∆I = 1 staggering we extracted the differences between the average transitions I + 2 → I → I - 2 energies in one band and the transition I + 1 → I - 1 energies in its signature partner. To describe ∆I = 2 staggering we calculated the deviation of transition energies from a smooth reference representing the finite difference approximation to the fourth derivative of the transition energies. We noticed transition energies in the nucleus 193Tl is identical to their N + 1, N + 2 neighbors. Also the analysis done allows us to confirm ∆I = 1 staggering in signature partners of 193Tl, 195Tl and ∆I = 2 staggering in SD3 band in 194Tl by performing a staggering parameter analysis.

A microscopic study on shape transition and shape coexistence in superdeformed nuclei

Superdeformed nuclei at high-spin states in several mass regions are investigated within a microscopic approach using cranked Nilsson-Strutinsky formalism to explore the equilibrium deformations in the ground state and their evolution with spin. Shape transition from normal deformed to superdeformed states with increasing spin is studied and a clear picture of shape coexistence is provided. Detailed information on spin, rotational energy, dynamical moment of inertia, and rotational frequency of superdeformed rotational bands is presented and the general features of superdeformed bands in certain mass regions are outlined. Rotational energy and dynamical moment of inertia are compared with available experimental data and the impact of temperature and pairing on superdeformed configuration are discussed.

Shell-Structure and Pairing Interaction in Superheavy Nuclei: Rotational Properties of theZ=104NucleusRf256

The rotational band structure of the Z=104 nucleus (256)Rf has been observed up to a tentative spin of 20ℏ using state-of-the-art γ-ray spectroscopic techniques. This represents the first such measurement in a superheavy nucleus whose stability is entirely derived from the shell-correction energy. The observed rotational properties are compared to those of neighboring nuclei and it is shown that the kinematic and dynamic moments of inertia are sensitive to the underlying single-particle shell structure and the specific location of high-j orbitals. The moments of inertia therefore provide a sensitive test of shell structure and pairing in superheavy nuclei which is essential to ensure the validity of contemporary nuclear models in this mass region. The data obtained show that there is no deformed shell gap at Z=104, which is predicted in a number of current self-consistent mean-field models.

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.

Tensor part of the Skyrme energy density functional. III. Time-odd terms at high spin

This article extends previous studies on the effect of tensor terms in the Skyrme energy density functional by breaking of time-reversal invariance. We have systematically probed the impact of tensor terms on properties of superdeformed rotational bands calculated within the cranked Hartree-Fock-Bogoliubov approach for different parameterizations covering a wide range of values for the isoscalar and isovector tensor coupling constants. We analyze in detail the contribution of the tensor terms to the energies and dynamical moments of inertia and study their impact on quasi-particle spectra. Special attention is devoted to the time-odd tensor terms, the effect of variations of their coupling constants and finite-size instabilities.

Effects of Training With a Dynamic Moment of Inertia Bat on Swing Performance

The purpose of this study was to investigate the effects of the 8-week dynamic moment of inertia (DMOI) bat training on swing velocity, batted-ball speed, hitting distance, muscle power, and grip force. The DMOI bat is characterized in that the bat could be swung more easily by reducing the moment of inertia at the initial stage of swing without decreasing the bat weight and has a faster swing velocity and lower muscle activity. Seventeen varsity baseball players were randomly assigned to the DMOI bat training group (n = 9) and the normal bat training group (n = 8). The training protocol was 7 swings each set, 5-8 sets each time, 3 times each week, and 8 weeks' training period. The results showed that the swing training with the DMOI bat for 8 weeks significantly increased swing velocity by about 6.20% (96.86 ± 8.48 vs. 102.82 ± 9.93 km·h(-1)), hitting distance by about 6.69% (80.06 ± 9.16 vs. 84.99 ± 7.26 m), muscle power of the right arm by about 12.04% (3.34 ± 0.41 vs. 3.74 ± 0.61 m), and muscle power of the left arm by about 8.23% (3.36 ± 0.46 vs. 3.61 ± 0.39 m) (p < 0.05). Furthermore, the DMOI bat training group had a significantly better change percentage in swing velocity, hitting distance, and grip force of the left hand than did the normal bat training group (p < 0.05). The findings suggested that the swing training with the DMOI bat has a positive benefit on swing performance and that the DMOI bat could be used as a new training tool in baseball.