Numerical calculation of energies of some excited states in a helium atom

The energies of some excited states with the total angular momentum L=0, 1 and 2. the total spin of two electrons S=0 and 1, and the even and odd parities are precisely calculated directly from the Schrödinger equation where the mass of the helium nucleus is finite. Moreover, we find that the solutions to the equation for the excited states have some more nodes, which can be used to distinguish the states with the same spectral term.     

Investigation of states in 30P via the 30Si(3He,t)30P reaction at 30 MeV

The ³⁰Si(³⁰He, t)³⁰P reaction has been measured for about 100 levels in ³⁰P with E_x < 8.8 MeV. Little selectivity in the population of states has been observed. For 75 levels angular distributions have been analysed using a “fingerprint method” by determining the L-value from a comparison in shape with transitions to states with known J^π. For possible mixed L-transitions a dominance of the higher L-value is observed for almost all cases. Coulomb displacement energy calculations utilizing shell-model wave functions have been used to identify T = 1 states.     

Study of the missing-mass spectra in the reactions π−d → K+ + MM and K−d → π+ + MM at 1.4 GeV/c to search for strange dibaryon states

The reactions π^?d → K⁺ + MM and K^?d → π⁺ + MM have been studied at 1.4 GeV/c to search for strange dibaryon states with quantum numbers Q = ?1, and S = ?1. No structures are found which could indicate the production of such states and upper limits for the cross sections are established.     

Coulomb Rydberg electron <Emphasis Type="Italic">L</Emphasis>-mixing in collisions with atomic ions

The cross sections of the Rydberg electron L-mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*(n, L) + A⁺ = H*(n, L′) + A⁺ without variation of the principal quantum number n. The probability of the L-mixing L → L′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(?i∫E _k (t)dt). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.     

Symmetrized harmonic oscillatorSU 3 states for multi-cluster systems

An algorithm is presented for the construction of single- and multi-cluster harmonic oscillator wave functions that are coupled into well-defined irreducible representations ofSU ₃ as well as of the symmetric groupS _N . The single-cluster harmonic oscillatorSU ₃ wave functions are constructed recursively, using theSU ₃ coefficients of fractional parentage. To construct multi-cluster wave functions with a well-defined permutational symmetry we diagonalize an appropriate set of single-cycle class operators of the symmetric group involving all the constituent particles. The formalism is applicable to the study of multi-cluster systems in nuclear physics where the wave functions are expressed in terms of harmonic oscillatorSU ₃ states     

Diploe-allowed optical absorption of an exciton in a spherical parabolic quantum dot

A investigation of the linear and nonlinear optical properties of an exciton in a spherical parabolic quantum dot has been performed by using the matrix diagonalization method. The optical absorption coefficients between the ground state (L=0,π=+1) and the first excited state (L=1,π=-1) have been examined based on the computed energies and wave functions. The results are presented as a function of the incident photon energy for the different values of the incident optical intensity and the confinement strength. We found the optical absorption coefficient is strongly affected by the incident optical intensity and the confinement strength.     

Two Types of Electronic States in One-Dimensional Crystals of Finite Length

Exact and general results on the electronic states in one-dimensional crystals bounded at τ and τ+L, where L=Na, N is a positive integer, and a is the potential period, are presented. Corresponding to each energy band of the Bloch wave, there are N−1 states in the finite crystal whose energies are dependent on L but not on τ and map the energy band exactly. There is always one and only one electronic state corresponding to each band gap of the Bloch wave, whose energy is dependent on τ but not on L. This state is either a constant-energy confined band-edge state or a surface state in the band gap.     

Superposition of two coherent states π out of phase with average photon number as relative phase

This paper discusses nonclassical features of the superposition of two coherent states π out of phase with each other and parameterized solely by amplitude α, that is, when the relative phase has a relationship with average photon number ∣α∣². In particular, it discusses oscillatory and sub-Poissonian photon statistics, degree of quadrature squeezing, and quasiprobability distribution functions. We examine that some nonclassical properties of these states are different from those of the even and odd coherent states.     

The non-resonant reaction γγ→K s K ±π∓ in perturbative QCD

The non-resonant reaction γγ→K _S K _π is studied in perturbative QCD. In order to reduce the required computer time the meson wave functions are approximated by sums of delta functions. Total cross sections, energy and angular distributions are presented.     

Low energy constraints on N = 2 supersymmetric models

We derive constraints on the masses of mirror particles in N = 2 supersymmetric theories. We consider the K_L?K_S mass difference, the π → ev/π → μv branching ratio and the anomalous magnetic moment of the muon. The K_L?K_S mass difference gives a lower bound of 15 TeV on the mirror gauge scalar and mirror gauge fermion masses, under suitable assumptions.     

Twenty-parameter eigenfunctions and energy values of the 23 S States of He and He-like Ions

Twenty-parameter calculations of the energies and wave functions of the first excited states 2³ S of He, Li⁺, Be⁺⁺, B⁺⁺⁺, O⁶⁺, Ne⁸⁺, Mg¹⁰⁺, have been carried out using Hylleraas' method. The energy values have been corrected for mass polarization. The coefficients of the best wave functions are listed. Similar calculations for the 2³ S state of the H^? ion yield an energy value which cannot be distinguished from the energy of a free H atom. For He and Li⁺, in addition, forty-parameter calculations have been carried out. The results compare well with the recent calculations of Pekeris using a somewhat different method. Even after the inclusion of the relativistic correction, the theoretical energy values deviate slightly from the observed. The differences, ?0·10±0·05 cm^?1 for He and ?1·07±0·10 cm^?1 for Li⁺, represent observed values of the Lamb shifts in the 2³ S states. These values agree within their uncertainties with the values predicted from quantum electrodynamics.     

A variational principle for band calculations in the kq-representation

A known variational principle satisfied by Wannier functions is extended to cover free electron-like solids. The extension is achieved by formulating the principle in the kq-representation where Wannier functions of a given band equal to Bloch functions of the same band.     

Antiproton-proton annihilation at rest intoπ + π − η ′ andπ + π − η from atomicS andP states

We have measured the branching ratios for \(\bar pp\) annihilation at rest intoπ ⁺ π ^? η andπ ⁺ π ^? η′ in hydrogen gas in two data samples that have different fractions ofS-wave andP-wave initial states. The branching ratios are derived from a comparison with the topological branching ratio for \(\bar pp\) annihilations into four charged pions of (49±4)% and the branching ratio intoπ ⁺ π ^? π ⁺ π ^? π ⁰ of (18.7±1.6)%. We find a significant reduction of the branching ratios fromP-states for \(\bar pp \to \pi ^ + \pi ^ - \eta \) andπ ⁺ π ^? η′ in comparison toS-state annihilation. $$\begin{gathered} BR(S - wave \to \pi ^ + \pi ^ - \eta ) = (13.7 \pm 1.46) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta ) = (3.35 \pm 0.84) \cdot 10^{ - 3} \hfill \\ BR(S - wave \to \pi ^ + \pi ^ - \eta ') = (3.46 \pm 0.67) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta ') = (0.61 \pm 0.33) \cdot 10^{ - 3} . \hfill \\ \end{gathered} $$ In a partial wave analysis of theπ ⁺ π ^? η Dalitz plot we find the following contributions: Phase space, \(a_2^ + (1320)\pi ^ \mp \) ,ηρ⁰ andf ₂(1270)η: $$\begin{gathered} BR(S - wave \to \pi ^ + \pi ^ - \eta PS) = (6.31 \pm 1.22) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta PS) = (0.47 \pm 0.26) \cdot 10^{ - 3} \hfill \\ BR(^1 S_0 \to a_2^ \pm (1320)\pi ^ \mp ) = (2.59 \pm 0.73) \cdot 10^{ - 3} \hfill \\ BR(^3 S_1 \to a_2^ \pm (1320)\pi ^ \mp ) = (1.31 \pm 0.48) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to a_2^ \pm (1320)\pi ^ \mp ) = (1.31 \pm 0.69) \cdot 10^{ - 3} \hfill \\ BR(^3 S_1 \to \rho \eta ) = (3.29 \pm 0.90) \cdot 10^{ - 3} \hfill \\ BR(^1 P_1 \to \rho \eta ) = (0.94 \pm 0.53) \cdot 10^{ - 3} \hfill \\ BR(^1 S_0 \to f_2 (1270)\eta ) = (0.083 \pm 0.086) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to f_2 (1270)\eta ) = (0.64 \pm 0.26) \cdot 10^{ - 3} . \hfill \\ \end{gathered} $$ We find a 2 σ effect for the reaction \(\bar pp \to a_0^ \pm (980)\pi ^ \mp \) , \(a_0^ \pm \to \eta \pi ^ \pm \) , with a branching ratio of (0.13±0.07)·10^?3. For η' production we give a branching ratio of \(\bar pp \to \rho \eta '\) of (1.81±0.44)·10^?3 from³ S ₁. We estmate a contribution of about 0.3·10^?3 for ρη' fromP-states. The ratio of ρη and ρη' rpoduction is used to test the validity of the quark line rule. In theπ ⁺ π ^? π ⁺ π ^? γ final state we do not observe the reaction \(\bar pp \to \pi ^ + \pi ^ - \omega \) , ω→π ⁺ π ^? λ and derive an upper limit of 3·10^?3 for decay modeω→π ⁺ π ^? λ.     

Dynamical calculation of the decay ψ′ → ψ + 2π

We calculate the ψ′ → ψ + 2π decay width on the basis of partial wave dispersion relations in the ππ channel. This is basically a coupled channel problem involving ππ, D$\text{D}$, etc. intermediate states. The calculation acquires anomalous thresholds due to the fact that the vertex ψ′ ψ (2π) is internally unstable. It is found that anomalous singularity contributions provide by far the most dominant contribution, which explains the rather large ψ′ → ψ + 2π decay mode. Very good agreement with the experimental width and mass distribution is achieved.     

Cusps in KL→3π decays

The pronounced cusp in K→3π decays which is generated by the pion mass difference is directly related to the ππS-wave scattering lengths. We apply a nonrelativistic effective field theory framework to evaluate the amplitudes for K_L→3π decays in a systematic manner. Electromagnetic effects in the neutral channel K_L→3π⁰ are also discussed.     

Observation of the decay Ks → 2γ and measurement of the decay rates KL → 2γ and KS → 2γ

The decay rates of K_L → 2γ and K_S → 2γ have been measured at the CERN SPS. The results are Γ(K_L→2γ)/χ(K_L→2π₀)=0.632±0.004±0.008 and Γ(K_S→2γ)/Γ(K_L→2γ)=2.3 ±1.0±0.4. This is the first observation of K_S→2γ decays.     

The reaction γ4He→3Hn π+ in impulse approximation

The reactionγ+⁴He→³H+n+π ⁺ is calculated in the impulse approximation. The influence of nuclear wave functions on the differential cross section is discussed numerically using Gaussian and Irving-Gunn wave functions for the triton and the α-particle. The differences are large enough to be looked for experimentally.     

Core excitons in the soft X-ray region: Solid argon

A theoretical calculation of core excitons is performed for the L_II,III soft X-ray threshold of solid argon at ～ 245 eV. The binding energies and the relative transition amplitudes for the lowest allowed exciton states are computed by formulating the problem in terms of Wannier functions and solving the resulting integral equation in the one-site approximation. The results obtained allow to locate the onset of interband transitions at an energy a few eV above previous theoretical determinations. Therefore, sharp structure previously interpreted in terms of conduction band density of states is attributed to discrete excitonic transitions, as strongly suggested by the close analogy with the atomic absorption spectrum. A comparison with the fundamental excitonic absorption in the vacuum ultra violet region is carried out in terms of the ratio of the electron-hole exchange interaction to the spin-orbit splitting of the hole states.     

Bound-pion absorption followed by emission of two nucleons

The bound-pion absorption reaction, viz. ¹²C(π^?, NN), is studied using Hartree-Fock (HF) wave functions obtained with the unitary-model-operator approach starting with the hard-core nucleon-nucleon (NN) interaction. The inequality of the energies of the two outgoing nucléons is treated exactly and calculations are done using the “1N model” for π-absorption. Other effects taken into account are: NN scattering in the final state, contributions of all excited states of ¹⁰B and ¹⁰Be with E < 5 MeV, and effects of the strong π-nucleus interaction and the finite nuclear size on the bound-π wave function. Branching ratios and angular distributions of absorption rates are in better agreement with experimental data. The correct order of magnitude of the total absorption rate is reproduced. Whatever the effects of short-range correlations present in the HF wave functions, they are not masked by the NN final-state interaction. The contribution of excited states in ¹⁰B and ¹⁰Be is found to be quite large. Absorption rates obtained with the HF and oscillator wave functions differ significantly both in size and shape.