Probing transition rates, nuclear moments and electric dipole polarizability in nobelium using multireference FSRCC and PRCC theories

TL;DR

This work applies all-particle two-valence FSRCC and PRCC theories to nobelium to compute IPs, excitation energies, E1 transition rates, hyperfine constants, and electric dipole polarizability, incorporating Breit, QED, and perturbative triples to capture strong relativistic effects. By benchmarking against Yb, the authors validate the accuracy of IPs, excitation energies, and alpha, then extract nuclear moments $\mu$ and $Q$ from hyperfine data for $^{253}$No and assess isotope shifts to infer mean-square radii changes. The results show substantial triple-excitation contributions to transition rates (≈10%), modest Breit+QED impact on hyperfine constants (≈4%), and robust agreement with experiment and prior theory for several properties, underscoring the importance of advanced correlation and relativistic treatments in superheavy elements. Overall, the work provides a comprehensive atomic-nuclear characterization of No and demonstrates the effectiveness of combining FSRCC and PRCC with QED corrections for high-precision predictions in the SHE regime, with implications for nuclear structure studies and future experimental planning.

Abstract

We employ an all-particle multireference Fock-space relativistic coupled-cluster (FSRCC) theory to compute the ionization potential, excitation energy, transition rate and hyperfine structure constants associated with $7s^2\;^{1}S_{0}\rightarrow 7s7p\;^{3}P_{1}$ and $7s^2\;^{1}S_{0}\rightarrow 7s7p\;^1P_{1}$ transitions in nobelium (No). Using our state-of-the-art calculations in conjunction with available experimental data \cite{raeder-18}, we extract the values of nuclear magnetic dipole ($μ$) and electric quadrupole ($Q$) moments for $^{253}$No. Further, information on nuclear deformation in even-mass isotopes is extracted from the isotope shift calculations. Moreover, we employ a perturbed relativistic coupled-cluster (PRCC) theory to compute the ground state electric dipole polarizability of No. In addition, to assess the accuracy of our calculations, we compute the ionization potential and dipole polarizability of lighter homolog ytterbium (Yb). To account for strong relativistic and quantum electrodynamical (QED) effects in No, we incorporate the corrections from Breit interaction, vacuum polarization and self-energy in our calculations. The contributions from triple excitations in coupled-cluster is accounted perturbatively. Our calculations reveal a significant contribution of $\approx$10\% from the perturbative triples to the transition rate of $7s^2\;^1S_{0}\rightarrow 7s7p\;^3P_{1}$ transition. The largest cumulative contribution from Breit+QED is observed to be $\approx$4\%, to the magnetic dipole hyperfine structure constant of $7s7p\;^1P_{1}$ state. Our study provides a comprehensive understanding of atomic and nuclear properties of nobelium with valuable insights into the electron correlation and relativistic effects in superheavy elements.

Figures (6)

• Figure 1: Convergence of (a) $\alpha$ of ytterbium and nobelium, (b) E1 transition amplitudes for ${^1}S_{0}\rightarrow {^3}P_{1}$ and ${^1}S_{0}\rightarrow {^1P}_{1}$ transitions of nobelium, and (c) magnetic dipole HFS reduced matrix elements (in the units of $10^{-6}$) of nobelium with basis size.
• Figure 2: (a) Relative error in the ionization potentials for Yb 1 and No 1. (b) Contributions from Breit interaction, self-energy and vacuum polarization to ionization potentials of Yb and No. (c), (d) Contributions from Breit interaction, self-energy, vacuum polarization and perturbative triples to transition rates of ${^1}S_{0}\rightarrow{^3}P_{1}$ and ${^1}S_{0}\rightarrow{^1}P_{1}$ transitions and magnetic dipole HFS constants of ${^3}P_{1}$ and ${^1}P_{1}$ states, respectively.
• Figure 3: (a), (b) Convergence trend for excitation energy and isotope shift parameters for $7s^2{\;^1}S_0 \rightarrow 7s7p{\;^1}P_1$ transition. (c), (d) The trend of electron correlation with different model configurations.
• Figure 4: (a) Contributions from Breit, QED and perturbative triples to the ground state $\alpha$ of Yb and No. (b), (c) The percentage contributions from DF, CP, and PC to the $\alpha$ of Yb and No.
• Figure 5: (a), (b) Five largest percentage contributions from the dipolar mixing of core and virtuals extracted from LO term for Yb and No. (c), (d) Five largest percentage contribution from the dipolar mixing of virtual-virtual orbitals of NLO terms for Yb and No.