Identification of Bandhead Spin and Identical Bands for Odd-A Nuclei in A-190 Superdeformed Mass Region

The dynamical moment of inertia is estimated with its even-power expansion of the rotational frequency and in accordance we determine the intermediate spins of the superdeformed(SD)rotational bands.Using Marquardt method of nonlinear least-squares routines,we determine the expansion coefficients by fitting the proposed dynamical moment of inertia with its recent experimental data of the SD nuclei in the A=190 mass region.The comparison between our theoretical and available experimental data for the dynamic moment of inertia and spin shows good agreements. Also,we have calculated the static moment of inertia at three alternative values of spin.The value of spin at which the two moments of inertia are nearly equals is to be regarded as a bandhead spin of the corresponding band.These studies are carried out for eighteen bands of odd-A nuclei of the superdeformed region 190,namely ~(189)Hg(b1),~(191)Hg(b1,b2, b3,b4),~(193)Hg(b2,b3,b5),~(195)Hg(b1,b2,b3,b4),~(193)Tl(b1,b2,b3,b5),~(189)Tl(b1),and~(197)Bi(b1).We also notice the occurrence of identical SD bands with near identical transition energies among the considered SD bands.

Description of Properties of Triaxial Superdeformed Bands in Odd-A Lu Isotopes

Properties of the triaxial superdeformed （TSD） bands of odd-A Lu isotopes are investigated systematically within the supersymmetry scheme including many-body interactions and a perturbation possessing the S0（5） （or SU（5）） symmetry on the rotational symmetry. Quantitatively good results of the γ-ray energies, the dynamical moments of inertia and the spin of the TSD bands in odd-A Lu isotopes are obtained. The calculation shows that the competition between the pairing and anti-pairing effects exists in these TSD bands. Meanwhile, the SU（3） symmetry in TSD bands are broken more seriously than in superdeformed （SD） bands.

Pairing phase transition in the odd-A nuclei: identification and classification

Research on the pairing phase transition in the odd-A nucleus ^(161)Dy is based on a sophisticated blend of the covariant density functional theory and the shell-model-like approach.It has been observed that variations in thermodynamic quantities at the critical temperature do not exclusively align with pairing phase transitions.The presence of an S-shaped heat capacity curve,often interpreted as an indicator of such transitions,does not offer a definitive confirmation.Additional factors,including the blocking effect,can modify the heat capacity curve and impede the transition process.The pairing phase transition in ^(161)Dy,which occurs approximately from 0.7 to 1.0 MeV,is unequivocally characterized as a first-order transition.Furthermore,the analysis of the impact of varying strengths of pairing correlations on these transitions reveals a nonlinear relationship,thereby adding complexity to the transition dynamics.

Magnetic moment predictions of odd-A nuclei with the Bayesian neural network approach

The Bayesian neural network approach has been employed to improve the nuclear magnetic moment predictions of odd-A nuclei.The Schmidt magnetic moment obtained from the extreme single-particle shell model makes large root-mean-square(rms)deviations from data,i.e.,0.949μN and 1.272μN for odd-neutron nuclei and odd-proton nuclei,respectively.By including the dependence of the nuclear spin and Schmidt magnetic moment,the machine-learning approach precisely describes the magnetic moments of odd-A uclei with rms deviations of 0.036μN for odd-neutron nuclei and 0.061μN for odd-proton nuclei.Furthermore,the evolution of magnetic moments along isotopic chains,including the staggering and sudden jump trend,which are difficult to describe using nuclear models,have been well reproduced by the Bayesian neural network(BNN)approach.The magnetic moments of doubly closed-shell±1 nuclei,for example,isoscalar and isovector magnetic moments,have been well studied and compared with the corresponding non-relativistic and relativistic calculations.

Magnetic moments and g-factors in odd-A Ho isotopes

The ground-state magnetic moment, g K factor and quenching spin gyromagnetic ratio have been calculated using the microscopic method based on the Quasiparticle Phonon Nuclear Model（QPNM） for ^155-169 Ho nuclei for the first time. It is shown that the residual spin-spin interactions are responsible for the core polarization,and because of the core polarization the spin gyromagnetic factors are quenched. By considering the core polarization effects, a satisfactory agreement is obtained for the computed ground state g K factor, which gives an intrinsic contribution to the magnetic moments. In order to assess the collective contribution to the magnetic moments, the rotational gyromagnetic factors g R have been also calculated within the cranking approximation using the single particle wave function of the axially symmetric Woods-Saxon potential. For the ground-state magnetic moments of odd-proton ^155-165 Ho nuclei, a good description of the experimental data is obtained with an accuracy of 0.01–0.1μN. From systematic trends, the quenching spin gyromagnetic factor, g K factor and magnetic moment have also been theoretically predicted for167,169 Ho where there is no existing experimental data.

Energy Level Statistics of SO（5） Limit of Super-symmetry U（6/4） in Interacting Boson-Fermion Model

We study the energy level statistics of the SO(5) limit of super-symmetry U(6/4) in odd-A nucleus using the interacting boson-fermion model. The nearest neighbor spacing distribution (NSD) and the spectral rigidity (△3)are investigated, and the factors that affect the properties of level statistics are also discussed. The results show that the boson number N is a dominant factor. If N is small, both the interaction strengths of subgroups SOB(5) and SOBF(5)and the spin play important roles in the energy level statistics, however, along with the increase of N, the statistics distribution would tend to be in Poisson form.

Projected 1+3 Quasiparticle-SU(5) Coupling Model Description of Some N=86 Isotones

-The calculation method for the transitional odd-A nuclei is studied.The theo-retical calculation of the energy level structure of 147pm and 149EU is performed bycoupling the 1+3 quasiparticles to the anharmonic vibration of the core.Aparticle-number-conservation treatment is made by means of the projection method.The effects of the particle-number projection,the three-d-boson excitation and residualinteraction on the lower excited states are discussed.

Gravitational Term in Semi Empirical Mass Formula

A new term was added to the well-known semi-empirical mass formula to account for the changes due to gravitational attraction between nucleons in the liquid drop, as well as, accommodates for the necessary corrections in the binding energy of a nucleus. The results of our calculations show a straight forward evidence that the gravitational attraction bears a reasonable contribution to the binding energy. On the other hand, employing the gravitational term in the semi empirical mass formula was led to the calculation of gravitational constant at subnuclear level.

Low-lying states of 92,93Nb excited in the reactions induced by the weakly-bound nucleus 6Li near the Coulomb barrier

Excited states of odd-odd nucleus 92Nb and odd-A nucleus 93Nb were populated in the 6 Li+ 89 Y reaction with an incident energy of 34 MeV. The processes that produce 92,93Nb and can be measured by a combination of light charged particle and gamma ray measurements are discussed. Twenty new transitions are observed and eight new levels are constructed in 92Nb, and in addition two new transitions are added to the level scheme of 93Nb. Using shell2 model calculations, the low-lying structure of 9 Nb is investigated and compared with the experimental results.