High-spin rotational bands and pairing reduction in 166Hf

Rotational properties of the ¹⁶⁶Hf nucleus have been studied by in-beam spectroscopic methods using the ¹⁵⁰Sm(²⁰Ne, 4n)¹⁶⁶Hf reaction. The ground band was observed up to the I^π = 18⁺ level, the s-band from the I^π = 12⁺ up to I^π = 22⁺ level; in addition two side bands were found. The results are interpreted in terms of the pairing-self-consistent Hartree-Fock-Bogolyubov cranking model. Quantitative agreement between theory and experiment is obtained for the crossing of the ground band and s-band. The calculations predict a reduction of about 50 % in the neutron pairing energy gap of yrast states in the crossing region. The kinematical ($\text{I}$⁽¹⁾) and dynamical ($\text{I}$⁽²⁾) moments of inertia are analysed.     

Evidence for band termination in118Xe

The yrast band of¹¹⁸Xe has been extended up to tentativelyI ^π = 34⁺ in a heavy-ion in-beam γ-spectroscopic study using the NORDBALL detector array. A band crossing is observed at the highest spins and interpreted within the Modified Oscillator Model as a transition to a terminating band.     

Recoil distance lifetime measurements in82Kr

The lifetimes τ=124±12, 6 _?2 ⁺⁴ and 380±100 ps of theE _x (I ^π )=3.46(8⁺), 2.92(6⁺) and 3.04(6^?) MeV states, respectively, populated by the reaction⁷⁶Ge(¹²C,α2n) were measured with the recoil distance method. In addition upper lifetime limits were obtained for nine states. The measured lifetimes and energies indicate a band crossing at aboutI ^π =8⁺, probably arising from the alignment of twog _9/2 neutrons. For the 3.04 MeV 6^? state as a second member of a band built on the 2.65 MeV 4^? state the measured lifetime points to a two-quasiparticle configuration. The positive-parity states have been discussed in the frame of the interacting boson approximation, nuclear field theory and the cranked shell model.     

High-spin states in 218Ra

Yrast states in ²¹⁸Ra up to spin and parity I^π = 17^? were identifíed by means of the ²⁰⁸Pb(¹³C, 3n) reaction and standard γ-ray spectroscopic techniques. The level scheme is characterized by two bands of opposite parity with nearly constant level spacing. A cascade of strong E1 interband transitions connects both bands.The results are discussed within the systematics of the even Ra isotopes. The negative-parity band which is observed from the I^π = 5^? to the I^π = 17^? state, is interpreted as an octupole vibrational band. The level scheme can be well reproduced in the vibrational limit of the interacting boson approximation (IBA1) which fails, however, to explain the strong E1 feeding of the negative-parity band from the ground-state band     

Magnetic rotation — past,present and future

Magnetic-dipole rotational (MR) bands were discovered about 15 years ago without any theoretical prediction in contrast to the super-deformed (SD) bands which were predicted long ago. First identification of a quasirotational structure as MR band occurred around 1992 although Kr isotopes probably have the first set of data having the signatures of MR bands as shown by us. Our first compilation of MR bands listed 120 MR bands in 56 nuclides which have now grown to more than 180 bands in 80 nuclides. We have observed new MR bands in the A = 130 mass region in ¹³⁷Pr, ¹³⁹Nd and ¹³⁵Ba nuclei. This led to the observation of the smallest MR bands in ¹³⁷Pr, multiple minima in the γ deformation in ¹³⁵Ba, coexistence of band structure based on these minima and band crossing of MR bands in A = 130 region. Some of these results have been reviewed in this paper along with theoretical calculations. There are still a number of questions related to MR bands which have not been fully resolved. The role of neutrons/protons in magnetic rotation still needs to be delineated. Do the MR bands follow the I(I + 1) behaviour? Are these structures as regular as normal rotational bands? How important is the existence of deformation for MR bands? We address some of these questions in this paper.     

Comments on the measurements of vibrational intensity in the photoelectron spectra of N2 and CO,for the ionic ground state

Over 50 experimental values of the photoelectron intensity I(v′ = 1) (normalized to I(v′ = 0) equal to 100) for the N₂⁺, X²Σ_g⁺ photoelectron band, as well as 17 values of I(v′ = 1) for CO⁺, X²Σ⁺, are gathered or calculated from literature data, compared and discussed. Differences in the types of analyzer used, the instrumental conditions, the character of the UV light employed and the type of possible intensity corrections make such a comparison difficult, leave unexplained discrepancies and show the necessity of more systematic experimental investigations.     

Search for missing predicted high-spin states in28Si

New shell model calculations have predicted several high-spin (I ^π=5⁺ and 6⁺) levels in²⁸Si near 10 MeV excitation energy which are missing from or ambiguous in existing experimental studies. Angular distributions, linear polarizations and Doppler-shifts ofγ-rays have been measured for theγ-decay of theE _p=1,911 and 2,073 KeV resonances of the²⁷Al(p, γ) reaction in an attempt to discover these missing states or confirm the discrepancies between experiment and theory. The excitation energies and spin-parities of the resonances were determined as 13,424.4±0.2 keV,I ^π=5⁺ and 13,582.3±0.5 keV,I ^π=6⁺. States populated in theγ-decay of these resonances were assigned spins and parities as follows: 11,777 keV,I ^π=5⁺; 11,331 keV,I ^π=6⁺; 10,417 keV,I ^π=5⁺; 9,417 keV,I ^π=4⁺ and 8,945 keV,I ^π=5⁺. On the basis ofγ-ray transition rates T=1 is assigned to the 13,424 keV level and T=0 to the 10,417 and 11,777 keV levels. With the new data excellent agreement is achieved between the experimental spectrum of²⁸Si and the new shell model predictions. These data provide evidence for aK ^π=3⁺ rotational band comprised by the 6,276, 6,889, 8,945 and 11,331 keV levels. This band emerges also from the shell model wave functions as do theK ^π=0⁺ bands based on the ground state and the 6,691 keV state.     

A study of branching ratios of cross sections in the charge symmetric reactions10B(d,p)11B and10B(d,n)11C

High-spin states in¹⁵⁶Er have been populated using the (α, 8n) and (¹⁶O, 4n) reactions. In the ground state band a strong backbending effect was observed atI ^π=12⁺. Four states of a secondK=0 band with spins 9, 11, 13 and 15 were found. This second band depopulates completely into the 8⁺ and 10⁺ members of the ground state band. This is explained by the fact that the upper states of this second band are yrast states and that this band crosses the (gsb)-line atI ?11.     

Investigation of the ground state rotational bands in233U and239Pu in the (α, 3n) reactions

The ground state rotational bands in²³³U and²³⁹Pu were investigated in (α, 3n) reactions. Conversion electrons were measured with an iron free orange spectrometer in order to suppress the background from fission. Levels up toI ^π=33/2⁺ of theK=5/2 band in²³³U andI ^π=31/2⁺ of theK=1/2 band in²³⁹Pu were identified ine ^?γ coincidence measurements. The level energies of both rotational bands can be well described up to the highest observed spins by a two-parameter angular velocity expansion. The electromagnetic properties of theK=1/2 band in²³⁹Pu are discussed.     

Loss of alignment gain in the πh 9/2[541 1/2−] ⊗ (νi 13/2)2 band in 167Tm and neighbouring odd-Z N = 98 nuclei

Theπh_9/2[541 1/2^?] band in ¹⁶⁷Tm has been studied through the ¹²⁴Sn(⁴⁸Ca, p4n)¹⁶⁷Tm reaction at E _beam = 210 MeV. The favoured signature of the πh_9/2[541 1/2^?] band is observed to spin 61/2h?. A remarkable small gain in aligned angular momentum at the AB-band crossing has been found. The crossing frequency and the gain in aligned angular momentum for ¹⁶⁷Tm are compared with data for the N = 98 isotones of Lu, Ta and Re, and contrasted with Cranked Shell Model predictions, based on frequency diabatic configurations. Large deviations are found for the gain in aligned angular momentum.     

On the coexistence of oblate and prolate deformed bands in83Zr

Deformation parameters of the positive parity yrast band and negative parity bands in⁸³Zr are deduced from lifetimes andE2/M1 mixing ratios. Lifetimes of high spin states have been determined from recoil distance Doppler shift and Doppler shift attenuation measurements using the⁵⁴Fe(³²S,2pnγ) ⁸³Zr reaction. Ten lifetimes and five lifetimes limits were determined. The positive parity band, built on theg _9/2 K=5/2 orbital has an average deformation ¦β ₂¦=0.28(2), and shows a reduction ofE2 transition strengths in the observed backbend region at I^π≈21/2⁺. In contrast, theE2 strengths in the negative parity states show a steady increase up to I^π≈=15/2^?. These states are more strongly deformed than the positive parity states (¦β ₂¦=0.33(3)). TheE2/M1 mixing ratios show that the negative parity band hasK=3/2 and is prolate, and favour oblate deformation for the positive parity yrast band. In theK=1/2^? band theE2 strength of the 7/2^?→3/2^? transition yields a deformation ¦β ₂¦=0.26(5). The band structure is compared with calculations within the Hartree-Fock Bogoliubov cranking model.     

Exciton molecule in semiconductors by phonon-assisted two-photon absorption

Direct creation of bi-excitonic states by photon-assisted two-photon absorption in indirect-gap semiconductors is investigated theoretically. The symmetry of the indirect bi-exciton states and of the phonon used are given for the case of Ge. A numerical application to the case of Si shows that the indirect two-photon absorption coefficient for bi-excitonic α²_I (bi-ex) transitions is several orders of magnitude larger than both indirect two-photon interband, α²_I (band), and excitonic, α²_I (exc), transitions. It becomes smaller than both indirect one-photon interband, α¹_I (band), and excitonic, α¹_I (exc), transitions for available laser intensities. The essential contribution to this enhancement of α²_I (bi-ex) is found to be from the resonance effect in the first process and from both the resonance effect and matrix elements included in the second process.     

Level structure of 184W from the 183W(n, γ) reaction

The level structure of ¹⁸⁴W has been studied from the prompt γ-rays emitted following the capture of both thermal and 2 keV neutrons by ¹⁸³W. Energies and intensities were measured for both the primary and the secondary (low-energy) prompt γ-rays. From these data, a level scheme is proposed for ¹⁸⁴W in which all the I^π = 0⁺, 1⁺ and 2⁺ states below ≈ 2.0 MeV are observed. Where possible, rotational-band assignments have been made to these and other levels. Additional evidence is presented which confirms the 1130 keV state as being the band head of a K^π = 2^? octupole vibrational band. Admixed K^π = 0⁺ and 2⁺ bands are established at 1322 and 1386 keV, respectively, with the I^π = 2⁺ states (at 1431 and 1386 keV) having a mutual admixture of ≈ 12%. In the energy region above 1.5 MeV, the following bands and band-head energies are identified: K^π = 1⁺, 1613 keV; K^π = 0⁺, 1614 keV; K^π = 1⁺, 1713 keV; K^π = 2⁺, 1877 keV. The neutron binding energy in ¹⁸⁴W has been determined to be 7411.1±0.6 keV. The band structure of the 1613 keV (1⁺) and 1614 keV (0⁺) bands is observed to be strongly distorted, the observed $\text{A (}\text{h}\text{?}{}^2\text{/2}\text{I}\text{)}$ values being ≈ 3.6 keV and ≈ 32 keV, respectively. This strong distortion is shown to be explainable in terms of Coriolis coupling of reasonable strength between the two bands. A similar explanation is shown to account for the somewhat less anomalous A-values (22.8 keV and 14.0 keV, respectively) of the 2⁺ band at 1386 keV and the 3⁺ band at 1425 keV. The results of a phenomenological fiveband-mixing analysis involving the K^π = 0⁺ and 2⁺ bands below ≈ 1.5 MeV are presented and discussed. These calculations indicate, among other things, that the direct E2 matrix element connecting the 1322 keV, K^π = 0⁺ band and the ground-state band is quite small, possibly zero. They also indicate that a nonzero E2 matrix element exists between this excited K^π = 0⁺ band and the γ-vibrational band and that the magnitude of this element is comparable with that between the γ-vibrational and ground-state bands. Arguments favoring and apparently refuting the interpretation of the 1322 keV, 0⁺ band as a “two-phonon γ-vibration” are presented.     

Investigation of 228Th in the (α, α'2n) reaction

The ²³⁰Th(α, α'2n)²²⁸Th reaction at E_α = 56 MeV was used to investigate states of moderately high spin in ²²⁸Th. Conversion electron and e^?-γ coincidence measurements were carried out, where the electrons were detected with an iron-free orange spectrometer. The ground state and low-lying K^π = 0^? rotational bands were observed up to I^π = 14⁺ and 13^?, respectively. The data are interpreted in terms of an ω-expansion for the ground-state rotational band, and an octupole vibrational band distorted by the Coriolis coupling to the K^π ? 1^? excitations for the K^π = 0^? band.     

High-spin states of 26Mg populated in the 12C(18O, α) reaction

The structure of ²⁶Mg has been investigated by means of the ¹²C(¹⁸O, α) reaction. Several previously unknown states were populated between excitation energies of 0 to 16 MeV. Excitation functions were measured for 126 states for bombarding energies between 43.2 and 45.9 MeV in 300 keV steps at a lab angle of 7°. The experimental energy averaged differential cross sections were compared with statistical model calculations and good agreement was obtained for the states whose spins and parities were previously established. The statistical model calculations were used to suggest the spins and parities for the rest of the states. In particular, candidates for 6⁺ and 8⁺ states were interpreted as members of three rotational bands in ²⁶Mg: the ground-state band, the K = 2⁺ band based on the 2.938 MeV 2⁺ state, and a K = 0⁺ band based on the 3.588 MeV 0⁺ state. Back bending of the yrast band is observed and it is suggested that it may be due to band crossing of the ground-state and first excited K = 0⁺ bands.     

High-spin yrast and non-yrast bands in 176Os, 178Os and 180Os

High-spin yrast and non-yrast states have been identified in ¹⁷⁶Os, ¹⁷⁸Os and ¹⁸⁰Os using (¹⁶O, xn) reactions, and γ-ray techniques. Band crossing anomalies are observed in each of the positive-parity yrast bands. The magnitude of these anomalies decreases with decreasing neutron number, an effect attributed to the change in the moment of inertia of the ground state rotational bands. A 23 ns isomer, predominantly K^π = 7^?, is identified at 1930 keV in ¹⁸⁰Os. The configuration of this isomer is discussed on the basis of the properties of its rotational band. Negative parity, odd and even spin, sideband sequences are observed in each isotope. Their relationship to rotation-aligned octupole and 2-quasiparticle bands is discussed from their excitation energies, band spacings, and decay properties. Detailed calculations for Coriolis mixed bands are carried out for the likely 2-quasiproton and 2-quasineutron configurations. An anomaly observed at spin 17 in the odd-spin negative-parity sequence in ¹⁸⁰Os is attributed to a band crossing with a fourquasiparticle configuration.     

Study of Three-Quasiparticle Band in 83 Kr

Excited states of ⁸³Kr, populated in the ⁷⁶Ge(¹¹B, 3npγ) reaction at a beam energy of 50 MeV, have been studied. The ΔI?=?1 band, built upon the 2,510.0 keV state, has been observed up to 5,639.4 keV with spin (27/2^???). Mean lifetimes have been measured up to spin 23/2^?? in ΔI?=?1 band using the Doppler shift attenuation method. The B(M1) rates derived from the measured lifetimes decrease smoothly with spin indicating that the angular momentum belonging to this band are generated by the shears mechanism.     

High-spin states in 232U investigated with the 232Th(α, 4nγ) reaction

The ground-state rotational band of ²³²U is established up to I^π = 16⁺ (tentatively 18⁺) through a study of the ²³²Th(α, 4nγ) reaction. Conversion electron spectroscopy is found to be especially useful in circumventing the difficulties caused by strong fission competition.     

On the nature of the superband in156Dy

Superbands, responsible for the backbending in¹⁵⁶Dy and other N=90 and N=88 nuclei, are proposed to be alignedn(i_13/2)² bands, whereas it is argued that the recently discovered positive parity band in¹⁵⁶Dy withI ^π= (2⁺) up to 10⁺ members does not constitute the low spin extension of the superband.     

Bandcrossing inK≠0 bands

It is shown that in the crossing of two bands withK≠0 in deformed nuclei, two new effects are observed that are not seen in the crossing ofK=0 bands; namely, a)I _critical at which the bands cross is lowered and b) Band crossing occurs at different values ofI _crit for oddI (orI+1/2 in oddA) and evenI (orI+1/2). These predictions are shown to be observed in the odd-A rare-earth nuclei where data are available to high spin.