On invariant states and the commutant of a group of quasi-free automorphisms of the car algebra

We study primary states of the CAR algebra which are left invariant under quasi-free automorphisms α_U corresponding to unitaries U of a von Neumann algebra $\text{M}$ on the one-particle Hilbert space, and show that they are quasi-free states ?_A corresponding to self-adjoint operators A in $\text{M}$′ with 0 ? A ? 1, under the assumption that $\text{M}$ does not contain any finite type Ifactor direct summands. Next we study automorphisms of the CAR algebra which commute with α_U for U in a von Neumann algebra $\text{M}$ and show that they are quasi-free automorphisms α_U with U in $\text{M}$′ under the same assumption on $\text{M}$ as above. Finally by using the latter result we obtain a generalization of a theorem of Hugenholtz and Kadison [3].     

The photoelectron angular distributions of HBr and HI AT hν = 21.2 eV

Photoelectron angular distributions for the ²Π_{$\text{3}\text{2}$, $\text{1}\text{2}$}(pπ)^?1 and ²Σ_{$\text{1}\text{2}$}⁺(pσ)^?1 ionic states of HBr and HI have been measured at a photon energy of 21.2 eV. The asymmetry parameters for the highly localized pπ orbitals closely follow those of the “lone-pair” orbitals of the related CH₃X molecules and the outer np atomic orbitals of the corresponding united atoms. Furthermore, the asymmetry parameters for the ²Π_{$\text{3}\text{2}$} and ²Π_{$\text{1}\text{2}$} states were found to be equal within experimental uncertainty, despite the large spin—orbit splittings of these heavy molecules. The asymmetry parameters for the ²Σ⁺(pσ)^?1 ionic states are significantly smaller than for the ²Π(pπ)^?1 states, in contrast to recent predictions based on angular momentum transfer theory.     

Analyzing powers for the (p, α) reactions on 58, 60, 62Ni at Ep = 22 MeV

Measurements of both the analyzing power and cross section were made for the (p, α) reactions on ^58,60,62Ni at an incident energy of 22 MeV. Data were taken for the strongly populated proton-hole states (0f_{$\text{7}\text{2}$}, 1s_{$\text{1}\text{2}$} and 0d_{$\text{3}\text{2}$}) in the residual cobalt isotopes and for 8 weakly populated low-lying states in ⁵⁵Co and ⁵⁹Co. Angular distributions were taken between θ_lab = 10° and 140° for the ground state and θ_lab = 10° and 80° for the excited states. Both the cross sections and analyzing powers exhibit a similar angular distribution for states having the same J^π values except in the transition to the $\text{3}\text{2}$^? state in ⁵⁹Co at 1.099 MeV. Using the observed J-dependence of the analyzing power, the unknown J^π values for the states at 2.982 MeV in ⁵⁵Co and 3.090 MeV in ⁵⁹Co are assigned to be $\text{9}\text{2}$^?. The shapes of the differential cross sections were well reproduced by the zero-range DWBA calculations using a triton-cluster form factor. However, all the measured analyzing powers could not be reproduced within the framework of such a simple DWBA calculation.     

Energy levels in 142Nd

The excited states of ¹⁴²Nd were studied by means of the decay of 40 sec ¹⁴²Pm and the ¹⁴²Nd(p, p') reaction via isobaric analog resonances. Approximately sixty levels of ¹⁴²Nd were observed below 5.3 MeV excitation, including several neutron particle-hole states excited strongly in (p, p') at f_{$\text{7}\text{2}$}, p_{$\text{3}\text{2}$}, p_{$\text{1}\text{2}$} and f_{$\text{5}\text{2}$} analog resonances. We have collected together all known energy levels in ¹⁴²Nd and have proposed J^π assignments for 22 excited states. We have also compared the experimental level spectrum (positive-parity states only) with a calculated one based on the shell model.     

Energies of the n2S12 and n2D32,52 states of Cs

Using the technique of Doppler-free two-photon spectroscopy the energies of the n²S_{$\text{1}\text{2}$} (12 ? n ? 35) and n²D_{$\text{3}\text{2}$,$\text{5}\text{2}$} (11 ? n ? 48) states of CsI have been measured with a thermionic detector. The absorption spectrum of molecular iodine was used as a reference giving us a total estimated accuracy of about 2 × 10^-7. Taking also into account the energies of the 7–11 ²S_{$\text{1}\text{2}$} and 5 and 6 ²D_{$\text{3}\text{2}$,$\text{5}\text{2}$} states measured by other authors and using an extended Ritz-formula we found the ionization limit to be E_i = 31406.468 ± 0.006 cm^-1.     

Properties of pp annihilations into strange particles at 702 and 757 MeV/c

$\text{p}\text{p}$ annihilations, leading to the production of at least one neutral K meson in the final state, have been studied in the incident momentum region of 700–760 MeV/c. Topological cross sections and cross sections for the various exclusive final states are presented. Detailed analyses of the different final states have been carried out to study the importance of resonance production and of quasi two-body and quasi three-body processes. A detailed study of the $\text{K}\text{K}\text{π}$ system in the four-body final states shows that the F₁ meson is a spurious effect due to systematic biases. In the momentum range investigated, the C = +1 final states are strongly suppressed.     

Polarization spectroscopy of ICl: The D′, a and a′ states

Three previously-unanalyzed states of ICl are reported, an ion-pair state D′(Ω =2) which converges to the limit I⁺(P₂+ Cl^-(S_o), and two shallow states a(Ω = 1) and a′(Ω = 0⁺) both of which converge to the ground states of separated atoms I(P_{$\text{3}\text{2}$}) + Cl(P_{$\text{3}\text{2}$}). The a(0⁺) state is responsible for the well-known interruption of the B(0⁺) state above υ_B = 3. Spectroscopic constants are given for the D′ and a′ states.     

Resonance photoelectron spectroscopy from autoionization states of CH3I

Resonance photoelectron spectra of methyl iodide have been taken by exciting individual autoionizing Rydberg states, and measuring the ejected electron energies by a time of flight technique. A number of spectra were obtained from autoionization states which are members of two series, converging respectively to the ²E_{$\text{1}\text{2}$} (ν = 0) and ²E_{$\text{1}\text{2}$} (ν₂ =1) states of the ion. In addition to observing vibrational bands not previously reported, we found that the peak intensities are consistent with Bardsley's formulation of the configuration interaction theory of autoionization.     

KMS condition in a Schrödinger picture of the dynamics

Given the C¹-algebra $\text{A}$ of observables, the KMS condition is formulated in terms of the time evolution α¹_t of a set $\text{S}$₀ ? $\text{S}$($\text{A}$) of “physical” states subject to certain natural conditions. α¹_t need not be defined by an automorphism group of $\text{A}$. It is shown that, for a KMS state ω, α¹_t induces a 1-automorphism α^ω_t of the von Neumann algebra π_ω($\text{A}$)″ generated by the representation π_ω belonging to ω.     

The microwave spectrum of the SiCl radical

The microwave spectrum of ²⁸Si³⁵Cl, the most abundant isotopic species of the silicon monochloride radical, was observed in both the ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ spin states of the ground vibronic state. The SiCl radical was produced in a flow cell by a dc discharge in SiCl₄. The observed transitions were $\text{J =}\text{7}\text{2}\text{←}\text{5}\text{2}\text{up to}\text{21}\text{2}\text{←}\text{19}\text{2}$ for both the spin states, and the observed frequencies were subjected to the least-squares analysis to yield accurate molecular constants as follows: B₀ = 7652.3048(23), D₀ = 0.007017(14), A_J = ?0.8392(16), p₀ + 2q₀ = 138.660(98), q₀ = 0.20(17), $\text{a + (b + c)}\text{2}\text{= 37.50(28)}$, $\text{a ? (b + c)}\text{2}\text{= 49.84(73)}$, b = 9(12), d = 46.40(94), and eQq₁ = ?23.13(96), all in MHz with 3σ in parentheses. The positive sign of the Λ-doubling constant, p₀, indicates that the contributions of ²Σ^? states dominate over those of ²Σ⁺ states. The spin and orbital averages of the unpaired-electron distribution were calculated from the observed hyperfine coupling constants and were discussed in terms of the electronic structure of the molecule.     

A new charge-correction method in X-ray photoelectron spectroscopy

The 2p_{$\text{3}\text{2}$} binding energy (242.3 eV) of Ar implanted in insulating materials is available to correct for charging shifts. Argon ions hav materials SiO₂ and soda glass. In each case the charging shift for Ar 2p_{$\text{3}\text{2}$} electrons agrees exactly with those for core-level elec The charge-corrected binding energies of the insulating materials permit the identification of atomic chemical states. Ion-induced reduction of the ins investigations.     

Relaxation of the 4G92 state of Nd3+ in LaCl3 and Nd3+ in La(Cl99.6Br0.4)3

The decay of the ⁴G_{$\text{9}\text{2}$} state of Nd³⁺ in LaCl₃ and La(Cl_99.6 Br_0.4)₃ was measured after pulsed laser excitation as a function of temperature. The decay rate is shown to depend besides the radiative transition on single-phonon relaxation between the states ⁴G_{$\text{9}\text{2}$} ($\text{μ =}\text{1}\text{2}$) and ⁴G_{$\text{9}\text{2}$} ($\text{μ =}\text{3}\text{2}$) and on multiphonon orbit-lattice relaxation from ⁴G_{$\text{9}\text{2}$} to ²G_{$\text{9}\text{2}$}. Partial substitution of Cl by Br only alters the radiative lifetime.     

The reaction 55Mn(d, t)54Mn

Neutron pick-up cross sections and vector analyzing powers have been measured for the reaction ⁵⁵Mn($\text{d}$, t)⁵⁴Mn at 17 MeV. The mixture of $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ to $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ transfer to the low-lying l_n = 1 states has been found. Evidence of the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ hole nature of several strong l_n = 3 states above 1 MeV has been obtained.     

Shallow acceptor bound exciton and free exciton states in high-purity zinc telluride

We investigated excitons bound to shallow acceptors in high-purity ZnTe and measured excitation spectra of two-hole luminescence lines at 1.6 K using a tunable dye-laser. The electron-hole coupling in the bound exciton (BE) states appears to be very different for the various acceptors even for almost identical exciton localisation energies. Three different types of BE are reported. For the Li-acceptor BE we observe three sub-components separated by 0.22 and 0.17 meV and interpreted as J = $\text{1}\text{2}$, $\text{3}\text{2}$, $\text{5}\text{2}$ states. The Ag-acceptor BE exhibits a strong ground state and a weak excited state at 1.3 meV higher energy. For the as yet unidentified k-acceptor we observe a single BE level, degenerate with the Ag-acceptor BE ground state. Dips in the excitation spectra due to absorption into free exciton 1S, 2S, and 3S states yield an exciton Rydberg R₀ = 12.8±0.3 meV and a free exciton binding energy FE(1S) = 13.2±0.3 meV.     

Experimental transition probabilities of some Xe(I) lines

Using the light absorption technique in a ¹³²Xe afterglow plasma, we have measured the relative transition probabilities for several xenon lines which have the metastable 6s[$\text{3}\text{2}$]₂ or the resonant 6s[$\text{3}\text{2}$]₁ states as their lowest transition level. Because the transition probabilities of the 8819 Å (6p[$\text{5}\text{2}$]₃ ? 6s[$\text{3}\text{2}$]²) and 8280 Å (6p[$\text{1}\text{2}$]₀ ? 6s[$\text{3}\text{2}$]₁) lines are relatively well known, we have chosen these as reference lines and have thus been able to determine the absolute values of the transition probabilities for 19 xenon lines corresponding to transitions from 6p, 6p′, 7p, 8p, 9p, 4f and 5f to 6s[$\text{3}\text{2}$]₂, and for four lines corresponding to the transitions 6p?6s[$\text{3}\text{2}$]₁.     

High-spin states in 24Mg and upper limits for particle spectroscopy of high spins by heavy-ion compound reactions

High-spin states in ²⁴Mg have been investigated by the reaction ¹⁰B(¹⁶O, d)²⁴Mg up to $\text{E}{}^1\text{≈ 24}\text{MeV}$. High-spin states with $\text{I ≧ 9}$ have been identified at $\text{E}{}^1\text{= 19.20, 20.26, 20.8, 21.6, 23.1,}\text{and}\text{23.5}\text{MeV}$. The 10⁺ yrast state in ²⁴Mg is probably located at 20.26 MeV. The upper limits with respect to spin and excitation energy of the applicability of heavy-ion compound reactions for particle spectroscopy of high-spin states are discussed. The main limitations result from the increasing continuum and from a decrease of the high-spin selectivity when the final spins approach the critical angular momentum for compound-nucleus formation. It will be shown that the difficulty in the analysis of the experiments arising from the decreasing probability of finding isolated yrast states at high excitation energies, i.e. from the increasing level density, can be overcome in such experiments. The decrease in the high-spin selectivity of the total cross section is compensated for spins up to J_max by the fact that the shape of the angular distributions depends on the final spin for states with I ～ J_max. This is caused by the decreasing alignment of the final nucleus with decreasing values of |I ? J_max| and can be used for high-spin spectroscopy.