Theoretical Study On Hyperfine Structure And Radiation Transition Properties Of Francium-Like Ra⁺ And Th³⁺

The Fr-like Ra⁺and Th³⁺are important candidates for precision measurement physic-s experiments,such as the development of high-precision optical frequency standard,the measurement of atomic symmetry breaking,and the exploration of the temporal and spa-tial changes of fundamental physical constants.Accurate knowledge about the electronic and nuclear structure properties of these two systems is an important prerequisite for carrying out the above-mentioned precise experiments.Although they all belong to francium-like sys-tems,their energy level structures and electronic correlation effects tend to be different from those of francium.The electronic structures of these two ionic systems are more complex,and the electronic correlation effect is stronger.The precise measurement and high-precision calculation of the electronic and nuclear structural properties are challenging.At present,the relevant high-precision atomic structure parameters and nuclear structure information are not sufficient.In this paper,starting from the first principles and using the Gaussian basis-based relativistic coupled cluster method,a series of theoretical studies on the electronic and nuclear properties of Ra⁺and Th³⁺are carried out.The main research contents are as follows:（1）Calculations of the hyperfine structure of Ra⁺and evaluations of the electric quadrupole moment Q of the^{209,211,221,223}Ra nuclei.The energies,magnetic dipole,electric quadrupole and magnetic octupole hyperfine-structure constants of the low-lying states of Ra⁺have been calculated.Combined with the our theoretical results and the available experimental values of the electric quadrupole hyperfine-structure constant,the electric quadrupole moment Q of the^{209,211,221,223}Ra nucleus are determined.Our Q(²²¹Ra)=1.968（34）and Q(²²³Ra)=1.248（22）are consistent with the referenced values 1.978（106）and 1.254（66）from a semi-empirical analysis（Z.Phys.D:At.,Mol.Clusters 11,105（1988））,but Q(²¹¹Ra)=0.33（2）is smaller than the referenced value 0.48（4）by about 30%.Furthermore,we also performed a procedure for assessing the contributions of magnetic octupole hyperfine interaction to the hyperfine splitting considering the preliminary value of magnetic octupole moment from the single-particle nuclear structure model.The sensitivity of hyperfine-structure interval mea-surements in²²³Ra⁺that can reveal the effect caused by the nuclear octupole moment are found to be on the order of k Hz.（2）Calculations of the hyperfine structure of ²²⁹Th³⁺and evaluations of electromag-netic nuclear moments of²²⁹Th.Combining the measured hyperfine structure constants[Phys.Rev.Lett.106.223001（2011）]and present atomic calculations,we extract the magnetic dipole moment,μ=0.359（9）,and the electric quadrupole moment,Q=2.95（7）,of the²²⁹Th nucleus.Our magnetic dipole moment is perfectly consistent with the recommended value from the all-order calculation by Safronova et.al.[Phys.Rev.A 88,060501（R）（2013）],but our electric quadrupole moment is smaller than their recommended value,by about 5%.A detailed analysis indicates that the non-linear terms of single and double excitations,not in-cluded in the all-order calculation,are crucial to produce a precise Q value of²²⁹Th.In addi-tion,we also report the magnetic octupole hyperfine-structure constants and some important non-diagonal hyperfine transition matrix elements,which are required for further extraction of the magnetic octupole moment?of²²⁹Th nucleus.（3）High-precision calculation of the energy levels and radiative transition properties of Ra⁺.The energies and radiation transition properties of Ra⁺are systematically calculated,involving ns_1/2（n=7-12）,np_1/2,3/2（n=7-12）,nd_3/2,5/2（n=6-10）30 energy levels in total.The accurate values along with uncertainties of the energies of Ra⁺and its electric dipole（E1）,electric quadrupole（E2）and some important magnetic dipole（M1）transition matrix elements are determined by the relativistic coupled-cluster method at different level approxi-mations.Using the E1,E2 and M1 matrix elements,the related radiation transition properties,including line strength,oscillator strength and transition probability,are further calculated.Furthermore,the effect of electron correlation effects on the properties of radiative transitions is systematically investigated.（4）High-precision calculation of the energy levels and radiative transition proper-ties of Th³⁺.Energies,Lande g factors,line strengths,transition probabilities,and oscillator strengths for electric dipole（E1）,electric quadrupole（E2）,and magnetic dipole（M1）transi-tions arising from the ns_1/2（n=7-10）,np_1/2,3/2（n=7-9）,nd_3/2,5/2（n=6-9）,nf_5/2,7/2（n=5-8）,and ng_7/2,9/2（n=5,6）energy levels in Th³⁺,are calculated.By comparing with the existing theoretical and experimental results,the uncertainties of the calculated results are evaluated.This work reports a high-precision atomic property calculation of Th³⁺and is of great signif-icance for future spectral analysis and precision experiments targeting various applications.