Spin alignment in the particle-rotor and cranking models

It is shown that the cranking model normally gives a smaller rotation-aligned spin for an odd quasiparticle than the particle-rotor model, especially at low rotational frequencies. The basic reason is found to be that the rotational frequency vector of the cranking model is “sharp”. This is an unphysical model property, and in the presence of a particle whose rotational motion is partly decoupled from the rotational motion of the average field its consequences become serious. A “sharp” rotational frequency corresponds to a neglect of the recoil effect that establishes coherence between the motion of the decoupled nucleon and the other nucleons and therefore is a prerequisite for the conservation of angular momentum. In conclusion the cranking model cannot be invoked to explain the so-called “Coriolis attenuation”, relative to the particle-rotor model, that is observed experimentally. Particle-rotor calculations are carried out into the backbending region of some well-deformed rare-earth nuclei, and the results indicate that the “Coriolis attenuation” effect is weak or absent at high rotational frequencies. However, the experimental $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$, unfavoured band of ¹⁶⁷Yb is found to exhibit an anomalous “downbending” behaviour.     

Rotation-vibration analysis of the Coriolis-coupled ν5g, ν6g, ν8g and ν9 bands of H2CCO

Medium resolution infrared grating spectra of gaseous ketene, H₂CCO were recorded between 1000 and 400 cm^?1, both at instrument temperature (40°C) and with cooling (?40°C). Interferometric Fourier spectra were also measured at ?70°C with resolution 0.22 cm^?1 between 450 and 330 cm^?1. The K structure of the fundamentals ν₅, ν₆, ν₈, and ν₉ was assigned. These fundamentals are coupled by a-axis Coriolis interactions. These couplings were analysed on the symmetric top basis for setting up the perturbation matrix and by utilizing the K-dependent Coriolis shifts of levels. A preliminary analysis of the Coriolis intensity anomalies was also undertaken.Band center values from combination differences are $\text{ν}{}_5{}^0\text{= 587.30 (27)}$ and $\text{ν}{}_6{}^0\text{= 528.36 (39)}\text{cm}{}^{\mathrm{?1}}$. Synthetic spectra indicate the band origins of ν₈ and ν₉ to be close to 977.8 and 439.0 cm^?1, respectively. Estimates of Coriolis coupling constants obtained from synthetic spectra are $\text{ζ}{}_{58}{}^{\mathrm{a}}\text{= + 0.33 (5)}$, $\text{ζ}{}_{68}{}^{\mathrm{a}}\text{= + 0.714 (20)}$, $\text{ζ}{}_{59}{}^{\mathrm{a}}\text{= ? 0.774 (20)}$, and $\text{ζ}{}_{69}{}^{\mathrm{a}}\text{= ? 0.30 (2)}$. Approximate ratios of unperturbed vibrational transition moments obtained from spectral simulations are $\text{M}{}_8{}^0\text{:±iM}{}_5{}^0\text{:±iM}{}_6{}^0\text{:M}{}_9{}^0\text{≈ +2:?9:+10:+0.5}$.     

Rotational bands in the odd-odd 152Eu nucleus

The ¹⁵⁰Nd(⁷Li, 5n) reaction has been used to study the high-spin states in the odd-odd nucleus ¹⁵²Eu. Two rotational bands of different behaviour have been identified: a rather regular band based on the I^π = 8^? isomeric state of configuration $\text{[413}\text{5}\text{2}\text{]}{}_{\mathrm{<mtext>p</mtext>}}\text{[505}\text{11}\text{2}\text{]n}$ and a strongly decoupled system belonging to the configuration $\text{[}\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{]}{}_{\mathrm{<mtext>p</mtext>}}\text{[i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}\text{]}{}_{\mathrm{<mtext>n</mtext>}}$.It is shown in this work that the aligned angular momentum carried by each two-quasiparticle configuration in ¹⁵²Eu is the sum of the alignment of the odd neutron and odd proton, which indicates a negligible influence of the neutron-proton residual interaction. Particular attention has been focused on the strong deviations of the moment of inertia of the core when different quasiparticle configurations are involved.     

Jahn-Teller analysis of the 3T1(P) absorption band of Ni2+ in GaP

Comparison between experimental absorption due to the ${}^3\text{T}{}_1\text{(F)?}{}^3\text{T}{}_1\text{(P)}$ transition of substitutional Ni²⁺(d⁸) in GaP and theoretical predictions based on the Jahn-Teller model is presented. Numerical solution of the Hamiltonian, in which spin-orbit interaction and T₂-mode Jahn-Teller coupling are included, is in very good agreement with the energy position and intensities of the observed absorption lines.     

Functional derivative δTc/δα2 (Ω)F(Ω) for weak coupling superconductors

We present approximate analytic calculation of the functional derivative $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω)}$, where T_c is the superconducting critical temperature and $\text{α}{}^2\text{(Ω)F(Ω)}$ is the electron-phonon spectral function, within the “square-well model” for the phonon mediated electron-electron interaction and weak coupling limit $\text{ω}{}_{\mathrm{D}}\text{(2πT}{}_{\mathrm{c}}\text{)? 1 (ω}{}_{\mathrm{D}}$ is the Debye energy). It is found that $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω) = (1 + λ)}{}^{-1}\text{G(Ω)}$ where λ is the familiar electron-phonon coupling parameter and $\text{G(Ω)}$ is a universal function of the reduced frequency $\text{Ω}\text{=}\text{Ω}\text{T}{}_{\mathrm{c}}$. We compare this formula with accurate numerical results for several weak coupling superconductors. The overall agreement is good     

E2 core polarization for sd-shell single-particle states calculated with a skyrme-type interaction

We have studied the core-polarization effect on the 1s0d-shell single-particle electromagnetic quadrupole transitions due to coupling with the quadrupole giant resonances. The self-consistent Hartree-Fock + RPA method is applied for the calculations of the single-particle wave functions and the response functions of the giant resonances. The particle-vibration-coupling model is used to calculate the core-polarization effect in the vicinity of ¹⁶O and ⁴⁰Ca. The effective coupling hamiltonian is determined by the SGII Skyrme-type interaction which is used in the HF + RPA and particle-vibration-coupling calculation. The results are discussed for the proton and neutron effective charges and for the longitudinal and transverse form factor for the $\text{0}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{→ 1}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ pro single-particle transition in ³⁹K. Good agreement with recent longitudinal data for this transition is obtained.     

Nuclear reaction studies of 168Tm

The intrinsic structure of ¹⁶⁸Tm has been studied using the (³He, d) and (α, t) proton stripping reactions as well as the (d, t) and (³He, α) neutron pick-up reactions. The beams of 24 MeV ³He particles, 25 MeV α-particles and 12 MeV deuterons were obtained from the McMaster tandem Van de Graaff accelerator. The reaction products were analyzed with an Enge-type magnetic spectrograph and detected with photographic emulsions. The spectra have been interpreted in terms of the coupling of an odd proton and an odd neutron, each moving independently in a spheroidal potential, which gives rise to intrinsic two-quasiparticle states with $\text{K = ¦Ω}{}_1\text{±Ω}{}_2\text{¦}$. The identification of the intrinsic states was made by comparing the experimental cross-section patterns with those predicted with the aid of Coriolis coupling and distorted-wave Born approximation (DWBA) calculations. Rotational bands superimposed on the K^π = 3⁺ and $\text{K}{}^{\mathrm{\pi }}\text{= 4}{}^{\mathrm{+}}\text{, {}\text{7}\text{2}{}^{\mathrm{+}}\text{[633]}{}_{\mathrm{n}}\text{±}\text{1}\text{2}{}^{\mathrm{+}}\text{[411]}{}_{\mathrm{p}}\text{}}$ configurations, the first of which is the ground state, ha been observed in the spectra of all four reactions. New assignments have been made for configurations resulting from coupling the $\text{1}\text{2}$^? [541], $\text{7}\text{2}$⁺ [404], $\text{5}\text{4}$⁺ [402] and $\text{1}\text{2}$^? [530] p to the $\text{7}\text{2}$⁺ [633] neutron state. The neutron pick-up measurements confirmed the earlier assignments based on (d, t) reaction studies and suggested tentative assignments for the {$\text{1}\text{2}$⁺ [400]_n±$\text{1}\text{2}$⁺ [411]_p} and {$\text{3}\text{2}$⁺ [402]_n±$\text{1}\text{2}$⁺ [411]_p}     

On the Zeeman effect of 2Π states in diatomic molecules

The theory of the Zeeman effect in ²Π states of diatomic molecules is reconsidered. Second order terms due to the interaction with ²Δ states, which were left out in a previous investigation, are now included. The total correlation between the spin-rotation coupling constant and the centrifugal distortion in the spin-orbit coupling renders the fitted molecular g factors somewhat ambiguous. This problem is handled by a transformation of the basis for the Hamiltonian matrix. The theoretical results are exemplified for the ²Π ground state of OH for which EPR data are available for both the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ substates. A combination of ab initio predictions and fitted values of the g factors finally yields new information concerning the separate contributions from ²Σ⁺, ²Σ^?, and ²Δ states to the contamination of the ²Π ground state in OH.     

The h112 and g72 band structures in 131Ce and 129Ce

High-spin levels in ^{129, 131}Ce have been produced by the reactions ^{116, 118}Sn(¹⁶O, 3n) ^{129, 131}Ce and studied by in-beam γ-ray spectroscopic techniques. Two strongly populated band structures are observed. The odd-parity levels based on a $\text{9}\text{2}{}^{\mathrm{?}}$ state constitute a system explained in the triaxial-rotor-plus-particle model as the result of the coupling of an $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ neutron-hole to a prolate-type triaxial core. The even-parity band built on a $\text{7}\text{2}{}^{\mathrm{+}}$ state corresponds to collective excitations associated with a neutron-hole in the $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ shell. Backbending effect observed in the yrast cascade is discussed.     

Quadrupole moment of the 5−2, 134 keV state in 197Hg

The quadrupole interaction for the $\text{5}{}^{\mathrm{?}}\text{2}\text{, 134}\text{keV}$ state of ¹⁹⁷Hg in solid Hg was observed by the e^?-γ time differential perturbed angular correlation method. The quadrupole coupling constant ν_Q=126 (2) MHz is derived. By comparison with experimental quadrupole coupling constants for ¹⁹⁹Hg in Hg and HgCl₂ as well as for ²⁰¹Hg in HgCl₂ the quadrupole moment of the $\text{5}{}^{\mathrm{?}}\text{2}\text{, 134}\text{keV}$ state in ¹⁹⁷Hg is related to that of the ²⁰¹Hg ground state, which is known. The value $\text{Q(}{}^{197}\text{Hg}\text{,}\text{5}{}^{\mathrm{?}}\text{2}\text{, 134}\text{keV}\text{)=0.47(6)}\text{b}$ is deduced. This value is not in agreement with the assumption of a $\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ shell-model configuration for the 134 keV state. It is consistent with an interpretation of the $\text{5}{}^{\mathrm{?}}\text{2}$ level in terms of the core coupling model of de Shalit.     

The (p, 2p) reaction on 6Li

The differential cross section for the quasi-elastic scattering of protons on ⁶Li is derived in the impulse approximation. The nucleus ⁵He is not treated as a bound nucleus in the derivation. Instead, the n-α interactions $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, $\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ in the final state are included. Fits to the unknown vertex functions appearing in the expression obtained for the momentum distribution at the “ground state” of ⁵He are given, showing that the n-α $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ interaction is important at the “ground state” of ⁵He. The consistency between the observed momentum distribution and the ⁶Li form factor at low momentum transfers is shown utilizing Elton's model.     

Two- and three-quasiparticle states in the interacting boson model and a unified description of even- and odd- mass Hg isotopes

The formalism of the interacting boson-fermion approximation is extended to include two- and three-quasiparticle states. This model is used in a systematic study of the high-spin states in even- and odd-mass ^189–198Hg isotopes. The positive-parity states in these nuclei are described by coupling $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron states to an O(6) core, which offers a simple and parameter-free test of the boson-fermion interaction. Good agreement is obtained between the recent experimental results and the calculated energies, transition rates and g-factors.     

Angular momentum projection corrections to transition densities in rare-earth nuclei

To describe the rotational levels of even-even nuclei in the rare-earth region, states of definite angular momentum are projected from an axially symmetric intrinsic Hartree-Pock wave function calculated with a density-dependent effective interaction. An expansion is obtained in which the rotational model approximation to the transition density, $\text{ρ}{}_{\mathrm{L}}\text{(r) = ? Y}{}_{\mathrm{Lo}}\text{(Ω)ρ(r)}\text{d}\text{ω}$, is corrected to leading order in $\text{1}\text{〈J}{}_{\mathrm{y}}{}^2\text{〉}$. Evaluation of the projection corrections in ¹⁵⁶Gd, ¹⁶⁶Er and ¹⁷⁶Yb yields negligible changes in low multipoles and a cross section increase of up to 15% in 6⁺ transitions. This effect is much too small to resolve the discrepancy between density-dependent Hartree-Fock predictions and experiment in high multipoles.     

High-resolution infrared spectrum of the ν2 and ν8 bands of CH2D2

A high-resolution infrared spectrum of methane-d₂ has been measured in the C-D stretching band region (2025–2435 cm^?1). Rotational structures of the ν₂ and ν₈ bands have been assigned by use of the ASSIGN-diagram method, and the c-type Coriolis interaction between ν₂ and ν₈ has been analyzed. The band origins, ν₂ = 2203.22 ± 0.01 cm^?1 and ν₈ = 2234.70 ± 0.01 cm^?1, the rotational constants and the centrifugal distortion constants for the two bands, and the Coriolis coupling constant, $\text{∥;ξ}{}_{28}{}^{\mathrm{c}}\text{∥; = 0.182 ± 0.015}\text{cm}{}^{\mathrm{?1}}$, have been determined.     

Decay of 185Au: Sign of shape coexistence in 185Pt

The decay of ¹⁸⁵Au has been studied on-line with mass-separated sources from the ISOCELE facility. Precise conversion-electron measurements have been performed with a 180° magnetic spectrograph. The level scheme of ¹⁸⁵Pt has been established, and the $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 33}$ min isomeric state has been located at 103.2 keV with respect to the $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 71}$ min ground state. Two highly converted transitions have been observed. The level scheme is discussed in the framework of an “axial-rotor + quasiparticle” approach: numerous states are interpreted assuming a prolate shape of the nucleus. Ten levels with low spin and negative parity ($\text{I ?}\text{7}\text{2}{}^{\mathrm{?}}$) decay mainly to the $\text{1}\text{2}{}^{\mathrm{?}}\text{[521]}$ band via strong M1 transitions and are not expected from the calculations performed with the prolate cores. The possibility of shape coexistence is discussed.