Relativistic many-body calculation of energies, oscillator strengths, transition rates, lifetimes, polarizabilities, and quadrupole moment of a Fr-like Thiv ion

Abstract

Atomic properties of the 24 low-lying ns, npj, ndj , nfj , and ngj states in Th IV ion are calculated using the high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric-dipole matrix elements, oscillator strengths, transition rates, and lifetimes. Scalar polarizabilities of the ground and six excited states (5fj , 6dj , 7pj, and 7s ), and tensor polarizabilities of the 5fj , 6dj , 7p 3/2 states of Th IV are evaluated. The uncertainties of the recommended values are estimated. These calculations provide recommended values critically evaluated for their accuracy for a number of Th IV atomic properties for use in theoretical modeling as well as planning and analysis of various experiments including development of ultra precise nuclear clock and RESIS studies of actinide ions.

Properties of Fr-like Th3+from rf spectroscopy of high-LTh2+Ryd

“…Estimates based on calculated dipole [11] and octupole matrix elements [12] indicate that the octupole-octupole terms are negligible but the octupole-dipole terms could be quite significant. Table III shows, for all the levels of this study, calculated values of the dipole-dipole and octupole-dipole second-order energies involving 6d core levels, assuming calculated values of the coupling matrix elements.…”

“…The quadrupole moment has been estimated to be 1.32 a.u. [13], and the adiabatic scalar and tensor dipole polarizabilities have been calculated to be (α D,0 , α D,2 ) = [4.5(8), −1.6(2)] [11]. Here again, the nonadiabatic coupling between the 6d 2 D 3/2 state and the ground state complicates the situation.…”

“…Since all of these levels have excitation energies >0.7 a.u. [11], an upper limit of their contribution is Taking (β Mod D,0 ) valence ∼ 0.6(6) a.u., we find β Mod D,0 = 3.6(6) a.u. Using that result it is possible to extract a value for the scalar quadrupole polarizability from the result of the fit of the data.…”

“…The present results are in good agreement with the less precise results inferred from the optical study, despite the sparse data pattern available in the optical study. The final column in Table VIII gives the most recent theoretical predictions for the Th 3+ properties reported here [11,12]. This recent theoretical study includes consideration of the various levels of theory that could be applied to this problem, ranging from a single configuration Dirac-Fock calculation to a sophisticated relativistic many body perturbation theory approach.…”

Laser-induced electronic bridge for characterization of the229mTh $ \rightarrow $229gTh nuclear transition with a tunable optical laser

“…A further advantage of using the s 7 state as the initial state is its metastability, i.e. very long lifetime of0.6s [25]. Note that since ñ |n is actually a virtual state, the energy of the M1 photon does not necessarily have to coincide with the energy of the M1 electronic transition, though the overall transition energy ñ  ñ | | i f has to be equal to the sum of the energies of the two photons (see figure 1).…”