Bulletin of the American Physical Society
53rd Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics
Volume 67, Number 7
Monday–Friday, May 30–June 3 2022; Orlando, Florida
Session U11: Focus Session: Few Body Problems and Long Range Interactions: Memorial for Richard DrachmanFocus Live Streamed

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Chair: Gordon Drake, Windsor Room: Grand Ballroom E 
Thursday, June 2, 2022 2:00PM  2:30PM 
U11.00001: Counterintuitive longrange interaction potentials Invited Speaker: Chris H Greene One of the topics where Richard Drachman made strong contributions concerns the longrange interaction between a distant electron and an atom or ion, a subject that always interested me greatly. In this presentation, I will point out one problem where the Drachman treatment predicted an energy dependent term[1] in the longrange effective potential that differed from an analogous term that arose in other derivations including my own with Shinichi Watanabe, a puzzling discrepancy that Richard Drachman subsequently resolved by showing that such terms are nonunique. Other examples of counterintuitive longrange interactions arise in Rydberg electron interactions with an anisotropic ionic core, where Bernard Zygelman predicted a term proportional to the scalar product of two angular momenta that arose from coupling to the open shell core and not from magnetic moment interactions. Research carried out in my group with graduate student William Clark showed that such terms arise from an adiabatic expansion of the longrange Hamiltonian,[2] and tested experimentally by Steve Lundeen's group. A final counterintuitive type of longrange interaction effect discussed in this presentation is the surprising one that can arise in a system of three or more particles having finite range interactions, called today the Efimov effect. In some very recent work, we see that long range adiabatic potentials computed in hyperspherical coordinates develop a modification of their longrange interaction when the scattering length or scattering volume is tuned to infinity. The talk will show examples of this long range modification including that predicted by Vitaly Efimov for three identical bosons, which produces an infinite number of Efimovian bound or resonant states. 
Thursday, June 2, 2022 2:30PM  3:00PM 
U11.00002: Precision calculations of fewbody atomic and molecular systems Invited Speaker: ZongChao Yan In this talk, I will present recent advances in highprecision calculations of fewbody atomic and molecular systems, including fewbody structure problems, Rydberg atoms, and longrange interactions, which have been influenced by Richard Drachman. Some of examples are QED calculations of Li^{+} to extract lithium nuclear properties, such as the nuclear charge radii and Zemach radii, and the exotic pionic helium atom (molecule) π^{}He^{+} with the potential to extract the π^{} mass at the ppb level, once experiments progress. 
Thursday, June 2, 2022 3:00PM  3:12PM 
U11.00003: Performance of Drachman's regularization in variational calculations of small atoms and molecules Sergiy Bubin Expectation values of singular operators, such as the Dirac delta function, evaluated with the wave function obtained in RayleighRitz variational calculations often exhibit poor convergence that is orders of magnitude worse than that for the energy. This is related to the fact that with such operators the expectation values sample the wave function locally rather than globally. One of the most practical approaches to deal with this issue was proposed by Richard Drachman and is based on using expectation value identities. For exact eigenfunctions, the approach gives the same expectation values as when the singular operator is used. However, in the case of approximate variational wave functions, it usually yields estimates that are much closer to the exact ones. In this talk I will review our recent studies where we investigated the performance of the regularization technique prescribed by Drachman in the case of fewelectron atomic and molecular systems. These studies provide some useful insight on when the Drachman’s regularization should work very well and when it may fail. 
Thursday, June 2, 2022 3:12PM  3:24PM 
U11.00004: High precision eigenvalues for the Rydberg sates of helium up to n = 16. Gordon W F Drake, Cody A McLeod, Lamies A Sati In previous work, high precision eigenvalues for all states of helium up to n = 10 and L = 7 have been obtained by the use of double basis sets in Hylleraas coordinates [1].. In the present work, we show that triple basis sets using three sets of individually optimized nonlinear parameters for different distance scales yield an order of magnitude improvement in accuracy for basis sets of the same size for the Rydberg Pstates states of helium. They also allow an extension of high precision calculations for the nonelativistic energies and wave functions up to at least n = 16 with little loss of accuracy. A summary of the methods used and a comparison with asymptotic expansions [2] will be presented. 
Thursday, June 2, 2022 3:24PM  3:36PM 
U11.00005: Manybody theory and calculations of positron scattering, binding and annihilation with atoms and polyatomic molecules Dermot G Green Pioneering technological developments have enabled the routine trapping, accumulation and beam delivery of lowenergy positrons for studies of fundamental atomic and molecular interactions, and the formation of positronium (Ps) and antihydrogen. The ability of positrons to annihilate with atomic and molecular electrons  to release two characteristic and detectable gamma rays  makes positrons and Ps unique probes of matter, and gives them important use across vast length scales, including as diagnositics of industrially important materials, in medical imaging (via PET, positron emission tomography), and in understanding the composition of the galaxy. 
Thursday, June 2, 2022 3:36PM  3:48PM 
U11.00006: Equivalent oneelectron BreitPauli operators for relativistic corrections to twophoton decay rates in helium Aaron T Bondy, Gordon W F Drake, Donald Morton Twophoton transition rates are important in determining astrophysical quantities such as population balance in planetary nebulae. We recently calculated twophoton decay rates in heliumlike ions including the finite nuclear mass effects [1]. We have now perturbatively added relativistic corrections to these results, giving the most precise and accurate calculations to date. We first tested the relativistic corrections to dipole transition integrals for the equivalent oneelectron case We derived (and will report on) oneelectron BreitPauli operators that are equivalent to the corresponding Dirac operators by expanding in powers of the finestructure constant α A continuous gauge parameter is used, and the operators are compared with the longwavelength QED operators derived previously for fewelectron atoms [2]. 
Thursday, June 2, 2022 3:48PM  4:00PM 
U11.00007: Longrange interactions of two Li atoms and a Li ion James F Babb, PeiGen Yan, LiYan Tang, ZongChao Yan A classic application of highprecision wave functions obtained using 
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