A shell-model study onM1 andE2 properties of Zn,Ga, and Ge

Electromagnetic properties of Zn, Ga, and Ge are studied by using the nuclear shell model. Empirically determinedM1 operators are found to be very successful to explainM1 transitions, moments, and mixing ratios. ManyE2 properties are also understood by the present shell-model calculations with effective charges.     

X-ray spectra of He-like ions of Ga and Ge,excited in the low-inductance spark plasma

The spectra of Ga XXX and Ge XXXI ions in the interval 1.2–1.4 Å excited in the low-inductance vacuum spark plasma have been obtained for the first time. The resonance line 1s²?1s2p of Ga XXX and Ge XXXI and a group of satellites, corresponding to transitions in Ga XXIX and Ge XXX can be seen distinctly in the spectra. The spectra were obtained by an electronic-optical image-intensifier tube for one discharge.     

Study of neutron-rich Mo isotopes by the projected shell model approach

The projected shell model (PSM) calculations have been performed for the neutron-rich even–even ^102?110Mo and odd—even ^103?109Mo isotopes. The present calculation reproduces the available experimental data on the yrast bands. In case of even–even nuclei, the structure of yrast bands is analysed and electromagnetic quantities are compared with the available experimental data. The g-factors have been predicted for high spin states. For the odd-neutron nuclei, the structures of yrast positive- and negative-parity bands are analysed and found to be in reasonable agreement with the experiments for ^103?107Mo. The disagreement of the calculated and observed plots for energy staggering quantity clearly establishes the occurrence of sizable triaxiality in ^103,105Mo and also predicts a decrease in the quantum of triaxiality with increasing neutron number and angular momentum for odd mass neutron-rich Mo isotopes.     

Analysis of the neutron single-particle energies of Zn, Ge, and Se isotopes within a mean field model with dispersive optical potential

The parameters of the neutron dispersive optical potential of even-even Zn, Ge, and Se isotopes (both stable and unstable) are determined from an analysis of experimental and estimated neutron single-particle energies. The imaginary part of the potential depends on the shell structure of the isotopes. The calculated energies are found to be in good agreement with the experimental and estimated energies.     

Even Zn isotopes in the cluster-vibration model

Even-A nuclear systems with two protons in the 28–50 valence shell (even Zn isotopes) are described in the cluster-vibration model. Energy spectra and electromagnetic properties are calculated and their qualitative features are discussed with emphasis on the coexistence between quasivibrational and quasirotational characteristics. The influence of possible cubic anharmonicities and of the presence of the$\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ configuration are investigated. For some states, pairing phonons are recognized as intrinsic building blocks created in the cluster-vibration model. The relation between this approach and recent shell-model calculations is discussed.     

Density and fluctuations in shell model spectra

A simple method, based on the Gram-Charlier expansion, to separate the smooth and fluctuating parts of the level density is developed. Applications to spectra arising from large shell model calculations are considered. Fluctuations in the energy levels are studied. It is found that with this proper decomposition, even long range correlations agree with the predictions of the random matrix theory.     

Shell model for rotation-like spectra of Sr isotopes

The isotopes of Sr are described by a shell-model with the proton-neutron configurations $\text{(2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{, 2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{, 1}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}{}_{\mathrm{<mtext>p</mtext>}}{}^{\mathrm{?2}}\text{× (1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}_{\mathrm{<mtext>n</mtext>}}{}^{\mathrm{?(50?N)}}$. The transition of the spectrum from a shell structure to a rotation-like structure which is experimentally observed in the Sr isotopes can be reproduced by the present model.     

Inner shell electron energy loss spectra of the methyl amines and ammonia

Electron energy loss Spectroscopy has been used to obtain the inner shell excitation spectra of the methyl amines CH₃NH₂, (CH₃)₂NH and (CH₃)₃N for both the N 1s and C 1s regions. A spectrum of the N 1s region of NH₃ is also presented at higher resolution than previously published data. The C ls spectra are all very similar and the discrete portions may be assigned to Rydberg transitions. However, features attributable to a σ^* shape resonance are observed just above the N 1s and C ls ionization edges. The NH₃ spectrum is ascribed to Rydberg transitions. The N 1s spectra of the methyl amines, however, become increasingly dominated by a σ* resonance in the continuum with increased methylation. The features in the inner-shell spectra are compared with the reported valence-shell optical absorption spectra and support the Rydberg assignment. The inner-shell spectra of (CH₃)₃N and NH₃ are also compared with previously published inner shell electron energy loss spectra of NF₃ and the third row phosphorus analogues PF₃,P(CH₃)₃andPH₃.     

Elastic and inelastic scattering of 22 MeV protons from natural even-even Zn and Ge isotopes: (II). Spectroscopy of the 68,70Zn and comparison between structure of low-lying states of Zn and Ge

The (p, p′) inelastic scattering on ⁶⁸Zn and ⁷⁰Zn has been measured at 22 MeV incident energy with an overall energy resolution of 14 keV for ⁶⁸Zn and 24 keV for ⁷⁰Zn using a tandem Van de Graaff and a split-pole magnetic spectrometer. Differential cross sections were obtained for levels up to 4.9 and 4.4 MeV excitation energy for ⁶⁸Zn and ⁷⁰Zn respectively. Experimental cross sections are compared with DWBA calculations, asymmetric rotor model, harmonic and anharmonic vibrational models coupled-channels calculations. Spin and parity assignments have been deduced for both isotopes. Results for ⁶⁴Zn, ⁶⁶Zn, ⁶⁸Zn and ⁷⁰Zn are discussed. Comparison between the deformation lengths deduced from these measurements and those derived from similar analysis using other projectiles, for the natural even-even Zn and Ge nuclei, are made; also, comparison between the structure of low-lying states of these nuclei are made.     

Discrete and continuum spectra in the unified shell model approach

A new version of the nuclear shell model unifies the consideration of the discrete spectrum, where the results reproduce the standard shell model, and continuum. The ingredients of the method are the non-Hermitian effective Hamiltonian, energy-dependent one-body and two-body decay amplitudes, and self-consistent treatment of thresholds. The results for helium and oxygen isotope chains reproduce the data well.     

Quasiparticle-phonon model calculations on doubly even Zn and Ge nuclei

The doubly even isotopes of Zn and Ge have been investigated in a model in which two quasiparticle excitations, constructed in a (0f _7/2), 1p _3/2, 0f _5/2, 1P _1/2, 0g _9/2 configuration space, are coupled with quadrupole vibrations of the core, viz.⁴⁰Ca or⁵⁶Ni. The 0f _7/2 orbit is excluded in case of a⁵⁶Ni core. The spectra, except for low-lying excited 0⁺ states, could be reproduced reasonably well. The calculatedE2 strengths and quadrupole moments are in fair agreement with experiment.     

Spectra of H-like Cu,Zn and Ga

The spectra of Cu XXIX, Zn XXX and Ga XXXI excited in a low-inductance vacuum spark plasma have been obtained for the first time. A mathematical noise-suppression method was used for the spectrum of Ga XXXI.     

The structure of neutron-rich calcium isotopes studied by the shell model with realistic effective interactions

We study the structure of neutron-rich calcium isotopes in the shell model with realistic interactions. The CD-Bonn and Kuo-Brown (KB) interactions are used. As these interactions do not include the three-body force, their direct use leads to poor results. We tested whether the adjustment of the single particle energies (SPEs) would be sufficient to include the three-body correlations empirically. It turns out that the CD-Bonn interaction, after the adjustment of SPEs, gives good agreement with the experimental data for the energies and spectroscopy. For the KB interaction, both the SPEs and monopole terms require adjustments. Thus, the monopole problem is less serious for modern realistic interactions which include perturbations up to the third order. We also tested the effect of the non-central force on the shell structure. It is found that the effect of the tensor force in the CD-Bonn interaction is weaker than in the KB interaction.     

Calculations of photoelectron spectra for tetrahedral oxyanions by the Hartree—Fock—Slater model

The electronic structures of typical oxyanions are studied using the discrete variational (DV)—Xα cluster method. The level structures calculated for the clusters correspond very well with the valence-state levels found in experimental XPS spectra. Theoretical intensities of the XPS peaks are evaluated, using the orbital populations obtained with the DV—Xα method together with atomic subshell photoionization cross-sections obtained in previous work with the same electron model. The results are in good agreement with experiment.     

The energy spectra and electromagnetic transitions of odd-a titanium isotopes

The isotopes ^{55, 47, 49, 51}Ti are studied in the framework of the deformed configuration mixing shell model. The calculated spectra and electromagnetic properties agree well with the observed ones. The calculations suggest the existence of an excited $\text{K =}\text{1}\text{2}$ band of states in ^{45, 47, 49}Ti and a $\text{K =}\text{7}\text{2}$ band in ⁵¹Ti. In ⁴⁹Ti this excited $\text{K =}\text{1}\text{2}$ band is more deformed than the “ground state band”. On the basis of the overall agreement between the calculated and experimental spectra and decay properties we suggest the spin assignments $\text{J =}\text{5}\text{2}$, $\text{7}\text{2}$, $\text{9}\text{2}$, $\text{5}\text{2}$ and $\text{7}\text{2}$ to the states in ⁴⁷Ti observed at 2.168, 2.97, 2.408, 2.835 and 3.223 MeV, respectively.     

Potential energy surfaces in the two-center shell model

The two-center shell model of two equal overlapping spheroids is combined with Lawrence's liquid-drop shapes. Within this framework, potential energy surfaces for nuclei from different mass regions are calculated. In particular, the transition of the ground state deformation from spherical to deformed is investigated for a sequence of ruthenium isotopes.     

Nuclear spectral energy functions beyond the shell model

We predictl=0 nucleons in¹²C to have a negative (binding) energy centered around –22 MeV with a full width at half-maximum of 5.3 MeV. Thel=1 (P _3/2 nucleons) are predicted to have a much narrower spectral energy function centered around –10.6 MeV. A strongly correlated translational invariant wave function was used to describe the ground state nucleus. A central two-nucleon potential was utilized in the hyperspherical harmonic method to approximately solve the Schrödinger equation for the ground state wave function. Both confirmation and failings of the independent particle shell model are exposed.     

(p,t) strengths in the Ga isotopes

The (p, t) reaction on the two stable Ga isotopes has been performed at 25 MeV, with 11 keV energy resolution. Levels up to 3.5 MeV in ⁶⁷Ga and 4.3 MeV in ⁶⁹Ga were measured. Differences observed between the distribution of the L = 2 (p, t) strength and the distribution of the B(E2)↑ strength may be explained by a mixed character of the $\text{7}\text{2}{}_2$^? level wave function. The distribution of the L = 0 strength indicates that the striking change in the ground-state structure shown between N = 40 and 42 already begins, although weakly, between N = 38 and 40.