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We report an improved variational upper bound for the ground state energy of H− using Hylleraas-like wave functions in the form of a triple basis set having three distinct distance scales. The extended precision DQFUN of Bailey, allowing for 70 decimal digit arithmetic, is implemented to retain sufficient precision. Our result exceeds the previous record [A. M. Frolov, Euro. J. Phys. D 69, 132 (2015)], indicating that the Hylleraas triple basis set exhibits comparable convergence to the widely used pseudorandom all-exponential basis sets, but the numerical stability against roundoff error is much better. It is argued that the three distance scales have a clear physical interpretation. The new variational bound for infinite nuclear mass is –0.527 751 016 544 377 196 590 814 478 a.u. New variational bounds are also presented for the finite mass cases of the hydrogen, deuterium, and tritium negative ions H−, D−, and T−. [ABSTRACT FROM AUTHOR]

We have calculated the electric dipole (E1) oscillator strengths and spontaneous decay rates for 12 spin-changing P-D transitions of atomic helium. We included the effects of the finite nuclear mass and the anomalous magnetic moment of the electron. The specific transitions for [sup.4]He are [n.sup.1][P.sup.o.sub.1] - [n'.sup.3] [D.sub.1,2] and [n.sup.3][P.sup.o.sub.2] - [n'.sup.1][D.sub.2] with n = 2, 3, 4 and n' = 3, 4. To include the effects of intermediate coupling between pure LS and jj, we used the Breit formulation for the spin-orbit and spin-other-orbit operators and combined the results of the exact diagonalization of the 2x2 energy matrix with pseudostate expansions to perform the perturbation sums over intermediate states. We calculated both the length and velocity gauges as a check on numerical accuracy and the validity of the transition operators. Key words: helium, atomic spectra, transition probabilities, nuclear mass, relativistic effects. Nous calculons les forces d'oscillateur dipolaires electriques (E1) et les taux de disintegration spontanee pour 12 transitions P-D a variation de spin de l'atome d'helium. Nous incluons les effets de la masse nucleaire finie et le moment magnetique anomal de l'electron. Specifiquement, les transitions etudiees dans [sup.4]He are [n.sup.1][P.sup.o.sub.1] - [n'.sup.3] [D.sub.1,2] and [n.sup.3][P.sup.o.sub.2] - [n'.sup.1][D.sub.2] with n = 2, 3, 4 and n' = 3, 4. Afin d'inclure les effets du couplage intermediate entre LS et jj purs, nous utilisons la formulation de Breit pour les operateurs de spin-orbite et de spin-autre-orbite et combinons les resultats de la diagonalisation exacte des matrices d'energie 2x2, avec expansion en pseudo-etats pour reussir les sommes de perturbation sur les etats intermediates. Nous calculons les jauges longueur et vitesse pour verifier la precision numerique et la validite des operateurs de transition. [Traduit par la Redaction] Mots-cles: helium, spectres atomiques, probabilites de transition, masse nucleaire, effets relativistes., 1. Introduction With this paper we wish to extend our previous calculations of spin-changing radiative transitions in neutral helium to P-D transitions and include the effects of the finite nuclear [...]

The relativistic corrections to the theoretical oscillator strengths of light elements such as helium are typically less than 0.1% and usually are ignored. However, they can be important for comparisons with the most accurate experiments, and they rapidly increase in magnitude with increasing nuclear charge. We have begun with the spin-forbidden electric-dipole transitions of neutral helium, using calculations consisting of (1) extremely accurate wave functions without relativistic corrections for both infinite and finite nuclear mass, (2) spin-changing matrix elements through the perturbations of the wave functions by the spin-orbit and spin-other-orbit Breit operators, (3) the use of pseudostates in the sums over all the intermediate states including the continuum, and (4) the inclusion as perturbers of the 1S0 and 3S1 states the pseudostates corresponding to the doubly excited npn'p ³[P.sup.e.sub.0] and npn'p ¹[P.sup.e.sub.1] terms, respectively. As examples of these calculations, we present oscillator strengths for the transitions 1 ¹[S.sub.0]-2 ³[P.sub.1], 2 ¹[S.sub.0]-2 ³[P.sub.1], 2 ³[S.sub.1]-2 ¹[P.sub.1], 2 ¹[P.sub.1-3] ³[D.sub.1,2], and 2 ³[P.sub.1,2]-3 ¹[D.sub.2]. PACS No: 32.70.Cs Les corrections relativistes aux forces d'oscillateur theeoriques d'eleements legers comme l'heelium sont typiquement plus petites que 0.1% et sont generalement ignorees. Cependant, elles peuvent etre importantes pour comparer avec les valeurs experimentales les plus precises et elles augmentent rapidement avec la charge nucleeaire. Nous deebutons avec les transitions dipolaires electriques spin interdites dans l'heelium neutre, a l'aide de calculs qui reposent sur, (1) des fonctions d'onde extrismement precises sans correction relativiste pour des masses nucleaires infinies et finies, (2) des elements de matrice de changements de spin via les perturbations de la fonction d'onde causees par les operateurs de Breit de spinorbite et de spin-autre orbite, (3) l'utilisation de pseudo etats dans la somme sur tous les etats intermediaries, incluant le continuum et (4) l'introduction, comme agents perturbant les etats ¹[S.sub.0] et ³[S.sub.1], des pseudo etats correspondant aux termes doublement excites npn'p ³[P.sup.e.sub.0] et npn'p ³[P.sup.e.sub.1] respectivement. Comme exemples de nos calculs, nous presenteras les forces d'oscillateur pour les transitions 1 ¹[S.sub.0]-2 ³[P.sub.1], 2 ¹-2 ³[P.sub.1], 2 ³[S.sub.1]-2 ¹[P.sub.1], 2 ¹pP.sub.1]-3 3 [D.sub.1,2] et 2 ³[P.sub.1,2]-3 ¹[D.sub.2]. [Traduit par la Redaction], 1. Introduction Although a three-body atomic system cannot be solved in closed analytical form, current computational techniques provide remarkable accuracies in the determination of energy levels, wave functions, and transition [...]

Abstract: This paper presents a review of recent progress in high-precision calculations for the ground state and low-lying excited states of helium, including the nonrelativistic energy, relativistic corrections of [α.sup.2] [...]

Abstract: We calculate very accurate ab initio ionization energies for both [sup.4]He I and ³He I as well as the isotope shifts for n = 1 to 10, L = [...]

Probabilities for electron shake-up and shake-off are calculated as relaxation processes following the beta decay of 6He to form 6Li, including corrections due to nuclear recoil. Within the sudden approximation, it is found that the correction due to nuclear recoil is nearly an order of magnitude less than that measured by Carlson et al. Phys. Rev. 129, 2220 (1963).

This paper reviews progress that has been made in obtaining essentially exact solutions to the nonrelativistic three-body problem for helium by a combination of variational and asymptotic expansion methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. As an example, the results are applied to the calculation of isotope shifts for the short-lived ''halo'' nucleus 6He relative to 4He in order to determine the nuclear charge radius of 6He from high precision spectroscopic measurements carried out at the Argonne National Laboratory. The results demonstrate that the high precision that is now available from atomic theory is creating new opportunities to create novel measurement tools, and helium, along with hydrogen, can be regarded as a fundamental atomic system whose spectrum is well understood for all practical purposes. [Copyright &y& Elsevier]

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The current theoretical status of the Lamb shift in He+ is discussed. Recent calculations of two-loop binding corrections to the Lamb shift significantly shift the theoretical value of the "classic" Lamb shift in He+, i.e., of the 2S1/2–2P1/2 interval. In this brief article, we present a new (theoretical) value for this interval that reads 14 041.474(42) MHz. The theoretical uncertainty is reduced as well as the discrepancy between theory and experiment. Planned measurements should be of help in further elucidating the situation.PACS Nos.: 31.15.–p, 12.20.Ds [ABSTRACT FROM AUTHOR]

The long-term goal of this work is to determine the fine-structure constant α from a comparison between theory and experiment for the fine-structure splittings of the helium 1s2p[sup 3] P[sub J] states. All known terms of order α[sup 5] a.u. (α[sup 7] mc[sup 2] ) arising from the electron–electron interaction, and recoil corrections of order α[sup 4] µ / M a.u. are evaluated and added to previous tabulation. The predicted energy splittings are ν[sub 0,1] = 29 616.946 42(18) MHz and ν[sub 1,2] = 2291.154 62(31) MHz. Although the computational uncertainty is much less than ±1 kHz, there is an unexplained discrepancy between theory and experiment of 19.4(1.4) kHz for ν[sub 1,2] .PACS Nos.: 31.30Jv, 32.10FnL'objectif à long terme de ce travail est la détermination de la constante de structure fine α à partir d'une comparaison entre la théorie et les mesures pour l'écartement de structure fine des états 1s2p[sup 3] P[sub J] dans l'hélium. Nous évaluons tous les termes connus à l'ordre α[sup 5] a.u. (α[sup 7] mc[sup 2] ) provenant des interactions électron–électron et les corrections de recul d'ordre α[sup 4] µ/M a.u. et nous les ajoutons aux valeurs antérieurement tabulées. Les écartements prédits en énergie sont ν[sub 0,1] = 29 616,946 42(18) MHz et η[sub 1,2] = 2291,154 62(31) MHz. Même si l'incertitude de calcul est beaucoup moindre que ± 1 kHz, il reste une différence inexpliquée de 19,4(1,4) kHz pour ν[sub 1,2] . [Traduit par la Rédaction] [ABSTRACT FROM AUTHOR]

Abstract: Penning trap mass measurements of 9Be, 10Be (), and the one-neutron halo nuclide 11Be () have been performed using TITAN at TRIUMF. The resulting 11Be mass excess () is in agreement with the current Atomic Mass Evaluation (AME03) [G. Audi, et al., Nucl. Phys. A 729 (2003) 337] value, but is over an order of magnitude more precise. The precision of the mass values of 9,10Be have been improved by about a factor of four and reveal a deviation from the AME mass values. Results of new atomic physics calculations are presented for the isotope shift of 11Be relative to 9Be, and it is shown that the new mass values essentially remove atomic mass uncertainties as a contributing factor in determining the relative nuclear charge radius from the isotope shift. The new mass values of 10,11Be also allow for a more precise determination of the single-neutron binding energy of the halo neutron in 11Be. [Copyright &y& Elsevier]