Intrinsic Structure of Light Nuclei in Monte Carlo Shell Model Calculation

Wavefunctions obtained from the Monte Carlo shell model (MCSM) calculation are investigated. It has been difficult to discuss the intrinsic structure of nuclei in conventional shell-model calculations. We propose a way to describe an intrinsic state in the MCSM and demonstrate the appearance of two-α-cluster structure in the ⁸Be ground state. The changes of cluster shape with respect to the number of major shell and basis is discussed. The shape of the ¹⁰Be ground state is also investigated. The behavior of valence neutron is consistent with the picture of molecular orbit state. The method is also applied to the ⁶He ground state, which is expected to have the asymmetric distribution of valence neutrons.     

Energy levels of the nucleus 250Bk from residual interaction studies

The bandhead energies of twenty two-quasiparticle states expected to occur in the low-energy excitation spectrum of the doubly odd nucleus ²⁵⁰Bk are calculated using a zero-range residual interaction and the results are compared with the available experimental information. Configuration assignments to nine intrinsic states reported in earlier studies are confirmed. Our calculations support the excitation energy of 115 keV for the K^π = 3⁺ state and also the characterisation of the 317 keV 5⁺ state as the K^π = 5⁺ bandhead. In addition, we suggest acceptable two-particle configurations for the 175 keV 1⁺ state and the 216 keV 0⁺ state. The expected location of eight as yet unobserved two-quasiparticle states is predicted.     

Bound states of 4He

The energies of the bound 0⁺ states of the α-particle are calculated on the basis of four body integral equations with separable ¹S₀ and ³S₁ pair interactions. We find the ground state at z₁ = ?45.73 MeV and an excited o⁺ level is found to be ?11.69 MeV.     

The effect of Fermi momentum cutoff on the binding energy of closed shell nuclei in the LOCV framework

The ground state binding energies of the light symmetric closed-shell nuclei, i.e., ⁴He, ¹²C, ¹⁶O and ⁴⁰Ca and the heavy asymmetric ones, i.e., ⁴⁸Ca, ⁹⁰Zr and ¹²⁰Sn are calculated in the harmonic oscillator (HOS) basis, by imposing the relative Fermi momentum cutoff of two point-like interacting nucleons on the density dependent average effective interactions (DDAEI). The DDAEI are generated through the lowest order constrained variational (LOCV) method calculations for the asymmetric nuclear matter with the operator and the channel dependent type bare nucleon-nucleon potentials, such as the Argonne $Av_{18}^{j_{\max } = 2}$ and the Reid soft core, Reid68, interactions. In the framework of harmonic oscillator shell model, the cutoff is imposed by defining the maximum value of the relative quantum numbers (RQN_max) in two ways: (1) The RQN_max of the last shell and (2) the RQN_max of each shell, in the ground state of the nucleus. It is shown that present results on the binding energies and the root means square radius are closer to the corresponding experimental data than, our previous works with the same DDAEI potentials, but without the cutoff constraint. However, for the light symmetric nuclei, the second scheme gives less binding energy and larger root mean square radius compare to the first one. While the situation is reversed for the heavier nuclei.     

Calculation of the magnetic hyperfine structure in the ground electronic state of HCCO

In this paper we analyze the spin-spin hyperfine interaction in the two components of the ground electronic state of the free π radical HCCO, A²A′[²Π] and X²A″. Electronic mean values of the Fermi contact constants of all magnetic nuclei [¹H, ¹³C₁, ¹³C₂,¹⁷O] are calculated using models that include the electron-correlation correction, primarily CCSD method in the cc-pwCVTZ basis set and B3LYP functional in the cc-pCVQZ basis set. Also, we have calculated components of the anisotropic hyperfine tensor for the ground X²A″ state. The dependence of hyperfine coupling constants (HFCCs) on the two bending coordinates is examined, and the results of HCC bending (vibrational) averaging of electronic mean values are presented for both states. It is demonstrated that electronic and subsequent vibrational averaging of the HFCCs suffices for obtaining results that are in good agreement with available experimental findings (for proton) in the X²A″ state, owing to a small geometry dependence of these quantities, and relatively distant minimum from linearity.     

A CASCI-MRMP method based on Kohn—Sham orbitals

Kohn-Sham orbitals are used in the previously proposed CASCI-MRMP scheme (a multi-reference M?ller-Plesset (MRMP) method with a complete active space configuration interaction (CASCI) reference function). That is, the CASCI wave function was constructed using the Kohn-Sham orbitals and used as a reference function of the MRMP to incorporate the remaining dynamical correlation. The scheme was applied to the potential curves of the ground and low-lying excited states of N₂, the potential curve of the ground state of CO, the barrier height of the H₂CO → H₂ + CO reaction, the valence π-π? and Rydberg excited states of benzene, and the low-lying excited states of ozone. Good agreement between the theory, experiment, and some benchmark calculations was obtained. The various orbitals which are investigated here do not give very different results. Rather, the choice of active space makes a considerable difference, and in particular the perturbation calculation is proved to be very important.     

Electronic structure and reactivity of the CNO/NCO/CON isomers

Three-dimensional potential energy surfaces (PESs) have been calculated for the lowest electronic states of NCO, CNO and CON isomers, using internally contracted Multi Reference Configuration Interaction (MRCI) and Coupled-Clusters RCCSD(T) ab initio methods. For the low lying doublet and quartet excited states of the three isomers, the N–CO, O–CN, C–NO and C–ON collinear dissociation paths were mapped by the Complete Active Space SCF (CASSCF) approach and the energy variations with the bending coordinate have been explored. Several regions of conical intersections have been located and the spin–orbit interactions between states of different spin symmetry have been evaluated in the region of intersections of these states. The analysis of the PESs allows one to identify the main interactions governing the reactivity of the lowest electronic states. The NCO and CNO isomers have stable X²Π electronic ground states, for CON the X²Π ground state is separated from the dissociative [CO?+?N] asymptote by a barrier of 0.11 eV and crosses the dissociative ⁴Σ ^- state close to its minimum. At their equilibrium ground state geometries the spin–orbit interactions A _SO between the two electronic components of the X²Π states were calculated to be -95.6, -109.6 and -57.1 cm^?1 for NCO, CNO and CON, respectively. The predissociation of the vibrational levels of the A²Σ⁺ and B²Π states of NCO has been explained.     

Crystal field theory and electric field gradients at 49Ti nuclei sites in LaTiO3

The energy level diagram and the wave functions for the Ti³⁺ ions (3d ¹) in LaTiO₃ are calculated using modern crystal-field theory. The relative orbital ordering of these ions in the ground state is obtained. It turns out that the states of the ground triplet are considerably split and therefore the effect of the electronic-vibrational interaction is suppressed despite the fact that the distortions of the TiO₆ building block seem to be small. The components of the electric field gradient tensor at the Ti³⁺ nuclei sites are calculated using the wave functions of the ground states obtained. The calculated asymmetry parameter agrees well with the experimental values, which demonstrates the adequacy of the proposed orbital-ordering pattern of the Ti³⁺ ions in the ground state.     

Ab initio SCF CI study of the electronic spectrum of s-tetrazine

Configuration interaction (CI) studies of ground, n→ π* and π→ π* electronically excited states are reported for s-tetrazine. The first n→ π* singlet excited state (¹ B _3u ), which is responsible for the purple-red colour of the molecule, is calculated at 2·80 eV, compared to the experimental transition energy of 2·22–2·70 eV. The singlet-triplet split of the first n→ π* states (¹ B _3u and ³ B _3u states) is calculated to be 0·76 eV.

The interaction of nitrogen lone pair orbitals (n-orbitals) is studied in terms of the ordering of the n π* excited states and found that the SCF orbital ordering is qualitatively in accord with the ordering of the n π* excited states in the CI level.

The first π→ π* excited state (¹ B _2u ) is calculated at 5·99 eV, slightly above the observed range of absorption. Numerous other high-lying singlet states as well as the triplet states have been calculated and they are used to verify several proposals relating to the excited state dynamics in the photo-physical studies of s-tetrazine.     

Study of electric monopole transitions between the ground state and the first excited 0+ state in 40, 42, 44, 48Ca with high resolution inelastic electron scattering

Monopole transitions from the 0₁⁺ ground states to 0₂⁺ excited states at 3.353 MeV (⁴⁰Ca), 1.837 MeV (⁴²Ca), 1.884 MeV (⁴⁴Ca) and 4.272 MeV (⁴⁸Ca) have been investigated with high resolution inelastic electron scattering (FWHM ≈ 30 keV) at low momentum transfer (0.29 ≦ q ≦ 0.53 fm^?1). The respective monopole matrix elements are 2.53 ± 0.41 fm², 5.24 ± 0.39 fm², 5.45 ± 0.41 fm² and 2.28 ± 0.49 fm². These results are used together with known ground state charge radii and the average number of holes in the sd shell in the ground state to estimate the number of particle-hole excitations in the wave functions of the excited 0⁺ states.     

Low-lying intrinsic energy levels in the nucleus170Ho

The band-head energies of the two-quasiparticle states expected in the doubly odd deformed nucleus¹⁷⁰Ho are calculated for a zero range residual interaction. The results are compared with the available experimental information. It is concluded that the ground state has the Nilsson configuration 6⁺{7/2^?[523↑] _p }+5/2[512↑] _n being the 2.76m isomer whereas the 43s isomer is the 1⁺ ∑=0 state arising from the same configuration and lies at about 100 keV excitation energy in agreement with the experiment. The first excited state in this nucleus is predicted to be the 4^?{3/2⁺[411↑] _p +5/2^?[521↑] _n } state close to the ground state with the corresponding 1^? ∑=0 member expected to appear well above the 1⁺ isomer.     

The electronic spectrum of AgBr2: Ab initio benchmark vs. DFT calculations on the lowest ligand-field states including spin-orbit effects

The X²Π_g, ²Σ_g⁺ and ²Δ_g states of AgBr₂ have been studied through benchmark ab initio CASSCF + Averaged Coupled Pair Functional (ACPF) and DFT calculations using especially developed valence basis sets to study the transition energies, geometries, vibrational frequencies, Mulliken charges and spin densities. The spin-orbit (SO) effects were included through the effective hamiltonian formalism using the |ΛSΣ〉 ACPF energies as diagonal elements. At the ACPF level, the ground state is ²Π_g, in contradiction with ligand-field theory and Hartree-Fock results. The ACPF adiabatic excitation energies of the ²Σ_g⁺ and ²Δ_g states are 3825 and 20 152 cm⁻¹, respectively. The inclusion of the SO effects leads to a pure Ω = 3/2 (²Π_g) ground state, a Ω = 1/2 (97% ²Π_g + 3% ²Σ_g⁺) A state, a Ω = 1/2 (3% ²Π_g + 97% ²Σ_g⁺) B state, a Ω = 5/2 (²Δ_g) C state and a Ω = 3/2 (99% ²Δ_g) D state. The B97, B3LYP and PBE0 functionals, which were shown to yield accurate transition energies for CuCl₂, overestimate the X²Π_g-²Σ_g⁺ T_e by around 25% but provide a qualitative energetic ordering in agreement with CASSCF and ACPF results. The nature of the bonding in the X²Π_g ground state is different from that of AgCl₂ since the Mulliken charge on the metal is 0.95 while the spin density is only 0.39. DFT strongly delocalizes the spin density providing even smaller values of around 0.13 on Ag not only for the ground state, but also for the ²Σ_g⁺ state.     

The KrXe molecule: Modification of potential curves of the ground and first excited electronic states

Potential curves of the ground state of the KrXe molecule and its excited states that converge to the Kr(4p ^{6 1} S ₀) + Xe(5p ⁵6s ³ P ₁) atomic states are corrected and tested using the results of modeling published vacuum ultraviolet spectra of a gas-discharge plasma of a krypton/xenon mixture.     

Conformation and dipole moment of tetrahydropyran-4-one by microwave spectroscopy

The microwave spectrum of tetrahydropyran-4-one has been studied in the frequency region 18 to 40 GHz. The rotational constants for the ground state and nine vibrationally excited states have been derived by fitting a-type R-branch transitions. The rotational constants for the ground state are (in MHz) A = 4566.882 ± 0.033, B = 2538.316 ± 0.003, C = 1805.878 ± 0.004. From information obtained from the gas-phase far-infrared spectrum and relative intensity measurements, these excited states are estimated to be ～ 100 cm^?1 above the ground state for the first excited state of the ring-bending and ～ 185 cm^?1 for the first excited state of the ring-twisting mode. Stark displacement measurements were made for several transitions and the dipole moment components determined by least-squares fitting of the displacements: (in Debye) |μ_a| = 1.693 (0.001), |μ_b| = 0.0, |μ_c| = 0.300 (0.013) yielding a total dipole moment μ_tot = 1.720 (0.003). A model calculation to reproduce the rotational parameters indicates that the data are consistent with the chair conformation.     

Stochastic autoionization of a relativistic two-electron atom

On the basis of the analysis of absorption spectra of Er³⁺:PbMoO₄ crystals made for the transitions from the ground ⁴ I _15/2 state to excited states of Er³⁺ ions by the Judd-Ofelt method, the main spectroscopic characteristics of the crystals were obtained, including the transition probabilities and the radiative lifetimes.     

Potential energy curves for the 48 lowest-lying molecular states of LiH+

The electronic energies of the 20 lowest lying ²Σ⁺ states, the 14 lowest lying ²Π states, and the 14 lowest lying ²Δ states of LiH⁺ have been calculated in the range 2 ≤ R ≤ 20 a.u. from a model potential approach and using truncated diatomic orbitals (TDO) as basis set. Results in very good agreement with the more recent literature were obtained for the spectroscopic constants, R_e and D_e, for the ground state X²Σ⁺.     

The 28Si(7Li, 7Be)28Al reaction at 36 MeV

The ²⁸Si(⁷Li, ⁷Be)²⁸Al reaction has been investigated at E_7Li = 36 MeV. States and groups of states were observed up to 5.3 MeV excitation in the ²⁸Al+⁷Be system. Experimental angular distribution for unresolved doublets of states at ≈ 0.0 and 0.44 MeV excitation, corresponding to ⁷Be in its ground state (⁷Be₀) and first excited states (⁷Be₁) with ²⁸Al in its ground state (3⁺) and first excited state (0.031 MeV, 2⁺) are compared with microscopic distorted wave approximation calculations.     

Doppler-free two-photon laser spectroscopy of barium I: Hyperfine splitting and isotope shift of high lying levels

The Doppler-free two-photon absorption method performed with a narrowbandc w dye laser permitted high resolution measurements of transitions from the Ba I ground state 6s ^{2 1} S ₀ to several highly excited states. The lifetimes and hyperfine splittings of these states as well as the isotope shifts of the transitions have been determined accurately. The lifetime values are in agreement with transition probability data; the hyperfine splitting results show considerable configuration interaction effects. A detailed discussion of the isotope shifts is given.     

Study ofpf-shell nuclei with a symmetry conserving generator coordinate method

Bands based on the 0⁺ ground state and the first excited 0⁺ pairing vibrational state of⁴⁸Ti,⁵²Cr and⁵⁶Fe are studied with the generator coordinate method. The generating wave functions for each value of the angular momentumJ are angular momentum and particle number projected selfconsistent Hartree-Fock-Bogoliubov states where the constrained amount of pairing correlations serves as the generator coordinate. The interaction is given by reaction matrix elements derived from the Hamada-Johnston force. The basis includes the four lowest oscillator shells. The excitation energies of the pairing vibrational states can be reproduced fairly well by the present choice of the generating wave functions, whereas the ground band is not much improved compared to projected Hartree-Bogoliubov calculations. We find that the strength of the pairing correlations in the 0⁺ and 2⁺ states of the ground state and the pairing vibrational bands can be related to data of two-particle transfer reactions. The angular momentum dependence of the pairing correlations and of the moments of inertia are studied. The results show that for a strongly paired ground state the ground state band and the pairing vibrational band intersect. This may produce in the yrast band the anomaly of the moment of inertia known from rare earth nuclei.     

Structure of 0+ states of 28Si and particle-hole conjugation

Full sd-shell calculations for the 0⁺ states of ²⁸Si have been performed in the SU(3) basis so that the intrinsic deformation of the shell model states can be deduced by inspection. The shell model Hamiltonian is decomposed in a symmetric part H_S and an antisymmetric part H_A with respect to particle-hole conjugation. It is shown that the splitting of prolate and oblate states is due to the spin-orbit part of H_A. The different prediction for ²⁸Si obtained with Kuo and with Preedom-Wildenthal matrix elements can be attributed to the difference in a single parameter: the strength of the spin-orbit part of H_A.