E1-M2-E3 mixing of the 1241.7 keV transition in147Yb

The half-life of theI,K ^π=2, 2^? state at 1318 keV in¹⁷⁴Yb has been measured in the¹⁷³Yb(n, γ) reaction to be 0.486±0.015 ns. This half-life determines the absolute transition probabilities of the gamma-ray transitions to the ground state rotational band yielding the following hindrance factors relative to the Weisskopf estimate:F _W(M 2; 2, 2^?→0, 0⁺)=350;F _W(M2; 2, 2^?→2, 0⁺)≧77F _W(M 2;2, 2^?→4, 0⁺)>740;F _W(E 1; 2, 2^?→2, 0⁺)=4.5×10⁶;F _W(E 3; 2, 2^?→2, 0⁺)≈0.1;F _W(E 3; 2, 2^?→4, 0⁺)≈0.4. These data are compared to analogous transitions in neighboring nuclei.     

On the Lie-Trotter theorems inL p -spaces

In this paper we consider operatorsH ₀ andV possessing the following properties:

1. H ₀ is a positive self-adjoint operator acting inL ²(M, γ) with γ a probability measure, so that exp(?tH ₀) is a contraction onL ¹(M, γ) for eacht>0.
2. V is a semibounded multiplicative operator acting inL ²(M, γ) {fx379-1}

Under these assumptions theorems of Lie-Trotter type are derived for the operatorsH, H ₀, V, whereH is a self-adjoint extension of the algebraic sumH ₀+V, and is built by the form method. Under the additional assumption thatV(·)∈L ²(M, γ) we prove an essential self-adjointness ofH ₀+V. The results obtained are applicable to non-relativistic quantum mechanics.     

Quadrupole moment of the first excited state of 32S

The static quadrupole moment and B(E2; 0⁺ → 2⁺) value for the first excited state of ³²S were measured using the reorientation effect in Coulomb excitation of ³²S projectiles. Silicon surface barrier detectors were used to detect ³²S ions scattered from ²⁰⁸Pb at mean laboratory angles of 90° and 174°, for bombarding energies in the range 122 to 160 MeV. The results for constructive (destructive) interference from the second 2⁺ state in ³²S are QP_2⁺ = ?16.0±2.2 (?13.3±2.2) e·fd² and B(E2; 0⁺ → 2⁺) = 292±17 (307±17) e²·fm⁴     

First observation of the production and decay of the Σc+

An event with the decay chain Σ_c⁺ → Λ_c⁺ + π⁰, Λ_c⁺ → K^? + p + π⁺, has been observed in an exposure of BEBC, equipped with a track sensitive target, to the wide band neutrino beam from the SPS at CERN. The event has a unique three constraint kinematic fit to the ΔS = ?ΔQ reaction v + p → μ^? + p + K^? + π⁺ + π⁺ + π⁰ with both gammas from the π⁰ decay detected. The proton and other final state particles are identified. The masses are M(Λ_c⁺) = 2290 ± 3 MeV/c², M(Σ_c⁺) = 2457 ± 4 MeV/c² and M(Σ_c⁺) ? M(Λ_c⁺) = 168 ± 3 MeV/c². Including other data one obtains M (Σ_c⁺⁺) ? M(Σ_c⁺) = 0 ± 4 MeV/c².     

Static quadrupole moments of the first excited states of 200Hg and 202Hg

The static quadrupole moments Q_2⁺ and B(E2; 0⁺ → 2⁺) values of the 2⁺ first excited states of ²⁰⁰Hg and ²⁰²Hg have been determined using the reorientation effect in Coulomb excitation. An annular silicon surface-barrier detector was used to detect backscattered ⁴He, ¹²C and ¹⁶O projectiles. It is found that for ²⁰⁰Hg, Q_2⁺ = +1.07 ± 0.19 e · b(+0.98 ± 0.19 e · b) for destructive (constructive) interference from the 2^+′ state, and B(E2; 0⁺ → 2⁺) = 0.853 ± 0.007 e² · b². For ²⁰²Hg, we find Q_2⁺ = +1.01 ± 0.13 e · b (+0.87 ± 0.13 e · b) and B(E2; 0⁺ → 2⁺) = 0.605 ± 0.005 e² · b². The Q_2⁺ value obtained for ²⁰⁰Hg is in agreement with previous work, but that for ²⁰²Hg is not. The results obtained are compared with the predictions of various nuclear models, and the mass dependence of Q_2⁺ in the region 182 ≦ A ≦ 206 is examined.     

A spectroscopic study of the D(0u+) ion-pair state of Br2 by the optical-optical double-resonance technique

An optical-optical double-resonance technique has been applied to study the D(0_u⁺) ion-pair state of Br₂ in a one-photon resonant three-photon absorption. The OODR transition proceeds through the high vibrational level of the B³Π(0_u⁺) state, which compromises a large Franck-Condon shift required for the excitation of Br₂ from the X¹Σ_g⁺ state to the D(0_u⁺) state. Dunham parameters of the D(0_u⁺) state, based on a global least-squares fit of 407 transitions (v′ = 0–16, J′ = 17–115), are Y₀₀ = 49928.443(41), Y₁₀ = 134.467(19), Y₂₀ = ?8.71(27) × 10^?2, Y₃₀ = ?3.36(10) × 10^?3, Y₀₁ = 4.2382(15) × 10^?2, Y₁₁ = ?1.061(36) × 10^?4, Y₂₁ = ?2.00(27) × 10^?6, and Y₀₂ = ?1.93(11) × 10^?8 for ⁷⁹Br₂ (all in cm^?1, and 3σ in parentheses). The single rovibronic fluorescence spectrum of the D(0_u⁺) state shows a transition terminating on the X¹Σ_g⁺ ground state, and establishes the absolute v′ numbering on the basis of the Franck-Condon factor calculations. The v′ = 2 and 3 levels of the D(0_u⁺) state are strongly perturbed due to the heterogeneous interaction with the 1_u state correlating with the same ionic products of the D(0_u⁺) state at the dissociation limit, $\text{Br}{}^{\mathrm{?}}\text{(}{}^1\text{S) +}\text{Br}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_2\text{)}$.     

Electric moments of the first excited state of 18O

The static quadrupole moment Q_2⁺ and the B(E2; 0⁺ → 2⁺) value of the first excited state of ¹⁸O at e_x = 1.982 MeV have been determined using the reorientation effect in Coulomb excitation. Surface-barrier detectors at laboratory angles of 90° and 174° were used to detect ¹⁸O ions elastically and inelastically scattered from ²⁰⁸Pb. At both angles, we determined experimentally the maximum bombarding energies at which nuclear interference effects were negligible. It is found that Q_⁺ = ?0.023 ± 0.021 e · b (?0.052 ± 0.021 e · b) for destructive (constructive) interference from higher states. This result is in good agreement with theoretical expectation. For the transition moment we find B(E2; 0⁺ → 2⁺) = 0.00390 ± 0.00018 e² · b² (0.00371 ± 0.00018 e² · b²) for destructive (constructive) interference.     

New data on the ternary fission of 252Cf from the Gammasphere facility

Ternary fission of ²⁵²Cf was studied at Gammasphere using eight ΔE×E particle telescopes. Helium, beryllium, boron, and carbon light charged particles (LCPs) emitted with kinetic energy more than 9, 21, 26, and 32 MeV, respectively, were identified. The 3368-keV γ transition from the first 2⁺ excited state in ¹⁰Be was found and the population probability ratio N(2⁺)/N(0⁺) = 0.160 ± 0.025 was estimated. No evidence was found for 3368-keV γ rays emitted from a triple molecular state. For the first time, charge distributions are obtained for ternary fission fragments emitted with helium, beryllium, and carbon LCPs.     

Mixed-symmetry states in the neutron-proton interacting boson model

States of mixed proton-neutron symmetry are investigated in different dynamical symmetries of the interacting boson model. We discuss in each of the limits the energy spectrum, the wave functions and the B(M1; 0₁⁺ → 1 _1⁺) values. We also study three classes of transitional nuclei namely the Pd nuclei [U(5) → O(6)], the Sm nuclei [U(5) → SU(3)] and the Pt nuclei [O(6) → SU(3)] with respect to the energy of the lowest non-symmetric J^π = 1⁺, 3⁺ levels as well as the M1 and M3 strengths for exciting these levels from the ground state. For ⁹⁸Pd we compare this calculation with a shell-model calculation. Finally, we adress the problem of the mixing of the non-symmetric J^π = 1⁺ state with nearby hexadecapole (g-boson) configurations.     

Investigation of the 2νEC/EC Decay of 106Cd

Search for the β⁺β⁺, β⁺ EC, and EC/EC modes of the ¹⁰⁶Cd decay was carried out with the TGV-2 (Telescope Germanium Vertical) low-background multidetector spectrometer installed at the Modane underground laboratory (4800 m w.e.). The measured foil samples ～50 μm thick and 52 mm in diameter were placed between the entrance windows of the neighboring detectors inside the cryostat. The total measurement time for 10 g of ¹⁰⁶Cd enriched to 75% was 8687 h. New limits (at the 90% confidence level, CL) were obtained for the ¹⁰⁶Cd half-lives against various branches of the decay to the ground state 0⁺ and excited states 2⁺ of the ¹⁰⁶Pd daughter nucleus. They are T _1/2(2νβ⁺β⁺) ≥ 6.0 × 10¹⁹ y, and T _1/2(2νβ⁺ EC) ≥ 5.9 × 10¹⁹ y, and T _1/2(2νEC/EC) ≥ 3.0 × 10²⁰ y for the transitions to the 0⁺ ground state of ¹⁰⁶Pd; T _1/2(2νβ⁺β⁺) ≥ 5.7 × 10¹⁹ y, T _1/2(2νβ⁺ EC) ≥ 5.9 × 10¹⁹ y, and T _1/2(2νEC/EC) ≥ 4.2 × 10¹⁹ y for the transitions to the 2⁺, 512-keV excited state of ¹⁰⁶Pd; and T _1/2(2νEC/EC) ≥ 3.1 × 10¹⁹ y for the transition to the 0 ₁ ⁺ , 1334-keV excited state of ¹⁰⁶Pd.     

L α emission from Ar++H2 collisions in the threshold energy region

In the energy range 2.4 to 33.3 eV_CM, relative cross sections have been measured forL _α emission from impact of Ar⁺ ions in a beam on a H₂ gas target. Absolute cross sections, obtained by normalization to literature data, are 1–10×10^?16cm² for metastable Ar⁺ and 1–20×10^?18cm² for ground state Ar⁺. In the former case, the dominant mechanism is probably dissociative electronic energy transfer, while in the latter case dissociative charge transfer is the most likely process. In addition, at the lowest energiesL _α resulting from a chemiluminescent rearrangement Ar⁺+H₂→ArH⁺+H(2p) has been observed.     

SU(7) Electroweak unification

Electroweak unification is obtained in anSU(7) model at a mass scale 3×10¹⁰≦M≦3×10¹⁶ GeV's, with left-right symmetric subgroups and sin² θ _w (M)=3/8. BelowM, the model reduces toSU(3) _L ×SU(3) _R , the flavor sector of the “trinification theory” of Glashow et al., or of theE ₆ grand unified theory. This model predicts a natural massless neutrino, and fractionally charged leptons with masses in theM regime.     

The quadrupole moment of 26Mg as a test of shell-model interactions

The static quadrupole moment Q_21⁺, and the B(E2; 0₁⁺ → 2⁺₁) value of the first excited state of²⁶Mg have been measured using the reorientation effect in Coulomb excitation of ²⁶Mg projectiles. It is found that Q_21⁺ = ?13.6±3.0 (?9.5±3.0) e ·fm² and B(E2; 0⁺₁ → 2⁺₁) = 322±16 (328±16) e² ·fm⁴ for constructive (destructive) interference from higher states. The result for Q₂ clearly differentiates among several alternative effective interactions which have been used in shell-model calculations.     

Signals of new gauge bosons at futuree + e − colliders

We analyze possible indirect signals of additional neutral gauge bosons at futuree ⁺ e ^? colliders, concentrating onSU(2) _L ×U(1) _y ×U(1) _y , andSU(2) _L ×SU(2) _R ×U(1) effective theories. We develop a simple formalism to describe these effects and make a careful study of radiative corrections, in particular initial state radiation, which will be shown to have important implications. To make realistic estimates of the sensitivity to the new gauge boson effects, we use a model detector fore ⁺ e ^? annihilation at a center of mass energy of 500 GeV. Using a number of selected physical observables we then show that masses considerably higher than the total energy (up to a factor of 6) can be probed and that distinction between various theoretical models is possible.     

Conversion coefficients and E0 transitions in102, 104, 106Pd

In in-beam (p, p′) experiments, electron and γ-spectra were measured in the electron energy range of 500-1840 keV for¹⁰²Pd and¹⁰⁴Pd, and 600–1580 keV for¹⁰⁶Pd. The conversion coefficients of all transitions in this range were obtained with accuracies of about 20%, in some favourable cases 10%. Special attention was given to 0⁺′-0⁺ transitions from the two-phonon triplets to the ground states with the following results for the branching ratios 0⁺′-0⁺ (ground state) to 0⁺′-2⁺ (one-phonon state):¹⁰²Pd:T _k (E0)/T _γ (E2)<(2.1±3.6)·10^{?7 104}Pd:T _k (E0)/T _γ (E2)=(6.0±1.4)·10^{?5 106}Pd:T _k (E0)/T _γ (E2)=(6.0±2.0)·10^?4     

Investigating the Double Beta Decay of <Superscript>58</Superscript>Ni

Double beta decay (β + EC, EC/EC) of ⁵⁸Ni is investigated at France’s Modane Underground Laboratory (4800 m water equivalent) using the OBELIX ultralow-background HPGe detector with a sensitive volume of 600 cm³ and a natural nickel sample of ~68% 58Ni with a mass of ~21.7 kg. After preliminary analysis of the experimental data accumulated over ~144 days, new experimental limits are obtained for the 2νβ⁺EC decay of ⁵⁸Ni to the 0⁺ ground state and the 2 ₁ ⁺ , 811 keV excited state of ⁵⁸Fe, and for the 2νEC/EC decay of ⁵⁸Ni to the 2 ₁ ⁺ , 811 keV and 2 ₂ ⁺ , 1675 keV excited states of ⁵⁸Fe. The limits are T_1/2(β⁺EC,0→0⁺) > 1.7 × 10²² yr, T_1/2(β⁺EC,0→2 ₁ ⁺ ) > 2.3 × 10²² yr, T_1/2(EC/EC,0→2 ₁ ⁺ ) > 3.3 × 10²² yr, and T_1/2(EC/EC,0→2 ₂ ⁺ ) > 3.4 × 10²² yr. Experimental limit T_1/2(0νEC/EC–res, 1918 keV > 4.1 × 10²² yr is obtained for resonant neutrinoless radiative EC/EC decay with an energy of 1918.3 keV. All limits are at 90% CL.     

Perturbation determinants for singular perturbations

Let A be a densely defined symmetric operator and let {Ã′, Ã} be an ordered pair of proper extensions of A such that their resolvent difference is of trace class. We study the perturbation determinant Δ_Ã′/Ã(·) of the singular pair {Ã′, Ã} by using the boundary triplet approach. We show that, under additional mild assumptions on {Ã′, Ã, the perturbation determinant Δ_Ã′/Ã(·) is the ratio of two ordinary determinants involving the Weyl function and boundary operators. In particular, if the deficiency indices of A are finite, then we obtain Δ_Ã′/Ã(z) = det (B′ - M(z))/det (B - M (z)), z ∈ ρ(Ã), where M(·) stands for the Weyl function and B′ and B for the boundary operators corresponding to Ã′ and à with respect to a chosen boundary triplet Π. The results are applied to ordinary differential operators and to second-order elliptic operators.     

The electric quadrupole moment of the first excited state of 204Hg

The static electric quadrupole moment Q₂₊ and the B(E2; 0⁺ → 2⁺) value of the 2⁺ first excited state of ²⁰⁴Hg have been determined using the reorientation effect in Coulomb excitation. An annular Si surface-barrier detector was used to detect back-scattered ⁴He, ¹²C and ¹⁶O projectiles. In a subsidiary experiment, spectra were obtained from ²⁰⁴Hg(p, p')²⁰⁴Hg using Si surface-barrier detectors, and the results were used in conjunction with previously existing data to provide information on higher states of ²⁰⁴Hg which might participate in the Coulomb excitation of the 2⁺ state. From a 3-level analysis, we find Q₂₊ = +0.40 ± 0.20 e · b and B(E2; 0⁺ → 2⁺) = 0.423 ± 0.005 e² · b². These results are in good agreement with the predictions of particle-vibrational coupling calculations. The value obtained for $\text{Q}{}_{\mathrm{2+}}\text{(}{}^{204}\text{Hg)}$ is substantially smaller in magnitude than values of Q₂₊ previously determined for ^{198, 200, 202}Hg.     

Equation of state and quantal crossover of the XY model in a longitudinal magnetic field

The equation of state of the XY model in a longitudinal (Γ) and transverse field (B) is investigated in the vicinity of a multicritical point (Γ_c, T =0) using the renormalization group method developed recently by the author and K. Walasek. For Γ = Γ_c a quantal crossover behaviour of the form H = M_{R³ψ (z)} is obtained, where H ～ B, M_R denotes the transverse magnetization, z ～ TM_R^?/βq, while ?,β_q are crossover and multicritical exponents, respectively.