Energetical structure of muonic molecular ions ddµ and dtµ

The long-lived states lying below then=2 threshold in muonic molecular ions ddµ and dtµ are reviewed. We have considered all the known long-lived states both of normal and anomalous spatial parity, the bound states as well as resonant three-body states of shape and Feshbach types. It is shown that these states could be satisfactorily classified in terms of the Born-Oppenheimer adiabatic theory. We calculate some characteristic properties of the Feshbach resonances, thus obtaining that the life-time of the 3d states is greater than 10^–11 s, and the fusion rate from these states less than 10⁹ s^–1. The geometry of the 4f(J=0,v=0) state shows that it does not obey approximate ungerade symmetry. On the contrary, the low vibrational 3d states are approximately of gerade symmetry, as a result these states decay ejecting dµ atoms in the same proportion as tµ atoms.     

A theoretical study of ion selectivity of zeolites—application to chabazite

As a contribution towards a better theoretical understanding of zeolite properties, the mechanism of ion migration through zeolite lattices has been studied with special reference to ion selectivity in chabazite. We have started from the Cartesian coordinates obtained by combining experimental data and the values for a model having standard bond lengths and angles. Then we have applied the Del Re method (with appropriate parameters for Si and Al⁻) to determine the net charges of the framework atoms. Then we have computed the potential energy profiles for one or more cations crossing the larger cavity of the chabazite unit cell (ca 200 atoms). The interaction energy contains electrostatic terms associated with point-charge interaction and polarization effects.Two different pictures have been analyzed: a totally idealized one, where ion motion takes place in the fully dehydrated zeolite, and a more realistic one, where the ion is seen as a moving aquo complex. In the latter case, the presence of the solvent has been taken into account by introducing a dielectric constant depending on ion size and channel diameter. Whereas no significant differences between ions having the same formal charges have been found in the dehydrated case, polarization effects being too small to bring about a distinct selectivity, the model taking solvation into account does predict the expected selectivity, and agrees well with available experimental results. Equilibrium sites, the corresponding free energies, and energy barriers between them have been used for the discussion.The value of the two models in attempts to understand elementary physico-chemical processes in zeolites is emphasized, with extensive reference to existing literature.     

Separation of different wave components in the Bethe–Salpeter wave function

The scalar products of polarization tensor and unit vectors are presented explicitly in spherical coordinate system expanded in terms of spherical harmonic functions. By applying the obtained formulae, different wave components in the Salpeter wave function can be shown explicitly, and the results are consistent with the results obtained by L–S coupling analysis. The cancelation formula is given, by which the terms with pure L = J + 1 wave components in the Salpeter wave function for the bound state with h_P=(-1)^J\eta_{\rm P}=(-1)^J can be obtained by separating the L = J − 1 wave components from mixing terms. This separation provides the basis for studying higher-order contributions from the coupling of L = J − 1 and J + 1 wave states, and for solving the Salpeter equation exactly without approximation.     

Studies on the analytical potential energy function of diatomic molecular ion XY~+ using variational method

It is well-known that the accurate behavior of potential energy function of molecular ion plays an important role in the studies such as solution chemistry, atmosphere chemistry, nebular medium, plasma physics, and gun powder, etc.[1, 2]. The values of potential energy function of diatomic molecular ion could significantly influence the optical efficiency of laser pump using ion vapors as working substrate[3]. The ionic potential is very important for the studies on low-energy ion-atom collisi…     

On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz

Making an ansatz to the wave function, the exact solutions of the D-dimensional radial Schrödinger equation with some molecular potentials, such as pseudoharmonic and modified Kratzer, are obtained. Restrictions on the parameters of the given potential, δ and ν are also given, where η depends on a linear combination of the angular momentum quantum number ? and the spatial dimensions D and δ is a parameter in the ansatz to the wave function. On inserting D = 3, we find that the bound state eigensolutions recover their standard analytical forms in literature.     

Sensitivity of the photon structure function F2 to the QCD scale parameter Λ

Initial optimism that the photon structure function F₂ would provide a sensitive measure of the QCD scale parameter Λ gave way to pessimism as the nature of the separation of point-like and hadronic parts of F₂ was understood. Building on previous work, this paper presents a quantitative analysis of the sensitivity of F₂ to Λ, and finds that at large Q² and x much of the sensitivity to Λ which gave rise to the initial optimism in fact survives the more sophisticated analysis.     

Binding energy and fine structure of the He^- ion

The variational method using a multiconfiguration wavefunction is carried out on the core-excited state 1s2s2p^4 p^0 for helium negative ion, including mass polarization and relativistic eorreetions. Binding energy and fine structure are reported. The results are compared with other theoretical and experimental date in the literature.     

A quantum Hamilton–Jacobi proof of the nodal structure of the wave functions of supersymmetric partner potentials

Quantum Hamilton–Jacobi formalism is used to give a proof for Gozzi’s criterion, which states that for eigenstates of the supersymmetric partners, corresponding to the same energy, the difference in the number of nodes is equal to one when supersymmetry (SUSY) is unbroken and is zero when SUSY is broken. We also show that this proof is also applicable to the case, where isospectral deformation is involved.     

Binding energy and fine structure of the He- ion

The variational method using a multiconfiguration wavefunction is carried out on the core-excited state 1s2s2p 4P0 for helium negative ion,including mass polarization and relativistic corrections.Binding energy and fine structure are reported.The results are compared with other theoretical and experimental date in the literature.     

The molecular structure and analytical potential energy function of HCO （X^2A＇）

In this paper the equilibrium structure of HCO has been optimized by using density functional theory （DFT）/ B3P86 method and CC-PVTZ basis. It has a bent （Cs, X^2A＇） ground state structure with an angle of 124.4095 °. The vibronic frequencies and force constants have also been calculated. Based on the principles of atomic and molecular reaction statics, the possible electronic states and reasonable dissociation limits for the ground state of HCO molecule have been determined. The analytic potential energy function of HCO （X^2A＇） molecule has been derived by using the many-body expansion theory. The contour lines are constructed, which show the static properties of HCO （X^2A＇）, such as the equilibrium structure, the lowest energies, etc. The potential energy surface of HCO （X^2A＇） is reasonable and very satisfactory.     

The influence of molecular structure of protein on the acoustic nonlinearity parameter B/A

I.IntroductionAcousticnonlinearityparameterB/Adescrjbesthenonlilleareffectsofasoundwavetrav-ellingthroughamedium.Withtheapplicationofhighmowerultrasonicwavetomedicine,thenonlineareffectsbecomemoreandmoreimportant.EspeciallybecauseB/Aissensitivetothepathologicalstateofbiologicaltissues[1-2])thisprovidesprospectiveapplicationinmedicaldiagnosis.Atpresent,thestudyinthisareaemphasizesontwoaspects.OneistodevelopnewmedicalimagingtechniquesbyusingthisnonlinearityparameterB/Al1'3-'];theotheristostu…     

The molecular structure and the analytical potential energy function of S2^- and S3^-

In this paper, the equilibrium geometry, harmonic frequency and dissociation energy of S2^- and S3^- have been calculated at QCISD/6-311＋＋G（3d2f） and B3P86/6-311＋＋G（3d2f） level. The S2^- ground state is of 2IIg, the S3^- ground state is of 2B1 and S3^- has a bent （C2v） structure with an angle of 115.65° The results are in good agreement with these reported in other literature. For S3^- ion, the vibration frequencies and the force constants have also been calculated. Base on the general principles of microscopic reversibility, the dissociation limits has been deduced. The Murrell-Sorbie potential energy function for S2^- has been derived according to the ab initio data through the least- squares fitting. The force constants and spectroscopic data for S2^- have been calculated, then compared with other theoretical data. The analytical potential energy function of S3^- have been obtained based on the many-body expansion theory. The structure and energy can correctly reappear on the potential surface.     

Excited states of the molecular ion (H2μ)+

The rotation-vibration spectrum of (H₂ )⁺ is computed. Radiative lifetimes of the excited states are of order 10^–4 s or more. These times can be considered infinite compared to the lifetime of ⁺. For the ion in a crystal the lifetimes are significantly decreased by interaction with polarized molecules of the lattice. Transition rates to the ground state are calculated for (H₂ )⁺ in a hydrogen crystal. The results make it possible to interpret the experimental data from SR investigations of hydrogen, deuterium and hydrogen-deuterium mixtures.     

Visualization of deficiencies in approximate molecular wave functions: the local orbital energy function for the matrix Hartree—Fock model

The local orbital energy function is used to assess the quality of approximate Hartree-Fock orbitals obtained by invoking the algebraic approximation and using a finite basis set expansion. Systematic sequences of distributed universal even-tempered basis sets of spherical-harmonic Gaussian-type functions are used to generate orbitals for which the corresponding total Hartree-Fock energy approaches the 1 μE_h level of accuracy. A pilot study of the behaviour of the local energy function is made for the hydrogenic atom described by a sequence of even-tempered Gaussian basis sets. The results of prototype calculations for the Hartree-Fock ground state of the BF molecule at its equilibrium geometry are presented. Sequences of calculations which use atom-centred basis sets are investigated as well as sequences which also include bond centred functions. The effects of the bond centred functions on the local orbital energy function are analysed. The local orbital energy function is seen as a measure of the quality of calculations carried out within the matrix Hartree-Fock approximation which can be employed in cases where the corresponding finite difference Hartree-Fock results are not available.     

New microscopic wave function of ��-condensation

We explain how to treat a microscopic wave function of ??-condensation taking a 3??-nucleus as a typical example. The wave function has been originally proposed ten years before by Horiuchi, R?pke, Schuck and the present author (Phys. Rev. Lett., 2001, 87: 192501). The microscopic model, which fully takes into account the Pauli principle between all the constituent nucleons, effective internucleon forces and the Coulomb force, can play an important role in reproducing an ??-gas nature thanks to ??-condensation as an excited state of ??-like nuclei. An essential point of the wave function is to describe their ground state simultaneously. We study its typical features by giving an analytical formula of the norm kernel and the kernel concerning the one-body operator for 3??-condensation.     

Bound states and resonance states of the plasma-embedded tdμ and ddμ molecular ions

We have investigated the bound states and resonance states of plasma-embedded tdμ and ddμ molecular ions using accurate correlated basis functions. The plasma effect has been taken care of by considering the Debye shielding approach of plasma modeling which admits a variety of plasma conditions. The density of resonance states are calculated using the stabilization method. The ground and excited states energies, and the S-wave resonance energies of tdμ and ddμ molecular ions immersed in plasmas are reported for various shielding parameters, along with the 1S and 2S threshold energies of the tμ and dμ atoms.     

Precise determination of the 4π-periodicity factor of a spinor wave function

The perfect crystal neutron interferometer is used to perform a precise determination of the 4-symmetry of a spinor. The high precision is gained by the use of very well defined magnetic fields within two magnetized Mu-metal sheets, which are rotated in opposite directions within the coherent neutron beams. The periodicity of a spinor is determined to a value of=716, 8±3, 8 deg., which is in agreement with the theoretical prediction.Work supported by Fonds zur Förderung der Wissenschaftlichen Forschung (Projekt 3185) and by Bundesminister für Forschung und Technologie 03-41A09     

Gluon distribution function from the Berger–Block–Tan form of the structure function F 2

Physics of Atomic Nuclei - We present a set of formulas to extract the gluon distribution function from the Berger–Block–Tan form of the deep inelastic structure function F 2 and its...