Multiplet States Research Articles

Excited States of 82Br from (p, nγ) Reaction

γ-ray and internal conversion electron spectra of the 82Se(p, nγ)82Br reaction were measured with Ge(Li) and superconducting magnet transporter Si(Li) spectrometers respectively, at 3.5 and 4 MeV bombarding proton energies. The level scheme of 82Br, multipolarities of 11 transitions, γ-branching ratios, level spin and parity values have been deduced. The energies of 82Br levels were calculated on the basis of the parabolic rule derived from the cluster-vibration model. This calculation provided a simple classification of several multiplet states in 82Br.

Semiempirical theory of shallow short‐range electron traps in silicon in a magnetic field

AbstractA theoretical investigation is made of the intervalley multiplet of electron states localized at short‐range traps in silicon placed in a magnetic field using an approximation of the zero‐short‐range potential. To describe the electron‐impurity interaction the intervalley and intravalley scattering lengths are introduced. They are considered as empirical parameters. It is shown that in crossed constant electric and magnetic fields the electric dipole transitions between multiplet states became available. The formulae describing the dependence of the probability of electric dipole transitions on the field strengths, on their orientation relative to crystallographic axes, and on the polarization of the variable electric field causing transitions, are derived.

The electronic states of oxygen in gallium phosphide an example of weak bonding

A number of important electronic properties of oxygen in GaP, which cannot be accounted for by existing theories, can be explained by a simple model based on the a1 and t2 spin orbitals formed from the four neighboring gallium valence bonds. I analyze this model and show that it provides a more realistic description of the physics of such a weakly coupled system than do conventional defect theories. I show further that in this model, for which two bonding electrons have been promoted to antibonding orbitals, the spin multiplet states are stabilized by the Coulomb and exchange energies of the Ga orbitals.

The empirical form of the effective nucleon-nucleon interaction in a model space with correlatedJ=0 pairs

Like in earlier work by Schiffer et al. the effective interaction is derived from experimental two-body multiplets. However, now the assumption is that a multiplet state is formed by two unpaired fermions relative to a core of correlatedJ=0 pairs. Then the need for two ranges, as proposed by Schiffer, disappears for the force between identical nucleons in a model space which is large enough to include pairing correlations. A form with a single attractive medium range is preferred for the identical nucleon interaction in order to reproduce collective 2+ states in even-even nuclei. In contrast, the proton-neutron force requires a very short range or two ranges to reproduce the empirical values of multipole coefficients, observed in odd-odd nuclei. Therefore we discuss the fact that the effective interaction is not always isospin invariant. As a typical case broken-pair calculations in theN=50 region are considered. But the conclusions drawn, will also apply to other regions of the periodic table.

On Λ - type doubling in multiplet states of diatomic molecules

Explicit expressions valid in the neighbourhood of Hund's case a/ and b/ are obtained for the width of Λ - type doubling of multiplet Π terms up to septet multiplicity. Moreover relation between the constants occurring in the expressions of Hund's case a/ and b/ is given.

Density matrix calculations for molecules and clusters II. First-row diatomic molecules

A modified version of the McWeeny density matrix method as described in I is used to calculate the binding characteristics of a number of first-row diatomic molecules. The exchange energy is approximated by the Xα expression. A similar formula is derived to include correlation. The properties of the deepest multiplet states of the molecules Be2, Be2+, B2, B2+, C2, C2+, C2-, O2, O2+ , CO, CO+ and CO- are studied and compared with other theoretical results obtained by different methods.

Neutron particle-hole multiplet states in 90Zr studied by proton inelastic scattering

The ν(g 9/2) −1(d 5/2) multiplet states in 90Zr have been identified using proton inelastic scattering at 65 MeV. The measured angular distributions were compared with microscopic DWBA calculations using simple shell-model wave functions. Remarkable agreement has been obtained for all the unnatural parity states of J π = 3 +, 5 + and 7 +.

Relativistic treatment of one- and many-electron contributions to hyperfine interactions in excitedSstates of rubidium atoms

The hyperfine structure of the rubidium atom in the excited $6^{2}S_{\frac{1}{2}}$, $7^{2}S_{\frac{1}{2}}$, and $8^{2}S_{\frac{1}{2}}$ states has been studied using the relativistic many-body perturbation procedure. The contributions from the different mechanisms, namely, the direct, the exchange core polarization (ECP), and the correlation effect are evaluated relativistically for each excited state. The contributions from these effects add up to net totals of 820 \ifmmode\pm\else\textpm\fi{} 16, 320 \ifmmode\pm\else\textpm\fi{} 6, and 156 \ifmmode\pm\else\textpm\fi{} 3 MHz, respectively, for the $6^{2}S_{\frac{1}{2}}$, $7^{2}S_{\frac{1}{2}}$, and $8^{2}S_{\frac{1}{2}}$ multiplet excited states, in excellent agreement with the experimental values of 809.1 (5.0), 318.1 (3.2), and 159.2 (1.5) MHz, respectively, similar to the situation for the ground $5^{2}S_{\frac{1}{2}}$ state found in an earlier investigation. The contribution from the ECP effect as compared to direct remains constant at about 16% as we go from the ground to the higher excited states. The correlation contribution, however, decreases dramatically as a ratio of the direct, from 32% in the ground state to 18, 14, and only 9%, respectively, in the excited multiplet states $6^{2}S_{\frac{1}{2}}$, $7^{2}S_{\frac{1}{2}}$, and $8^{2}S_{\frac{1}{2}}$. The physical reasons for the observed trends in the contribution from the ECP and correlation effects is discussed, as is the implications of our results for the expected trends for these contributions in related systems like the ground and excited states of other alkali-metal atoms and noble-metal atoms, and the Knight shifts in nuclear magnetic resonance experiments on alkali metals.

On Λ-type doubling in multiplet states of diatomic molecules

Explicit expressions valid in the neighborhood of Hund's case ( a) and ( b) are obtained for the width of Λ-type doubling of multiplet Π terms up to septet multiplicity. Moreover, a relation between the constants occurring in the expressions of Hund's cases ( a) and ( b) is given.

Self-consistent second-order perturbation treatment of multiplet structures using local-density theory

Various ways of calculating the multiplet structure from a local-density theory are discussed. They are based on a second-order expansion of the total energy in the changes of the occupation numbers from a given reference state. The method is first applied to single determinantal states whose energies are considered as averages over the true multiplet states. In this case, the problem is reduced to the evaluation of a few fundamental parameters which, in general, must be calculated self-consistently. For states which are degenerate by symmetry it is shown that internal consistency imposes relationships between these parameters. These relationships have a unique solution for the ${A}_{1}^{2}{T}_{2}^{2}$ configuration in ${T}_{d}$ symmetry. This example includes the neutral vacancy in silicon and, as a limiting case, the ${s}^{2}{p}^{2}$ configurations of column-IV atoms. An extension of the method is then proposed to treat directly linear combinations of Slater determinants. This leads to a formalism which closely parallels term-dependent Hartree-Fock theory. Finally, the method is extended to include configuration interaction. A unique solution is again possible for the free carbon atom yielding improved term values.

An energy- B(E2) generalized vibrational rule for one-phonon multiplets in odd- A nuclei

The rule is derived for the energies of one-phonon multiplet states and for the transition moments for the ground-state E2 transitions. Selected leading diagrams with the particle-vibration interaction and nuclear anharmonicities have been included; these are not affected by the nuclear Ward identities. The asymptotic complementarity of corrections to the energies and transition moments is derived. The rule is exemplified for 87Sr, with the quadrupole moment of the phonon as a free parameter. For Q(2 1) ≈ + 0.2 e · b the experimental data are reproduced; qualitatively, they also resemble the asymptotic limit.

The effect of the parity violating electron–nucleus interaction on the spin–spin coupling Hamiltonian of chiral molecules

We show that the form of the parity violating electron–nucleus interactions permits construction of an additional contribution to the effective spin–spin coupling Hamiltonian in spin multiplet states of chiral molecules. The ratio of the difference of the zero field splittings of optical isomers to the unperturbed zero field splitting is estimated to be 105 as large as the optical frequency ratios which have previously been investigated.

Unified description of odd-mass In nuclei. III. Application toIn119,121

We describe the odd-mass indium nuclei A=119, 121 within the framework of the unified-model taking into account the coupling of single-hole and one-particle--two-hole proton configurations with quadrupole and octupole vibrations of the underlying core. Besides the energy spectra, spectroscopic factors for pickup and electromagnetic transition properties (branching ratios, T/sub 1/2/(1/2/sup +//sub 1/); delta(3/2/sup -//sub 1/..-->..1/2/sup -//sub 1/)) are calculated and compared with experimental data, mainly for /sup 119/In. The yrast structure of the vibrational multiplet states has also been studied in lowest order perturbation theory and in the unified-model description. These calculations are also approached from a deformed zero-order description giving the total potential energy surfaces of all odd-mass In nuclei. Extensive band-mixing calculations produce energy spectra for the 1/2/sup +/ rotational-like band and are used to calculate static moments and transition rates. The equivalence with the former, spherical description is pointed out.

SCF Theory of multiplet states

AbstractThe SCF theory of multiplet monodeterminantal states is described from a comprehensive viewpoint. In this context, the formalism and derived theorems are developed, as well as the description of a SCF closed‐shell‐like structure, namely the hypermultiplet. Numerical applications are discussed taking as a model the H2O molecule and its first positive ion. Wave functions of double ζ‐quality, with computed molecular properties of 16 states are given.

Application of the nuclear field theory to superfluid nuclei: The quasiparticle-phonon multiplet

The quasiparticle-phonon multiplet of superfluid spherical nuclei is investigated in the framework of the nuclear field theory (NFT), using the pairing plus quadrupole force. In leading order of the NFT expansion there exists a simple relation between the energy splitting of the multiplet and the ground state B(E λ) transitions from the multiplet. This relation states that the reduced matrix elements for the B(E λ) transition decrease linearly with increasing energies of the multiplet states. The extent to which this relation is fulfilled by available experimental data is checked. The influence of the spurious correlations involved in the NFT treatment due to the BCS approximation is estimated. The numerical calculations are performed for 93Nb where the ground state B(E λ) transitions are measured for all multiplet states.

Photoexcitation and ionization in molecular oxygen: Theoretical studies of electronic transitions in the discrete and continuous spectral intervals

Theoretical studies of valence-electron (1πg, 1πu, 3σg) photoexcitation and ionization cross sections in molecular oxygen are reported employing separated-channel static-exchange calculations and the Stieltjes–Tchebycheff moment-theory technique. As in previously reported investigations of photoexcitation and ionization in small molecules following this approach, canonical Hartree–Fock orbitals, large Gaussian basis sets, and many-electron eigenstates of correct symmetry are used in defining appropriate noncentral static-exchange potentials and in computations of the appropriate discrete and continuum transition strengths. It is particularly important in molecular oxygen to incorporate the appropriate ionic parentages of the various photoionization multiplet states in order to obtain the correct partial-channel cross sections. The calculated discrete series associated with 1πg excitation are found to be in good agreement with available experimental assignments and previously reported theoretical studies, and the predicted states associated with 1πu and 3σg excitations are in general accord with assignments for the higher series based on spectral and quantum-defect analysis. Although the observed photoelectron spectra and photoionization cross sections are relatively complex, the calculated total vertical electronic photoabsorption cross section and the partial-channel photoionization cross sections for production of X 2πg, a 4πu, A 2πu, 2 2πu, 3 3Πu, b 4Σg−, and B 2Σg− ionic states are found to be in good accord with recent synchrotron radiation, line-source, electron-impact, and (e,2e) dipole oscillator-strength measurements when proper account is taken of the parentages of the various multiplet states. The partial-channel cross sections exhibit resonancelike structures that can be attributed to contributions from diabatic valencelike virtual states that appear in the appropriate photoionization continua, rather that in the corresponding discrete spectral intervals. These features in the dipole spectrum of molecular oxygen are discussed and are contrasted and compared with the results of previously reported related studies in molecular nitrogen and carbon monoxide.

Baryonium masses in a quark model

We derive certain mass relations among the various isospin multiplets of the baryonium states in a quark model. The mass spectrum for these states is also predicted by identifying the interquark-interaction-potential parameters used for this calculation with those used previously for the calculation of the masses of mesons and baryons. We predict two spin-1 states at 1497 and 1799 MeV, which could be identified with the experimentally observed states at 1495 and 1820 MeV, respectively. Three other spin-1 states are calculated to have masses of 1692, 1898, and 1932 MeV. These are very close to the mass values of the experimentally found states 1684, 1897, and 1935 MeV.

Electronic structures of aromatic hydrocarbons with high spin multiplicities in the electronic ground state

Abstract It has been established experimentally that there are alternant hydrocarbons (AH) with high spin multiplicities in the electronpic ground state, the highest multiplicity known up to date being septet. Such electronic structures are rationalized by utilizing the degeneracy of non-bonding pi molecular orbitals (NBMO) predictable from the theory of Longuet-Higgins in conjunction with the non-bonding orbitals of divalent carbon atoms which are perpendicular to p-orbitals and are nearly degenerate with NBMO. The degeneracy of NBMO is determined by the topological nature of molecules which permits the ground state with high spin multiplicities according to Hund's rule in spite of their low molecular symmetries. The nature of AH having high spin multiplicities in the ground state reported so far is understood in this manner. It was found, however, that for some AH the high spin multiplet states are unexpectedly not the ground states although they lie very close to the singlet ground state. The difference between these two types of AH with high spin multiplicities is associated with the fact that the spin distribution of NBMO is alternant in the former AH, but not in the latter. To the latter AH the weak interaction model was found to apply in which a molecule is divided into two units weakly interacting with each other.

A method for merging the results of separate least-squares fits and testing for systematic errors

A method is presented for merging the results of separate least-squares fits to obtain the most precise, single values for each of the molecular constants of a spectroscopic system. The output molecular constants and accompanying variance-covariance matrices from each of the separate fits are taken together as input to a correlated least-squares fit, which then yields the desired merged single values. The method is applied to a 1Σ- 1Σ diatomic model band system using well-defined synthetic data as an example. Other currently used, multistate methods of obtaining molecular constants for a spectroscopic system are special cases of the method described here. For the nonlinear least-squares fits required for multiplet states, the merge method is particularly advantageous. The properties of the merged values of the molecular constants and their standard errors are examined with regard to forming confidence limits for these estimates and it is shown that, in most spectroscopic applications, the confidence limits have their usual meaning. Furthermore, it is similarly shown that the confidence limits for the variance of the merged fit provide a simple and convenient test for the presence of relative systematic errors between the separate least-squares results being merged. Although the method is illustrated here by merged separate band-by-band results, it also can be applied to any type of spectroscopic results.

A study of 64Cu, 66Cu, 68Cu and 70Cu by (t, 3He) reactions

Levels in 64,66,68,70Cu that are populated in the 64,66,68,70Zn (t, 3He) reactions at 24 MeV triton energy have been studied. Mass excesses for the lowest states observed in 68Cu and 70Cu are found to be −65576±20 keV and −62982±20 keV, respectively. A multiplet of states, populated with large intensities, is observed to move systematically towards decreasing excitation energy as the neutron number approaches 40. It is concluded that this multiplet has a π p 3 2 ν g 9 2 configuration.