放射性核束的库仑激发

综述了利用中、高能放射性核束的库仑激发方法研究位于N＝20和28主壳隙附近的丰中子核结构所取得的进展．系统的实验结果清晰地表明,在离开β稳定线区域时N＝20兰壳隙突然消失和N＝28主壳隙的减弱过程．提出了利用兰州放射性束流线开展双幻核Ni50附近核素的低位能级核结构研究的构想． The study of coulomb excitation of the neutron-rich nuclei around N=20 and 28 shell closure with radioactive ion beam at intermediate energy is reviewed. The systematics of the measured energy of the 2+1 state shows that the N=20 shell closure in neutron-rich isotopes with Z≤12 disappears suddenly and N=28 shell elosure appears to be weak for 44S.The coulomb excitation studies of the exotic nuclei around the double magic 7828Ni50 at RIBLL are proposed.     

Properties and structure of N=Z nuclei within relativistic mean field theory

The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48.Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square (rms) radii of charge and neutron, and shell gaps have been calculated.The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42.The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43.The evolution of shell gaps with proton number Z can be clearly observed.Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region.In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.     

Coulomb excitation of neutron-rich Zn isotopes: first observation of the 2(1)+ state in 80Zn

Neutron-rich, radioactive Zn isotopes were investigated at the Radioactive Ion Beam facility REX-ISOLDE (CERN) using low-energy Coulomb excitation. The energy of the 2(1)+ state in 78Zn could be firmly established and for the first time the 2+ --> 0(1)+ transition in 80Zn was observed at 1492(1) keV. B(E2,2(1)+ --> 0(1)+) values were extracted for (74,76,78,80)Zn and compared to large scale shell model calculations. With only two protons outside the Z=28 proton core, 80Zn is the lightest N=50 isotone for which spectroscopic information has been obtained to date. Two sets of advanced shell model calculations reproduce the observed B(E2) systematics. The results for N=50 isotones indicate a good N=50 shell closure and a strong Z=28 proton core polarization. The new results serve as benchmarks to establish theoretical models, predicting the nuclear properties of the doubly magic nucleus 78Ni.     

Z = 50 shell gap near 100Sn from intermediate-energy Coulomb excitations in even-mass 106-112Sn isotopes

Rare isotope beams of neutron-deficient 106,108,110Sn from the fragmentation of 124Xe were employed in an intermediate-energy Coulomb excitation experiment. The measured B(E2,0(1)(+)-->2(1)(+)) values for 108Sn and 110Sn and the results obtained for the 106Sn show that the transition strengths for these nuclei are larger than predicted by current state-of-the-art shell-model calculations. This discrepancy might be explained by contributions of the protons from within the Z = 50 shell to the structure of low-energy excited states in this region.     

Enhanced core polarization in (70)Ni and (74)Zn

The reduced transition probabilities B(E2;0(+) --> 2(+)(1)) of the neutron-rich (74)Zn and (70)Ni nuclei have been measured by Coulomb excitation in a (208)Pb target at intermediate energy. These nuclei have been produced at Grand Accélérateur National d'Ions Lourds via interactions of a 60A MeV (76)Ge beam with a Be target. The B(E2) value for (70)Ni(42) is unexpectedly large, which indicates that neutrons added above N=40 strongly polarize the Z=28 proton core. In the Zn isotopic chain, the steep rise of B(E2) values beyond N=40 continues up to (74)Zn(44). The enhanced proton core polarization in (70)Ni is attributed to the monopole interaction between the neutron in the g(9/2) and protons in the f(7/2) and f(5/2) spin-orbit partner orbitals. This interaction could result in a weakening of magicity in (78)Ni(50).     

香港大学在束伽玛谱学研究与新一代伽玛探测器阵列(英文)

探索原子核的壳层演化,验证奇特核的幻数结构是香港大学核物理研究的重要方向。目前,科研团队利用在束伽玛谱学技术已经研究了30Ne的N=20幻数消失和78Ni（Z=28,N=50）附近原子核的双幻数结构,而即将开展的53,56Ca在束伽玛谱学实验会对新幻数N=34的定量研究,以及到N=40核的壳层演化提供重要的数据。下一步的研究目标是探索100Sn（N=Z=50）的奇特结构,特别是研究它的第一个2+激发态与其邻近原子核的低激发态性质。100Sn处于质子滴线以及核天体快质子俘获路径上,因此,它的幻数结构及其临近原子核单粒子性能研究将会极大增强对核力和核合成机制的认识。为了进一步提高物理实验统计,香港大学在数量上增加了30% NaI（Tl）晶体从而全面升级了DALI2伽玛探测阵列。此外,为了探索远离稳定线核区的新物理,开展更高精度在束伽玛谱学实验,香港大学与中国科学院近代物理研究所、中国原子能科学研究院计划合作研制基于溴化镧晶体的新一代伽玛探测器阵列。这套阵列主要在兰州重离子加速器（HIRFL）和将来建成的强流重离子加速器（HIAF）等大科学装置上开展实验,从而在奇特核研究方面取得大量重要的成果,促进科研人员全面认识、理解核力以及天体核合成过程。Exploring the evolution of shell closures and examining the magicity of extremely exotic nuclei are the main research interests of HKU (University of Hong Kong) experimental nuclear physics group. The group has employed in-beam gamma-ray spectroscopy technique to investigate the vanishing of N=20 magicity in 30Ne (N=20) and the strong magicity in nuclei around 78Ni (Z=28, N=50). The approved future's experiment on spectroscopy of 53,56Ca, proposed by HKU, will give quantitative information for the "magic index" of N=34 and shell evolution toward N=40. The next goal is to investigate the structure of 100Sn (N=Z=50), particularly the energy of the first 2+ state, and the low-lying states in the neighboring nuclei. 100Sn lies on the proton drip-line and on the astrophysical rp-process path. Characterizing the magicity of 100Sn and the nature of single-particle states in its neighboring nuclei is therefore essential to the fundamental understanding of nuclear forces and nucleo-synthesis. To significantly increase the data statistics for our physics goals, HKU group has prepared the upgrade of gamma-ray spectrometer DALI2 with 30% more NaI(Tl) detectors integrated into a new array configuration. On the other hand, next significant insights into the structure of nuclei would require new gamma-ray detection array capable for higher precision gamma-ray spectroscopy. HKU group in collaboration with IMP and CIAE therefore proposes to construct a new-generation gamma-ray detection array based on the novel scintillator LaBr₃(Ce) to explore the new physics in nuclei far from the valley of stability. Utilizing the radioactive beams at the Chinese large-scale facilities such as the Heavy Ion Research Facility in Lanzhou (HIRFL) in IMP and the future's High Intensity heavy-ion Accelerator Facility (HIAF), this novel LaBr₃(Ce) array would lead to a significant boost to the frontiers of exotic-nuclei research, which will guide scientists towards the comprehensive and even beyond-traditional understanding of nuclear forces and nucleosynthesis.     

Vanishing N = 20 shell gap: study of excited states in (27,28)Ne

This Letter reports on the (1)H((28)Ne, (28)Ne) and (1)H((28)Ne, (27)Ne) reactions studied at intermediate energy using a liquid hydrogen target. From the cross section populating the first 2(+) excited state of (28)Ne, and using the previously determined BE(2) value, the neutron quadrupole transition matrix element has been calculated to be M(n)=13.8 +/- 3.7 fm(2). In the neutron knockout reaction, two low-lying excited states were populated in (27)Ne. Only one of them can be interpreted by the sd shell model while the additional state may intrude from the fp shell. These experimental observations are consistent with the presence of fp shell configurations at low excitation energy in (27,28)Ne nuclei caused by a vanishing N=20 shell gap at Z=10.     

Gamow-Teller strengths in the A = 14 multiplet: a challenge to the shell model

A new experimental approach to the famous problem of the anomalously slow Gamow-Teller (GT) transitions in the beta decay of the A=14 multiplet is presented. The GT strength distributions to excited states in 14C and 14O were studied in high-resolution (d,2He) and (3He,t) charge-exchange reactions on 14N. No-core shell-model calculations capable of reproducing the suppression of the beta decays predict a selective excitation of Jpi=2+ states. The experimental confirmation represents a validation of the assumptions about the underlying structure of the 14N ground state wave function. However, the fragmentation of the GT strength over three 2+ final states remains a fundamental issue not explained by the present no-core shell model using a 6homega model space, suggesting possibly the need to include cluster structure in these light nuclei in a consistent way.     

Interplay between single-particle and collective effects in the odd-A Cu isotopes beyond N=40

Collective properties of the low-lying levels in the odd-A 67-73Cu were investigated by Coulomb excitation with radioactive beams. The beams were produced at ISOLDE and postaccelerated by REX-ISOLDE up to 2.99 MeV/u. In 67,69Cu, low-lying 1/2(-), 5/2(-), and 7/2(-) states were populated. In 71,73Cu, besides the known transitions deexciting the single-particle-like 5/2(-) and core-coupled 7/2(-) levels, gamma rays of 454 and 135 keV, respectively, were observed for the first time. Based on a reanalysis of beta-decay work and comparison with the systematics, a spin 1/2(-) is suggested for these excited states. Three B(E2) values were determined in each of the four isotopes. The results indicate a significant change in the structure of the odd-A Cu isotopes beyond N=40 where single-particle-like and collective levels are suggested to coexist at very low excitation energies.     

Tabletop nucleosynthesis driven by cluster Coulomb explosion

Coulomb explosion of completely ionized (CH4)n, (NH3)n, and (H2O)n clusters will drive tabletop nuclear reactions of protons with 12C6+, 14N7+, and 16O8+ nuclei, extending the realm of nuclear reactions driven by ultraintense laser-heterocluster interaction. The realization for nucleosynthesis in exploding cluster beams requires complete electron stripping from the clusters (at laser intensities I(M) > or = 10(19) W cm(-2)), the utilization of nanodroplets of radius 300-700 A for vertical ionization, and the attainment of the highest energies for the nuclei (i.e., approximately 30 MeV for heavy nuclei and approximately 3 MeV for protons).     

B(E2) upward arrow measurements for radioactive neutron-rich ge isotopes: reaching the N=50 closed shell

The B(E2;0(+)(1)-->2(+)(1)) values for the radioactive neutron-rich germanium isotopes (78,80)Ge and the closed neutron shell nucleus 82Ge were measured at the HRIBF using Coulomb excitation in inverse kinematics. These data allow a study of the systematic trend between the subshell closures at N=40 and 50. The B(E2) behavior approaching N=50 is similar to the trend observed for heavier isotopic chains. A comparison of the experimental results with a shell model calculation demonstrates persistence of the N=50 shell gap and a strong sensitivity of the B(E2) values to the effective interaction.     

Probing shell structure and shape changes in neutron-rich sulfur isotopes through transient-field g-factor measurements on fast radioactive beams of 38S and 40S

The shell structure underlying shape changes in neutron-rich nuclei near N = 28 has been investigated by a novel application of the transient-field technique to measure the first-excited-state g factors in 38S and 40S produced as fast radioactive beams. There is a fine balance between proton and neutron contributions to the magnetic moments in both nuclei. The g factor of deformed 40S does not resemble that of a conventional collective nucleus because spin contributions are more important than usual.     

Influence of Isotope on Shell Effects of Pre-scission Particle Evaporation

The shell effects on the particle evaporation prior to fission for three Pb isotopes, 204pb, 20sPb, and 212pb,as well as three Sn isotopes, 128Sn, 132Sn, and 136Sn, are explored by a diffusion model. Calculations show that the magnitude of shell effects in the emission of particles changes with the neutron-to-proton ratio N/Z of these fissioning nuclei, and this change is affected significantly by the spin and excitation energy of the system. It is shown that high angular momentum enhances the dependence of shell effects on the N/Z while high excitation energy weakens such a dependence.     

Improved isospin dependent quantum molecular dynamics model and its application to fusion reactions near Coulomb barrier

The isospin dependent quantum molecular dynamics model is developed by introducing switch function method which deals with correctly the surface interaction and shell effect in the process of projectile and target approaching. The fusion excitation functions for ⁴⁰Ca + ⁴⁰Ca, ⁴⁰Ca + ⁴⁸Ca and ⁴⁸Ca + ⁴⁸Ca at energies in the vicinity of the Coulomb barrier are studied. The experimental data of the fusion cross sections for these three systems can be regenerated very well. It is found that the fusion cross sections for neutron-rich system increase obviously. The static and dynamical Coulomb barriers are studied in order to clarify the phenomena. The neutron to proton ratio (N/Z ratio) at neck region is also studied, which apparently presents isospin effects of projectile-target combinations.     

Influence of Isotope on Shell Effects of Pre-scission Particle Evaporation

The shell effects on the particle evaporation prior to fission for three Pb isotopes, ^204Pb, ^208Pb, and ^212pb,as well as three Sn isotopes, ^128Sn, ^132Sn, and ^136Sn, are explored by a diffusion model. Calculations show that the magnitude of shell effects in the emission of particles changes with the neutron-to-proton ratio N/Z of these fissioning nuclei, and this change is affected significantly by the spin and excitation energy of the system. It is shown that high angular momentum enhances the dependence of shell effects on the N/Z while high excitation energy weakens such a dependence.     

Enhanced quadrupole collectivity at N = 40: the case of neutron-rich Fe isotopes

The transition rates for the 2(1)+ states in (62,64,66)Fe were studied using the recoil distance Doppler-shift technique applied to projectile Coulomb excitation reactions. The deduced E2 strengths illustrate the enhanced collectivity of the neutron-rich Fe isotopes up to N = 40. The results are interpreted using the generalized concept of valence proton symmetry which describes the evolution of nuclear structure around N = 40 as governed by the number of valence protons with respect to Z ≈ 30. The trend of collectivity suggested by the experimental data is described by state-of-the-art shell-model calculations with a new effective interaction developed for the fpgd valence space.     

A search for an \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathcal{N} =2 $\end{document} inflaton potential

We consider $ \mathcal{N} =2 $ supergravity theories that have the same spectrum as the R + R² supergravity, as predicted from the off‐shell counting of degrees of freedom. These theories describe standard $ \mathcal{N} =2 $ supergravity coupled to one or two long massive vector multiplets. The central charge is not gauged in these models and they have a Minkowski vacuum with $ \mathcal{N} =2 $ unbroken supersymmetry. The gauge symmetry, being non‐compact, is always broken. α‐deformed inflaton potentials are obtained, in the case of a single massive vector multiplet, with α = 1/3 and 2/3. The α = 1 potential (i.e. the Starobinsky potential) is also obtained, but only at the prize of having a single massive vector and a residual unbroken gauge symmetry. The inflaton corresponds to one of the Cartan fields of the non‐compact quaternionic‐Kähler cosets.     

质子数Z 分别位于Ru 之上和之下的A~(100~126) 丰中子原子核三轴形变在原子核形状变迁和共存中的重要作用(英文)

基于Ru (Z = 44) 丰中子同位素中存在最大三轴形变的理论预言和实验证据,综述了近年来Rh (Z = 45),Pd (Z =46), Ag (Z =47), Cd (Z =48)(质子数Z 位于Ru,Z =44 之上)及Zr (Z =40), Nb (Z =41), Mo (Z =42),Tc (Z =43)(质子数Z 位于Ru,Z =44 之下) 的A~ (100~126) 丰中子同位素中关于三轴形变的形状变迁和形状共存系统性研究的重要进展。252Cf 自发裂变瞬发 射线-- 三重符合、特别是新建立的--- 四重符合数据的系统观测和研究,在Ru, Pd, Cd 和Nb 丰中子同位素中显著扩展或首次观测到了一系列能带,为这个核区原子核形状的研究提供了新的、重要的实验数据。联系此前报道的有关进展,使用PES, TRS, PSM, CCCSM 和SCTAC 理论模型计算拟合新的实验数据,在该核区沿同中素和同位素链,并随自旋和激发能变化各自由度,跟踪原子核形状渐进变化,获得了新的系统性研究成果,显著扩展和深化了人们对原子核形状变迁和形状共存的认知。对于Ru 及其上的Rh (Z = 45), Pd (Z = 46), Ag (Z = 47) 和Cd (Z = 48) 丰中子同位素的研究表明:Rh 丰中子核具有比最大值稍小的三轴形变,γ = 28°,并在103{106Rh 同位素链上鉴别出了手征对称破缺;在三轴形变核112Ru和114Pd(N = 68)中发现了三轴原子核的摆动运动,该摆动运动也可能在114Ru (N = 70)中存在;观察到了从具有最大三轴形变的110,112Ru 中手征破缺到稍小三轴形变的112,114,116Pd 中扰动的手征破缺的过渡;在较软的Ag 核中观察到了丰富的谱学结构,在104,105Ag 中鉴别出了可能的手征对称破缺,在较重的115,117Ag 中提出了趋于三轴形变的软度;具有小形变的Cd核的能级结构被解释为准粒子耦合、准转动和软三轴形变;最近的库伦激发的研究提供了Z = 50, N = 82满壳附近122,124,126Cd 核中出现核集体性的实验和理论证据;上述研究成果展现出从Ru中的最大三轴形变(γ=30°,三轴形变极小增益为0.67 MeV), 经具有大三轴形变的Rh核γ=28°),到Pd核中的稍小、但稳定于中等自旋到高自旋区的三轴形变(γ~41°,三轴形变极小增益为0.32 MeV),再经Ag核中的软度,最后到具有很小形变、但仍出现集体性质、包括软三轴形变的Cd核的过渡。对于Pd核转动带交叉系统性的研究揭示了其第一带交叉(νh_11/2)2 中子转动顺排的上行驱动,和第二带交叉(πg_9/2)2质子转动顺排的下行驱动效应,成功地解释了114Pd 中的三轴摆动运动,并给出了110-118Pd同位素链中理论早已预言、而比早期理论预言更为完整准确的形状渐进变迁和形状共存的图像。根据该核区的系统研究,发现最大三轴形变出现在112Ru,而在相邻的偶Z(Pd)同位素链,三轴形变极小的中心在114Pd, 两者均为N = 68。上述系统性研究沿相邻的Ru和Pd偶Z同位素链,在N =68同中素中鉴别出最大三轴形变,均比理论预言的108Ru 和110Pd 多4个中子。在Z值位于Ru (Z = 44) 之下的Zr (Z = 40), Nb (Z = 41), Mo (Z = 42) and Tc (Z = 43) 丰中子同位素中,Y和Zr核具有很强的轴对称四极形变,而在较重的Zr同位素中出现了自由度;较重的Nb核(A = 104~106) 基态具有中等程度的软三轴形变和强四极形变,随着自旋和激发能的增加,过渡到接近于轴对称的强四极形变;而较轻的Nb核(A≤103) 基态均接近轴对称形状;在Nb同位素链上基态由球形到强四极形变的形状突变发生在100Nb(N = 59),在100-106Nb同位素链中基态的软三轴形变随中子数增加而增加;在Nb核中还观察到关于软三轴形变的形状共存;Mo核具有大的三轴形变,观察到了振动和手征对称破缺;Tc核具有比最大值稍小的三轴形变,γ=26°,并观察到了手征对称破缺。质子数Z从41到48的A~(100~126)丰中子同位素,特别是Pd和Nb 同位素,呈现出关于三轴形变的过渡特征。This paper reviews the systematic investigations and understanding for the shape transitions and coexistence with regard to triaxial deformations in A s 100 to 126 neutron-rich Rh (Z = 45), Pd (Z = 46), Ag (Z = 47), Cd (Z = 48) and Zr (Z = 40), Nb (Z = 41), Mo (Z = 42), Tc (Z = 43) isotopes with Z beyond and below Ru (Z = 44), respectively, in Ru the maximal triaxial deformation having been predicted and deduced. The recent measurements and studies of prompt triple- and four-fold, γ-γ-γ and γ-γ-γ-γ, coincidence data from the spontaneous fission of 252Cf using Gammasphere have yielded considerable expansion and extension or first observation of the bands in Ru, Pd, Cd, and Nb isotopes,which provided important data for the studies of nuclear shapes in this region. Combined with previous investigations, recent systematic studies of the new data well reproduced by PES, TRS, PSM, CCCSM and SCTAC model calculations have traced shape changes along the isotonic and isotopic chains, respectively,and with changing excitations/spins as well, significantly expanding our knowledge of shape transitions/coexistence in nuclei.For the neutron-rich Ru and beyond, Rh, Pd, Ag and Cd isotopes, triaxial deformations γ= 28°,slightly smaller than the maximal value, were deduced in Rh (Z = 45) isotopes, with chiral symmetry breaking proposed in 103-106Rh; onset of wobbling motions were identified in 112Ru and 114Pd (N =68),and probably also in 114Ru (N =70); evolution from chiral symmetry breaking in 110,112Ru with maximal triaxial deformations to disturbed chirality in 112,114,116Pd with less pronounced triaxial deformations was proposed; rich nuclear structure was proposed in soft Ag isotopes with possible chiral doubling structure suggested in 104,105Ag, and softness towards triaxial deformation proposed in heavier 115,117Ag;quasi-particle couplings, quasi-rotations and soft triaxiality were suggested in Cd (Z =48) isotopes with small deformations; onset of collectivity was recently suggested in 122,124,126Cd in the vicinity of Z =50 and N = 82 closed shells by studies of Coulomb excitations; shape evolutions from maximal triaxial deformations in Ru (γ=30°, with triaxial minimum energy gain of 0.67 MeV), through Rh with large triaxial deformations ( γ=28°), to less pronounced triaxiality in Pd (with triaxial minimum energy gain of 0.32 MeV), then soft triaxiality in Ag, and finally to slightly deformed Cd isotopes but with emergence of collectivity and soft triaxiality were proposed. The systematic studies of the band crossings in Pd revealed up-rising drivings of the first band crossings caused by (νh_11/2)2 and down-sloping drivings of the second band crossings by (πg_9/2)2, explained the onset of wobbling motions in 114Pd,and showed a long-sought picture of shape evolution and coexistence in the Pd isotopic chain which is more complete but complex than earlier predictions. Based on the systematic studies in the mass region,maximal triaxial deformation is found to be reached in 112Ru and less-pronounced triaxiality centered at 114Pd, both for N =68, four neutrons more than predicted in earlier theoretical calculations.In the neutron-rich Zr (Z =40), Nb (Z =41), Mo (Z =42) and Tc (Z =43) isotopes with Z just below Ru, large quadrupole deformations of axially symmetric shapes were deduced in Y and Zr isotopes, with emergence of the degree of freedom having been suggested for heavier Zr isotopes; medium triaxial deformations were deduced for the ground states of heavier (A > 104) Nb isotopes, and, with increasing excitations and spins, evolution from medium triaxial deformations with strong quadrupole deformations at ground states to nearly axially-symmetric shapes were deduced; light Nb isotopes (A6103) have near axially-symmetric shapes with strong quadrupole deformations; combining with the identification of onset of strong quadrupole deformation at 100Nb in the Nb isotopic chain, an increase of soft triaxiality with increasing neutron number was proposed in 100-106Nb. Shape coexistence with regard to soft triaxiality is also proposed in Nb isotopes; large triaxial deformations, vibrations and chiral doublets were proposed in Mo isotopes; chiral doubling and large triaxial deformations (γ ~26°) slightly smaller than the maximal triaxiality were suggested in Tc isotopes.The neutron-rich nuclei with Z ranging from 41 through 48 and A ~100 to 126, especially the Pd and Nb isotopes are thus found to be transitional nuclei with regard to triaxiality.     

DFT calculation of core– and valence–shell electron excitation and ionization energies of 2,1,3-benzothiadiazole C6H4SN2, 1,3,2,4-benzodithiadiazine C6H4S2N2, and 1,3,5,2,4-benzotrithiadiazepine C6H4S3N2

The vertical core– and valence–shell electron excitation and ionization energies of the three title molecules, 1–3, were calculated by density functional theory (DFT) using adequate functional for each type of processes and atoms under study. The inner shells treated were C1s, N1s, S1s, S2s, S2p. Molecular geometry was optimized by DFT B3LYP/6-311 + (d,p). The basis set of triple zeta plus polarization (TZP) Slater-type orbitals was employed for DFT calculations. The ΔSCF method was used to calculate ionization energies. The average absolute deviation (AAD) from experiment of 26 valence-electron ionization energies calculated by DFT for the three molecules 1–3 was 0.14 eV; while that of 24 calculated core-electron binding energies (CEBEs) from experiment was 0.4 eV. Selected core excitation energies were calculated by the multiplet approximation for the three molecules. The AAD of twelve calculated core excitation energies by the multiplet approximation that exclude S2s cases was 0.56 eV. Time-dependent DFT (TDDFT) was employed to calculate the excitation energies and corresponding oscillator strengths of core- and valence-electrons of the molecules. Some selected occupied core orbitals were used to calculate the core-excitation energies with the TDDFT (Sterner–Frozoni–Simone scheme). The core excitation energies thus calculated were in an average error of ca. 28 eV compared to observed values. They were shifted to the value calculated by the multiplet approximation. Convoluted spectra based upon the shifted energies and accompanying oscillator strengths reproduce low-energy region of observed spectra reasonably well, whereas they deviate from experiment in high-energy region. Reasonable agreement between theory and experiment was obtained for the valence electron excitations of the molecules.