Quantization of the potential amplitude in the one-dimensional Schrödinger equation

A consistent scheme is proposed for quantizing the potential amplitude in the one-dimensional Schrödinger equation in the case of negative energies (lying in the discrete-spectrum domain). The properties of the eigenfunctions ?_n(x) and eigenvalues α_n corresponding to zero, small, and large absolute values of energy E < 0 are analyzed. Expansion in the set ?_n(x) is used to develop a regular perturbation theory (for E < 0), and a general expression is found for the Green function associated with the time-independent Schrödinger equation. A similar method is used to solve several physical problems: the polarizability of a weakly bound quantum-mechanical system, the two-center problem, and the tunneling of slow particles through a potential barrier (or over a potential well). In particular, it is shown that the transmission coefficient for slow particles is anomalously large (on the order of unity) in the case of an attractive potential is characterized by certain critical values of well depth. The proposed approach is advantageous in that it does not require the use of continuum states.     

Adsorption of nitrogen on platinum

The adsorption and desorption of nitrogen on a platinum filament have been studied by thermal desorption techniques. Nitrogen adsorption becomes significant only after any carbon contamination is removed from the surface by heating the platinum filament in oxygen, and after the CO content in the background gas is reduced substantially. At room temperature nitrogen populates an atomic tightly bound β-state, E^≠ = 19 kcal mole^?1. The saturation coverage of the (3-state is 4.5 × 10¹⁴ atoms cm^?2. Formation of the (β-state is a zero order process in the pressure range studied. At 90 K two additional α₁- and α₂-desorption peaks are observed. The activation energy for desorption for the α₂-state is 7.4 kcal mole^?1 at low coverage decreasing to 3 kcal mole^?1 at saturation of this state, 6 × 10 molecules cm^?2. The maximum total coverage in the α-states was 1.2 × 10¹⁵ molecules cm^?2. A replacement process between the β- and α-states has been observed where each atom in the (β-state excludes two molecules from the α-state.     

An ab initio investigation of the low-lying electronic states of BeH

Potential energy curves(PECs) for the ground state(X 2 Σ +) and the four excited electronic states(A 2 Π,B 2 Π,C 2 Σ +,4 Π) of a BeH molecule are calculated using the multi-configuration reference single and double excited configuration interaction(MRCI) approach in combination with the aug-cc-pVTZ basis sets.The calculation covers the internuclear distance ranging from 0.07 nm to 0.70 nm,and the equilibrium bond length R e and the vertical excited energy T e are determined directly.It is evident that the X2Σ+,A2Π,B2Π,C2Σ+ states are bound and 4Π is a repulsive excited state.With the potentials,all of the vibrational levels and inertial rotation constants are predicted when the rotational quantum number J is set to be equal to zero(J = 0) by numerically solving the radial Schr¨odinger equation of nuclear motion.Then the spectroscopic data are obtained including the rotation coupling constant ω e,the anharmonic constant ωexe,the equilibrium rotation constant Be,and the vibration-rotation coupling constant αe.These values are compared with the theoretical and experimental results currently available,showing that they are in agreement with each other.     

ΛΛ 6 He and Λ 9 Be systems in the three-body cluster model treated on the basis of differential Faddeev equations

The _ΛΛ ⁶ He and _Λ ⁹ Be hypernuclei are treated as the S=0, T=0 (for the former) and S=1/2, T=0 (for the latter) bound states of the three-cluster systems ΛΛα and Λαα, respectively. The cluster-reduction method is used to solve the s-wave differential Faddeev equations for these systems. On the basis of the MT I–III model, the ΛΛ interaction potential is specified in the form $V_{\Lambda \Lambda } = \frac{2}{3}V_{NN} $ . Phenomenological potentials are used to describe Λα and αα interactions. The binding energies of the _ΛΛ ⁶ He and _Λ ⁹ Be hypernuclei and the parameters of low-energy Λ-hyperon and α-particle scattering on a _Λ ⁵ He hypernucleus are calculated. It is shown that the proposed ΛΛ interaction potential makes it possible to reproduce faithfully the binding energy of the _ΛΛ ⁶ He hypernucleus and that scattering in the Λ _Λ ⁵ He system is similar to neutron scattering on a deuteron.     

Ground state(s) of the spin-boson hamiltonian

We establish that the finite temperature KMS states of the spin-boson hamiltonian have a limit as the temperature drops to zero. Using recent advances on the one-dimensional Ising model with long range, 1/r ², interactions, we prove qualitative properties of the ground state(s) in the ohmic case. We show (i) the asymptotics of the critical coupling as the bare energy gap goes to zero and to infinity, (ii) a jump in the order parameter, and (iii) that the number of bosons is finite below and infinite at and above the critical coupling strength.     

On the elastic characteristics of graphene and silicene

Analytical expressions for the central k ₀ and noncentral k ₁ force constants of two-dimensional (graphene, silicene) and three-dimensional (diamond, silicon) structures have been obtained within the previously proposed model of the binding energy of carbon atoms in graphene. The Kleinman internal displacement parameter of the two-dimensional structure has been determined. It has been shown that the ratio k ₀/k ₁ depends only on the dimension of the structure.     

On the hydrodynamic theory of central peak in displacive structural phase transitions

A model involving nonlinear coupling between the overdamped phonon mode and temperature fluctuations is studied using the dynamic renormalization group method. It is shown that the behavior of the central peak in the dynamic form factor depends on the specific heat exponent α. For α < 0 and as T → T_c the central peak is found to merge with the over-damped phonon mode and the coupling goes to zero at T_c as (T ? T_c)^?α. An argument on the intensity of the central peak in the critical region in presented and it is concluded that the hydrodynamic coupling may not be the dominant mechanism of the central peak in SrTiO₃.     

Chemical reaction of sputtered Cu film with PI modified by low energy reactive atomic beam

Polyimide (PMDA-ODA) surface was irradiated by low energy reactive atomic beam with energy 160-180 eV to enhance the adhesion with metal Cu film. O₂⁺ and N₂⁺ ions were irradiated at the fluence from 5 × 10¹⁵ to 1 × 10¹⁸ cm⁻². Wetting angle 78° of distilled deionized (DI) water for bare PI was greatly reduced down to 2-4° after critical ion flounce, and the surface energy was increased from 37 to 81.2 erg/cm. From the analysis of O 1s core-level XPS spectra, such improvement seemed to result from the increment of hydrophilic carbonyl oxygen content on modified PI surface. To see more carefully correlation of the peel strength with interfacial reaction between Cu and PI, flexible copper clad laminate with Cu (9 μm)/Cu (200 nm) on modified PI substrate (25 μm) was fabricated by successive sputtering and electroplating. Firstly, peel strength was measured by using t-test and it was largely increased from 0.2 to 0.5 kgf/cm for Ar⁺ only irradiated PI to 0.72-0.8 kgf/cm for O₂⁺ or N₂O⁺ irradiated PI. Chemical reaction at the interface was reasoned by analyzing C 1s, O 1s, N 1s, and Cu 2p core-level X-ray photoelectron spectroscopy over the as-cleaved Cu-side and PI side surface through depth profiling. From the C 1s spectra of cleaved Cu-side, by the electron transfer from Cu to carbonyl oxygen, carbonyl carbon atom became less positive and as a result shifted to lower binding energy not reaching the binding energy of C₂ and C₃. The binding energy shift of the peak C₄ as small as 1.7 eV indicates that carbonyl oxygen atoms were not completely broken. From the analysis of the O 1s spectra, it was found that new peak at 530.5 eV (O₃) was occurred and the increased area of the peak O₃ was almost the same with reduced area of the peak carbonyl oxygen peak O₁. Since there was no change in the relative intensity of ether oxygen (O₂) to carbonyl oxygen (O₁), and thus O₃ was believed to result from Cu oxide formation via a local bonding of Cu with carbonyl oxygen atoms. Moreover, from X-ray induced Auger emission spectra Cu LMM which was very sensitive to chemical bonding, Cu oxide or CuOC complex formation instead of CuNO complex was clearly identified by the observation of the peak at 570 eV at higher 2 eV than that of metal Cu. In conclusion, when Cu atoms were sputtered on modified PI by low energy ion beam irradiation, it can be suggested that two Cu atoms locally reacted with carbonyl oxygen in PMDA units and formed Cu⁺O⁻C complex linkage without being broken from carbon atoms and thus the chemically bound Cu was in the form of Cu₂O.     

Continuum resonances with shielded Coulomb-like potential and Efimov effect

Motivated by the possibility of the second energy level (0 ₂ ⁺ ) of ¹²C (in a three-alpha model) to turn into an Efimov state, we study a simple non-realistic toy model formed by three bosons interacting by the phenomenological s-wave Ali-Bodmer potential plus a Coulomb interaction. An artificial three-body potential was used to create a resonance with energy close to the energy of the 0 ₂ ⁺ of ¹²C, 0.38 MeV. The strength of the Coulomb potential is decreased until the energies of the two alpha pairs are zero. The system was placed inside a harmonic trap and a stabilization method has been used to calculate the energies of the resonances. We found that the shielded-Coulomb potential, which keeps the long tail, is not able to produce the Efimov effect. The energy of the three alphas decreases only to 0.19 MeV when the two-body energy crosses the threshold to become bound.     

A Mathematical Representation of Quantizing the Motion of Relativistic Electrons in a Magnetic Field

It is shown that the quadratic component of the kinetic energy of continuous longitudinal motion of relativistic electrons in the external magnetic field is varied continuously between 0 and 2(2m _e c ²_B H) within each Landau energy level, undergoing an abrupt change at the boundaries of the levels. This results in the fact that in the quantum limit of a superstrong magnetic field where all electrons are at the zero Landau level, the maximum quadratic component of the kinetic energy of free longitudinal electron motion along the direction of the magnetic field is twice as high as the maximum quadratic component of the kinetic energy of its bound transverse motion.     

Split-shell molecular orbital calculations on the heteronuclear alkali metal diatomics

One of the radicals formed in irradiated 5-iododeoxyuridine is shown unambiguously to be the α-iodo radical RCH₂-?(I)R′ formed by hydrogen atom addition to C₆. The ¹²⁷I hyperfine tensor components, A_x = + 90 G, A_y = (-) 50 G, A_z = (-)40 G are proposed as being characteristic of the coupling to be expected for α-iodo alkyl radicals. Hence a radical recently detected in irradiated iodoacetamide with a maximum hyperfine coupling of 250 G cannot have this structure. Possible alternative structures are discussed.

The way in which the E.S.R. spectra for the α-iodo radica in 5-iododeoxyuridine are modified by the quadrupole interaction from ¹²⁷I is described and hence an estimate of the quadrupole coupling is obtained.     

Variational calculations of the static polarizability of H2 and of the dipole-dipole contribution to the dispersion energy between two hydrogen molecules

The convergence of variation-perturbation calculations using non-linear variation parameters has been examined for the static polarizability of H₂ and for the coefficient (C₆) of the R ^-6 term in the multipole expansion of the H₂-H₂ dispersion energy. Using a correlated ground state wavefunction, and one excited state for each of the parallel and perpendicular components of the polarizability, a single variational parameter for each state gave 96 per cent of the exact value of α_⊥ and 91 per cent of the exact value of α_‖. A second variational parameter for the parallel component gave 94 per cent of α_‖. The same procedure gave the spherical average and anisotropy of C₆ to an accuracy of about 90 per cent. By extending the calculations into the region where overlap of the orbitals of the two molecules becomes significant, it is shown for the end-on configuration that the C₆ R ^-6 term underestimates the dispersion energy near the van der Waals' minimum by roughly 10 per cent.     

Schrödinger operators with magnetic fields

We prove a large number of results about atoms in constant magnetic field including (i) Asymptotic formula for the ground state energy of Hydrogen in large field, (ii) Proof that the ground state of Hydrogen in an arbitrary constant field hasL _z = 0 and of the monotonicity of the binding energy as a function ofB, (iii) Borel summability of Zeeman series in arbitrary atoms, (iv) Dilation analyticity for arbitrary atoms with infinite nuclear mass, and (v) Proof that every once negatively charged ion has infinitely many bound states in non-zero magnetic field with estimates of the binding energy for smallB and largeL _z .On leave at Department of Mathematics, California Institute of Technology, Pasadena, CA 91125 for 1980/81Supported by USNSF Grant MCS-78-00101Supported by USNSF Grant MCS-78-01885; on leave at Department of Mathematics, California Institute of Technology, Pasadena, CA 91125 for 1980/81     

Stability of the positively charged manganese centre in GaAs heterostructures examined theoretically by the effective mass approximation calculation near the Γ critical point

This paper describes an n-i-p-i-n model heterostructure with a manganese (Mn)-doped p-type base region to check the stability of a positively charged manganese A_Mn⁺ centre with two holes weakly bound by a negatively charged 3d⁵(Mn) core of a local spin S=5/2 in the framework of the effective mass approximation near the Γ critical point (k～0). By including the carrier screening effect, the ground state energy and the binding energy of the second hole in the positively charged centre A_Mn⁺ are calculated within a hole concentration range from 1 × 10¹⁶ cm^-3 to 1 × 10¹⁷ cm^-3, which is achievable by biasing the structure under photo-excitation. For comparison, the ground-state energy of a single hole in the neutral A_Mn⁰ centre is calculated in the same concentration range. It turns out that the binding energy of the second hole in the A_Mn⁺ centre varies from 9.27 meV to 4.57 meV. We propose that the presence of the A_Mn⁺ centre can be examined by measuring the photoluminescence from recombination of electrons in the conduction band with the bound holes in the A_Mn⁺ centre since a high frequency dielectric constant of varepsilon _∞ =10.66 can be safely adopted in this case. The novel feature of the ability to tune the impurity level of the A_Mn⁺ centre makes it attractive for optically and electrically manipulating local magnetic spins in semiconductors.     

Magneto-optical signature of broken mirror symmetry of two-dimensional conductors

An unusual aspect of macroscopic electrodynamics of two-dimensional mirror-odd conducting structures bound up with the band spin–orbit coupling H _so = α(p × c) · σ of current carriers (where c is one of two none-quivalent normals to a given structure) is pointed out. Namely, it is shown that due to the spin–orbit coupling the presence of the in-plane magnetic field H ₀ gives rise to a dependence of the reflection/transmission amplitudes on the structure orientation c, the wave vector of the incident radiation q, and H ₀ of the form q · (c × H ₀). This q- and H ₀-odd dependence can be the foundation of the optical way to determine the value of the spin–orbit coupling α.     

Photoassociation experiments with ultracold metastable helium

The present article gives a review of various photoassociation (PA) experiments performed at ENS with a gas of ultracold atoms of metastable helium in the 2³S₁ state, using a PA laser beam red-detuned from the 2³S₁-2³P transitions. Molecular spectra close to the D₂ atomic line (2³S P₂) are presented. All the measured lines are identified as a signature of molecular bound states having a strong (if not pure) quintet spin character at short interatomic distance. Close to the D₀ atomic line (2³S P₀), giant helium dimers can be produced [see Phys. Rev. Lett. 91, 073203 (2003)]. A laser set-up improved recently allows us to measure very accurately the binding energy of the ro-vibrational ground state of the 0 _u ⁺ purely long-range potential and the agreement with the theory published previously is excellent. Finally, preliminary results on 2 photon PA spectroscopy are given.Received: 1 July 2004, Published online: 26 October 2004PACS: 32.80.Pj Optical cooling of atoms trapping - 33.20.Kf Visible molecular spectra - 34.50.Gb Electronic excitation and ionization of molecules - 34.20.Cf Interatomic potentials and forcesJ. Léonard: Present address: Van der Waals-Zeeman Institute, Universiteit van Amsterdam, The Netherlands.M. Walhout: Permanent address: Calvin College, Grand Rapids, MI, USA.     

Solutions for the T = 0 quantum spin glass transition in a metallic model with spin-charge coupling

We solve several low temperature problems of an infinite range metallic spin glass model. A compensation problem of T 0 divergencies is solved for the free energy which helped to extract the quantum critical behaviour of the spin glass order parameters as a function of δJ = J – J_c (T = 0). The critical value J_c(T = 0) = 3/16p_F^?1 of the frustrated spin coupling J, which separates spin glass from nonmagnetic (spin liquid) phase, is determined exactly in the static saddle point solution for a semielliptic metallic band model in terms of the density of states at the Fermi level. In addition to the replica-overlap order parameter 〈Q^ab〉, a ≠ b, the diagonal 〈Q^aa〉 is confirmed as order parameter by the result 〈Q^aa〉 _SP ～ (δJ)^β, β = 1, and its susceptibility χ^aaaa ～(-δJ)^?γ with γ = 1/2 at T = 0. The value for γ agrees with the one for the transverse field Ising spin glass. The low γ decay of 〈Q^aa〉, ～ T is obtained exactly in the whole quantum disordered phase including the critical value.     

Electron correlations and instability of a two-center bipolaron

The energy of a large bipolaron is calculated for various spacings between the centers of the polarization potential wells of the two polarons with allowance made for electron correlations (i.e., the explicit dependence of the wave function of the system on the distance between the electrons) and for permutation symmetry of the two-electron wave function. The lowest singlet and triplet 2³S states of the bipolaron are considered. The singlet polaron is shown to be stable over the range of ionic-bond parameter values η≤η_m≈0.143 (η=?_∞/?₀, where ?_∞ and ?₀ are the high-frequency and static dielectric constants, respectively). There is a single energy minimum, corresponding to the single-center bipolaron configuration (similar to a helium atom). The binding energy of the bipolaron for η → 0 is J_bp=?0.136512e⁴m^*/?²? _∞ ² (e and m* are the charge and effective mass of a band electron), or 25.8% of the double polaron energy. The triplet bipolaron state (similar to an orthohelium atom) is energetically unfavorable in the system at hand. The single-center configuration of the triplet bipolaron corresponds to a sharp maximum in the distance dependence of the total energy J_bp(R); therefore, a transition of the bipolaron to the orthostate (e.g., due to exchange scattering) will lead to decay of the bound two-particle state. The exchange interaction between polarons is antiferromagnetic (AFM) in character. If the conditions for the Wigner crystallization of a polaron gas are met, the AFM exchange interaction between polarons can lead to AFM ordering in the system of polarons.     

ESR and Chemical Bonding of Some Copper Complexes

ESR spectra of copper (II) was measured in 33 copper complexes which were synthesized in this laboratory and the bonding parameter α²of copper was calculated according to the method proposed by Kivelson. ⁽¹⁾ The results of these calculations are classified, together with the data quoted from the literature,^1-5into four groups according to the kinds of ligand atoms, i.e., α²is 0.72 to 0.87 for 0₄ - type complexes, 0.69 to 0.86 in N₂O₂, 0.74 to 0.82 in N₄, and 0.54 to 0.62 in S₄ and S₂₃N₂ type complexes, where 0, H and S refer the oxygen, nitrogen and sulfur atoms of ligands, respectively, that directly coordinate with copper.     

Improved condition for the absence of bound states and converging analytic bounds to critical screening parameter

Converging lower bound to the critical screening parameterD _c associated with the ground state of a two-particle system interacting through a cut-off Coulomb potential is obtained analytically using an improved condition for the absence of bound states. The predicted numerical result for the lower bound is found to be within 10⁻³% of the exact result. On the other hand, a multi-parameter variational approach yields a tight upper bound, within 0.54% of the exact result. It is shown that the critical screening parameter for the exciteds-states can also be determined in an approximate way. We obtainD _c ^ms ≈ [0.764435n ⁻²+0.617737n ⁻³]⁻¹ wheren is the principal quantum number. The predictedD _c for various quantum states (n=1 to 8) are in good agreement with the values obtained numerically by Singh and Varshni.