Nuclear Angular Momentum Research Articles

Coherent excitation and isotope selective photoionization of cadmium

Coherence between the magnetic sub-levels of the 5s5p3P1 level of cadmium is induced by excitation. A second excitation step and photo-ionization are used to detect the coherence and perturbations by the nuclear angular momentum. The ionization probability of even isotopes is suppressed with respect to the odd isotopes by a factor 59.

The light magnet, coupling of electronic and nuclear angular momenta in optical NMR and ESR: Quantum theory

Optical NMR and ESR is a recently introduced technique in which a circularly polarized laser (a “light magnet”) is used in an NMR or ESR spectrometer to induce magnetization. The spectral consequencies are developed with a quantum theory similar to the rigorous theory of Zeeman splitting of Russell-Saunders states, a theory which is suitable for atoms and molecules with net electronic angular momentum, and in which the antisymmetric electronic polarizability is finite. The optical NMR and ESR Hamiltonians are developed with the Wigner-Eckhart Theorem. The circularly polarized laser shifts the original NMR or ESR resonance lines, and splits the shifted lines into analytically useful patterns. The theory gives Landé factors which are in agreement with an earlier, simple, semiclassical theory ( J. Phys. Chem. 95, 2256–2260 (1991)).

Optical NMR and ESR Dipole-dipole and Fermi contact interactions

The quantum theory of nuclear magnetic dipole/laser induced electronic magnetic dipole interactions in optical NMR is developed for atoms in terms of the interaction between the total electronic and nuclear spin angular momenta. It is shown that a circularly polarised laser co-axial with the static magnetic flux density of a conventional NMR spectrometer (of any type) induces an electronic magnetic dipole moment in an atom or molecule, a moment which sets up a magnetic field at the nucleus, thus changing the effective magnetic field and NMR resonance frequency. This mechanism appears to be comparable in magnitude to Landé coupling between the anisotropic, or vectorial, polarisability of the atom and the nuclear spin angular momentum. Dipole-dipole and Fermi contact interaction between the vectorial polarisability and the nuclear spin angular momentum is explored through the appropriate terms in the ONMR interaction energy. Fermi contact interaction is nonzero, generally in a liquid sample.

Magnetic-field decoupling of an alkali-metal excited-state hyperfine structure.

The theory of how excited-state hyperfine structure can be determined using a magnetic field to decouple the nuclear and electronic angular momentum is presented. The initial excited state is assumed to have an anisotropic Zeeman sublevel population distribution, which can be conveniently created by a laser-induced multiphoton excitation of an unpolarized atom. The Zeeman sublevel populations are subsequently mixed by the hyperfine interaction. The degree of mixing is controlled by a magnetic field applied along the quantization axis. The relative Zeeman sublevel populations can be monitored by detecting the polarization of fluorescence emitted when the excited state radiatively decays. It is convenient to take the ratio of two time-integrated fluorescent signals measured for orthogonal linear polarizations, since this is independent of the excited-state number density. The plot of this ratio versus magnetic field is very well approximated by a Lorentzian curve whose half-width is proportional to the magnetic dipole hyperfine coupling constant. This method was used to determine the magnitude of the magnetic dipole constant of the cesium 8${\mathit{D}}_{3/2}$ state to be 3.92\ifmmode\pm\else\textpm\fi{}0.10 MHz, which is in excellent agreement with previous results.

Potential energy and dipole moment functions of the HCS radical

The three-dimensional MCSCF CI potential energy, electric dipole and electronic transition moment functions have been calculated for the X 2A′ and A 2A″ electronic states of the HCS radical. These states adiabatically correlate with the two components of a 2Π electronic state for linear configurations and their ro-vibronic spectra exhibit the Renner-Teller effect. Such spectra have been evaluated from variational ro-vibronic wavefunctions, which take into account both anharmonicity effects and rotation-vibration coupling. The nuclear and electronic angular momentum couplings have also been considered. Spectroscopic constants for the X 2A′ and A 2A″ states calculated by perturbation theory are given. The calculated equilibrium geometries are: R e CH: 1.083 Å (X), 1.063 Å (A), R e CS: 1.573 Å (X), 1.557 Å (A) and α e HCS: 131.8° (X), 180° (A), respectively. The electronic barrier to linearity in the electronic ground state is calculated to be 3063 ± 200 cm −1. The fundamental vibrational band origins and intensities (at 300 K) in the electronic ground state of HCS are predicted to be: 3104 cm −1/6 cm −2 atm −1 (CH stretch), 1165 cm −1/43cm −2 atm −1 (CS stretch) and 871 cm −1/54 cm −2 atm −1 (bend). The fundamental frequencies are expected to be accurate to within about 30 cm −1, the vibrational intensities to within about 10 to 20%. The electric dipole moment μ 0 (X) is calculated to be 0.85 ± 0.05 D. The K-reordering due to the electronic angular momentum coupling is discussed. Absolute line intensities (up to J″ = 9) have been calculated and are given for a few intense lines.

Quantum studies of inelastic collisions of O2(X 3Σ−g) with He: Polarization effects and collisional propensity rules

We investigate rotationally inelastic cross sections of O2(X 3Σ−g) with He at a collision energy of 27 meV. Theoretical cross sections obtained from close-coupled (CC) calculations are compared with results from the infinite-order sudden (IOS) approximation. Both the CC and IOS fine-structure state-resolved cross sections exhibit a strong ΔN=ΔJ Fi conserving collisional propensity. An analysis of the general expression for state-resolved cross sections in terms of spin-independent tensor opacities clearly establishes, without the introduction of dynamical approximations, the direct connection between this propensity rule and the collisional propensity for the conservation of the orientation of the nuclear rotational angular momentum vector N. In the low-N limit, Fi changing O2–He collisions are much more strongly depolarizing than collisions that conserve the Fi symmetry level. This enhanced collisional depolarization of an initial distribution of the total molecular angular momentum vector J is related to the collisional reorientation of N that must occur in Fi changing transitions.

H and H2 NMR properties in amorphous hydrogenated silicon (a-Si:H).

It is shown that the basic NMR properties of ortho-${\mathrm{H}}_{2}$ molecules with a rotational angular momentum J and a spin angular momentum I under the influence of a completely asymmetric crystalline field in an amorphous matrix can be described by an effective nuclear spin Hamiltonian which contains only the nuclear spin angular momentum operators (${I}_{i}$), but is independent of the molecular rotational angular momentum operators (${J}_{i}$). By directly applying the existing magnetic-resonance theories to this effective nuclear spin Hamiltonian, a simple description is presented for various static and dynamic NMR properties of the ortho-${\mathrm{H}}_{2}$ NMR centers in amorphous hydrogenated silicon (a-Si:H), thereby resolving many difficulties and uncertainties encountered in understanding and explaining the H and ${\mathrm{H}}_{2}$ NMR observations in a-Si:H.

Gamma decay of isovector giant resonances built on highly excited states in 111Sn.

Gamma-ray transition-energy spectra up to ${E}_{\ensuremath{\gamma}}\ensuremath{\simeq}33$ MeV have been measured for the decay of the compound nucleus $^{111}\mathrm{S}\mathrm{n}*$ populated at excitation energies up to ${E}^{*}\ensuremath{\simeq}100$ MeV. Above ${E}_{\ensuremath{\gamma}}\ensuremath{\simeq}20$ MeV an excess of gamma rays over the contribution from the isovector giant dipole resonance is observed in the energy range where the isovectors giant quadrupole resonance built on excited states is expected. The width of the giant dipole resonance in $^{108,111}\mathrm{S}\mathrm{n}*$ shows a large increase with increasing nuclear temperature and angular momentum.

On the physical origin of propensity rules in collisions involving molecules in 2Σ electronic states

A general quantum treatment of the collision dynamics of 2S+1Σ-state diatomic molecules is developed, with particular emphasis given to the physical origin of the collisional propensity for conservation of the e/f molecular symmetry label. State-resolved integral cross sections are expressed as a weighted sum of tensor opacities which are related to the probability that a collision will reorient the nuclear rotational angular momentum vector. Previous derivations of the propensity rules for collisions of 2S+1Σ-state diatomic molecules were restricted to the sudden or Born approximations. Here a general derivation is developed that is free of dynamical approximations, and that clearly establishes the direct connection between the observed propensity for the conservation of the e/f molecular symmetry and the collisional propensity for the conservation of the orientation of the nuclear rotational angular momentum vector. A power-law model suggested by previous semiempirical fits to cross sections for 1Σ+-state molecules is extended to open-shell molecules. This simple model allows us to predict semiquantitatively the degree to which the e/f symmetry index is conserved without performing a full dynamical calculation.

Hyperfine interaction constants and lifetime of the 62D3/2and 62D5/2states of39K measured by the quantum beam method

The hyperfine structure and lifetime of the 62D3/2 and 62D5/2 states in 39K are studied experimentally. The states were excited from the ground state by two-photon absorption of the laser light pulses. The hyperfine-structure intervals, and hence the hyperfine-structure interaction constants, were obtained from the numerical analysis of the zero-field quantum beat signals. The unmodulated component of the fluorescence decay curve served to determine the lifetime. In a separate experiment a magnetic field was applied to induce partial decoupling of the electronic and nuclear angular momenta in the 62D states. The sign of the magnetic dipole interaction constants was deduced from the resulting difference between the intensities of sigma + and sigma - polarised fluorescence.

Finite-nucleus treatment of the response to σμτλprobes and pion-like excitations

Presents an exact finite-nucleus treatment of the response to spin-isospin-sensitive probes. Since linear momentum is not a good quantum number here, the author adopts a formalism suggested by Toki and Weise (1980) which incorporates an expansion in partial waves of good nuclear total angular momentum. The author starts from the pion self-energy Pi , which is non-local in momentum space. Iterations of this quantity lead to the response function R, obtained by solving a matrix integral equation exactly (using numerical methods). R is used to renormalise the matrix element of a spin-isospin ( sigma mu tau lambda ) probe and find large effects for intermediate and large momenta (q>mpi ). These effects are unimportant for very low momenta. He also finds very important effects of the non-locality in momentum space. The formalism is applied to the JP=1+, T=1 level in 12C. The results are compared with approximations in current use: the infinite nuclear matter approximation, the local density approximation and the approximations of Toki and Weise. All these approximations are found to be unsatisfactory, especially for q to 0 and near the critical momentum region (q approximately (2-3)mpi ).

Response to spin-isospin transverse probes and pionlike excitations in finite nuclei

We treat the response in a finite nucleus to spin-isospin sensitive probes in the transverse spin channel. Since linear momentum is here not a good quantum number, we adopt a formalism suggested by Toki and Weise, which incorporates an expansion in partial waves of good nuclear total angular momentum. The pion self-energy Pi is nonlocal in momentum space; iterations of this quantity give the response function R, which is obtained by solving a matrix integral equation exactly (using numerical methods). We use R to renormalize the matrix element of a transverse spin-isospin probe and find large effects near the critical momentum region (qapprox.2--3 m/sub ..pi../) and almost no effects for a small momentum transfer. We also find very important effects of the nonlocality in momentum space. We apply our formalism to the level with J/sup P/ = 1/sup +/; T = 1 in /sup 12/C. The results are compared with currently used approximations: the local density approximation, the infinite nuclear matter approximation, and the approximations of Toki and Weise. All these approximations fail to reproduce the exact results, especially for q..-->..0 and near the critical momentum region. Using the infinite nuclear matter approximation, we find the best agreement for themore » equivalent constant density rho-bar = 0.08 fm/sup -3/ for low q; this agreement is not found, however, for any particular value of rho-bar when the value of q is either tiny or big. The approximation of Toki and Weise cannot be reliably used in our case, except possibly for qroughly-equalm/sub ..pi../. The finite-nucleus results obtained are compared with the corresponding longitudinal response.« less

Response to spin-isospin longitudinal probes and pionlike excitations in finite nuclei

We treat the response in a finite nucleus to longitudinal spin-isospin probes. Since linear momentum is here not a good quantum number, we adopt a formalism suggested by Toki and Weise, which incorporates an expansion in partial waves of good nuclear total angular momentum. The basic quantity involved is the pion self-energy II, which is nonlocal in momentum space. This quantity peaks at diagonal momentum distribution only for momentum $q\ensuremath{\approx}{k}_{c}$, where ${k}_{c}$ is the critical momentum for pion condensation precursor features, ${k}_{c}\ensuremath{\sim}2\ensuremath{-}3{m}_{\ensuremath{\pi}}$. To solve for the response function $\mathcal{R}$, we iterate II by solving an integral equation exactly (using numerical methods). The response $\mathcal{R}$ is singular for criticality (Migdal parameter ${g}^{\ensuremath{'}}\ensuremath{\approx}0.4$ and momentum $q\ensuremath{\approx}{k}_{c}$). We use $\mathcal{R}$ to renormalize the matrix element of a longitudinal spin-isospin probe and find, as expected, a large effect near criticality as well as a very significant effect of nonlocality in general. We apply our formalism to levels with ${J}^{P}={0}^{\ensuremath{-}},T=1$ in $^{16}\mathrm{O}$ and ${J}^{P}={1}^{+},T=1$ in $^{12}\mathrm{C}$. The results are compared with currently used approximations. The local density approximation employed in this context gives semiquantitative agreement only. Using infinite nuclear matter, we find the best agreement for the equivalent constant density $\ensuremath{\rho}=0.12$ ${\mathrm{fm}}^{\ensuremath{-}3}$ for $^{16}\mathrm{O}$; this agreement remains only qualitative, however. We give a detailed test of the model interactions suggested by Meyer-ter-Vehn in which it emerges that the value of ${k}_{c}$ is not correctly produced. The approximations of Toki and Weise are satisfactory for ${g}^{\ensuremath{'}}\ensuremath{\gtrsim}0.6$ and $k\ensuremath{\approx}{k}_{c}$. Approximations cannot be reliably used, however, for small ${g}^{\ensuremath{'}}$ or far from the critical momentum transfer. This is especially the case for the description of the nonlocality of II in momentum space through the use of a Bessel-function distribution, which is unreliable throughout the relevant range of parameters.

The giant quadrupole resonance in highly excited, rotating nuclei

The giant quadrupole resonance in highly excited, fast rotating nuclei is studied as a function of both the nuclear temperature and the nuclear angular momentum. The photo-absorption cross sections for quadrupole radation in 156Dy, 160Er and 164Er are evaluated within the linear response theory. The strength functions of the γ-ray spectrum obtained from the decay of highly excited nuclear states by deexcitation of the isoscalar quadrupole mode show a fine structure, which depends on the temperature T, the angular momentum I and the deformation of the nucleus β. The splitting of the modes associated with the signature-conserving and signature-changing components of the quadrupole field is discussed.

Quantum mechanical calculations of symmetric molecular charge exchange and vibrational excitations in O+2+O2 collisions

A scattering formulation is presented for symmetric molecular charge exchange treating the internal vibrational degrees of freedom and translation quantum mechanically. A unitary transformation is found to reduce the 2n coupled radial equations to two sets of n coupled equations. The formulation is applied to O2+(X 2Πg, v)+O2(X 3Σg−, v′) at 1, 8, and 36 eV center-of-mass collision energies. Convergence with respect to vibrational basis set size is found to be slower at lower energy. Integral cross sections and transition probabilities as a function of nuclear orbital angular momentum are presented. The integral cross sections summed over final levels for vibrational excitation and de-excitation and for charge transfer are on the order of 10 Å2. Comparisons of earlier classical path calculations with the present results do not show quantitative agreement at these energies.

Rotationally inelastic collisions between a diatomic molecule in a2Π electronic state and a structureless target

We present the full close-coupling formulation of the collision between a diatomic molecule in a 2Π state in the Hund’s case (a) limit and a structureless target. Due to the possibility of transitions between spin-orbit and/or Λ-doubling states the scattering displays an additional degree of complexity not seen in rotationally inelastic collisions of 1Σ+ molecules. The well-known coupled states and infinite-order-sudden (IOS) approximation techniques can be applied in a straightforward manner. The factorization and scaling relations between the various cross sections, which are valid in the energy sudden limit, are explored. For transitions within either spin-orbit manifold (Ω = 1/2, Ω = 3/2), these scaling relations allow both matrices of cross sections, for parity conserving the parity violating transitions, to be expressed in terms of the cross sections for parity conserving transitions out of the Ω = 1/2, J = 1/2 level. Under conditions in which either a Born or sudden formulation of the collision dynamics is appropriate, we show that at large values of the total angular momentum, transitions which conserve the parity index of the molecular wave functions will be strongly favored, a propensity rule which has been seen in previous experimental studies of rotational relaxation in 2Π molecules. A scaling relation is also derived for the cross sections for transitions between the two spin-orbit manifolds. For these processes, however, the propensity toward conservation of the parity index only occurs in the case of transitions which are elastic in the total angular momentum. The IOS formulation of the collision dynamics is then extended to a Hund’s case (b) representation of the molecular wave function. Although a complete factorization is no longer possible, one can still show that at large J there will exist a strong propensity toward conservation of the alignment between S (the spin-angular momentum of the molecule) and N (the vector sum of the nuclear rotational angular momentum R and the z-component Λ of the electronic orbital angular momentum). In the case (b) limit a propensity toward conservation of the parity index will still exist, but less strongly than in the case (a) limit.

Atomic spectra for nuclear studies

The atom, through its spectrum, reveals some of the key features of its nucleus. From the earliest days of nuclear physics, high‐resolution measurements of the hyperfine structure of atomic energy levels have provided reliable data on nuclear angular momenta (spins) and electric and magnetic multipole moments. Shifts in atomic energy levels from isotope to isotope—the “isotope shifts”—have given information about the change of the mean‐square radius of the nuclear charge as a function of neutron number. Often the optical spectrum of bound electrons provides the only probe of these nuclear properties. Magnetic dipole moments and spins have played an important role in clarifying the individual‐particle aspects of the nucleus, described by the shell model, while electric quadrupole moments and isotope shifts have dramatically demonstrated the collective nuclear degrees of freedom. To perform systematic studies of these effects over long sequences of isotopes, to shed as much light as possible on the structure of the nucleus, one must be able to make measurements with radioactive nuclei. This requirement has posed a challenge to atomic spectroscopists to develop new high‐resolution techniques suitable for studies of nuclear structure with the very minute or dilute samples that can be produced with accelerators or reactors. Notable advances were made in the past thirty years in working with small samples—and particularly the small radioactive samples produced at accelerators—and by the introduction of radio‐frequency and level‐crossing techniques.

An NMR study of solvent interactions in paramagnetic system

The temperature dependence of the proton nmr spectra of dithiocarbamato iron(III) complexes is markedly solvent dependent. A study is made of the temperature dependence of the nmr shifts for the NCH 2 protons in tris(N, N-dibutyldithiocarbamato)iron(III) in acetone, benzene, carbon disulphide, chloroform, dimethylformamide, pyridine and some mixed solvents. This contribution shall outline first how the nmr shifts may be interpreted in terms of the Fermi contact interaction and the dipolar term in the multipole expansion of the interaction of the electron orbital angular momentum and the electron spin dipolarnuclear spin angular momentum. This analysis yields a direct measure of the effect of the solvent systems on the environment of the transition metal ion. The results are analysed in terms of the crystal field environment of the transition metal ion with contributions from ( a) the dithiocarbamate ligand ( b) the solvent molecules and ( c) the interaction of the effective dipole moment of the polar solvent molecule with the transition metal ion complex. The model yields not only an explanation for the unusual nmr results but gives an insight into the solventsolute interactions in such systems.

Hindered rotational energy levels of the ammonium ion in alkali halide lattices

The hindered rotational energy levels of the ammonium ion in alkali halide lattices have been computed by assuming a ’’single approach model,’’ i.e., that one of the N–H bonds points toward the halide ion. The barrier to rotation about the threefold axis is small. Therefore, the tunneling frequencies for these solids are much larger than for other ammonium compounds. The Hamiltonian that describes the motion of the ammonium ion in alkali halide lattices is invariant under the direct product group ?×C3, where ? is the tetrahedral group of rotations around body-fixed axes and C3 the trigonal group of rotations about space-fixed axes. For high barriers to rotation, closed mathematical expressions have been derived for the librational frequencies. Experimental determination of the low temperature heat capacity or the mean square value of the nuclear angular momentum <I (I+1) ≳ is shown to provide a method for determining the barrier to rotation.

Tunneling states and nuclear spin conversion in solid CH3D

Total neutron cross section measurements have been made on condensed CH3D over the temperature region 0.75<T<100 K. The neutron wavelength was sufficiently long (4.7 Å) so that, in the low temperature region, the cross section was proportional to 〈I (I+1) 〉, the mean squared proton nuclear angular momentum per molecule, where I = total nuclear spin. 〈I (I+1) 〉 was determined to an accuracy of 1% or better and was only found to change significantly in the region T<10 K where conversion between nuclear spin symmetry species becomes appreciable. In contrast to the example of CH4, the rate of conversion appears to be rather insensitive to the amount of O2 impurity. For pure CH3D, the rate of conversion is rapid and is shown to correspond closely to the rate of thermal relaxation observed in calorimetric measurements on the solid at low temperatures. Estimates of low-lying tunneling states are made from the complementary calorimetric and neutron cross section results. There is a slight indication that the energy levels dilate in the region T<1.6 K, as has been predicted to occur in solid CH4. It is concluded that the unexpectedly rapid conversion between nuclear spin symmetry species in CH3D is a consequence of an accidental degeneracy between an A and an E tunneling level in each of two manifolds. Analysis of the thermodynamic data shows that the lowest temperature phase (phase III) of solid methane is not fully orientationally ordered.