Level-Crossing-Untersuching der Stark-Aufspaltung der tiefsten1 P 1-Terme von Ca,Sr und Ba

Using the level-crossing technique, magnitude and sign of the tensor polarizability α_ten of the lowest¹ P ₁-levels of Ca, Sr, and Ba have been measured by investigating the splitting into Zeeman-sublevels in superimposed homogeneous electric and magnetic fields. The experimental results are: α_ten/g _J =?13.6(3) kHz/(kV/cm)² for Ca α_ten/g _J =?14.32(15) kHz/(kV/cm)² for Sr α_ten/g _J =?10.72(10) kHz/(kV/cm)² for Ba, where theg _J -values are approximatelyg _J≈1. With greater accuracy the ratios of these constants have been determined by eliminating the electric-field strength measurement: (α_ten(Sr)/g _J (Sr))/(α_ten(Ca)/g _J (Ca))=1.050(8) (α_ten(Sr)/g _J (Sr))/(α_ten(Ba)/g _J (Ba))=1.336(2). The polarizability constants are discussed with regard to the state vectors of the lowestsp ¹ P ₁- and³ P ₁-levels. The tensor polarizability of the 6s 6p¹ P ₁-level of Ba I is considered in relation to oscillator strengths of electric dipole transitions to neighbouring levels.     

Effective operators of the spin correlated crystalline electric field

The effective operators of the spin correlated crystal field have been formed by coupling the exchange with the crystal field. The exchange field is a scalar in spin space so the effective operators will still have the same rank as that of the crystal field but will give non-zero matrix elements between the states ^2S+1L_J of the half filled shells, contrary to the zero value obtained for a pure crystal field tensor.     

Measurement of Δ1J(199Hg, 31P) in [HgPCy3(OAc)2]2 and relativistic ZORA DFT investigations of mercury–phosphorus coupling tensors

Using ³¹P solid-state NMR spectroscopy, anisotropy in the indirect ¹⁹⁹Hg-³¹P spin–spin coupling tensor (ΔJ) for powdered [HgPCy₃(OAc)₂]₂ (1) has been measured as 4700±300 Hz. Zeroth-order regular approximation (ZORA) density functional theory (DFT) calculations, including scalar and spin-orbit relativistic effects, performed on 1 and a series of other related compounds show that ΔJ(¹⁹⁹Hg, ³¹P) arises entirely from the ZORA Fermi-contact–spin-dipolar cross term. The calculations validate assumptions made in the spectral analysis of 1 and in previous determinations of ΔJ in powder samples, namely that J is axially symmetric and shares its principal axis system with the direct dipolar coupling tensor (D). Agreement between experiment and theory for various ¹⁹⁹Hg, ³¹P spin–spin coupling anisotropies is reasonable; however, experimental values of ¹J(¹⁹⁹Hg, ³¹P)_iso are significantly underestimated by the calculations. The most important improvements in the agreement were obtained as a result of including more of the crystal lattice in the model used for the calculations, e.g., a change of 43% was noted for ¹J(¹⁹⁹Hg, ³¹P)_iso in [HgPPh₃(NO₃)₂]₂ depending on whether the two or three nearest nitrate ions are included in the model. Finally, we have written a computer program to simulate the effects of non-axial symmetry in J and of non-coincidence of the J and D on powder NMR spectra. Simulations clearly show that both of these effects have a pronounced impact on the ³¹P NMR spectrum of ¹⁹⁹Hg–³¹P spin pairs, suggesting that the effects should be observable experimentally if a suitable compound can be identified.     

Quantitative Measurement of Transverse and Longitudinal Cross-Correlation between13C–1H Dipolar Interaction and13C Chemical Shift Anisotropy: Application to a13C-Labeled DNA Duplex

Measurement of both longitudinal and transverse relaxation interference (cross-correlation) between¹³C chemical shift anisotropy and¹³C–¹H dipolar interactions is described. The ratio of the transverse to longitudinal cross-correlation rates readily yields the ratio of spectral densitiesJ(0)/J(ω_C), independent of any structural attributes such as internuclear distance or chemical shift tensor. The spectral density at zero frequencyJ(0) is also independent of chemical exchange effects. With limited internal motions, the ratio also enables an accurate evaluation of the correlation time for overall molecular tumbling. Applicability of this approach to investigating dynamics has been demonstrated by measurements made at three temperatures using a DNA decamer duplex with purines randomly enriched to 15% in¹³C.     

A microscopic analysis of moments of inertia

A microscopic analysis of moments of inertia is performed within the cranked Nilsson model. Special emphasis is put on the second-derivative moment of inertia, J⁽²⁾. Contributions to this from changes of rotational frequency and deformation are separately discussed. A simple expression for the latter is derived and it is for a studied series of Yb isotopes usually found to contribute with less than 10% to the total J⁽²⁾ value. J⁽¹⁾, J⁽²⁾ and J_rigid are calculated as functions of spin at the appropriate equilibrium deformations for the even-even nuclei ^160–176Yb. Variations of J⁽²⁾ with particle number and spin are discussed. Relations between J⁽²⁾ and the deformation are studied in detail, especially in connection with the super-backbending.     

Irreducible U(3) tensor interactions in the symplectic collective model

The potential V(β, γ) of the Bohr-Mottelson and symplectic collective models is expressed as a linear combination of U(3) irreducible tensor operators in the symplectic enveloping algebra. This many-body collective potential is then projected onto the symplectic two-body tensor operators. The projected two-body potential is shown to give results similar to the many-body potential in ²⁰Ne. Hence, in the symplectic shell model, one has obtained a collective model with two-body forces.     

A method for evaluation of fixed-J traces

Traces of operators in fixed-J spaces are of interest in statistical nuclear theory. A method, based on polynomial expansions inJ(J+1), is given here for the evaluation of such traces and is illustrated by some examples.     

Theoretical ab initio calculation of the indirect nuclear spin-spin coupling constants of monohetero cyclopropanes and cyclopropenes via the equations-of-motion method

Nonempirical calculations using the equations-of-motion approach, which includes the main portion of electron correlation effects, are reported for the one-bond coupling constants in the three-membered rings borirane, cyclopropane, azirane, oxirane, silirane, phosphirane, and thiirane and related double-bond analogs. The important overall result is that the ¹J(CC) and ¹J(CC) constants are spread over broad ranges, much wider in the case of the double-bond species, with a nearly regular increase with the electronegativity of the central heteroatom. For the boron cycles the smallest ¹J(CC)'s are predicted, with ¹J(CC) surprisingly lower than ¹J(CC). This exceptional pattern is accounted for in terms of the peculiar electronic structure of these rings formed by the electron-deficient B atom. The ¹J(Heteroatom-C), ¹J(Heteroatom-H) and ¹J(CH) couplings correlate correctly with the available experimental data.     

Diode laser spectroscopy of the ν6 band of 12CH3I

The vibration-rotation spectrum of the ν₆ fundamental of methyl iodide has been recorded in the 824 to 862 cm^?1 region by using a tunable semiconductor diode laser spectrometer. The rotational analysis performed for six Q branches ^pQ(J,3), ^pQ(J,4), ^pQ(J,5), ^pQ(J,6), ^pQ(J,7), and ^qQ(J,8) led to accurate values for several molecular constants. The nuclear quadrupole splitting arising from the spin of iodine has been observed very clearly in the low J transitions and for various K values.     

Effective dynamic moment of inertia of 118Xe and 130Ba

The effective moment of inertia J_eff⁽²⁾ of ¹¹⁸Xe and ¹³⁰Ba has been measured using sum-spectrometer techniques. The data are discussed using arguments based on particle alignments and results of cranking calculations. J_band⁽²⁾ and J_eff⁽²⁾ are compared in order to estimate the contribution of particle alignments to the total increase in angular momentum.     

Construction of a finite energy momentum tensor

A non-perturbative approach, postulating the existence of a family of Zimmermann normal products, certain linear relations among field operators, and the Wilson short distance expansion, is used to construct a finite energy momentum tensor. The dependence of the tensor on the field operators is made explicit by a suitable limit procedure. The calculations are performed in a scalar A⁴ model as an example. The results obtained are generalizations of the perturbation theory treatment of products of operators.     

Gauge symmetry and the EMC spin effect

We emphasise the EMC spin effect as a problem of symmetry and discuss the renormalisation of theC=+1 axial tensor operators. This involves the generalisation of the Adler-Bell-Jackiw anomaly to each of these operators. We find that the contribution of the axial anomaly to the spin dependent structure functiong ₁(x, Q ²) scales at O(α_s). This means that the anomaly can be a largex effect ing ₁. Finally we discuss the jet signature of the anomaly.     

Contact terms in E.M. decays of mesons

The ratios R_J(P)Γ(J)→P⁺P^?), P = π or K, have been evaluated ad due to contact interactions genrated by gauge invariance, for mesons with natural J^P. R_J increases rapidly with J. This provides unambigous tests for the model and indicates that contact terms are prolific sources of photons and leptons in hadron collisions.     

Iterative Lineshape Fitting of MAS NMR Spectra: A Tool to Investigate HomonuclearJCoupling in Isolated Spin Pairs

Possibilities and limitations of iterative lineshape fitting procedures of MAS NMR spectra of isolated homonuclear spin pairs, aiming at determination of magnitudes and orientations of the various interaction tensors, are explored. Requirements regarding experimental MAS NMR spectra as well as simulation and fitting procedures are discussed. Our examples chosen are the isolated³¹P spin pairs in solid Na₄P₂O₇· 10H₂O, (1), and Cd(NO₃)₂· 2PPh₃, (2). In both cases the two³¹P chemical shielding tensors in the molecular unit are related byC₂symmetry, and determination of the orientations of these two tensors in the molecular frame is possible. In addition, aspects of homonuclearJcoupling will be addressed. For 1, both magnitude and sign of²J_iso(³¹P,³¹P) (J_iso= −19.5 ± 2.5 Hz) are obtained; for 2, (J_iso= +139 ± 3 Hz) anisotropy ofJwith an orientation of theJ-coupling tensor collinear, or nearly collinear, with the dipolar coupling tensor can be excluded, while absence or presence of anisotropy ofJwith any other relative orientation of theJ-coupling tensor cannot be determined.     

Hadronic gauge couplings in meson decays

The branching ratiosR(J→ππρ)≡Γ(J→ππρ)/Γ(J→ππ) for naturalJ ^P mesons have been evaluated under the assumption that theT(J→ππρ) amplitudes are generated by the gauge principle for ρ-mesons originally proposed by Sakurai in his approach to VMD. The ratios are predicted to increase withJ and are compatible with the present-day data. This suggests that the hadronic interactions of the photon proceed exclusively through its hadronic (VMD) component.     

Operators in a translation invariant two-dimensional bag model

Operator matrix elements are studied in a translation invariant version of the bag model in two-dimensional space time. In particular we calculate the matrix elements of quark fields Q(x), currents J_μ(x), and bilocal currents Q(x)γ_μλ^aQ(0) whose Taylor expansion yields the twist two operators of leptoproduction. The structure functions of this model are related to those of a naive cavity approximation by a particularly simple transformation.     

On the spaces of positive and negative frequency solutions of the Klein-Gordon equation in curved space-times

In a space-time $\text{(V}{}_{\mathrm{n}}\text{×}\text{R}\text{;g)}$ with V_n closed (n ≠ 2) satisfying certain global conditions, we can write the Klein-Gordon equation, relative to a suitable class of atlases, in the evolution form du/dt = T^-1(t)u, on Sobolev spaces K^l(V_n) = H^l(V_n) × H^l?1(V_n), where the spectrum of T^-1(t) is imaginary. Following papers by T. Kato and J. Kisyński we prove the existence of the evolution operator for this equation. The space $\text{K}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(V}{}_{\mathrm{n}}\text{)}$ has a natural strongly-symplectic structure ω. We determine the explicit form of complex-structure-positive operators of this structure. We prove that any two such operators, say J₁, J₂, are symplectically equivalent, (i.e. there is a symplectic transformation S such that J₂ = SJ₁S^-1). Spaces of positive and negative frequency solutions are then unique modulo symplectic equivalence. Each operator J determines a regular kernel on space-time which satisfies the properties of the kernel postulated by A. Lichnérowich in his program of quantization of fields in curved space-times. We carry out explicit calculations in the case of Robertson-Walker space-times. If an additional condition is satisfied by the given space-time, a unique complex-structure-positive operator can be selected in a natural way. This condition is satisfied by globally stationary space-times.     

Study of excited states in49V with the48Ti (p, γ)49V reaction

In the⁴⁸Ti(p, γ)⁴⁹V reaction gamma decays of thirteen resonances betweenE _p =960 and 1570 keV are investigated. Level energies within ±0.5–±2.0 keV andQ-value 6756.8±1.5 keV are obtained. Branching ratios for the resonance states and strongly populated bound states are given. Gamma-ray angular distribution measurements yield the followingJ(keV) assignments of⁴⁹V bound and resonance states:J(1140)=5/2,J ^π(2235)=5/2^(?),J(2264)=(3/2),J(2308)=3/2,J(3912)=3/2,J(8105,Ep=1374keV)=(1/2) andJ ^π(8289,E _p =1564keV)=3/2^(?). Multipolarity mixing ratios for all measured primary and secondary gamma rays are tabulated. Dopplershift attenuation measurements yield the mean lifetimes τ _m (keV) of the following bound states in⁴⁹V:τ _m (748)=(200± ₁₀₀ ⁴⁰⁰ )fs, τ _m (1140)=(250± ₁₀₀ ⁵⁰⁰ )fs, τ _m (1155)>400 fs, τ _m (1515)=(45± ₂₀ ³⁰ )fs, τ _m (1644)=(55± ₂₀ ³⁰ )fs, τ _m (1661)=(25±5)fs, τ _m (1994)>400 fs, τ _m (2235)=(30± ₁₅ ³⁰ )fs, τ _m (2264)=(45± ₁₅ ³⁰ )fs and τ _m (2308)=(20±10)fs.     

Measurements of theg J -factors of12C in the3 P 1 and3 P 2 states

Using the atomic beam magnetic resonance method the Zeeman interactions of¹²C in the³ P ₁ and³ P ₂ states at magnetic fields of about 3.4 kOe have been measured. The measured quantities areg _J (³ P ₁)?g_J(³ P ₂)=15.4(1.0)·10^?6 g _J (³ P ₂)=1.5010616 (50), from which the following value for g_J(³P₁) can be calculated:g _J (³ P ₁)=1.5010770 (50). The experimental results are in moderate agreement with theoretical calculations.     

Electric dipole moments and nuclear hyperfine interactions for H2S,HDS, and D2S

Electric dipole moments and nuclear hyperfine coupling constants for several low-energy rotational states of the ground vibrational state of H₂S, HDS, and D₂S have been determined by molecular beam electric resonance spectroscopy. Analysis of the Stark effects for radiofrequency spectra of the lowest rotational levels gives dipole moments of 0.978325 (10) D for H₂S (J = 1, τ = 0), 0.977294 (20) D for D₂S (J = 1, τ = 0), and 0.977484 (60) D for HDS (J = 1, τ = 1 and J = 2, τ = 0). The electric field gradient tensor at the deuterium nucleus, the nuclear spin-spin tensor, and the spin-rotation tensor were evaluated from the hyperfine components of the radiofrequency spectra. The accuracy of these tensors was moderately improved over earlier measurements. From the H₂S spin-rotation tensor, the average paramagnetic shielding for the protons was found to be σ_av^p = ?104.84 (40) ppm. Combining this result with the proton NMR absolute chemical shift allowed the average diamagnetic shielding to be calculated as σ_av^d = 135.7 (5) ppm.