VAMPIR calculations for 128Ba and 130Ce: Two mechanisms of backbending

Hartree-Fock-Bogoliubov calculations with spin and number projection before the variation (VAMPIR) are performed for the nuclei ¹²⁸Ba and ¹³⁰Ce using a slightly renormalized Brueckner G-matrix as effective interaction in a rather large single-particle basis. The results are compared to those of Hartree-Fock-Bogoliubov calculations with projection after the variation, those of multiconfiguration calculations (MONSTER) and to experiment. In both nuclei the VAMPIR and the MONSTER approaches turn out to be of about the same quality and agree rather well with the experimental data. Analysis of the VAMPIR mean fields reveals that two somewhat different mechanisms are responsible for the backbending observed in the yrast bands of the two nuclei. While in ¹³⁰Ce the well-known alignment of two high-j quasiparticles (proton $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$) is found, in ¹²⁸Ba first a neutron pair is scattered from the $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ to the $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ orbit, and then the larger alignment energy of the less occupied neutron $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ states produces the backbend. This latter effect is in agreement with the predictions of a simple model presented by us some years ago.     

Band crossing and the prealignment B(E2) anomaly in 126Ba

A theoretical interpretation of the reduction in E2 strengths in ¹²⁶Ba prior to backbending is presented. A shell model basis is built from normal parity orbilals organized into multiplets of a pseudo SU(3) symmetry coupled to $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ configurations restricted to states of seniority zero and two. Within the framework of the model the scattering of a pair of protons from normal parity to the $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ orbital produces band crossing and a corresponding reduction in E2 transition strengths prior to pair alignment which is the principal mechanism of the backbending.     

Band structure in 131,132,133Ba observed by (12C,xn) reactions

High-spin levels in Ba isotopes are observed in the reactions ^122,124Sn(¹²C,3nγ)^131,133Ba and ¹²⁴Sn(¹²C,4nγ)¹³²Ba. They are studied by in-beam spectroscopic methods such as prompt and delayed spectra, excitation functions, γ-γ coincidences and angular distributions. Bands are found on the $\text{11}{}^{\mathrm{?}}\text{2}$ isometric state in ¹³³Ba and on the $\text{9}{}^{\mathrm{?}}\text{2}$ isomeric state in ¹³¹Ba which are in agreement with the structure of other nuclei with 77 and 75 neutrons and with prolate deformation. A negative-parity band with both even- and odd-spin members from 5^? to 9^? is found in ¹³²Ba.     

The decay scheme of 127Ba and half-lives of some low-lying excited states in 123, 125, 127, 129Cs

Radioactive sources of ^{123, 125, 127, 129}Ba obtained in the spallation reaction have been studied with Ge(Li), Si(Li), NaI(Tl) and plastic detectors. On the basis of γ-ray energies, intensities, energy sums and coincidence information, the decay scheme has been proposed for ¹²⁷Ba. No high-spin isomer of ¹²⁷Ba has been observed. The lifetimes of $\text{5}\text{2}$⁺ → $\text{1}\text{2}$⁺ transitions in ^{123, 125, 127, 129}Cs have been measured. No evidence for the shape isomerism in ¹²⁷Cs has been found.     

The reaction 36S(p, γ)37Cl: (II). Lifetimes,spins and parities of 37Cl levels

Analysis of the γ-ray angular distributions measured at 16 ³⁶S(p, γ)³⁷Cl resonances yields the spins and/or parities of 21 bound states of ³⁷Cl in addition to the resonance spins. Among the latter are four $\text{J =}\text{1}\text{2}$ resonances. For several other bound states the possible spins have been restricted. Multipolarity mixing ratios have been deduced from the same data. Lifetimes (or lifetime limits) of 29 bound states have been deduced from DSA measurements.This extensive experimental information allows a comparison with the results of a shell-model calculation for both the even- and odd-parity states of ³⁷Cl. In this calculation either zero, one or two particles are promoted from the 2s_{$\text{1}\text{2}$} or 1d_{$\text{3}\text{2}$} to the 1f_{$\text{7}\text{2}$} or 2p_{$\text{3}\text{2}$} subshells. Up to an excitation energy of about 5 MeV a one-to-one correspondence is found between experimental and calculated levels.     

Triaxial shape and onset of high-spin bands in 129Ba

High-spin states in ¹²⁹Ba have been studied by the ¹²⁰Sn(¹²C, 3n)¹²⁹Ba reaction. The onset of a system of bands parallel to the yrast band is observed. The negative parity states ($\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{system}$) break up into two substructures based upon the lowest $\text{I = j =}\text{11}\text{2}\text{and the}\text{I = j ? 1 =}\text{9}\text{2}$ states. In addition to the $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ system, a new positive parity structure is seen which is built on the $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{shell}$. The results are in qualitative agreement with the triaxial core model.     

Many-body theory for simultaneous photoionization and photoexcitation of helium

Brueckner-Goldstone many-body perturbation theory is applied to study the simultaneous photoionization and photoexcitation (SSP) of helium. The results are used to examine the validity and limitations of other approaches to the problem. The oscillator strengths ($\text{d}\text{?}\text{?}$) for the transition 1s²→(2s ?p)¹P and 1s²→(2p ?s)¹P are compared with the results of Brown. The cross section for SPP at the photoexcitation threshold (65.399 eV) is found to be in agreement with the experimental result of Samson.     

Totally polarized electrons from photoionization of outer p12 subshells of rare gases: a relativistic random phase approximation calculation

Photoelectrons ejected from the outer $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ subshells of the rare gases Ar, Kr, and Xe are shown to be totally polarized at certain energies in the vacuum ultraviolet region of the spectrum. These photoelectrons may provide a favorable source of polarized electrons.     

A direct comparison between gas-phase and solid-state Hg 5d photoionization processes

We present an experimental study of the Hg 5d spin-orbit intensity branching ratio in the photon energy range 18–100 eV. The results obtained on cleaved α-HgS exhibit strong differences with respect to the recent gas-phase data by Shannon and Codling. This is the first time that $\text{experimental}$ results on gas-phase photoionization and $\text{experimental}$ results on solid-state photoionization of the same core levels are directly compared to each other. The evidence we provide for solid-state effects in the photoionization process is, therefore, independent of any particular theoretical interpretation of the data.     

Observation of particle alignment in the octupole band of 172Yb

Members of the octupole band up to spin 14^? have been identified with the ${}^{170}\text{Er}\text{(α,2}\text{n}\text{)}{}^{172}\text{Yb}$ reaction. The band is strongly perturbed by Coriolis effects and has a high moment of inertia with variations characteristic of particle alignment. Vabrational alignment is insufficient to explain the data.     

The effect of oxygen on the sputtering of metastable atoms and ions from Ba metal

By means of the Doppler-Shift-Laser-Fluorescence technique we have measured the effect of oxygen coverage on the velocity distributions and relative yields of sputtered Ba atoms and ions in both the ground and metastable excited states. Our measurements show no evidence that the excitation probabilities are correlated with the magnitude of the electric-dipole-moment matrix element to the ground state. We also find that the excitation probability of the Ba(¹ D) state from a clean metal surface depends strongly on the emission velocity υ and approaches the functional form exp$\text{(}\text{?A}\text{av}\text{)}$ at higher velocities.     

Negative ion calculations based on many-body theory

We apply many-body theory techniques, particularly the Dyson equation, to interactions of an electron with an atom having filled subshells. This method is a unified treatment of different but related problems; electron scattering, negative ions, and photoionization of negative ions. We present calculated results for these problems: the systems electron + He(³S), Pd, Ca, Sr, and Ba, scattering phases, electron binding energy, wave functions, and photoemission.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 86–96, August, 1990.     

keV Neutron capture cross sections of 134Ba and 136Ba

The neutron capture cross sections of ¹³⁴Ba and ¹³⁶Ba have been measured in the energy region 3 to ¹⁰⁰keV. The following average quantities were deduced from the extracted resonance parameters: 〈D〉 = 127±10eV, 10⁴S₀ = 0.85±0.3, 10⁴S₁ = 0.8, 〈Γ_γ〉 = 120±20 meV for ¹³⁴Ba. Analysis of the ¹³⁶Ba data gave 〈Γ_γ〉 = 125±30meV for s-wave neutrons. The average 30 keV capture cross sections for these two s-process nuclei were found to be $\text{225±35}\text{mb}\text{for}{}^{134}\text{Ba and}\text{61±10}\text{mb}\text{for}{}^{136}\text{Ba}$.     

The systematics of h112 proton alignment in 157, 158, 159Er

Rotational bands have been observed in ^{157, 158, 159}Er to very high spin ($\text{J ～ 41}\text{h}\text{?}$). Upbends are found, due to the alignment of two h_{$\text{11}\text{2}$} protons at $\text{0.40 ?}\text{h}\text{?}\text{ω ? 0.46}\text{MeV}$ in all bands. A systematic shift with neutron number of the band-crossing frequency is observed and is related to a change in quadrupole deformation ?₂.     

Neutron and proton alignment at high spin in 168W

Excited states in the neutron-deficient nucleus ¹⁶⁸W, populated in the ¹⁴⁸Sm(²⁴Mg, 4n)¹⁶⁸W reaction, have been studied using γ-ray spectroscopy. The yrast band, which is identified up to about spin 28, shows a very strong backbend at low frequency, $\text{h}\text{?}\text{ω}{}_{\mathrm{c}}\text{= 0.235}\text{MeV}$, attributed to the $\text{(i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}\text{)}{}^2$ neutron alignment. Evidence for a second backbend is also observed. A strongly populated odd-spin (probably negative-parity) sideband is also identified to the spin, and shows several band-crossing anomalies. The characterisation of the anomalies is made by comparison with CSM calculations. Proton and neutron alignments are probably present in the sideband, and the second backbend in the yrast sequence may be due to alignment of $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ protons.     

High resolution spectroscopy using photodeflection

Isotope separation by laser deflection of an atomic beam, combined with simultaneous mass spectroscopy, has been used to determine optical frequency shifts and to assign mass numbers to all components of the $\text{Ba 6s}{}^2{}^1\text{S}{}_0\text{?6s6p}{}^1\text{P}{}_1$ 5536 Å resonance. Several components which cannot be resolved optically without the use of enriched samples, were resolved with the technique described. They are ${}^{135}\text{Ba}\text{(F=}\text{5}\text{2}\text{)}$ at 120 MHz, ¹³⁶Ba at 128 MHz and ¹³⁴Ba at 138 MHz.     

Influence of protons on backbending

Backbending in (at least the first half of) the rare earth nuclei seems to be determined by the alignment of an $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron pair. This is supported by the disappearance of backbending due to the blocking of an $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ level by an odd neutron for example in ¹⁶⁵Yb. Contrary to expectations backbending disappears also by adding an odd $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$,proton to ₇₀¹⁶⁶Yb in ₇₁¹⁶⁷Lu for this state (but is present if the odd proton is in the $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ level). A theory is presented which explains the odd neutron and the odd proton nuclei. It turns out that the odd proton in ¹⁶⁷Lu serves only as a type of catalyst for the alignment of an $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron pair. The odd proton changes the deformation and moves the Fermi surface nearer ($\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$) or farther away ($\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$) from the nearest $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron level. In one case one finds backbending and in the other case no backbending in ¹⁶⁷Lu.