Effect of correlations on nuclear muon capture

The process μ⁻+¹²C→¹²B+v _μ is studied using the modified Hartree Fock wavefunction obtained with the unitary-model-operator-approach starting from the realistic hardcore nucleon-nucleon interaction, with the aim of testing the wavefunctions and obtaining a numerical value for the induced pseudoscalar coupling constant (g _P ). These observables, namely, the partial capture rate to the¹²B(1⁺; g.s), its recoil nuclear polarisation and the total capture rate, which exhaust the available experimental data in the above process have been calculated and compared with the other theoretical and experimental results. As far as the partial capture rate is concerned the use of the unitary-model operator approach wave functions for¹²C withb=2.09 fm and Cohen-Kurath wave function for¹²B(1⁺; g.s) reduces the pure shell model capture rate by about 30%. The effect of strong configuration mixing in the ground state of¹²C in taken into account by introducing a scale factor ξ similar to the ‘amplitude reduction factor’ of Donnelly and Walecka. With this ξ the agreement with the experiment both for the partial capture rate and the beta decay ‘ft’ value is found to be satisfactory. The¹²B(1⁺; g.s) recoil polarisation is found to be insensitive to the use of the unitary-model-operator-approach wave functions. When compared with the experimental data, we obtaing _P =(14.9±1.9)g _A . The total capture rate is found to be sensitive to the use of the unitary-modeloperator-approach wave functions which contain the effect of nucleon-nucleon short range correlations and we obtain a satisfactory agreement with the experiment for¹⁶O and¹²C, thereby revealing the importance of the effect of such correlations in the total capture rate studies.     

Rotational analysis of the 0–9, 0–10 and 0–11 bands of theA 2II u -X 2II g band system of (16O18O)+

High-resolution spectra of the 0–9, 0–10 and 0–11 bands of theA ²II _u —X ²II _g system of (¹⁶O¹⁸O)⁺ ion have been studied for their rotational structure. This study enables a direct determination of the Λ-doubling parameters of theA ²II _u andX ²II _g states. The model of ‘pure precession’ explains, though not entirely, the Λ-doubling of theX ²II _a state as arising out of its interaction with theB ² Σ _g ⁻ state. The Λ-doubling in theA ²II _u state was found insignificant.     

Reinvestigation of the second negative (A 2 Π u−X 2 Π g) band system of O 2 +

TheA ² Π _ustate of O₂ ⁺ was earlier established as an inverted state contrary to previous assumptions. The rotational analysis of a few more bands of theA-X system of O₂ ⁺ has now been completed. These studies show that the spin-orbit coupling constantA in theA ² Π _ustate gradually varies with the vibrational quantum numberν and is found to be positive forν⩾6. It has also been observed that the spia-rotation interaction is not negligible in theA ² Π _ustate. The spin splitting constantγ is reported for various vibrational levels of this electronic state.     

Properties of synchrotron radiation

Muon capture on hydrogen gives a unique possibility for a measurement of the pseudo-scalar form factor g _p (q _c ² = -0.88 m _μ ² ) of the nucleonic weak current, thus providing a sensitive test of the QCD chiral symmetry perturbation theory which predicts the value of this form factor with a precision of Δg _p /g _p ≃ 2%. For adequate comparison with theory, the muon capture rate Λ_c should be measured with a precision of ΔΛ_c/Λ_c ≤ 1%, that is an order of magnitude better than the precision of the present world data. We report on the project of an experiment designed to provide the required precision. Also, we present the final result of our previous experiment on a high precision measurement of the μ³He capture rate and compare this result with the PCAC prediction. This revised version was published online in August 2006 with corrections to the Cover Date.     

Electronic states of C2H6 +

The complete photoelectron spectrum of ethane has been measured in the valence region using Ne, He I, and He II resonance radiation. The resolution of these spectra is sufficient to partially resolve vibronic structure accompanying the transition to the ground ionic state. The similarity of this structure with that obtained from model calculations using the Jahn-Teller theorem strongly suggests that the active vibration in this transition is a doubly degenerate CH₃ deformation mode and that the ground ionic state is a Jahn-Teller split ² E _g state. These experiments suggest a ² A _1g term for the first excited ionic state. The transition to the ² A _2u state of the ion contains evidence for two active vibrations v ₁ (C–H stretch) and v ₃ (C-C stretch).     

Correlation between fractional independent yields and neutron-to-proton ratio of fission products in low energy fission

Fractional independent yields of fission products in the thermal neutron-induced fission of²³³U,²³⁵U,²³⁹Pu,²⁴¹Pu and in the spontaneous fission of²⁵²Cf have been correlated with the neutron-to-proton ratio of the fission products. The yields of the products from a fissioning system, when plotted as a function of neutron-to-proton (N/Z) ratio of fission preducts, fall on two Gaussian distribution corresponding to light and heavy fission products. The centroids of the distribution or the most probable value of neutron-to-proton ratio is found to be very close to theN/Z of the fissioning nucleus. From the most probable value ofN/Z the various parameters of charge distribution e.g. most probable massA _p, most probable chargeZ _p, the mass dispersionσ _Aand the charge dispersionσ _Zhave been obtained and are in good agreement with the experimental values ofA _pandZ _p.     

The X2Π and A2Σ+ states of FH+, ClH+ and BrH+: theoretical study of their g -factors and fine/hyperfine structures

Theoretical calculations on the fine, hyperfine and Zeeman (g-factor) parameters are reported for the X²Π and A²Σ⁺ states of FH⁺, ClH⁺ and BrH⁺. The fine-structure constants [spin–orbit (A), Λ-doubling (p, q) and spin–rotation constants (γ _Π, γ _Σ)] are evaluated up to second order (via SO/L couplings with several excited states) using a multireference configuration interaction (MRCI) method, a Breit–Pauli Hamiltonian and 6-311++(2d,2pd) basis sets. Hyperfine constants of magnetic and electric type [Frosch–Foley (a, b, c, d) and nuclear quadrupole (eQq ₀, eQq ₂)] are studied with density functional methods and various basis sets. Magnetic dipole moments (parameterized via g-factors) are calculated in second order like the fine structure constants. The situation is somewhat complex for X²Π since no less than five different g’s have to be evaluated in second order. In general, our results are in good agreement with those reported in the literature, mostly limited to the ground state. Our calculations confirm that, at equilibrium, all second-order properties are dominated by the couplings between the electronic states X and A.     

Theoretical studies of the local structures and electron paramagnetic resonance parameters for Cu2+ center in Zn(C3H3O4)2(H2O)2 single crystal

The electron paramagnetic resonance (EPR) parameters (g factors g_xx, g_yy, g_zz and hyperfine structure constants A_xx, A_yy, A_zz) are interpreted by taking account of the admixture of d-orbitals in the ground state wave function of the Cu²⁺ ion in a Zn(C₃H₃O₄)₂(H₂O)₂ (DABMZ) single crystal. Based on the calculation, local structural parameters of the impurity Cu²⁺ center were obtained (i.e. R_a≈1.92 Å, R_b≈1.96 Å, R_c≈1.99 Å). The theoretical EPR parameters based on the above Cu²⁺?O^2? bond lengths in the DABMZ crystal show good agreement with the observed values and some improvements have been made as compared with those in the previous studies.     

ΛN Space-exchange effects in thes-shell hypernuclei and Λ 9 Be

Variational Monte Carlo calculations of the ground state separation energiesB _Λ of thes-shell hypernuclei and also of _Λ ⁹ Be have been made for an Urbana-type central space-exchange ΛN potential consistent with Λp scattering, and also including three-body ΛNN forces. Thes-shell hypernuclei are treated asA-body systems (A = baryon number), and _Λ ⁹ Be is analysed as a partially nine-body problem in the Λ — 2α model. The reduction ofB _Λ due to the space-exchange ΛN potential has been calculated for thes-shell hypernuclei for a range of interactions: both ΛN and ΛN + ΛNN forces. ForA = 3,4,5 the exchange energy is approximately, 0.04, 0.15 and 0.50 MeV, respectively. For _Λ ⁹ Be a much more limited study gives ≅ 1.3 MeV. These values are much larger than that for ‘soft’ ΛN +NN potentials when the correlations are weak. Preliminary results were presented at the DAE Symp. on ‘Nuclear Physics’ Vol. 32B (1989).     

Singlet-triplet pseudo Jahn-Teller centers in copper oxides

One of the most interesting attributes of a hole CuO ₄ ⁵ center in doped cuprates is the complexity of the ground state as a result of electronic pseudodegeneracy. An extra hole injected into the initial CuO ₄ ⁶ cluster with a b _1g hole can occupy not only the very same hybrid Cu 3d-O 2p orbital state, producing a Zhang-Rice A _1g singlet, but also the pure oxygen e _u state, generating a singlet or triplet ^1,3 E _u term, with close energies. The pseudo Jahn-Teller effect induced by pseudodegeneracy of the singlet ¹ A _1g and ¹ E _u terms is analyzed in detail. Fiz. Tverd. Tela (St. Petersburg) 40, 1795–1804 (October 1998)     

Magnetic circular dichroism of the first spin-forbidden transition in 2[Cr(en)3Cl3] . KCl . 6H2O

The longitudinal Zeeman effect of the ² E ←⁴ A ₂ transition of the Cr⁺³ ion in single crystals of 2[Cr(en)₃Cl₃] . KCl . 6H₂O has been measured using circularly polarized light as a function of magnetic field strength between 0 and 160 kgauss at ～80 K. The g factor for the ground state was determined to be g _‖(⁴ A ₂) = 2·01±0·05, in agreement with the E.S.R.-determined value. The ratio between the excited state g values and that of the ground state was determined; using the value g _‖(⁴ A ₂) = 1·99, the g factors g _‖(2) = 2·61±0·04 and g _‖() = 1·47±0·04 were obtained.     

EPR,FTIR, Powder XRD and Optical Absorption Studies of Cu(II) Ion in Triaqua(1,10-Phenanthroline-k<Superscript>2</Superscript><Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>′)(Sulfato-kO)Zinc(II)

Electron paramagnetic resonance (EPR), optical, Fourier-transform infrared (FTIR) and powder X-ray diffraction (XRD) studies have been carried out on Cu(II)-doped triaqua(1,10-phenanthroline-k² N,N′)(sulfato-kO)zinc(II) to get information about the position and spin Hamiltonian parameters of the dopant. Angular variation of copper hyperfine structure lines in EPR study shows the presence of a single site with g and A values as: g _xx  = 2.003, g _yy  = 2.001, g _zz  = 2.223; A _xx  = 4.41 mT, A _yy  = 2.39 mT and A _zz  = 12.16 mT. The slightly lower parallel value obtained for the copper nucleus has been explained by considering admixture of the ground state with the excited state. The direction cosines of principle g and A values suggest that the impurity is present interstitially. Admixture coefficients and additional parameters (P, k, α ², α′) have also been evaluated. Optical, FTIR and powder XRD techniques have been used to reconfirm the structure of the host lattice.     

Characterization of isomers of the nucleus154Pm

Consideration of the expected two-quasiparticle structures and their estimated band head energies, and the selection rules for beta transition rates for the¹⁵⁴Nd →¹⁵⁴Pm →¹⁵⁴Sm decays are used to deduce the configurations for the isomers and the low-spin structures in the neutron rich doubly odd nucleus ₆₁ ¹⁵⁴ Pm₉₃. The 2.68 m high spin isomer and the 1.73 m low spin isomer are respectively assigned the spin-parity 4⁺ and 1⁺ with the configuration {p:5/2⁻ [532↑] +n:3/2⁻ [521↑]} with the 2.68 m isomer lying lower in energy, and thus forming the¹⁵⁴Pm ground state. Two-quasiparticle character of the beta-connected states in¹⁵⁴Nd decay and¹⁵⁴Pm decay is discussed.     

Covalent binding parameters and the ground state wavefunctions of vanadyl ion complexes

The Steven’s method of molecular orbitals for octahedral complexes containing transition metal ions has been used for estimating the binding parameters and interpreting theg factors of VO ₂ ⁺ ion in single crystals. The expressions forg factors have been given in terms ofK _‖ andK _⊥ taking into account the tetragonal crystalline field and covalent binding effects. Computations show thatK _⊥ should be less than 0.066 in order to fit the experimentalg values. The ground state wave function (GSWF) of VO ₂ ⁺ ion doped in different single crystals has been estimated using crystal field theory. The GSWF is found to be ind _xy state with slight admixture of the excited states ,d _xz andd _yz. The hyperfine interaction parameterP and Fermi contact termX have also been estimated.     

Spectroscopic and structural proprieties of LiAr and LiAr<Subscript>2</Subscript> molecules

We determined and tried to understand the spectroscopic and structural properties of small LiAr and LiAr₂ molecules within a simple model considering LiAr as a result of interaction between a valence electron and a LiAr⁺ molecular ion. Potential energy curves, spectroscopic constants, and vibrational levels corresponding to the Li(2s, 2p, 3s, and 3p)+Ar dissociation are reported for the LiAr molecule. The depth of the potential well for the X ²Σ⁺ ground state is found to be 50 cm⁻¹ (the corresponding experimental value is (42.5±1.2) cm⁻1 [1]). R _e is determined to be 9.36 a.u. (the experimental value is 9.24 a.u.). For the first excited state A, R _e = 4.97 a.u. and D _e = 993cm ⁻¹ (the corresponding experimental values are 4.68 a.u. and (925−40) cm⁻¹, respectively [1]). The spacing between the vibrational levels for the ground and first excited states is in very good agreement with the experiment. For the ground state, the difference between our results and the data of the most recent experiment is about 1 cm⁻¹. The model has been extended to study the LiAr₂ molecule in two forms (linear and triangular). We have determined the potential energy surfaces of the states dissociating to Li(2s, 2p)+Ar₂ and thus found the triangular form to be more stable as compared to the linear one. We have also calculated the transition energy between the ground state and first excited states of this molecule. The emission spectrum of the Li(2s)+Ar₂→Li(2p)+Ar₂ transition in both forms redshifts as compared to the Li(2s)→Li(2p) atomic transition.     

EPR studies of Cu2+ and V4+ ions in phosphate glasses

Two lead-phosphate glass systems doped with both copper and vanadium ions in different ratios were studied by EPR (electron paramagnetic resonance) method. EPR spectra and parameters (g_‖ = 2.44, g_⊥ = 2.08 andA _‖ = 117.6 · 10⁻⁴ cm⁻¹) obtained for x(CuO · V₂O₅)(l−x)[2P₂O₅ · PbO] glasses withx ≤ 10 mol% suggest a tetrahedral (Td) coordination of Cu²⁺ ions and not a tetragonally elongated octahedron as has been assumed in previous works. The ground state of the paramagnetic electron is thed _xy copper orbital with a 4p_z contribution of 6%. For 20 ≤x ≤ 40 mol% a broad line (ΔB = 307 G) characteristic for clustered ions appears atg = 2.18. The V⁴⁺ ions are evidenced only in the spectra of x(CuO · 2V₂O₅)(1 −x)[2P₂O₅ · PbO] glasses and the resonance parameters suggest a pentacoordinated C_4v local symmetry for these ions. The hyperfine structures characteristic for Cu²⁺ and V⁴⁺ ions disappear for 10 ≤x ≤ 40 mol% due to the mixed exchange Cu²⁺−V⁴⁺ pair formation in these glasses.     

Pseudo-Jahn–Teller effect in Si4X4 (X = F,Cl, Br,I) molecules: a theoretical investigation

ABSTRACT

The variability of planar rings in Si₄X₄ (X?=?F, Cl, Br, I) molecules caused by the pseudo-Jahn–Teller impact (PJTE) was evaluated as an original PJTE work. Optimisation and the following frequency calculations in these molecules illustrated that in high-symmetry planar (with D_4h symmetry) geometry, all of these compounds were unstable and their structures were puckered to lower C_2h symmetry stable geometry. Furthermore, the vibronic coupling interaction between ¹A_1g ground and the first ¹E_g excited states through (¹A_1g?+?¹E_g) ? e_g PJTE problem was the cause of non-planarity of the four-member ring and the symmetry breaking phenomenon in those series. The calculated gaps (Δ) between the ground state and the E_g excited state, the vibronic coupling (F) and ground state primary force constant values (k₁) were obtained from the numerical fitting of the ground state adiabatic potential energy surface with the analytical expressions of these molecules. Finally, natural bond analysis (NBO) was used for the design of the strongest interaction and natural atomic charges of these structures.     

Low-energy electron spectrum in copper oxides in the multiband p-d model

An exact diagonalization of the Hamiltonian in the p-d model of a CuO₆ cluster was used to obtain dependences on the model parameters of the lowest-energy two-hole terms: the energy difference between the 2p orbitals of planar and apical oxygen Δ(apex)=ε(2p)−ε[2p(apex)], the crystal field parameter , and the ratio of the distances between the copper atom and the apical and planar oxygen atoms d(apex)/d(pl). In the limit of large d(apex)/d(pl) and Δ_d, our model is equivalent to the three-band p-d model and, in this case, large singlet-triplet splitting Δε⩾1 eV is also observed. As the parameters decrease, a singlet-triplet crossover is observed. Two mechanisms are identified for stabilization of the triplet term ³ B _1g (0) as the ground state. It is shown that for realistic values of the parameters, reduction of the p-d model to the three-band model is limited by the low energies of the current excitations because of the presence of the lower excited ³ B _1g and ¹ A _1g cluster states. Intercluster hopping causes strong mixing of singlet and triplet states far from the G point. The results of the calculations are compared with data obtained by angle-resolved photoelectron emission in Sr₂CuO₂Cl₂. Fiz. Tverd. Tela (St. Petersburg) 40, 184–190 (February 1998)     

ESR study of exchange coupled pairs in copper diethyldithiocarbamate

ESR investigations on exchange coupled pairs of Cu ions in single crystals of Cu(dtc)₂, isomorphously diluted with the corresponding diamagnetic zinc salt, are reported. The spin Hamiltonian parameters for the coupled species (S=1) are:g _‖=2.1025,g ₊=2.031,A=75.1×10⁻⁴ cm⁻¹,B=14.8×10⁻⁴,D=276.0×10⁻⁴ cm⁻¹ andE=46.7×10⁻⁴ cm⁻¹. While theg andA tensors show tetragonal symmetry, the zeor-field splitting tensor is rhombic and has principal axes different from those of theg andA tensors. Intensity measurements made down to 4.2 K indicate that the exchange is ferromagnetic with |FFF| ∼ 10 cm⁻¹. Direct dipole-dipole interaction appears to be the major contribution to the zero-field splitting. A calculation on the distributed point dipole model shows that dipolar interaction is considerably modified by the high covalency of the Cu-S bond and accounts for the rhombic nature of the tensor. The possible exchange mechanisms in Cu(dtc)₂—direct exchange and superexchange through the bridging sulphurs—are discussed.     

Temperature dependence of Rb2 molecule formation rate constant in a magneto-optical trap

In this paper, we report the measurement of Rb₂ molecule formation rate constant due to a two body process in a magneto-optical trap as a function of the sample temperature. The ground state molecules are detected by two-photon ionization, through the intermediate a ³Σ _u ⁺ → 2³Π _g molecular band. Our results show that the Rb₂ molecules formed in the MOT could be due to a wave shape resonance, which enhances the molecule formation rate. This effect may be used to enhance the molecule production; and therefore it maybe important to future experiments involving production and trapping of cold ground state molecules.