Статті в журналах: "Low-Lying Excitation Energies"

1

Cheng, Y. Y., S. Q. Zhang, X. Q. Li, H. Hua, C. Xu, Z. H. Li, P. W. Zhao, et al. "Systematics on the low-lying spectra in N = 78 ~ 80 isotones." International Journal of Modern Physics E 23, no. 08 (August 2014): 1450037. http://dx.doi.org/10.1142/s0218301314500372.

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Combining the new spectroscopy results of 144 Tb and previous spectroscopy studies of neighboring nuclei, a systematic investigation on the low-lying spectra in N = 78 ~ 80 isotones is performed. Good systematics have been found for the coupling patterns which couple the odd nucleon(s), such as πh11/2, [Formula: see text], to the 2+, 4+, 6+ and 3- core excitations. It is found that the relative excitation energies of the states formed by coupling h11/2 proton(s) to the 2+, 4+ core excitations are pushed up, in contrast with those formed by coupling h11/2 neutron hole(s) to the 2+, 4+ core excitations, which are pulled down. According to the systematics, the interpretation that the 17/2+ states observed in 141 Sm and 143 Gd are the fully aligned member of coupling the odd h11/2 neutron hole to the octupole 3- core excitation, is explored to the isotones 145 Dy , 142 Eu , and 144 Tb .

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2

Ramı́rez, Rafael, and Telesforo López-Ciudad. "Low lying vibrational excitation energies from equilibrium path integral simulations." Journal of Chemical Physics 115, no. 1 (July 2001): 103–14. http://dx.doi.org/10.1063/1.1378318.

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3

SCHNACK, JÜRGEN, MARSHALL LUBAN, and ROBERT MODLER. "ROTATIONAL BAND STRUCTURE OF LOW-LYING EXCITATIONS IN SMALL HEISENBERG SYSTEMS." International Journal of Modern Physics B 17, no. 28 (November 10, 2003): 5053–57. http://dx.doi.org/10.1142/s0217979203020193.

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We derive the low-temperature properties of the giant molecular magnet { Mo 72 Fe 30}, where 30 Fe 3+ paramagnetic ions occupy the sites of an icosidodecahedron and interact via isotropic nearest-neighbour antiferromagnetic Heisenberg exchange. The key idea of our model is that the low-lying excitations form a sequence of "rotational bands", i.e. for each such band the excitation energies depend quadratically on the total spin quantum number. As rotational bands characterise the spectra of many magnetic molecules our method opens a new road towards a description of their low-temperature behaviour which is not accessible otherwise.

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4

TAKEUCHI, S., N. AOI, H. BABA, T. KUBO, T. MOTOBAYASHI, K. TANAKA, K. YAMADA, et al. "STUDY OF LOW-LYING STATES IN 32Mg." International Journal of Modern Physics E 18, no. 10 (November 2009): 2025–29. http://dx.doi.org/10.1142/s0218301309014226.

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Proton inelastic scattering on the neutron-rich nucleus 32 Mg has been experimentally studied at E lab = 46.5 MeV / nucleon in inverse kinematics. The energies of excited states in 32 Mg were obtained by measuring de-excitation γ rays. Several new states were identified by γ-γ coincidence analysis. Their spins and parities were restricted and the deformation parameters βp,p′ were extracted from the measured angular distribution of the proton inelastic scattering. The present analysis favors 4+ for the spin and parity of the 2321-keV state.

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5

Mardyban, M. A., D. A. Sazonov, E. A. Kolganova та R. V. Jolos. "SHAPE EVOLUTION OF 96ZR AND 96MО WITH EXCITATION ENERGY INCREASE". Bulletin of Dubna International University for Nature, Society, and Man. Series: Natural and engineering sciences, № 2 (43) (24 грудня 2019): 37–41. http://dx.doi.org/10.37005/1818-0744-2019-2-37-41.

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The observed properties of the low-lying collective excitations of 96Zr and 96Mo are investigated in the framework of the collective quadrupole nuclear model with the Bohr Hamiltonian, whose potential energy has two minima – spherical and deformed. Satisfactory description of the excitation energies and E2 transition probabilities is obtained. It is shown that in the case of 96Zr both minima are sufficiently deep. However, in the case of 96Mo a deformed minimum is only outlined.

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6

Barreto, M. T., A. Canal Neto, and F. E. Jorge. "Gaussian basis sets for low-lying excited states of neutral atoms with 2 ≤ Z ≤ 36." Canadian Journal of Chemistry 82, no. 8 (August 1, 2004): 1237–43. http://dx.doi.org/10.1139/v04-084.

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The improved generator coordinate HartreeFock method is used to generate Gaussian basis sets for low-lying excited states of neutral atoms from He (Z = 2) to Kr (Z = 36). Then, excitation energies and orbital energies of the outermost orbitals of each symmetry are calculated and compared with the corresponding values obtained with numerical HartreeFock calculations. Besides this, the basis sets for Be (3P) and F (2P) are contracted by a standard procedure and, then, enriched with polarization functions. From these basis sets, total energies, dissociation energy, and bond length for BeF are calculated and compared with results obtained with other basis sets and with experimental values. The sets for HeKr are useful in constructing basis sets for molecular calculations. Key words: improved generator coordinate HartreeFock method, Gaussian basis sets, low-lying excited states, neutral atoms.

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7

Dimitrova, Sevdalina, and Nicola Lo Iudice. "Large–scale shell model calculations for 140Xe." EPJ Web of Conferences 194 (2018): 01004. http://dx.doi.org/10.1051/epjconf/201819401004.

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This paper presents the results of a large-scale shell model calculations of the yrast spectrum of 140Xe. We extend the previous calculations confined to low-lying angular momenta to high-spin states apply- ing the same importance sampling iterative matrix diagonalization algorithm. Excitation energies and transi- tion probabilities are obtained by using an effective nucleon-nucleon interaction derived from the CD-Bonn nucleon-nucleon potential. A satisfactory agreement with the experimental data and the previous results for low lying states is achieved.

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8

Cave, Robert J., and Ernest R. Davidson. "Non-vertical excitation energies for low-lying singlet states of butadiene and hexatriene." Chemical Physics Letters 148, no. 2-3 (July 1988): 190–96. http://dx.doi.org/10.1016/0009-2614(88)80297-5.

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9

Ürer, Güldem, and Leyla Özdemir. "Energies and Electric Dipole Transitions for Low-Lying Levels of Protactinium IV and Uranium V." Zeitschrift für Naturforschung A 67, no. 1-2 (February 1, 2012): 89–98. http://dx.doi.org/10.5560/zna.2011-0066.

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We have reported a relativistic multiconfiguration Dirac-Fock (MCDF) study on low-lying level structures of protactinium IV (Z =91) and uranium V (Z =92) ions. Excitation energies and electric dipole (E1) transition parameters (wavelengths, oscillator strengths, and transition rates) for these low-lying levels have been given. We have also investigated the influence of the transverse Breit and quantum electrodynamic (QED) contributions besides correlation effects on the level structure. A comparison has been made with a few available data for these ions in the literature.

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10

PAAR, N., T. NIKŠIĆ, D. VRETENAR, and P. RING. "RELATIVISTIC DESCRIPTION OF EXOTIC COLLECTIVE EXCITATION PHENOMENA IN ATOMIC NUCLEI." International Journal of Modern Physics E 14, no. 01 (February 2005): 29–37. http://dx.doi.org/10.1142/s0218301305002746.

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The low-lying dipole and quadrupole states in neutron rich nuclei are studied within the fully self-consistent relativistic quasiparticle random-phase approximation (RQRPA), formulated in the canonical basis of the Relativistic Hartree–Bogoliubov model (RHB), which is extended to include the density dependent interactions. In heavier nuclei, the low-lying E1 excited state is identified as a pygmy dipole resonance (PDR), i.e. as a collective mode of excess neutrons oscillating against a proton–neutron core. Isotopic dependence of the PDR is characterized by a crossing between the PDR and one-neutron separation energies. Already at moderate proton–neutron asymmetry the PDR peak is calculated above the neutron emission threshold, indicating important implications for the observation of the PDR in (γ, γ′) scattering, and on the theoretical predictions of the radiative neutron capture rates in neutron-rich nuclei. In addition, a novel method is suggested for determining the neutron skin of nuclei, based on measurement of excitation energies of the Gamow–Teller resonance relative to the isobaric analog state.

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11

GRASSO, M., D. GAMBACURTA, and F. CATARA. "COLLECTIVE MODES WITHIN SKYRME-SECOND RPA." Modern Physics Letters A 25, no. 21n23 (July 30, 2010): 1919–22. http://dx.doi.org/10.1142/s0217732310000642.

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Second RPA calculations with a Skyrme force are performed to describe both high- and low-lying excited states in 16 O . The coupling between 1 particle-1 hole and 2 particle-2 hole as well as that between 2 particle-2 hole configurations are fully taken into account and the residual interaction is never neglected. For the rearrangement terms in the matrix elements beyond standard RPA two approximations are employed: they are either neglected or evaluated with the RPA procedure. A several-MeV shift of the strength distribution to lower energies is systematically found with respect to RPA distributions. A better description of the excitation energies of the low-lying 0+ and 2+ states is obtained with second RPA with respect to RPA.

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12

BEREZHNOY, YU A., and V. YU KORDA. "DEUTERON-NUCLEUS INTERACTION AT INTERMEDIATE ENERGIES." International Journal of Modern Physics E 03, no. 01 (March 1994): 149–70. http://dx.doi.org/10.1142/s021830139400005x.

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The deuteron-nucleus interaction has been studied in the approximation where the deuteron radius and the nuclear surface diffuseness are small compared with the nuclear radius. The closed formulae have been derived for the integrated cross-sections of different deuteron-nucleus interaction processes and for differential cross-sections of the deuteron elastic scattering and the deuteron inelastic scattering with excitation of the low lying vibrational states of nuclei. It is shown that the allowance for nuclear surface diffuseness substantially influences the values of the different deuteron-nucleus reaction cross-sections.

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13

Kamleh, Waseem, Derek Leinweber, Zhan-wei Liu, Finn Stokes, Anthony Thomas, Samuel Thomas, and Jia-jun Wu. "Structure of the Nucleon and its Excitations." EPJ Web of Conferences 175 (2018): 06019. http://dx.doi.org/10.1051/epjconf/201817506019.

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The structure of the ground state nucleon and its finite-volume excitations are examined from three different perspectives. Using new techniques to extract the relativistic components of the nucleon wave function, the node structure of both the upper and lower components of the nucleon wave function are illustrated. A non-trivial role for gluonic components is manifest. In the second approach, the parity-expanded variational analysis (PEVA) technique is utilised to isolate states at finite momenta, enabling a novel examination of the electric and magnetic form factors of nucleon excitations. Here the magnetic form factors of low-lying odd-parity nucleons are particularly interesting. Finally, the structure of the nucleon spectrum is examined in a Hamiltonian effective field theory analysis incorporating recent lattice-QCD determinations of low-lying two-particle scattering-state energies in the finite volume. The Roper resonance of Nature is observed to originate from multi-particle coupled-channel interactions while the first radial excitation of the nucleon sits much higher at approximately 1.9 GeV.

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14

HUO, YANLI, MEISHAN WANG, CHUANLU YANG, HONGFEI WANG, and ZIXIA MA. "THE STUDY OF THE PROPERTIES OF THE GROUND- AND LOW-LYING EXCITED STATES OF ASH2, ${\rm ASH}_{2}^{+}$ AND ${\rm ASH}_{2}^{-}$." Journal of Theoretical and Computational Chemistry 12, no. 02 (March 2013): 1250115. http://dx.doi.org/10.1142/s0219633612501155.

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The properties of the ground and excited states of AsH2 , [Formula: see text] and [Formula: see text] have been investigated by using symmetry-adapted-cluster (SAC)/symmetry-adapted-cluster configuration interaction (SAC-CI) method. The geometry of the ground state of AsH2 is optimized at SAC method with different basis sets. The calculated results with cc-pVTZ and cc-pVQZ basis sets are in very good agreement with the experimental and previous theoretical data. The geometry and the properties of eight low-lying electronic excited states of AsH2 are obtained at SAC-CI/cc-pVTZ and SAC-CI/cc-pVQZ level, including geometries, vertical excitation energies, adiabatic excitation energies, transition dipole moments, and oscillation strengths. Employing the same theoretical level as AsH2 , the geometries, adiabatic ionization potentials (AIPs), and vertical ionization potentials (VIPs) of the ground and eight low-lying electronic states of [Formula: see text] are investigated as well as the geometries, vertical detachment energies (VDEs) and adiabatic detachment energies (ADEs) of nine electronic states of [Formula: see text]. Comparing with the available experimental or previous theoretical data, the SAC/SAC-CI/cc-pVTZ and SAC/SAC-CI/cc-pVQZ results are reliable for AsH2 , [Formula: see text] and [Formula: see text]. The predicted results can afford the useful information for one to deeply investigate them from the spectral experiment.

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15

CAO, LI-GANG, and ZHONG-YU MA. "SOFT DIPOLE MODES IN NEUTRON-RICH Ni-ISOTOPES IN QRRPA." Modern Physics Letters A 19, no. 38 (December 14, 2004): 2845–56. http://dx.doi.org/10.1142/s0217732304015233.

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The soft dipole modes in neutron-rich even–even Ni-isotopes are investigated in the quasiparticle relativistic random phase approximation. We study the evolution of strengths distribution, centroid energies of dipole excitation in low-lying and normal GDR regions with the increase of the neutron excess. It is found in the present study that the centroid energies of the soft dipole strengths strongly depend on the thickness of neutron skin along with the neutron-rich even–even Ni-isotopes.

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16

Ganev, H. G. "Proton-neutron symplectic model description of ²⁰Ne." Chinese Physics C 46, no. 4 (April 1, 2022): 044105. http://dx.doi.org/10.1088/1674-1137/ac42be.

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Abstract A microscopic description of the low-lying positive-parity rotational bands in 20Ne is given within the framework of the symplectic-based proton-neutron shell-model approach provided by the proton-neutron symplectic model (PNSM). For this purpose, a model Hamiltonian is adopted. This includes an algebraic interaction lying in the enveloping algebra of the dynamical group of the PNSM, which introduces both horizontal and vertical mixings of different irreducible representations within the irreducible collective space of 20Ne. A good overall description is obtained for the excitation energies of the ground and first two excited β bands, including the ground state intraband quadrupole collectivity and the known interband transition probabilities between the low-lying collective states, without utilizing an effective charge.

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17

ZHANG, XIAOYU, WEIPING ZHANG, and FANKAI MENG. "TIME-DEPENDENT DENSITY FUNCTIONAL THEORY STUDY ON DYNAMICS OF HYDROGEN BONDING IN EXCITED STATES OF TRANS-ACETANILIDE IN METHANOL SOLVENT." Journal of Theoretical and Computational Chemistry 11, no. 02 (April 2012): 421–35. http://dx.doi.org/10.1142/s0219633612500290.

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The hydrogen-bonding dynamics in both singlet and triplet excited states of the trans-acetanilide ( AA ) in methanol ( MeOH ) solvent was investigated using the time-dependent density functional theory (TDDFT) method. Geometric optimizations of the hydrogen-bonded AA–MeOH complexes considered here as well as the isolated AA and MeOH molecules were performed using density functional theory (DFT) method. At the same time, the TDDFT method was performed to calculate the electronic transition energies and corresponding oscillation strengths of all the compounds in the low-lying electronically excited states. In this study, only the intermolecular hydrogen bonds C=O⋯H–O and N–H⋯O–H can be formed. A theoretical forecast that changes of hydrogen bonds in the low-lying electronic excited states was proposed. We discussed not only ground-state geometric structures and electronic excitation energies but also frontier molecular orbitals and electron density transition. The intermolecular hydrogen bonds between AA and MeOH molecules play an important role in the geometric structures and electronic excitation energies. Zhao et al. have put forward the relationship between the electronic spectra and hydrogen bonding dynamics for the first time. According to Zhao's rule, a redshift of the relevant electronic spectra will appear if hydrogen bond is strengthened, while the hydrogen bond weakening can make an electronic spectra shift to blue.

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18

Balasi, K. G., T. S. Kosmas, P. C. Divari та V. C. Chasioti. "Cross sections for the neutral current νe - 116Cd scattering reaction". HNPS Proceedings 16 (1 січня 2020): 97. http://dx.doi.org/10.12681/hnps.2586.

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The cross sections for neutrino scattering off the 116Cd nucleus have been computed by utilizing the Quasi-particle Random Phase Approximation (QRPA). An- gular and initial energy dependence of the neutrino-nucleus cross sections have been calculated at low and intermediate electron neutrino energies up to 100 MeV. By solving the QRPA equations and fixing the appropriate parameters the lowest lying excitation energies spectrum was reproduced. The contributions from multipole ex- citations was examined. The obtained results could be used for studying the nuclear response of this isotope to supernova neutrino spectra.

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19

Siregar, R. E., and M. O. Tjia. "The low-lying excitation energies of polyenes investigated with a chain-length-dependent screened potential." International Journal of Quantum Chemistry 48, no. 4 (November 10, 1993): 267–76. http://dx.doi.org/10.1002/qua.560480408.

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20

Sormova, Hanka, Roberto Linguerri, Pavel Rosmus, Jürgen Fabian, and Najia Komiha. "On the Electronic States of S4+ and S4- Isomers." Collection of Czechoslovak Chemical Communications 72, no. 1 (2007): 83–99. http://dx.doi.org/10.1135/cccc20070083.

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For three energetically most stable structures of tetrasulfur, S4, S4+ and S4- (cis-chain, rectangular, and trans-chain forms), equilibrium geometries, harmonic wavenumbers, ionization energies, electron affinities, electronic vertical and adiabatic excitation energies, and electronic transition moments were calculated by ab initio methods. It was found that similarly to the ground state of S4, the S4+ cis-isomer could interconvert, perturbed, however, by vibronic coupling with a very close-lying excited state and large-amplitude vibrations. Moreover, the cis- and rectangular minima are calculated to be energetically degenerated. The ω values in all three species agree reasonably well with existing experimental and theoretical data. The calculated patterns of harmonic modes suggest the existence of very complex low-lying anharmonic polyads in all three species. The calculated ionization energies reported previously are compared with the present more accurate data. Also the electronic transition moments and the energy positions of the electronic states with higher spin multiplicities are given.

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21

Vaval, Nayana, Prashant Manohar, and Sourav Pal. "Electronic Spectra and Ionization Potentials of Halogen Oxides Using the Fock Space Coupled-Cluster Method." Collection of Czechoslovak Chemical Communications 70, no. 7 (2005): 851–63. http://dx.doi.org/10.1135/cccc20050851.

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The ionization potentials and excitation energies of halogen monoxides and dihalogen oxides are studied using fully size-extensive Fock space version of multi-reference coupled-cluster theory. The low-lying excited states of ClO-, FO-, Cl2O and F2O are obtained along with the ionization spectra of Cl2O and F2O. The adiabatic electron affinity of ClO, FO and the vertical detachment energy of ClO- and FO- are also presented.

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22

Asakawa, Hitoshi, and Masuo Suzuki. "Finite-Size Corrections in the Supersymmetric t–J Model with Boundary Fields." International Journal of Modern Physics B 11, no. 09 (April 10, 1997): 1137–51. http://dx.doi.org/10.1142/s0217979297000575.

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The supersymmetric t–J model with boundary fields is discussed. Using the exact solution of the present model, the finite-size corrections of the ground-state energy and the low-lying excitation energies are calculated. The partition functions are evaluated in the scaling limit to obtain the conformal weights of the primary fields in the present model. A surface critical exponent and the ground-state degeneracy are also derived.

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23

NAKAMURA, TAKASHI, YOSHITERU SATOU, TAKASHI SUGIMOTO, and YOSUKE KONDO. "BREAKUP REACTIONS AND EXOTIC STRUCTURES OF HALO NUCLEI." International Journal of Modern Physics E 18, no. 10 (November 2009): 2071–76. http://dx.doi.org/10.1142/s0218301309014317.

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We have performed breakup experiments of halo nuclei: 11 Li with a Pb target, 14 Be with 12 C and proton targets, and 19 C on a proton target at approximately 70 MeV/nucleon at RIKEN. These experiments aim at investigating the E1 response of 11 Li , and at searching for the low-lying discrete resonances of 14 Be and 19 C above the neutron decay threshold. The former results shows the strong E1 transitions at low excitation energies (soft E1 excitation), which suggests the spatial neutron-neutron correlation. The latter revealed the first 2+ state of 14 Be , and the second 5/2+ state of 19 C for the first time.

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24

Belyaev, A. K., D. V. Vlasov, A. Mitrushchenkov, and N. Feautrier. "Quantum study of inelastic processes in low-energy calcium–hydrogen collisions." Monthly Notices of the Royal Astronomical Society 490, no. 3 (October 12, 2019): 3384–91. http://dx.doi.org/10.1093/mnras/stz2763.

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ABSTRACT Cross-sections and rate coefficients for the partial inelastic processes in calcium–hydrogen collisions are calculated by means of the quantum reprojection method for nuclear dynamics based on the accurate ab initio electronic structure data. That is, the atomic data for the 110 inelastic processes of excitation, de-excitation, ion-pair formation, and mutual neutralization in Ca + H and Ca+ + H− collisions are computed for all transitions between the 11 low-lying CaH(2Σ+) molecular states including ionic one. The quantum chemical data are used in a hybrid diabatic representation, which is derived from the adiabatic representation. It is found that the largest rate coefficients correspond to the mutual neutralization processes. At the temperature 6000 K, the maximal rate is equal to $4.37 \times 10^{-8}\, \mathrm{cm}^{3}\,\mathrm{s}^{-1}$. It is shown that the large-valued rates are determined by long-range ionic–covalent interactions with final binding energies from the optimal window, while moderate- and low-valued rates by both long- and short-range non-adiabatic regions with final energies outside of the optimal window.

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25

Wu, Yingxin, Aoxue Li, Feng Pan, Lianrong Dai, and Jerry P. Draayer. "The Rotor-Vibrator Plus Multi-Particle-Hole Description of 154Gd." Symmetry 14, no. 12 (December 10, 2022): 2620. http://dx.doi.org/10.3390/sym14122620.

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Анотація:

Based on the well-known rotor-vibrator model and the particle-plus-rotor model, multi-particle-hole excitations from a collective even-even core described by the rotor-vibrator is considered to describe well-deformed even-even nuclei. Like the particle-plus-rotor model, the intrinsic Vierergruppe (D2) symmetry is still preserved in the rotor-vibrator plus multi-particle-hole description. It is shown that a series of experimentally observed 0+ states in these nuclei may be interpreted as the multi-particle-hole excitations in a complementary manner to the beta and gamma vibrations described by the rotor-vibrator model. As a typical example of the model application, low-lying positive parity level energies below 1.990 MeV in the eight experimentally identified positive parity bands; a series of 0+ excitation energies up to 016+; and some experimentally known B(E2) values, E2 branching ratios, and E2/M1 and E0/E2 mixing ratios of 154Gd are fitted and compared to the experimental data. The results suggest that the multi-particle-hole-pair configuration mixing may play a role in these 0+ states.

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26

Li, Wei, Xuan Cai, Yaogai Hu, Yong Ye, Mingdao Luo, and Jiming Hu. "A TDDFT study of the low-lying excitation energies of polycyclic cinnolines and their carbocyclic analogues." Journal of Molecular Structure: THEOCHEM 732, no. 1-3 (November 2005): 21–32. http://dx.doi.org/10.1016/j.theochem.2005.06.042.

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27

KAKAVAND, T., and K. P. SINGH. "LIFETIMES OF LEVELS IN 71Ge." International Journal of Modern Physics E 11, no. 04 (August 2002): 347–58. http://dx.doi.org/10.1142/s0218301302000855.

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The low-lying states of 71Ge have been studied the via the 71Ga (p,n γ)71Ge reaction using proton beam energies of 2.5–4.3 MeV. The angular distributions have been used to assign the spins and the multipole mixing ratios using statistical theory for compound nuclear reactions. The ambiguity in the spin values for the various levels has been removed. The multipole mixing ratios for a few γ-transitions have been newly measured. The lifetimes of the levels at 747.0, 808.0, 831.1, 1377.8, 1406.6, 1414.4, 1422.1, 1558.8 and 1566.1 keV excitation energies have been measured for the first time using the Doppler shift attenuation method.

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28

CENEVIVA, C. A. P., L. LOSANO, and H. DIAS. "NUMBER-PROJECTED QUASIPARTICLE PHONON COUPLING APPLIED TO ODD-MASS Te ISOTOPES." International Journal of Modern Physics E 04, no. 02 (June 1995): 419–29. http://dx.doi.org/10.1142/s0218301395000146.

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Анотація:

The structure of low-lying levels in odd-mass Te isotopes (115≤A≤131) is examined in the framework of the projected-quasiparticle-phonon coupling model (PQPC). Effects of particle number symmetry restoration are discussed through the comparison with usual quasiparticle phonon coupling calculations (QPC). Excitation energies, dipole and quadrupole moments are calculated and compared with the experimental data. Nuclear Structure: 115−131 Te ; calculated levels J, π, S, μ, and Q. Number-projected quasiparticle-phonon coupling.

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29

Murray, Lionel P., та Robert R. Birge. "Two-photon spectroscopy of the Schiff base of all-trans-retinal. Nature of the low-lying π π* singlet states". Canadian Journal of Chemistry 63, № 7 (1 липня 1985): 1967–71. http://dx.doi.org/10.1139/v85-325.

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The two-photon excitation spectrum of all-trans-N-retinylidene-n-butylamine (ATRSB) in EPA at 77 K is obtained over the wavelength region from 370 to 455 nm (λex/2) using linearly polarized light. The two-photon excitation maximum is observed at ~422 nm (λex/2) and is red shifted ~2800 cm−1 from the one-photon absorption maximum at ~377 nm. We assign the two-photon excitation spectrum to the "1Ag*−" ← S0 transition which indicates that the "1Ag*−" π π* state lies below the "1Bu*+" π π* state in ATRSB. Comparisons of the one-photon absorption, two-photon excitation, and fluorescence spectra of ATRSB with the corresponding spectra of all-trans-retinal are presented. PPP-CISD calculations correctly predict the directions but not the magnitudes of the blue shifts of the π π* excited state transition energies in going from all-trans-retinal to ATRSB. We postulate that the "1Ag*−" π π* state is preferentially stabilized relative to both the ground state and the nearby "1Bu*+" state by hydrogen bonding to solvent molecules. Comparison of the spectra reported here with the two-photon spectra of rhodopsin provides further evidence that the chromophore in rhodopsin is protonated.

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30

Yu, Angyang. "The ground state and low-lying excited states of CCCN radical and its ions: a CASSCF/CASPT2 study." Canadian Journal of Physics 94, no. 9 (September 2016): 803–7. http://dx.doi.org/10.1139/cjp-2016-0176.

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The ground state and low-lying excited states of the CCCN radical and its ions have been investigated systematically using the complete active space self-consistent field (CASSCF) and multi-configuration second-order perturbation theory (CASPT2) methods in conjunction with the ANO-RCC-TZP basis set. The calculated results show that the state 12Σ+ has the lowest CASPT2 energy among the electronic states. By means of the geometric optimization of this radical, it could be found that the molecule exhibits linear structure, with the bond lengths R1 = 1.214 Å, R2 = 1.363 Å, R3 = 1.162 Å, which are very close to the experimental values. The calculated vertical excitation energies and the corresponding oscillator strengths show that there are three relatively strong peaks at energies 0.63, 4.04, and 5.49 eV, which correspond to the transitions 12Σ+ → 12Π, 12Σ+ → 22Π, and 12Σ+ → 22Σ+, respectively. Additionally, the electronic configuration and the harmonic vibration frequencies of each state are also investigated.

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31

Shimizu, Noritaka, Yutaka Utsuno та Tomoaki Togashi. "β-decay half-lives of neutron-rich N=82,81 isotones by shell-model calculations". EPJ Web of Conferences 260 (2022): 11049. http://dx.doi.org/10.1051/epjconf/202226011049.

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We perform large-scale shell-model calculations and successfully describe the low-lying spectra and half-lives of neutron-rich N = 82 and N = 81 isotones with Z = 42 − 49 in a unified way. Shell-model study shows that their Gamow-Teller strength distribution has a peak in the low-excitation energies, which significantly contributes to the half-lives. This peak is dominated by the ν0g7/2 → π0g9/2 transition and enhanced on the proton deficient side of these isotones due to the Pauli blocking effect and the change of the effective single-particle energy of the ν0g7/2 orbit.

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32

Li, Dongkang, Tao Wang, and Feng Pan. "Shape Phase Transitions in Even–Even 176–198Pt: Higher-Order Interactions in the Interacting Boson Model." Symmetry 14, no. 12 (December 9, 2022): 2610. http://dx.doi.org/10.3390/sym14122610.

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Dynamical symmetry plays a dominant role in the interacting boson model in elucidating nuclear structure, for which group theoretical or algebraic techniques are powerful. In this work, the higher-order interactions required in describing triaxial deformation in the interacting boson model are introduced to improve the fitting results to low-lying level energies, B(E2) values and electric quadrupole moments of even–even nuclei. As an example of the model application, the low-lying excitation spectra and the electromagnetic transitional properties of even–even 176−198Pt are fitted and compared to the experimental data and the results of the consistent-Q formalism. It is shown that the results obtained from the model are better than those of the original consistent-Q formalism, indicating the importance of the higher-order interactions in describing the structure and the shape phase evolution of these nuclei.

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33

Mandaglio, Giuseppe, Orest Povoroznyk, Olga K. Gorpinich, Olexiy O. Jachmenjov, Antonio Anastasi, Francesca Curciarello, Veronica De Leo та ін. "First measurement of the 2.4 MeV and 2.9 MeV 6He three-cluster resonant states via the 3H(4He, pα)2n four-body reaction". Modern Physics Letters A 29, № 19 (12 червня 2014): 1450105. http://dx.doi.org/10.1142/s0217732314501053.

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Two new low-lying 6 He levels at excitation energies of about 2.4 MeV and 2.9 MeV were observed in the experimental investigation of the p-α coincidence spectra obtained by the 3 H (4 He , p α)2 n four-body reaction at E4 He beam energy of 27.2 MeV. The relevant E* peak energy and Γ energy width spectroscopic parameters for such 6 He * excited states decaying into the α+ n+n channel were obtained by analyzing the bidimensional (E p , Eα) energy spectra. The present new result of two low-lying 6 He * excited states above the 4 He +2 n threshold energy of 0.974 MeV is important for the investigation of the nuclear structure of neutron-rich light nuclei and also as a basic test for theoretical models in the study of the three-cluster resonance feature of 6 He .

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34

Zawadzki, Mateusz, Murtadha A. Khakoo, Ahmad Sakaamini, Logan Voorneman, Luka Ratkovich, Zdeněk Mašín, Amar Dora, Russ Laher та Jonathan Tennyson. "Low energy inelastic electron scattering from carbon monoxide: II. Excitation of the b³Σ⁺, j³Σ⁺, B¹Σ⁺, C¹Σ⁺ and E¹Π Rydberg electronic states". Journal of Physics B: Atomic, Molecular and Optical Physics 55, № 2 (19 січня 2022): 025201. http://dx.doi.org/10.1088/1361-6455/ac37f3.

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Abstract In this second part of a two part paper (first part: Zawadzki et al (2020 J. Phys. B: At. Mol. Opt. Phys. 53 165201)) we present differential scattering cross sections for excitation of several Rydberg electronic states of carbon monoxide by electron impact. The first part concerned the low-lying valence states of CO. In the present study cross sections are obtained experimentally using low-energy electron energy-loss spectroscopy and theoretically using the R-matrix method. Incident electron energies range from near-threshold of 12.5 eV to 20 eV while the scattering angles range from 20° to 120°. The R-matrix calculations use three distinct close-coupling models and their results are compared to available experimental and theoretical cross sections. The overall comparison leads to significantly improved description of the excitation cross sections for this target.

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35

Ajitha, Devarajan, Kimihiko Hirao, and Sourav Pal. "Energies and Dipole Moments of Excited States of Ozone and Ozone Radical Cation Using Fock Space Multireference Coupled-Cluster Analytical Response Approach." Collection of Czechoslovak Chemical Communications 68, no. 1 (2003): 47–60. http://dx.doi.org/10.1135/cccc20030047.

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Using the Fock space multireference coupled-cluster (FS-MRCC) analytical linear response approach, we report the dipole moments of low-lying singlet and triplet excited states of ozone. The low-lying singlet and triplet excited states are calculated at the ground-state geometry and at the adiabatic geometry for the 1A2 and 1B1. For comparison we also calculate at the ground-state geometry the dipole moments of the 1A2, 1B1 and 1B2 using multireference configuration interaction (MRCI) with a bigger VQZ basis and complete active space. We also report as by-product the excitation energy values in the singles and doubles approximation. At the ground-state geometry we also report the energy and the dipole moments of the 2A1, 2A2 and 2B1 states of the ozone radical cation. The energy of the ozone cation radical is compared with the other correlated approaches. It matches well with the experimental values.

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36

Záliš, Stanislav, Antonín Vlček, and Chantal Daniel. "The Character of Low-Lying Excited States of Mixed-Ligand Metal Carbonyls. TD-DFT and CASSCF/CASPT2 Study of [W(CO)4L] (L = ethylenediamine, N,N'-dialkyl-1,4-diazabutadiene) and [W(CO)5L] (L = pyridine, 4-cyanopyridine)." Collection of Czechoslovak Chemical Communications 68, no. 1 (2003): 89–104. http://dx.doi.org/10.1135/cccc20030089.

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This contribution presents the results of the TD-DFT and CASSCF/CASPT2 calculations on [W(CO)4(MeDAB)] (MeDAB = N,N'-dimethyl-1,4-diazabutadiene), [W(CO)4(en)] (en = ethylenediamine), [W(CO)5(py)] (py = pyridine) and [W(CO)5(CNpy)] (CNpy = 4-cyanopyridine) complexes. Contrary to the textbook interpretation, calculations on the model complex [W(CO)4(MeDAB)] and [W(CO)5(CNpy)] show that the lowest W→MeDAB and W→CNpy MLCT excited states are immediately followed in energy by several W→CO MLCT states, instead of ligand-field (LF) states. The lowest-lying excited states of [W(CO)4(en)] system were characterized as W(COeq)2→COax CT excitations, which involve a remarkable electron density redistribution between axial and equatorial CO ligands. [W(CO)5(py)] possesses closely-lying W→CO and W→py MLCT excited states. The calculated energies of these states are sensitive to the computational methodology used and can be easily influenced by a substitution effect. The calculated shifts of [W(CO)4(en)] stretching CO frequencies due to excitation are in agreement with picosecond time-resolved infrared spectroscopy experiments and confirm the occurrence of low-lying M→CO MLCT transitions. No LF electronic transitions were found for either of the complexes studied in the region up to 4 eV.

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37

Zhang, Haifeng, Jiubo Cui, Weiwei Pei, and Dongfang Wang. "A CASSCF/CSAPT2 Study on the Reaction Pathways From HOSS to HSSO Radicals." E3S Web of Conferences 165 (2020): 05025. http://dx.doi.org/10.1051/e3sconf/202016505025.

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In this paper, we used the CASSCF/CASPT2 method to study the low-lying electronic states of the HOSS and HSSO radicals. Based on the Cs and C1 symmetries, the geometrical parameters, total energies, configurations, oscillator strengths, excitation energies, oscillator strengths and harmonic vibrational frequencies of the HOSS and HSSO radicals were calculated. We found that the ground state of HSSO radical with C1 symmetry has multi-configurational character, which leads to a significant difference of dihedral angles of HSSO radical among at our work and at References. Moreover, a transition state was given out in the pathway for the reaction from HOSS to HSSO. This transition state produces relatively high-energy barrier of 30.5 Kcal/mol corresponding to the gradual changes of the S2-H-O angle.

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38

Meo, F. Di, P. Trouillas, C. Adamo, and J. C. Sancho-García. "Application of recent double-hybrid density functionals to low-lying singlet-singlet excitation energies of large organic compounds." Journal of Chemical Physics 139, no. 16 (October 28, 2013): 164104. http://dx.doi.org/10.1063/1.4825359.

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39

MATTIS, DANIEL C. "ABSENCE OF A GAP IN THE EXCITATION SPECTRUM (PHONONS) OF ANHARMONIC SOLIDS." Modern Physics Letters B 01, no. 01n02 (May 1987): 1–5. http://dx.doi.org/10.1142/s0217984987000028.

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Acoustic phonons are the suitably quantized low-lying normal modes of elastic solids. Their energies ε(k) are given by ε(k)=ħω(k), where the frequencies ω(k) are proportional to k (k=wavevector, or inverse wavelength) and vanish as w=sk (s=speed of sound) in the limit k→0. Here we prove a similar result for a reasonably general class of anharmonic solids, applicable even to such solids as the various He4 phases, H2 molecular solid, etc., which are in the extreme quantum limit. We show that the spectrum of elementary excitations in the harmonic solid provides an upper bound to the spectrum of elementary excitations in the similar anharmonic solid having the same ground state interatomic spring constantsK.

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40

Orce, J. N. "Polarizability effects in atomic nuclei." International Journal of Modern Physics E 29, no. 03 (March 2020): 2030002. http://dx.doi.org/10.1142/s0218301320300027.

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This work sheds light upon how the atomic nucleus polarizes throughout the nuclear chart. Deviations from the well-known behavior of the nuclear dipole polarizability — which smoothly increases with increasing atomic mass number — are investigated. Relative enhancements are found for light nuclei as the nuclear symmetry energy decreases and, within a nucleus, as its excitation energy increases. These two properties are related by a diminishing binding energy of the nuclear system. Contrarily, hindrances of nuclear polarizability are observed in the photo-neutron cross-section data and photon-strength functions of semi-magic nuclei with [Formula: see text], 50 and 82, which support the presence of shell effects at low-lying excitations and — assuming validity of the Brink-Axel hypothesis — at high-excitation energies up to the quasi-continuum region. These features assign the nuclear dipole polarizability as a sensitive measure of the long-range correlations of the nuclear force, and provide a new spectroscopic probe to investigate collective phenomena, shell closures, and the elusive nuclear symmetry energy. Particular cases of quadrupole collectivity are also discussed in terms of the available, and yet so scarce, information on nuclear polarizability (e.g. Sn and Ni isotopes).

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41

Karna, S. P., P. J. Bruna, and F. Grein. "Configuration interaction study of the electronic spectrum of methinophosphide, HCP." Canadian Journal of Physics 68, no. 6 (June 1, 1990): 499–507. http://dx.doi.org/10.1139/p90-078.

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Ab initio configuration interaction (CI) studies were performed on low-lying linear and nonlinear states of methinophosphide (HCP), using large basis sets with polarization and s, p Rydberg functions, and extensive multireference CI wave functions. Potential curves for linear states of HCP as functions of RCP and RCH and for nonlinear states as functions of αHCP were obtained, from which spectroscopic constants Te, Re, and ωe were evaluated. For the X1Σ+ ground state, the energy of dissociation into H + CP and the dipole moment were also calculated. The assignment of states based on the observed spectrum had to be revised in several instances. The ã state remained 13Σ+ (or 13A′), but the [Formula: see text] state became 13A″, the [Formula: see text] state, 13Δ, the Ã and [Formula: see text] states remained 11A″ and 21A′, respectively, [Formula: see text] was not seen as a seperate state, and [Formula: see text] became 13Σ−. In the energy range from 0 to 8 eV, 22 linear and 11 nonlinear stable states were found. Nonlinear states were stabilized for excitations from π(9a′, 2a″) into the in-plane component of π*, 10a′. Several doubly excited states of the type π2 → π*2 were bound, lying at relatively small excitation energies.

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42

Hashemi, Zohreh, and Linn Leppert. "Assessment of the Ab Initio Bethe–Salpeter Equation Approach for the Low-Lying Excitation Energies of Bacteriochlorophylls and Chlorophylls." Journal of Physical Chemistry A 125, no. 10 (March 3, 2021): 2163–72. http://dx.doi.org/10.1021/acs.jpca.1c01240.

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43

Grein, Friedrich. "Theoretical studies on ClOO — electronic spectra, ionization potential, and electron affinity." Canadian Journal of Physics 89, no. 8 (August 2011): 891–97. http://dx.doi.org/10.1139/p11-076.

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Vertical excitation energies and oscillator strengths of doublet and quartet states of ClOO, covering doublet states up to 7.5 eV and quartet states up to 9 eV, were obtained by multireference configuration interaction calculations. Strong absorptions from the X2A″ ground state are predicted at 186 and 235 nm. Experimentally, a maximum has been found near 248 nm. The grouping of excited states, with twelve low-lying doublet states and three low-lying quartet states, is explained by the interaction of the 2P ground state of Cl with the π*2 states 3Σg–, 1Δg, and 1Σg+ of O2. Potential energy curves for Cl–O separation at fixed O–O distance and ClOO angle show the lower states to be repulsive (with the exception of the ground state), and higher states to have minima due to avoided crossings. The lowest Rydberg states are expected around 8.5 eV. Adiabatic ionization potentials (IP) and electron affinities (EA) of ClOO were obtained by density functional and coupled cluster methods, with values of 11.60–11.79 eV for IP and 3.56–3.79 eV for EA.

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44

Wang, Yu-Wen, Hong-Yuan He, and Wei-Hai Fang. "An accurate prediction of adiabatic excitation energies to the low-lying electronic states for acetophenone and the related carbonyl compounds." Journal of Molecular Structure: THEOCHEM 634, no. 1-3 (September 2003): 281–87. http://dx.doi.org/10.1016/s0166-1280(03)00380-4.

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45

McKeon, Caroline A., Samia M. Hamed, Fabien Bruneval, and Jeffrey B. Neaton. "An optimally tuned range-separated hybrid starting point for ab initio GW plus Bethe–Salpeter equation calculations of molecules." Journal of Chemical Physics 157, no. 7 (August 21, 2022): 074103. http://dx.doi.org/10.1063/5.0097582.

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The ab initio GW plus Bethe–Salpeter equation (GW-BSE, where G is the one particle Green's function and W is the screened Coulomb interaction) approach has emerged as a leading method for predicting excitations in both solids and molecules with a predictive power contingent upon several factors. Among these factors are the (1) generalized Kohn–Sham eigensystem used to construct the GW self-energy and to solve the BSE and (2) the efficacy and suitability of the Tamm–Dancoff approximation. Here, we present a detailed benchmark study of low-lying singlet excitations from a generalized Kohn–Sham (gKS) starting point based on an optimally tuned range-separated hybrid (OTRSH) functional. We show that the use of this gKS starting point with one-shot G0W0 and G0W0-BSE leads to the lowest mean absolute errors (MAEs) and mean signed errors (MSEs), with respect to high-accuracy reference values, demonstrated in the literature thus far for the ionization potentials of the GW100 benchmark set and for low-lying neutral excitations of Thiel’s set molecules in the gas phase, without the need for self-consistency. The MSEs and MAEs of one-shot G0W0-BSE@OTRSH excitation energies are comparable to or lower than those obtained with other functional starting points after self-consistency. Additionally, we compare these results with linear-response time-dependent density functional theory (TDDFT) calculations and find GW-BSE to be superior to TDDFT when calculations are based on the same exchange-correlation functional. This work demonstrates tuned range-separated hybrids used in combination with GW and GW-BSE can greatly suppress starting point dependence for molecules, leading to accuracy similar to that for higher-order wavefunction-based theories for molecules without the need for costlier iterations to self-consistency.

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46

Yuan, Cenxi. "Systematic shell-model study on spectroscopic properties from light to heavy nuclei." EPJ Web of Conferences 178 (2018): 02016. http://dx.doi.org/10.1051/epjconf/201817802016.

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A systematic shell-model study is performed to study the spectroscopic properties from light to heavy nuclei, such as binding energies, energy levels, electromagnetic properties, and β decays. The importance of cross-shell excitation is shown in the spectroscopic properties of neutron-rich boron, carbon, nitrogen, and oxygen isotopes. A special case is presented for low-lying structure of 14C. The weakly bound effect of proton 1s1/2 orbit is necessary for the description of the mirror energy difference in the nuclei around A=20. Some possible isomers are predicted in the nuclei in the southeast region of 132Sn based on a newly suggested Hamiltonian. A preliminary study on the nuclei around 208Pb are given to show the ability of the shell model in the heavy nuclei.

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47

Cao, Jianfang, Hongmei Wu, Yue Zheng, Fangyuan Nie, Ming Li, and Chenchen Zou. "Hydrogen-bonding study of photoexcited 4-nitro-1,8-naphthalimide in hydrogen-donating solvents." Open Physics 14, no. 1 (January 1, 2016): 621–27. http://dx.doi.org/10.1515/phys-2016-0071.

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AbstractThe solute–solvent interactions of 4-nitro-1,8-naphthalimide (4NNI) as a hydrogen bond acceptor in hydrogen donating methanol (MeOH) solvent in electronic excited states were investigated by means of the time-dependent density functional theory(TDDFT). We calculated the S0 state geometry optimizations, electronic transition energies and corresponding oscillation strengths of the low-lying electronically excited states for the isolated 4NNi and hydrogen-bonded 4NNi-(MeOH)1,4 complexes using the density functional theory (DFT) and TDDFT methods. The electronic excitation energies of the hydrogen-bonded complexes are correspondingly decreased compared to that of the isolated 4NNi, which revealed that the intermolecular hydrogen bond C=O···H–O and N=O···H–O in the hydrogen-bonded 4NNi-(MeOH)1,4 are strengthened in the electronically excited state. The calculated results are consistent with the mechanism that hydrogen bond strengthening will induce a redshift of the corresponding electronic spectra, while hydrogen bond weakening will cause a blueshift. Furthermore, we believe that the deduction we used to depict the trend of the hydrogen bond changes in excited states exists in many other fuorescent dyes in solution.

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48

Burrill, S., and F. Grein. "Multireference configuration interaction studies of HCBr." Canadian Journal of Physics 86, no. 11 (November 1, 2008): 1333–43. http://dx.doi.org/10.1139/p08-079.

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Multireference configuration interaction (MRCI) potential curves were obtained for six 1A′, 1A′′, 3A′, and 3A′′ states of bromomethylene, HCBr, as functions of RCBr for bond angles of 102.9° and 130°, and as functions of the bond angle for RCBr = 1.8682 Å. Besides the well-known X1A′, a3A′′ and A1A′′ states, 21A′(3.26), 31A′(4.48), 41A′′(5.05), 41A′(5.06), 51A′(5.65), 43A′(6.00), 51A′′(6.60), 61A′′(6.60), 63A′′(6.61) (with estimated upper limits to the adiabatic transition energies in eV in parentheses), as well as several 5s and 6s Rydberg states, were found to be stable or metastable. Estimated spectroscopic constants for bound and metastable states, as well as vertical excitation energies for repulsive or quasi repulsive states are listed. The CH+Br dissociation energy of the ground state is about 3.5 eV, and 3.3 eV for a3A′′, whereas it is about 3.6 eV for CBr–H dissociation. It follows that photodissociation of ground-state HCBr by sunlight (up to 4.4 eV) can lead to both Br and H radicals. Photodissociation via several low-lying states is also possible. PACS Nos.: 31.10.+z, 31.15.Ar, 31.25.–v, 31.25.gf, 31.25.Qm, 31.50.Df, 31.15.Dj, 31.15.Fm

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49

Al Mogren, M. Mogren, D. Ben Abdallah, S. Dhaif Allah Al Harbi, M. S. Al Salhi, and M. Hochlaf. "Collisional (de-)excitation of protonated cyanoacetylene (HC3NH+) by helium at low and moderate temperatures." Monthly Notices of the Royal Astronomical Society 503, no. 2 (March 27, 2021): 2902–12. http://dx.doi.org/10.1093/mnras/stab450.

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ABSTRACT Protonated cyanoacetylene, HC3NH+, is detected in astrophysical media, where it plays a key role as an intermediate in the chemistries of HCN/HNC and of cyanopolyynes. We first generated a potential energy surface (PES) describing the intermonomer interaction between HC3NH+ and He in Jacobi coordinates using the highly correlated CCSD(T)-F12/aug-cc-pVTZ ab initio methodology. Then, scattering calculations based on an exact close-coupling quantum-scattering technique were done to obtain pure rotational cross-sections for the rotational (de-)excitation of HC3NH+ after collision with He for total energies up to 2500 cm−1. These cross-sections are used to deduce the collision rates in the 5–350 K temperature range for the low-lying rotational levels of HC3NH+ (up to $j\,\, = \,\,15$). In addition, we generated an average PES for the HC3NH+–H2 system. The preliminary results show that the H2($j_{\mathrm{H_2}} = 0$) and He state-to-state de-excitation cross-sections have similar magnitudes, even though the H2 cross-sections are larger by a factor of 2–2.5. This work should help with the accurate derivation of protonated cyanoacetylene abundances in non-local thermodynamical equilibrium astrophysical media. These will put more constraints on the chemical pathways involving the formation and destruction of HC3NH+ while going back to the cyanopolyyne family and more generally those parts of nitrogen-containing molecular chemistry.

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50

Hu, Feng, Yan Sun, and Maofei Mei. "Systematic calculations of energy levels and transitions rates in Mo XXVIII." Zeitschrift für Naturforschung A 75, no. 8 (September 25, 2020): 739–47. http://dx.doi.org/10.1515/zna-2020-0119.

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AbstractComplete and consistent atomic data, including excitation energies, lifetimes, wavelengths, hyperfine structures, Landé gJ-factors and E1, E2, M1, and M2 line strengths, oscillator strengths, transitions rates are reported for the low-lying 41 levels of Mo XXVIII, belonging to the n = 3 states (1s22s22p6)3s23p3, 3s3p4, and 3s23p23d. High-accuracy calculations have been performed as benchmarks in the request for accurate treatments of relativity, electron correlation, and quantum electrodynamic (QED) effects in multi-valence-electron systems. Comparisons are made between the present two data sets, as well as with the experimental results and the experimentally compiled energy values of the National Institute for Standards and Technology wherever available. The calculated values including core-valence correction are found to be in a good agreement with other theoretical and experimental values. The present results are accurate enough for identification and deblending of emission lines involving the n = 3 levels, and are also useful for modeling and diagnosing plasmas.

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