Polarizabilities and other properties of the tdµ molecular ion

2001 ◽  
Vol 79 (9) ◽  
pp. 1149-1158
Author(s):  
A K Bhatia ◽  
R J Drachman
Keyword(s):  
Energy Levels ◽  
Molecular Ions ◽  
Muon Catalyzed Fusion ◽  
Oppenheimer Approximation ◽  
Good Energy ◽  
Cusp Conditions ◽  
Fermi Contact ◽  
Muonic System ◽  
Three Body ◽  
Contact Parameters

Wave functions of the Hylleraas type were used earlier to calculate energy levels of muonic systems. Recently, we found in the case of the molecular ions H2+, D2+, and HD+ that it was necessary to include high powers of the internuclear distance in the Hylleraas functions to localize the nuclear motion when treating the ions as three-body systems without invoking the Born–Oppenheimer approximation. We tried the same approach in a muonic system, tdµ– (triton, deuteron, and muon). Improved convergence was obtained for J = 0 and 1 states for shorter expansions when we used this type of generalized Hylleraas function, but as the expansion length increased the high powers were no longer useful. We obtained good energy values for the two lowest J = 0 and 1 states and compared them with the best earlier calculations. Expectation values were obtained for various operators, the Fermi contact parameters, and the permanent quadrupole moment. The cusp conditions were also calculated. The polarizability of the ground state was then calculated using second-order perturbation theory with intermediate J = 1 pseudostates. (It should be possible to measure the polarizability by observing Rydberg states of atoms with tdµ– acting as the nucleus.) In addition, the initial sticking probability (an essential quantity in the analysis of muon catalyzed fusion) was calculated and compared with earlier results. PACS Nos.: 30.00, 36.10-k, 02.70-c

Excitation of muonic molecules ddμ and dtμ by super-intense attosecond soft X-ray laser pulses: Shaped post-laser-pulse muonic oscillations and enhancement of nuclear fusion

2014 ◽  
Vol 23 (09) ◽  
pp. 1430014 ◽  
Author(s):  
André D. Bandrauk ◽  
Guennaddi K. Paramonov
Keyword(s):  
Laser Pulse ◽  
Quantum Dynamics ◽  
Power Spectra ◽  
Laser Pulses ◽  
Molecular Ions ◽  
Intense Laser ◽  
Muon Catalyzed Fusion ◽  
Three Dimensional Model ◽  
Intense Laser Pulses ◽  
Oppenheimer Approximation

The quantum dynamics of muonic molecular ions ddμ and dtμ excited by linearly polarized along the molecular (z)-axis super-intense laser pulses is studied beyond the Born–Oppenheimer approximation by the numerical solution of the time-dependent Schrödinger equation within a three-dimensional model, including the internuclear distance R and muon coordinates z and ρ. The peak-intensity of the super-intense laser pulses used in our simulations is I0 = 3.51 × 1022 W/cm2 and the wavelength is λl = 5 nm. In both ddμ and dtμ, expectation values 〈z〉 and 〈 ρ 〉 of muon demonstrate "post-laser-pulse" oscillations after the ends of the laser pulses. In ddμ post-laser-pulse z-oscillations appear as shaped nonoverlapping "echo-pulses". In dtμ post-laser-pulse muonic z-oscillations appear as comparatively slow large-amplitude oscillations modulated with small-amplitude pulsations. The post-laser-pulse ρ-oscillations in both ddμ and dtμ appear, for the most part, as overlapping "echo-pulses". The post-laser-pulse oscillations do not occur if the Born–Oppenheimer approximation is employed. Power spectra generated due to muonic motion along both optically active z and optically passive ρ degrees of freedom are calculated. The fusion probability in dtμ can be increased by more than 11 times by making use of three sequential super-intense laser pulses. The energy released from the dt fusion in dtμ can by more than 20 GeV exceed the energy required to produce a usable muon and the energy of the laser pulses used to enhance the fusion. The possibility of power production from the laser-enhanced muon-catalyzed fusion is discussed.

Some properties of three body resonances of dtμ related to muon-catalyzed fusion

1988 ◽  
Author(s):  
P. Froelich ◽  
K. Szalewicz ◽  
H. J. Monkhorst ◽  
W. Kolos ◽  
B. Jeziorski
Keyword(s):  
Muon Catalyzed Fusion ◽  
Three Body

BORN–OPPENHEIMER APPROXIMATION FOR THE BROWN–RAVENHALL EQUATION

2001 ◽  
Vol 13 (08) ◽  
pp. 921-951
Author(s):  
VANIA SORDONI
Keyword(s):  
Semiclassical Limit ◽  
Energy Levels ◽  
Mass Ratio ◽  
Nuclear Mass ◽  
Oppenheimer Approximation ◽  
Brown And Ravenhall

In this paper we study the pseudo-relativistic Hamiltonian proposed by Brown and Ravenhall in the semiclassical limit when the mass ratio h2 of electronic to nuclear mass tends to zero. We show that the relativistic contribution of the nuclei on WKB-type expansions of the first energy levels are of order o(h2), as h→0.

Three-body molecular states of the LiH2+ system in the Born-Oppenheimer approximation

2018 ◽  
Vol 118 (15) ◽  
pp. e25611 ◽  
Author(s):  
Juan M. Randazzo ◽  
Antonio Aguilar-Navarro
Keyword(s):  
Oppenheimer Approximation ◽  
Three Body

Ionization of alkaline earth additives in hydrogen flames - I. Hydrogen atom concentrations and ion stabilities

1974 ◽  
Vol 338 (1613) ◽  
pp. 155-173 ◽  
Keyword(s):  
Alkaline Earth ◽  
Molecular Ions ◽  
The Other ◽  
Hydrogen Atoms ◽  
Ion Hydration ◽  
Atomic Ions ◽  
Charged Species ◽  
Hydration Energies ◽  
Three Body ◽  
Species Being

The ions present in flames of H 2 +O 2 + N 2 with trace quantities of an alkaline earth M ( = Ca or Sr) added to them have been studied mass spectrometrieally. Those detected were principally MOH + and M + , the only negatively charged species being the free electron. It was established that the reaction M + +H 2 O = MOH + +H was rapid enough to be balanced everywhere in a flame. Detailed studies of (I) provided a means for measuring the concentration of hydrogen atoms at the point of sampling in the flame from observations of [M + ]/[MOH + ]. It proved possible to make absolute determinations of [H]. In addition, the ionization potentials of CaOH and SrOH were measured as 5.7 ± 0.3 and 5.4 ± 0.3 eV, which values are slightly less than those for the corresponding alkaline earth atoms. Hydrates of MOH + and M + were observed, but it was concluded that ion-hydration is not an important flame process in this case, but rather one associated with cooling of gases as they are sampled into the mass spectrometer. It appears that molecular ions hydrate in a two-body process, e. g. MOH + + H 2 O → MOH + . H 2 O with a velocity constant, which is independent of temperature and approximately 1 x 10 –10 ml molecule –1 s –1 . Atomic ions on the other hand initially undergo hydration by a slower three-body step requiring a chaperon molecule. The first hydration energies at absolute zero for CaOH + and SrOH + were measured to be 120±20 and 109±15 kJ mol –1 respectively. These exceed the corresponding quantities for Ca + and Sr + , which were found to be 75±16 and 60±16 kJ mol –1 .

scholarly journals Molecular Data for Stellar Opacities

1995 ◽  
Vol 10 ◽  
pp. 576-578
Author(s):  
Uffe Gråe Jørgensen
Keyword(s):  
Ab Initio ◽  
Energy Levels ◽  
Laboratory Data ◽  
Molecular Data ◽  
Molecular Ions ◽  
Molecular Constants ◽  
Excitation Energies ◽  
Line Intensities ◽  
Lower Accuracy ◽  
Ab Initio Computations

In total, 40 neutral diatomic molecules, 2 molecular ions, and 7 polyatomic molecules are known from observed photospheric stellar spectra. Line data for opacity computations (i.e., lists of line frequencies, intensities, and excitation energies) exist for 17 of these molecules, although the data are complete only for a handful of them. A detailed description of stellar photospheric molecules can be found in Tsuji (1986), and the existing opacity data have been reviewed by Jorgensen (1995).Listed line frequencies in the data bases are either the measured values, or based on computed molecular constants obtained from fits to measured values. Attempts to compute ab initio line frequencies have so far resulted in lower accuracy than what is obtained by use of molecular constants. Published line strengths include measured values as well as ab initio values. For strong bands the ab initio intensities are as accurate as the laboratory values, whereas measured values for weak bands are generally more accurate than the ab initio values. The primary advantage of ab initio computations is therefore that the complete set of all transitions can be obtained. Exploratory studies have shown that completeness of the line data is crucial for the obtained stellar photospheric structure.As an alternative to the ab initio computations of the line intensities, fits to experimental data have been attempted. The most promising method seems to be to fit the dipole function by use of a Padé approximant. Combined with a potential fitted to experimental energy levels, such a dipole function can in principle be used to predict the complete list of band intensities and line intensities for all bands with energies up to the molecular dissociation energy. The part of the dipole function which corresponds to the largest stretching (or bending) of the molecule is the most uncertain in such fits as well as in ab initio computations. This part is responsible for most of the many weak transitions, and large uncertainties are therefore to be excepted in the computed intensities of the weak spectral bands. As these are of major importance for the stellar photospheric structure (due to their huge number and their pseudo continuous appearance in the spectrum), a particularly large effort is desirable in comparing computed intensities with laboratory data for a representative sample of weak bands. Unfortunately, only few measurements of weak bands exist.

EPR AND OPTICAL STUDIES OF VANADYL IONS IN ALKALI LEAD BOROTELLURITE GLASSES

2005 ◽  
Vol 19 (13n14) ◽  
pp. 643-653 ◽  
Author(s):  
R. P. SREEKANTH CHAKRADHAR ◽  
G. SIVARAMAIAH ◽  
J. LAKSHMANA RAO ◽  
N. O. GOPAL
Keyword(s):  
Optical Absorption ◽  
Molecular Ions ◽  
Tetragonal Symmetry ◽  
Spin Hamiltonian ◽  
Paramagnetic Resonance ◽  
Fermi Contact Interaction ◽  
Fermi Contact ◽  
Hamiltonian Parameters ◽  
Electron Paramagnetic ◽  
Boltzmann Law

Electron Paramagnetic Resonance (EPR) and optical absorption spectra of VO 2+ ions in different alkali lead borotellurite glasses have been studied. The spin-Hamiltonian parameters (g and A), bonding parameter [Formula: see text] and Fermi contact interaction parameter k have been calculated. The values of spin-Hamiltonian parameters confirm that the vanadyl ions are present in the glasses as VO 2+ molecular ions in an octahedral site with a tetragonal compression. The number of spins (N) participating in resonance is calculated as a function of temperature (123–393 K) for 9 mol% of VO 2+ ions in lithium lead borotellurite glass sample. It is observed that N obeys the Boltzmann law. From EPR data, the paramagnetic susceptibility (χ) is calculated at various temperatures and the Curie constant has been evaluated from 1/χ–T graph. The optical absorption spectrum exhibits two bands characteristic of VO 2+ ions in tetragonal symmetry. The band gap (E opt ) and the Urbach energies (ΔE) have been determined from the ultraviolet absorption edges and are found to be dependant on the size of the alkali ion. The theoretical values of optical basicity (Λ th ) of these glasses have also been evaluated.

ROVIBRATIONAL BOUND STATES OF THE Ar2Ne COMPLEX

2013 ◽  
Vol 12 (01) ◽  
pp. 1250107 ◽  
Author(s):  
BENHUI YANG ◽  
BILL POIRIER
Keyword(s):  
Quantum Dynamics ◽  
Bound States ◽  
Energy Levels ◽  
Effective Potentials ◽  
Spectral Transform ◽  
Physical Insight ◽  
Rovibrational States ◽  
Three Body ◽  
Massive Parallelization ◽  
Variable Representation

We report exact quantum dynamics calculations of the eigenstate energy levels for the bound rovibrational states of the Ar2Ne complex, across the range of J values for which such states are observed (J = 0–35). All calculations have been carried out using the ScalIT suite of parallel codes. These codes employ a combination of highly efficient methods, including phase-space optimized discrete variable representation, optimal separable basis, and preconditioned inexact spectral transform (PIST) methods, together with an effective massive parallelization scheme. The Ar2Ne energy levels were computed using a pair-wise Aziz potential plus a three-body correction, in Jacobi co-ordinates. Effective potentials for the radial co-ordinates are constructed, which reveal important physical insight into the two distinct dissociation pathways, Ar2Ne → NeAr + Ar and Ar2Ne → Ar2 + Ne . A calculation of the bound vibrational (J = 0) levels, computed using the Tang–Toennies potential, is also performed for comparison with results from the previous literature.

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