Ground and excited S1 states of the beryllium atom

Abstract

Benchmark calculations of the total and transition energies of the four lowest 1 S states of the beryllium atom are performed. The computational approach is based on variational calculations with finite mass of the nucleus. All-particle explicitly correlated Gaussian (ECG) functions are used to expand the total non-Born-Oppenheimer nonrelativistic wave functions and the ECG exponential parameters are optimized using the standard variational method. The leading relativistic and quantum electrodynamics energy corrections are calculated using the first-order perturbation theory. A comparison of the experimental transition frequencies with the ones calculated in this work shows an excellent agreement. The deviations of 0.02 − 0.09 cm −1 are well within the estimated error limits for the experimental values.

Hylleraas-Configuration Interaction (Hy-CI) Non-Relativistic Energies for the 3 1S, 4 1S, 5 1S, 6 1S, and 7 1S Excited States of the Beryllium Atom

“…The result of the 99,965 term Be 5 1 S calculation is tabulated in Table 3 and turns out to be, as noted previously, within 46 nHa of the recent, best results of Ref. [21].…”

“…Term types (psps+d pps) (1+r 12 +r 13 ) are much more important here than in Be 3 1 S and also are indicative of how the nature of the correlation changes as the outermost electron becomes more diffuse. Table 3 shows that the current best Be 3 1 S 82,807 expansion result is 18 nHa below the ECG results of Stanke et al [19] and of Pachucki [32], and within 18 nHa of the most recent, best calculation [21]. Similarly, the current best Be 4 1 S 99,874 expansion result is 14 nHa below the ECG result of Stanke et al [19], and within 40 nHa of the most recent, best 4 1 S calculation [21].…”

“…Table 3 shows that the current best Be 3 1 S 82,807 expansion result is 18 nHa below the ECG results of Stanke et al [19] and of Pachucki [32], and within 18 nHa of the most recent, best calculation [21]. Similarly, the current best Be 4 1 S 99,874 expansion result is 14 nHa below the ECG result of Stanke et al [19], and within 40 nHa of the most recent, best 4 1 S calculation [21]. This table includes the results for the 5 1 S and 6 1 S states, which will turn out to be within 46 nHa of the most recent, best 5 1 S result and 26 nHa better than the best previous calculation for the 6 1 S state.…”

“…For Be, Adamowicz and co-workers [19] reported ECG results for the five lowest 1 S states of the Be atom, i.e., for ground and 2s → ns (n = 3-6) Rydberg excited states 2 . In two recent papers ( [20,21]), Adamowicz and co-workers extended these calculations to include the lowest ten 1 P Rydberg states and re-examined the ground and 2s → ns (n = 3-5) Rydberg excited states. In this work, we treat the same 2s → ns (n = 3-6) Rydberg excited states and then use that methodology to extend the calculations to include the 7s Rydberg excited state of Be.…”

Resonant two-photon spectroscopy of the 2s3d 1D2 level of neutral BeCook1, Vira2, Williams3 2020Phys. Rev. A7230View full textAdd to dashboardCite

“…Precision spectroscopy of the light elements serves an important role in aiding and refining theoretical methods of atomic structure calculation. While the theoretical precision for beryllium still lags behind the other light elements, recent improvements in theoretical models have resulted in predictions for several energy levels that exceed current experimental results [1][2][3]. Measurements of the 2s 2 1 S 0 − 2s2p 1 P 1 transition energy and ionization threshold of neutral 9 Be hold particular interest in serving as tests of the latest nonrelativistic wavefunction calculation methods and incorporation of leading relativistic and quantumelectrodynamic (QED) corrections.…”