Theoretical Study Of The Static Dipole Polarizabilities And Hyperpolarizability Of B²⁺ And B⁺ Ions

When atoms are in an external electric field,the deviation of the electron cloud from the normal distribution is described as the polarizability and hyperpolarizability.The polarizability and hyperpolarizability can be used for development of atomic optical clocks,precise measurement of radiation spectra,and calculation of supercooled atoms and quantum information.Such as the polarizability of atoms can be used to calculate blackbody radiation（BBR）shifts of the clock transition,to construct long-range interaction potentials in supercooled environments,and to evaluate low order Stark shifts.However,accurate measurement of atomic polarizability and hyperpolarizability in experiments is very difficult.It is necessary to provide accurate atomic polarizability,hyperpolarizability and other basic parameters in theory.In this paper,the energy levels,matrix elements,oscillator strength,polarizability,and hyperpolarizability of B²⁺and B⁺ions are studied using the relativistic configuration interaction model potential（RCICP）method.The main research contents are as follows:1.The B²⁺ion is a three-electron system,with a ground state of 1s²2s ²S_1/2,which is a very important research system for precision measurement physics.The energy levels,matrix elements and oscillator strengths of B²⁺ions are calculated in detail.The static electric dipole polarizabilities of the 2s_1/2,2p_1/2,2p_3/2,3s_1/2,and 3p_1/2 states of the B²⁺ions are determined.We can find that the polarizability of the ground state 2s_1/2 is dominated by the 2s_1/2→2p_1/2,3/2 transitions.The polarizability of the 2p_1/2 state is dominated by the2p_1/2→2s_1/2 and 2p_1/2→3d_3/2 transitions.However,the contribution of 2p_1/2→2s_1/2transition to the polarizability of the 2p_1/2 state is negative,so the polarizability of the2p_1/2 state is negative.The polarizability of the 2p_3/2 state is dominated by the 2p_3/2→2s_1/2and 2p_3/2→3d_5/2 transitions.Due to the contribution of the 2p_3/2→2s_1/2 transition to the polarizability of the 2p_3/2 state is negative,the polarizability of the 2p_3/2 state is less than zero.The hyperpolarizability of the ground state 2s_1/2 is further calculated,and the contributions of intermediate states are studied in detail.The hyperpolarizability is mainly determined by the¹₀（¹ is the static electric dipole polarizability and₀ is the first order non-adiabatic correction of¹）.2.The ground state is 2s^{2 1}S₀and the 2s2p ³P₀ state is a metastable state with a long lifetime of the B⁺ion.The clock transition 2s2p ³P₀→2s^{2 1}S₀ is good candidate systems for the development of precision optical clocks.The energy levels,matrix elements and oscillator strengths of B⁺ions are calculated based on the monovalent electronic system B²⁺ions.The static electric dipole polarizabilities of the 2s_1/2,2p_1/2,2p_3/2,3s_1/2,and 3p_1/2states of the B²⁺ions are determined.The electric dipole polarizabilities of 2s^{2 1}S₀,2s2p³P₀,2s2p ³P₁ and 2s2p ¹P₁states of the B⁺ions are determined.The polarizabilities of the2s^{2 1}S₀ and 2s2p ³P₀ states are very close,they are 9.6220 a.u.and 7.7594 a.u.,respectively.The BBR shift of the clock transition 2s2p ³P₀→2s^{2 1}S₀ at room temperature is calculated.This BBR value（0.01605 Hz）is one order of magnitude smaller than the BBR shift of the clock transition ²D_5/2→²S_1/2 of Ca⁺and Sr⁺ions,which are two orders of magnitude smaller than the BBR shift of the clock transition ³P₀→¹S₀ of Ca,Sr and Yb atoms.