Bound and Resonant States of the Hulthén Potential Investigated by Using the Complex Scaling Method with the Oscillator Basis

Bound and resonant states of the Hulthén potential are studied. The complex scaling method is used to achieve the energy spectrum. The oscillator basis is used to expand the radial wave function. Conforming to the standard feature of the complex scaling method, the bound energies do not change and the continuums change with the rotational angle. With tables and graphs, the interesting properties of the energy spectrum for various physical parameters are presented. The Gauss quadrature integral approximation is used to deal with the potential integral term.     

Exploration of Pseudospin Symmetry in the Resonant States

Taking ^120Sn as an example, we discuss the pseudospin symmetry in the single proton resonant states by examining the energies, widths and the wavefunctions. The information of the single proton resonant states in spherical nuclei are extracted from an analytic continuation in the coupling constant method within the framework of the self-consistent relativistic mean field theory under the relativistic boundary condition. We find small energy splitting in a pair of pseudospin partners in the resonant states. The lower components of the Dirac wavefunctions of a pseudospin doublet agree well in the region where nuclear potential dominates. It is concluded that the pseudospin symmetry is also well conserved for the resonant states in realistic nuclei.     

Construction of AFLT States for W_NH Symmetry,Analytic Continuation and Integrability on AGT Relation

We propose a Hamiltonian to the construction of the AFLT states for WNsymmetry. We generalize the AGT relation to generic(extended) conformal field theory with 1 ≤ c ∞. We analyze the triangular structure hidden in the AGT relation with WNsymmetry in detail and the triangular structure implies the integrability.     

Bound States of the S-Wave Equation with Equal Scalar and Vector Standard Eckart Potential

A supersymmetric technique for the bound-state solutions of the s-wave Klein-Gordon equation with equal scalar and vector standard Eckart-type potential is proposed. Its exact solutions are obtained. Possible generalization of our approach is outlined.     

Calculation of Quantum‐Chemical Characteristics of the Ground and Excited Electronic States of Porphin and Its Tetrapyrrole Isomers

Using the CNDO/S method, we have performed quantumchemical calculations of the ground and excited electronic states of porphin molecules (symmetry D _2h ) and a number of porphin isomers: porphycene (C_2h ), hemiporphycene, corphycene (C_2v ), isoporphycene, and three nonsynthesized structural isomers of the porphin skeleton by its bridge groups —(CH) _meso —. The results of the calculations are compared with the corresponding data for the freebase porphin molecule (H₂P). Near the boundary between the occupied and vacant orbitals the isomers form rows of singleelectron levels with similar energy characteristics. For the MOs of these isomers, the H₂P MOs closest in distribution on the comparable atomic centers are given. The weak (Q) and strong (B) transitions in the visible and near UV regions point to the porphyrin type of spectra of all the isomers. The calculation data on the excited electronic states of N, g, and ntype H₂P near and above the B states are given; the presence of such states in other isomers is shown. The calculation does not point to a difference in the position of the first singlet transitions in the first five isomers. The calculation data on the lower singlettriplet transitions are also reported.     

One-Dimensional Relativistic Problems on the Bound States and Degradation for a Superposition of Two δ Potentials

For a superposition of two potentials, exact one-dimensional wave functions of the bound states with quantization conditions and exact wave functions of the degradation state with transmission and reflection coefficients have been found. The phenomenon of complete reflection taking place for potentials of this type is investigated.     

Formation of η′(958) Meson Bound States and Chiral Symmetry In-Medium

We theoretically discuss the feasibility to observe the η′(958)-mesic nuclei by using the missing mass spectroscopy. We evaluate the η′-nucleus optical potential including the contribution of lowest order in density together with the second order terms account for η′ absorption by two nucleons, based on a recent model of the η′N interaction. We show the calculated formation cross section of the η′ bound states from (π, N) reaction with pion beam momentum p _π = 1.8 GeV/c and (p, d) reaction with proton kinetic energy T _p = 2.5 GeV.     

Analysis of Y（4660） and Related Bound States with QCD Sum Rules

In this article, we take the vector charmonium-like state Y（4660） as a φ＇ fo（980） bound state （irrespective of the hadro-charmonium and the molecular state） tentatively, and study its mass using the QCD sum rules. The numerical value My = 4.71 ±0.26 GeV is consistent with the experimental data. Considering the SU（3） symmetry of the light flavor quarks and the heavy quark symmetry, we also study the bound states φ＇a（400-1200）, γ′″ fo（980）, and γ′″σ（400-1200） with the QCD sum rules, and make reasonable predictions for their masses.     

Decay of the Bethe–Salpeter Kernel and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We consider lattice classical ferromagnetic spin systems at high temperature (1) with nearest neighbor interactions and even single-spin distributions (ssd). Associated with each system is an imaginary time lattice quantum field theory. It is known that there is a particle of mass m–ln in the energy-momentum spectrum. If s ⁴–3s ²²<0, where s ^k is the kth moment of the ssd, and is sufficiently small, we show that in the two-particle subspace there is no mass spectrum up to 2m. For >0 we show that the only mass spectrum in (m, 2m) is a bound state of mass m _b=2m+ln(1–)+O(), where =(+2s ²²)^–1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results.     

Characteristics of scattering of Λ hyperons from nuclei within the potential model

The characteristics of bound states of hypernuclei were calculated in [1] in a wide range of mass numbers within the potential model for three different potentials. In this study, the phase shifts and low-energy parameters for scattering of Λ hyperons from core nuclei, considered in [1], have been calculated for the same potentials. The calculated scattering lengths and effective radii are compared with their values found in [1] on the basis of the data on the binding energies and vertex constants of hypernuclei.     

Correspondence of Fluorescing States of Naphthols and Naphtholate Anions and its Effect on the Calculation of pKa∗ from Spectral Shifts

The validity of dissociation constants of electronically excited acids and bases, calculated from spectral shifts^1,2 accompanying protolytic dissociation, especially where shifts of fluorescence spectra are employed, is dependent, among other factors, upon fluorescence orginating from excited states of the same electronic configuration in both acid and conjugate base.³ In some of the molecules whose excited state acid-base properties have been most extensively studied, notably some derivatives of naphthalene, energy level reversals have been shown to accompany dissociation in the lowest excited singlet state in aqueous solutions.⁴ The spectroscopic properties and excited state dissociation phenomena of the naphthols have been studied extensively from several points of view.^5-9 While the calculation of the excited state dissociation properties of β-naphthol, in which fluorescence occurs from the ¹L_b state in both anion and neutral molecule, presents no particular problem with regard to correspondence of the lowest excited singlet states of conjugate acid and base, it appeared that in α-naphthol, by analogy with α-naphthylamine⁴, fluoescence might occur from the ¹L_a state in the conjugate base and from the ¹L_b state in the conjugate acid. Thus it seemed that a careful consideration of the states from which the fluorescences of the conjugate species derived from α-naphthol in fluid aqueous solutions orginated, would be useful.     

Resonant structure due to the 3p→3d transition in the photoionization of Ca+

Many-body perturbation theory has been used to calculate the resonance structure (3p→3d) into the photoionization (4s→kp) for ion Ca⁺. This resonance structure results from the interference between a photoionization process or a photoionization with excitation process and a resonant Auger process. The coupled equation method has been improved to calculate this interference by the summation of specific classes of diagrams of perturbation theory to infinite order. The resonance structure in the region of the 3p threshold is enhanced via a super-Coster–Kronig transition. The theoretical results are in good agreement with experiment.     

Resonant Raman Scattering Spectra of Zn‐Phthalocyanine and Zn‐Phthalocyanine‐d 16

We obtained the resonant Raman scattering spectra of Znphthalocyanine and of its fully deuterated analog, Znphthalocyanined ₁₆. We performed calculation of normal vibrations and using it, interpreted the Raman scattering spectra. We characterized the form of vibration with the aid of potential energy distribution. For the majority of vibrations the calculation adequately describes the observed isotropic shifts. The correspondence between the vibrational states of Znphthalocyanine and metal complexes of tetrabenzoporphin has been established in confirmation of the proposed detailed interpretation of the spectra.     

Dimers based on the α + α potential and chain states of carbon isotopes

Using the well established binding energies of one and two valence neutrons in the two-center α+α system (forming the states in ⁹Be and ¹⁰Be*) the structure of these nuclear dimers and their rotational bands including those with more than 2 nucleons are discussed using published transfer reaction data for Be and Boron isotopes. Based on the 0 ₂ ⁺ state in ¹²C which is supposed to be an 3α particle chain at an excitation energy of 7.65 MeV and using the binding energy of these valence neutrons in ⁹Be and ¹⁰Be*, chain states in the system ¹²C* + x neutrons are constructed. The energy position of the lowest chain states are estimated and ways for their population in reactions on ⁹Be and using radioactive beams are proposed. It is expected that these states are metastable and could have appreciable branches for γ-decay. Further extrapolations to longer chain states (polymers) in neutron rich light isotopes are made.     

Measurement of the sizes of a source of α particles from the collisions of relativistic 22Ne and 24Mg nuclei with photoemulsion nuclei

The correlation of two α particles has been measured. In the case of a one-dimensional parameterization of the correlation function, the size of the source of the α particles is R(α) = 2.84 ± 0.28_stat ± 0.23_sist fm. This result is compared to similar measurements for protons and deuterons.     

Rheo-optical and dielectric studies of the α loss region of low-density polyethylene

The α mechanical loss region of low-density polyethylene has been studied by vibrational and relaxational X-ray diffraction, birefringence, IR dichroism, light-scattering, and dielectric methods. These experiments are consistent with the proposal of Takayanagi that the α₁ process is intercrystalline in nature and exhibits an activation energy of about 25 kcal/mole, where the α₂ loss is intracrystalline and possesses an activation energy of about 50 kcal/mole.     

Current Filamentation and Resonant Transport of the Relativistic Electron Beam in Dense Plasmas

The transport of a relativistic electron beam in dense plasmas with a cold return electron current is examined by two-dimensional particle-in-cell simulation.The filamentation and coalescence of currents and related magnetic field patterns,caused by the electromagnetic-benm-plasma instability,are observed.In the later simulation time,the electrons of the relativistic electron beam are trapped into the potential wells of the wave excited by the instability,and transport resonantly with the wave.