Ab initio calculations of the hyperfine structure of Ra⁺ and evaluations of the electric quadrupole moment Q of the ^{209,211,221,223}Ra nuclei

Abstract

The relativistic coupled-cluster method has been employed to calculate the energies, magnetic dipole, electric quadrupole and magnetic octupole hyperfine-structure constants of the low-lying states of Ra + . The validity of our calculations is substantiated by comparing the calculated binding energies and magnetic dipole hyperfine-structure constants with the corresponding available experimental results. The combination of our theoretical results with the available experimental values of the electric quadrupole hyperfine-structure constant, makes it possible to extract the electric quadrupole moments Q of the 209,211,221,223 Ra nuclei. Our Q( 221 Ra) = 1.968(34) and Q( 223 Ra) = 1.248( 22) are consistent with the referenced values 1.978(106) and 1.254(66) from a semi-empirical analysis (1988 Z. Phys. D 11 105), but Q( 211 Ra) = 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 measurements in 223 Ra + that can reveal the effect caused by the nuclear octupole moment are found to be on the order of kHz.

Relativistic coupled-cluster calculation of hyperfine-structure constants of $^{229}$Th$^{3+}$ and evaluation of the electromagnetic nuclear moments of $^{229}$Th

“…Furthermore, the contribution of non-linear terms account for approximately a quarter of the total correlation effect in 5f states, but less than a tenth in 6d states. Both the total correlation effects and the non-linear terms corrections are significantly larger than those in A/µ for each state, which is opposite of Ra + [18]. Such strong and unusual correlation effects mean that it is more difficult to accurately calculate the B/Q of ground state of 229 Th 3+ .…”

“…( 4), one would obtain the transition matrix element within the CCSD or LCCSD approximation, respectively. The specific calculation steps are described in detail in our previous work [18,21].…”

“…In the present work, we employed a finite basis set composed of even-tempered Gaussian-type functions expressed as G i = N i r ℓ+1 e −ηir 2 , to expand the Dirac radial wave function P and Q as in Ref. [18,21,22], where N i is the normalization factor, and In our calculations, the no-pair Dirac Hamiltonian is set as the starting point. Breit interaction and the lowerorder quantum electrodynamics (QED) radiative potential proposed by Flambaum and Ginges [23] are considered at the same foot as coulomb interaction.…”

“…In their calculations, all possible single and double excitations are iterated to all orders of perturbation theory, and a part of triple excitations are included perturbatively, thus it is termed as SDpT method. However, only the linear coupled-cluster terms of single-and double-excitations are included in the SDpT method, and we notice that the correlation effects represented by the nonlinear terms play a crucial role in the precise prediction for the hyperfine structure of Fr or Fr-like monovalent systems [17,18]. Thus it is necessary and important to accurately assess the contribution of nonlinear terms in the HFS calculations of Fr-like 229 Th 3+ .…”

Natural Orbitals and Targeted Non-Orthogonal Orbital Sets for Atomic Hyperfine Structure Multiconfiguration Calculations

“…The hyperfine interaction not only splits and broadens spectral lines, but also redistributes the radiation and may even open new decay channels that are useful for diagnosing electron densities in low-density astrophysical plasmas [3]. In nuclear physics, calculated hyperfine interaction constants, related to detailed electron-nucleus interactions [4], have been combined with high-precision measurements to extract nuclear information such as magnetic dipole, electric quadrupole [5][6][7], and magnetic octupole [8] moments.…”