Application of Pseudospectral Methods to Beta Decay, Two-photon Decay, and Tune-out Frequencies in Helium

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 \u3e 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 \u3c 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

Photodisintegration of lithium isotopes

We have performed a measurement of the photodisintegration of the lithium isotopes, ⁶Li and ⁷Li, using a monochromatic, polarised photon beam and a segmented neutron detector array which covers approximately ¼ of 4π srad. Using time-of-flight and scintillator light-output spectra we separate the data into individual reaction channels. This work is motivated by the need to compare with recent theoretical predictions and to provide data for future theoretical work. For the photodisintegration of ⁶Li we took data at 12 photon energies between 8 and 35 MeV. We describe the data using a model consisting of two-body reaction channels and obtain angular distributions and absolute cross sections for many of these reaction channels. We compare our results with a recent Lorentz integral transform calculation (Bacca et al. Phys. Rev. C 69, 057001 (2004)). Our results are in reasonable agreement with the calculation, in contradiction with previous experimental results. For the photodisintegration of ⁷Li, we took data at 9 photon energies between 10 and 35 MeV. We obtain cross sections for the reaction channel ⁷Li + γ → n + ⁶Li(g.s.) at all photon energies with angular distributions at all but the highest energy. We obtain angular distributions and total cross sections for reaction channels involving excited states of the daughter nucleus, ⁶Li, at select energies. We hope that these measurements will provide incentive for new theoretical calculations. We observe neutrons that can only be described by the reaction channel ⁷Li+γ → n+⁶Li(10.0) which necessitates an excited state of ⁶Li with excitation energy Eₓ = 10.0±0.5 MeV that is not in the standard tables of excited states