Tests of interacting boson model wave functions from measured gyromagnetic ratios of states in the even Os isotopes

The gyromagnetic ratios of the 2₁⁺, 2₂⁺, and 4₁⁺ states in ^188,190,192Os were experimentally measured. It is shown that the hamiltonians of standard interacting boson models (IBM-1 and -2) fit to level spectra and B(E2) rates fail to account for either the intra-nucleus or mass-dependent g-factor variations of these states in these Os isotopes.     

Charmed Deuteron

Possible existence of bound states of a charmed baryon, Λ _c , Σ _c , Σ* _c with a nucleon, N, as well as two charmed baryons, Λ _c Λ _c , etc., are examined in the meson exchange potential approach. The heavy quark spin symmetry induces a strong tensor coupling between Λ _c N, Σ _c N and Σ* _c N states, which causes a bound state of Λ _c N (J = 0⁺ and 1⁺) states. Such a bound state is also seen in the spin-singlet Λ _c Λ _c channel, which resembles the H dibaryon in the strange sector.     

194Pt(12C, 12C′) reaction and the triaxial-rotor model

Elastic and inelastic scattering differential cross sections for the ¹⁹⁴Pt(¹²C, ¹²C′) reaction at a bombarding energy of 78 MeV have been measured. Data have been obtained for 0⁺, 2⁺, 4⁺, and 2^+′, states in ¹⁹⁴Pt. The data have been analyzed using a rigid asymmetric-rotor model in coupled-channels reaction calculations. It is found that satisfactory fits to all data can be obtained but only if the hexadecapole deformation is included in the asymmetric-rotor model.     

High-resolution optogalvanic study of the c4(0)1Πu, c′5(0)1Σu+, and a″(0)1Σg+ Rydberg states of N2

A new optogalvanic technique with an rf discharge was applied to a high-resolution study of the Rydberg states of N₂. The Ledbetter band, c₄(0)¹Π_u ← a″(0)¹Σ_g⁺, and a new visible band, c′₅(0)¹Σ_u⁺ ← a″(0)¹Σ_g⁺, were studied at a Doppler-limited resolution of 0.05 cm^?1. A Doppler-free method was also applied to resolve overlapped lines. Precise wavenumbers were determined for the rotational transitions of the two Rydberg bands. The rotational and the centrifugal constants for the lowest Rydberg state, a″(0)¹Σ_g⁺, were determined to be B₀ = 1.913748(42) cm^?1 and D₀ = 6.088(99) × 10^?6 cm^?1, where the numbers in parentheses are the standard deviation and apply to the last digits.     

A partial-wave analysis of the neutral 3π system produced in the reaction π−p → (π+π−π0) n at 12 and 15 GeV/c

Data on the charge-exchange reaction π^?p → (π⁺π^?π⁰)n have been taken at beam momenta of 12 and 15 GeV/c, using the CERN Omega Multiparticle Spectrometer. A partial-wave analysis has been made of the (3π)⁰ system. We observe both natural and unnatural spin-parity production. The natural parity states can be identified with established resonances. In addition a natural spin-parity enhancement is observed at a mass of about 2 GeV/c² with J^P = 4⁺ preferred. We have called this effect the A₂¹ (2030). The unnatural spin-parity production found is consistent with reggeized Deck model predictions. No unambiguous A₁ or A₃ production is observed.     

Transition densities between the 01+, 21+, 41+, 02+, 22+, 11− and 31− states in 12C derived from the three-alpha resonating-group wave functions

All the multipole transition densities between the seven T = 0 states in ¹²C are calculated with the use of the microscopic 3α resonating-group wave functions which are obtained by dynamically solving the 3α relative motion with the total antisymmetrization taken into account exactly. The observed elastic and inelastic electron scattering form factors for the transition to the 2₁⁺, 4₁⁺, 0₂⁺, 1₁^?and 3₁^? states are well reproduced with no additional effective charge. The existence of a deformed intrinsic state for the 0₁⁺, 2₁⁺and 4₁⁺states is deduced by the analysis of the transition densities between them which are derived by the weak-coupling-type 3α wave functions; the intrinsic density distribution is illustrated. The monopole density distribution of the 0₂⁺, 2₂⁺ and 1₁^?, states is found to be much longer ranged than that of the 0₁⁺, 2₁⁺ and 4₁⁺ states; the 3₁^? state case is intermediate. On the basis of the transition densities between the 0₁⁺, 2₁⁺, 0₂⁺ and 2₂⁺ states, analysis is made of the transition between the shell-like states and the molecule-like states with a large spatial-structure change. Specific, effective nucleon-nucleon interactions are folded into the transition densities here obtained. The evident dependence of the radial shape of the folded nucleon-¹²C form factors on the choice of the interactions and the multi-step form factors for the excitation of the 0₂⁺, 1₁^? and 3₁^? states are discussed.     

Oblate shapes of200, 202, 204Hg

Measurements of the reorientation effect for the first excited 2⁺ states in^{200, 202, 204}Hg were performed by exploiting the dependence of theγ-ray yield on Q₂+ for different projectiles. For²⁰⁰Hg, a positive quadrupole moment of Q₂=0.96±0.11 eb (for negative interference) or Q₂=1.11±0.11 eb (for positive interference) was determined indicating an oblate shape. Small positive Q₂ values were also found for²⁰²Hg and²⁰⁴Hg. Nine B(E2) values for excitation of the 2⁺, 2⁺′ and 4⁺ states in^196–204Hg measured.     

Electron scattering from transitional nuclei

An electron scattering experiment on ¹⁸⁸Os, ¹⁹⁰Os, ¹⁹²Os, ¹⁹⁴Pt and ¹⁹⁶Pt has been performed at momentum transfers q = 0.6 to 3.2 fm⁻¹. Transition charge densities have been determined for the low-lying 2⁺, 3⁻ and 4⁺ states. The 2⁺ densities are well reproduced within the framework of the interacting boson model 2, where we have determined the boson densities α_ν, α_π, β_νv and β_π. The 4⁺ transition densities could not be reproduced indicating the need for including a g-boson. The ground and transition charge densities of ¹⁸⁸Os, ¹⁹²Os and ¹⁹⁶Pt have been compared with a microscopic calculation. The total binding energies and the intrinsic wave functions have been calculated for different values of β and γ with the constrained triaxial Hartree-Fock-Bogoliubov method using the finite range interaction D1SA. These energies are interpreted as potential energy surfaces and used in the Bohr hamiltonian in order to obtain the total nuclear wave functions. We obtain very good agreement with experiment. The calculated potential energy surfaces show these nuclei to be γ-soft with a shallow minimum for triaxial deformations and rigid in the β direction.     

Magnetic hyperfine interaction in muonic indium,osmium and mercury

The magnetic hyperfine interaction in several muonic atoms has been measured. The magnetic splittings of the 1s _1/2, 2s _1/2 and 2p _1/2 muon states in the 9/2⁺ ground state of¹¹⁵In, determined by measuring muonic X rays areΔE _mag(1s _1/2,¹¹⁵In 9/2⁺)=3580±70 eVΔE _mag(2s _1/2,¹¹⁵In 9/2⁺)=525±120 eVΔE _mag(2p _1/2,¹¹⁵In 9/2⁺)=850±180 eV. The magnetic splitting of nuclearγ rays in the presence of a muon in the 1s _1/2 state yields for the 1/2^? ground state in¹⁹⁹HgΔE _mag(1s _1/2,¹⁹⁹Hg 1/2^?)=468±115 eV and the following values for the first excited 2⁺ states in the nuclei^190,192Os and²⁰⁰Hg:ΔE _mag(1s _1/2,¹⁹⁰Os 2⁺)=665± ₄₀ ⁸⁰ eVΔE _mag(1s _1/2,¹⁹²Os 2⁺)=800±80 eVΔE _mag(1s _1/2,²⁰⁰Hg 2⁺)=655± ₇₅ ¹⁰⁵ eV. These data are compared with calculations using different nuclear models.     

The study of the proton-proton collisions at the beam momentum 1581 MeV/c

The new data on the elastic pp and single-pion production reaction pp → pnπ ⁺ taken at the incident proton momentum 1581 MeV/c are presented. To extract contributions of the leading partial waves the single-pion production data are analyzed in the framework of the event-by-event maximum-likelihood method together with pp → ppπ ⁺ data measured earlier and the pp → pnπ ⁺ data taken at 1628 MeV/c. The analysis shows that at 1581 MeV/c the largest contributions stem from the ³ P ₂, ³ P ₁, ³ P ₀ and ³ F ₂ initial partial waves. From these partial waves we also deduce contributions for the production of the Δ(1232) and N(1440) states.     

Observation of the second 4+ state in 28Si by means of proton inelastic scattering and analysis of the Kπ = 01+and 31− bands

High-resolution data from the ²⁸Si(p, p′) reaction have been obtained at E_p = 26.3 MeV. Separate cross sections for the 3₁^? and 4₂⁺ states at 6.879 and 6.889 MeV have been obtained. The strength of the 4₂⁺ state is much larger than reported in previous experimental papers. The 3₁^? state is well described in a coupled-channels calculation based on the rotation-vibration model.     

Application of atom-photon coincidence techniques to the determination of the differential cross section for excitation ofK(42 P) in low-energy K-N2, CO collisions

The differential cross section for the processK(4² S)+N₂, CO→K(4² P)+ N₂, CO is presented for reduced scattering angles τ<2·10⁴ eV deg. The inelastic process is identified by determining the time-correlation between the inelastically scattered potassium atom and the emittedK(4² P→4² S)photon. The performance of different coincidence techniques is compared. From the differential cross sections values for the position of the curve crossing responsible for the excitation process are derived (R _c=2.77, 2.48 Å andV(R _c )=0.55, 1.00 eV for K-N₂, CO respectively). The values indicate that the lowest ionic intermediate state of the form K⁺-N ₂ ^? , CO^? is responsible for the excitation process.     

Theoretical investigation of the molecular structure and transition dipole moments of the NaK low lying electronic states

The electronic structure and the spectroscopic constants of the low lying electronic states of the NaK⁺ ionic molecule have been determined through using an ab initio approach involving a non-empirical pseudopotential for the Na and K cores and core valence correlation correction. The potential energy of nearly 26 electronic states of ²Σ⁺, ²Π, and ²Δ symmetries has been calculated up to their dissociation limit Na(4d) + K⁺ and Na⁺ + K(6s). Their spectroscopic constants (R_e, D_e, T_e, ω_e, ω_eχ_e, and B_e) are derived and compared with the few available theoretical studies. A good agreement has been found for the ground state and few excited states with previous works. New potential energy curves were presented, for the first time, for the higher excited states. Numerous avoided crossing between electronic states of ²Σ⁺, ²Π symmetries have been localized and analyzed. Their existences are related to the charge transfer between the two ionic molecules Na⁺K and NaK⁺. Furthermore, we have determined the transition dipole moments for several states and analyzed the avoided crossings related to charge transfer between alkaline atoms.     

Vibration-rotation bands of nitrous oxide: 4.1 micron region

The infrared spectrum of nitrous oxide has been measured and analyzed from 2265 cm^?1 to 2615 cm^?1. Newly refined effective rotational constants for twenty-one vibrational states of ¹⁴N₂O, three vibrational states each of ¹⁴N₂¹⁸O and ¹⁵N¹⁴N¹⁶O, two states of ¹⁴N¹⁵N¹⁶O and one state of ¹⁴N₂¹⁷O have been calculated.The most interesting features observed are two Δ-Σ “forbidden” bands, 04^2c0-00⁰0 and 12^2c0-00⁰0. These bands occur because of Coriolis interaction between unperturbed vibrational states having l = 0 and l = 2.     

Eigenvalues, eigenfunctions, and surface states in finite periodic systems

Using a simple approach that requires neither the Bloch functions nor the reciprocal lattice, new, compact, and rigorous analytical formulas are derived for an accurate evaluation of resonant energies, resonant states, energy eigenvalues and eigenfunctions of open and bounded n-cell periodic systems with arbitrary 1D potential shapes, provided the single cell transfer matrix is given. These formulas are applied to obtain the energy spectra and wave functions of a number of simple but representative open and bounded superlattices. We solve the fine structure in bands and exhibit unambiguously that the true eigenfunctions do no not fulfill the periodicity property |Ψ_μ,ν (z + l_c)|² = |Ψ_μ,ν (z)|², with l_c the single cell length. We show that the well known surface states and surface energy levels come out naturally. We analyze the surface repulsion effect and calculate exactly the surface energy levels for different potential discontinuities an the ends.     

AB initio calculations of the electronic properties of N4− in KN3

The energies of the ground state and low-lying excited states of the N₄^? defect in KN₃ have been calculated using ab initio techniques. A rectangular equilibrium geometry with dimensions X = 2.76 and Z = 2.47 a.u. and ground state symmetry of Γ₄⁺ was determined by calculating N₄^? as a free radical. For this ground state the unpaired electron is in a π orbital which is consistent with the experimental hyperfine tensor only if one edge of the N₄^? radical is parallel to the c axis in KN₃. These results were used to calculate the X²Γ₄⁺ state of N₄^? in the crystal field of KN₃, yielding an energy of ?217.899 Hartrees. The isotropic hyperfine constant was calculated to be a = 2.1 G and the components of the anisotropic hyperfine tensor as B_xx = ?3.4 G, B_yy = 7.0 G and B_zz = ?3.6 G, in good agreement with experimental and INDO results. Several excited states were calculated for the N₄^? defect in KN₃. When an estimate was made of the correlation energy, the transition energy of the X²Γ₄⁺→A²Γ₃^? transition agreed well with the peak energy of the 780 nm absorption band which has been attributed to N₄^?.     

A study of s - wave π π scattering in the reaction πn → ππp at 2.15 GeV/c

We have studied the 2_π⁰ final states in the reaction π⁺d → π⁰π⁰p(p) at 2.15 GeV/c in a 2 million picture exposure of the PPA rapid cycling deuterium bubble chamber. Two tantalum plates were added to the bubble chamber to convert γ rays which were kinematically constrained to a 2π⁰ hypothesis. The 2π⁰ mass spectrum is observed to saturate s-wave unitarity in the ππ mass region between 0.6 and 0.9 GeV/c², clearly favoring the ‘up-down’ or broad resonance solution for s-wave, I = 0, ππ scattering.