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On the bound triplet states in the Be atom

Alexei M. Frolov, María Belén Ruiz

Published Oct 9, 2013• 0 citations
OpenAlex

Abstract

The bound state spectrum of the low-lying triplet states in the Be atom is investigated. In particular, we perform accurate computations of the bound triplet $S$, $P$, $D$, $F$ and $G$ states in the four-electron Be atom. The results of these calculations are employed to draw the spectral diagram which contains the energy levels of the triplet states of Be atom. Based on our computational results we can observe transitions from the low-lying bound states to the weakly-bound, Rydberg states. For the $2^3S$ and $3^3S$ states in the Be atom we also determine a number of bound states properties and discuss the hyperfine structure by using our results of highly accurate computations.

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Rydberg atoms

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Introduction Series of atomic spectral lines had been studied by emission from excited vapors even before Balmer described the regularity of the visible lines of hydrogen in 1884. However, direct excitation had been restricted to the few lowest-lying levels, particularly those accessible by electric dipole transitions from the ground state using classical light sources. The advent of tunable lasers in the 1970s changed such spectroscopic limitations enormonsly, allowing excitation to a very much larger number of states. Atoms in highly excited states, typically with principal quantum numbers n ≥ 10, are called Rydberg atoms. They are oversize, fragile states of significant intrinsic interest. They are very rare in nature because of their size and fragility, but they are found in interstellar space (H I regions). One of the best sources for comprehensive descriptions of Rydberg atoms and references to the literature describing their exploration is Ref. [120]. It describes their characteristic properties and behavior both classically and quantum mechanically, and especially their strongly enhanced interactions with external fields. The first thing to note is that Rydberg atoms are usually characterized by a single, highly excited electron while all the other electrons remain in their original states. Thus their properties are very nearly classical, and the atoms are much closer to the ideal hydrogen-like model of Chap. 7, along with appropriate quantum defects (see Chap. 10). The spectroscopy of such states is especially interesting because the active electron is much less perturbed by the other electrons in the atom than when it is in lower states. Moreover, there are some special circumstances in which the energy of a Rydberg state is degenerate with an atomic state having two electrons excited to lower levels, and such configurations yield further new information. Second, Rydberg atoms do not usually decay back to the ground state by emission of characteristic radiation, so their study is mediated by other techniques that reveal new and interesting properties. Such properties arise because Rydberg atoms have a huge dipole moment and very low binding energy resulting from the large average distance between the excited electron and the nucleus-plus-core of the rest of the atom with net charge e . Third, transitions between Rydberg states are quite different from those connecting to the ground state for at least three reasons.

Cambridge University Press eBooks•Dec 31, 2015•0 citations
The bound state spectrum of the low-lying triplet states in the Be atom is investigated. In particular, we perform accurate computations of the bound triplet SSS, PPP, DDD, FFF and GGG states in the four-electron Be atom. The results of these calculations are employed to draw the spectral diagram which contains the energy levels of the triplet states of Be atom. Based on our computational results we can observe transitions from the low-lying bound states to the weakly-bound, Rydberg states. For the 23S2^3S23S and 33S3^3S33S states in the Be atom we also determine a number of bound states properties and discuss the hyperfine structure by using our results of highly accurate computations.
Hyperfine structure of the 23S−2^3S-23S−state in the 9{}^99Be atom
A number of bound states properties and the hyperfine structure of the 23S(L=0)-state in the Be atom are determined from the results of highly accurate computations. The energies of the hyperfine structure levels for this state are ε(F=12) = -13725.635(7) MHz, ε(F=32) = -5490.254(7) MHz and ε(F=52) = 8235.381(7) MHz, respectively. The hyperfine structure splittings are Δ12 = 8235.381(7) MHz and Δ23 = 13725.635(7) MHz, respectively. The spectrum of low-lying (bound) triplet states in the Be atom is briefly investigated.
The bound state properties of the ground 1 1S(L=0) state and the lowest triplet 2 3S(L=0) state of the 3He, 4He, and infinityHe helium atoms are determined to very high accuracy from the results of direct numerical computations. To compute the bound state properties of these atoms the author applied his exponential variational expansion in relative/perimetric three-body coordinates. For the ground 1 1S(L=0) state and the lowest triplet 2 3S(L=0) state of the 3He, 4He, and infinityHe atoms the author also determined the lowest order QED corrections and the field component of isotopic shift (=field shift). For the 2 3S(L=0) state of the 3He atom the hyperfine structure splitting is evaluated. The considered properties of the ground 1 1S state and the lowest 2 3S state in the 3He and 4He atoms are of great interest in a number of applications.
We perform accurate calculations of energy levels as well as fine and hyperfine splittings of the lowest 1,3PJ,3S1,3PJe^{1,3}P_{J}, ^{3}S_{1}, ^{3}P_{J}^{e}1,3PJ​,3S1​,3PJe​, and 1,3DJ^{1,3}D_{J}1,3DJ​ excited states of the 9Be^{9}\mathrm{Be}9Be atom using explicitly correlated Gaussian functions, and we report on the breakdown of the standard hyperfine structure theory. Because of the strong hyperfine mixing, which prevents the use of common hyperfine constants, we formulate a description of the fine and hyperfine structure that is valid for an arbitrary coupling strength and may have wide applications in many other atomic systems.
A combined experimental and theoretical spectroscopic study of high-$n, 30\ensuremath{\lesssim}n\ensuremath{\lesssim}100$, triplet SSS and DDD Rydberg states in 87Sr^{87}\mathrm{Sr}87Sr is presented. 87Sr^{87}\mathrm{Sr}87Sr has a large nuclear spin I=9/2I=9/2I=9/2, and at high-nnn the hyperfine interaction becomes comparable to, or even larger than, the fine structure and singlet-triplet splittings, which poses a considerable challenge both for precision spectroscopy and for theory. For high-nSn SnS states, the hyperfine shifts are evaluated nonperturbatively, taking advantage of earlier spectroscopic data for the I=0I=0I=0 isotope 88Sr^{88}\mathrm{Sr}88Sr, which results in good agreement with the present measurements. For the DDD states, this procedure is reversed by first extracting from the present 87Sr^{87}\mathrm{Sr}87Sr measurements the energies of the 3D1,2,3{}^{3}{D}_{1,2,3}3D1,2,3​ states to be expected for isotopes without hyperfine structure (88Sr^{88}\mathrm{Sr}88Sr), which allows the determination of corrected quantum defects in the high-nnn limit.
We present high-resolution spectroscopy of Rb2{\mathrm{Rb}}_{\text{2}}Rb2​ ultralong-range Rydberg molecules bound by mixed singlet-triplet electron-neutral atom scattering. The mixing of the scattering channels is a consequence of the hyperfine interaction in the ground-state atom, as predicted recently by Anderson et al. [Phys. Rev. A 90, 062518 (2014)]. Our experimental data enable the determination of the effective zero-energy singlet sss-wave scattering length for Rb. We show that an external magnetic field can tune the contributions of the singlet and the triplet scattering channels and therefore the binding energies of the observed molecules. This mixing of molecular states via the magnetic field results in observed shifts of the molecular line which differ from the Zeeman shift of the asymptotic atomic states. Finally, we calculate molecular potentials using a full diagonalization approach including the ppp-wave contribution and all orders in the relative momentum kkk, and compare the obtained molecular binding energies to the experimental data.
Introduction Series of atomic spectral lines had been studied by emission from excited vapors even before Balmer described the regularity of the visible lines of hydrogen in 1884. However, direct excitation had been restricted to the few lowest-lying levels, particularly those accessible by electric dipole transitions from the ground state using classical light sources. The advent of tunable lasers in the 1970s changed such spectroscopic limitations enormonsly, allowing excitation to a very much larger number of states. Atoms in highly excited states, typically with principal quantum numbers n ≥ 10, are called Rydberg atoms. They are oversize, fragile states of significant intrinsic interest. They are very rare in nature because of their size and fragility, but they are found in interstellar space (H I regions). One of the best sources for comprehensive descriptions of Rydberg atoms and references to the literature describing their exploration is Ref. [120]. It describes their characteristic properties and behavior both classically and quantum mechanically, and especially their strongly enhanced interactions with external fields. The first thing to note is that Rydberg atoms are usually characterized by a single, highly excited electron while all the other electrons remain in their original states. Thus their properties are very nearly classical, and the atoms are much closer to the ideal hydrogen-like model of Chap. 7, along with appropriate quantum defects (see Chap. 10). The spectroscopy of such states is especially interesting because the active electron is much less perturbed by the other electrons in the atom than when it is in lower states. Moreover, there are some special circumstances in which the energy of a Rydberg state is degenerate with an atomic state having two electrons excited to lower levels, and such configurations yield further new information. Second, Rydberg atoms do not usually decay back to the ground state by emission of characteristic radiation, so their study is mediated by other techniques that reveal new and interesting properties. Such properties arise because Rydberg atoms have a huge dipole moment and very low binding energy resulting from the large average distance between the excited electron and the nucleus-plus-core of the rest of the atom with net charge e . Third, transitions between Rydberg states are quite different from those connecting to the ground state for at least three reasons.