Date of Award

10-11-2024

Publication Type

Dissertation

Degree Name

Ph.D.

Department

Physics

Keywords

Beta decay;Helium;High-precision atomic theory;Hylleraas coordinates;Tune-out frequency;Two-photon decay

Supervisor

Gordon Drake

Abstract

We extend the widespread use and versatility of pseudostates in the theoretical char- acterization of properties of two-electron atoms and ions by using them in calculations for three distinct physical processes. Atomic systems have infinitely many bound and continuum states, posing a computational challenge for calculations involving per- turbation sums over intermediate states. In this work, we construct two-electron pseudostates variationally using a doubled basis set of correlated Hylleraas functions. The first process we consider is the beta decay of 6He, an isotope of helium with a halo nucleus that lives for 0.8 s. The electron-antineutrino correlation coefficient, a?⌫, is related to the kinematics following this decay and is a frequent subject of low- energy tests of the Standard Model—exotic interactions beyond vector–axial-vector would signal new physics. The Coulomb pulse resulting from the change in nuclear charge from Z = 2 to Z = 3 can shake off one or both of the atomic electrons of the 6Li+daughter ion. The precise charge state fractions of the daughter ion affect the kinematics of the decay, which are used to obtain a?⌫. We treat the shake-up and shake-off processes in the beta decay of 6He by developing two-electron, con- figuration interaction (CI) projection operators capable of distinguishing single- and double-ionization channels [A. T. Bondy and G. W. F. Drake, Atoms 11, 41 (2023)]. The CI-like projection operators are formed using products of one-electron Sturmian pseudostates that have a fascinating “triangular” structure, with a wide range of nonlinear parameters, capable of spanning many distance scales and producing very- high-energy (E > 1030 a.u.) pseudostates. We have reduced a theory-experiment discrepancy by an order of magnitude and predict the charge-state fraction of 6Li3+ following this decay to be 0.35(5)% and 0.53(7)% for the 1 1S0 and 2 3S1 states of 6He, respectively—still much larger than the measured 0.018(15)% [T. A. Carlson et al., Phys. Rev. 129, 2220 (1963)] and < 0.01% [R. Hong et al., Phys. Rev. A 96, 053411 (2017)]. vi Secondly, we perform high-precision variational calculations which include finite- nuclear-mass effects for spontaneous two-photon (2E1) decay rates in heliumlike ions in the metastable 21S state, including the heavy species of muonic, pionic and an- tiprotonic helium [A. T. Bondy, D. C. Morton, and G. W. F. Drake, Phys. Rev. A 102, 052807 (2020)]. This critical process helps determine population balances and serves as a temperature and pressure probe in low-particle-density regimes such as astrophysical planetary nebulae. In calculating the finite-nuclear-mass effects, mass polarization was treated as a gauge-dependent power series in μ/M, leading to novel algebraic relationships that test for gauge equivalence—for 20Ne8+ the length and velocity gauge of the two-photon decay rates agree to 1 ppb. We generalize the alge- braic relationships to test for agreement when finite-nuclear-mass effects are included between length, velocity, and acceleration gauges for any nE1-photon transitions [A. T. Bondy and G. W. F. Drake, Phys. Rev. A 108, 022807 (2023)]. These general relations are tested and verified for three cases of spontaneous decay in heliumlike ions: the E1 decays 2 1P – 1 1S and 2 3P – 2 3S and the 2E1 decay 2 1S – 1 1S. They provide a powerful new way to test the accuracy of calculations involving approximate wave functions. Finally, the tune-out frequency near 726 THz for the 2 3S1 state of helium, which corresponds in lowest order to a zero in the frequency-dependent polarizability, is calculated as part of a joint theoretical-experimental effort [B. Henson et al., Science 376, 199 (2022)]. This provides a novel test of QED for a physical effect other than the traditional energy level measurements, such as the Lamb shift. The problem is reformulated as a zero in the Rayleigh scattering cross section to include higher- order retardation effects. We present high-precision, variational calculations of the Rayleigh scattering cross section in helium within the framework of nonrelativistic- QED, including higher-order corrections due to relativistic, QED, and retardation effects. This theoretical-experimental comparison tests QED effects and retardation effects at the 30? and 2? level, respectively. The tune-out frequency is calculated to be 725 736 252(9) MHz, while the measured value is 725 736 700(260) MHz, leaving a 1.7? discrepancy.

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