An experimental investigation of the radiative structure decay K+ → e+υγ

The decay K⁺ → e⁺υγ has been investigated. For the structure-dependent part with positive γ-helicity (SD₊) the branching ratio $\text{Γ(}\text{SD}{}_{\mathrm{+}}\text{)}\text{Γ(}\text{K}{}_{\mathrm{\mu 2}}\text{) = (2.33 ± 0.42) × 10}{}^{\mathrm{?5}}$ is obtained from 51 ± 3 events observed in the kinematical region E_e ? 235 MeV, E_γ > 48 MeV and θ_eγ > 140°. For the corresponding part with negative γ-helicity we obtain an upper limit Γ(SD_?)/Γ(SD₊) < 11 (90% CL) from the sample of electrons with energies 220 MeV ? E_e < 230 MeV and with no γ in the backward direction. This upper limit implies that the ratio of structure-dependent axial vector amplitudes lies outside the region $\text{?1.8 < a}{}_{\mathrm{<mtext>K</mtext>}}\text{υ}{}_{\mathrm{<mtext>K</mtext>}}\text{< ?0.54}$.For the decay $\text{K}{}^{\mathrm{+}}\text{→}\text{e}{}^{\mathrm{+}}\text{νν}\text{ν}$ the limit $\text{Γ(}\text{K}{}^{\mathrm{+}}\text{→}\text{e}{}^{\mathrm{+}}\text{νν}\text{ν}\text{)/Γ(}\text{K}{}_{\mathrm{e2}}\text{) < 3.8}$ 90% confidence level) was found.     

On the continuity of generalized eigenfunctions of the Schrödinger operator

We prove that the generalized eigenfunctions of the Schrödinger operator are continuous for potentials obeing the following assumptions: V=V⁺?V^?,V^±≥0,$\text{V}{}^{\mathrm{+}}\text{∈L}{}^{\mathrm{p}}{}_{\mathrm{<mtext>loc</mtext>}}\text{(}\text{R}{}^{\mathrm{l}}\text{)}$, $\text{V}{}^{\mathrm{?}}\text{∈L}{}^{\mathrm{p}}\text{(}\text{R}{}^{\mathrm{l}}\text{)}$,$\text{p >}\text{l}\text{2}$.     

Nuclear orientation study of the excited states of 129I populated in the decay of 129gTe and 129mTe

From the angular distributions of γ-rays emitted by oriented ^129gTe and ^129mTe nuclei implanted in iron by isotope separator, unique spin assignments could be made for the excited states of ¹²⁹I at 487.4 keV $\text{(}\text{5}\text{2}{}^{\mathrm{+}}\text{)}$, 696.0 keV $\text{(}\text{11}\text{2}{}^{\mathrm{+}}\text{)}$, 729.6 keV $\text{(}\text{9}\text{2}{}^{\mathrm{+}}\text{)}$, 768.9 keV $\text{(}\text{7}\text{2}{}^{\mathrm{+}}\text{)}$, 1050.4 keV $\text{(}\text{7}\text{2}{}^{\mathrm{+}}\text{)}$ and 1111.8 keV $\text{(}\text{5}\text{2}{}^{\mathrm{+}}\text{)}$. In addition, E2/M1 amplitude ratios for the following ¹²⁹I γ-rays (energies are in keV) are derived: δ(459.6) = ?(0.076^+0.037_?0.148); δ(487.4) = 0.50^+0.17_?0.10 or δ^? = 0.35^+0.15_?0.09; δ(556.7) = 0.06±0.02 or δ^? = ?(0.10±0.02); δ(624.4) = 0.10±0.26 or δ^? > 0.4; the 696.0 keV γ-ray is pure E2; δ(729.6) = ?(0.34±0.06) or δ^?1 = 0.55±0.05; δ(741.1) = ?(0.27±0.10) or δ^?1 = ?(0.43±0.12); δ(817.2) = 0.46±0.04 or δ^?1 =0.20±0.03 if $\text{I}{}^{\mathrm{\pi }}\text{(845}\text{keV}\text{) =}\text{7}\text{2}{}^{\mathrm{+}}$; δ(1022.6) = ?(0.02 ±0.02) or δ^?1 = ?(0.23±0.02); $\text{δ(1084) = 0.56}{}^{\mathrm{+0.04}}{}_{\mathrm{?0.14}}$; δ(1111.8) = 0.06±0.05 or δ^?1 = ?(0.08±0.05). The anisotropy of the 531.8 keV γ-ray excludes $\text{1}\text{2}{}^{\mathrm{+}}$ as a possible spin assignment for the 559.6 keV level, so that no $\text{1}\text{2}{}^{\mathrm{+}}$ level is fed in the decay from ¹²⁹Te. Anisotropies for the 209, 250.7, 278.4 and 281.1 keV γ-rays are also measured. Comparison of the level scheme is made with theoretical predictions from both the pairing-plus-quadrupole model and the intermediate coupling unified model.     

Investigation of rare non-strange decay modes of the f meson in Π+p interactions at 5GeVc

Rare decay modes of the f meson are studied in the final states Δ⁺⁺π⁺π^?π⁺π^?, Δ⁺⁺π⁺π^?MM and Δ⁺⁺π⁺π^?π⁺π^?MM. The ratio $\text{Γ (f → π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^0\text{π}{}^0\text{)}\text{Γ(f → π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{)}$ is 0.23 ± 0.09 and Γ(f → 4 π) saturates the f inelasticity. A 2 s.d. upper limit of 0.09 is found for the branching ratio $\text{(f → ηη)}\text{(f → 2π)}$.     

The irreducible Raman scattering tensor operator for the 32 crystallographic point groups and its application to the resonance and electronic Raman effect

The irreducible components of the Raman scattering tensor operator $\text{α}\text{?}{}_{\mathrm{\gamma }}{}^{\mathrm{<mtext>\Gamma </mtext>}}\text{(}\text{Γ}{}_{\mathrm{ks}}\text{Γ}{}_{\mathrm{k\prime s\prime }}\text{)}$ under the symmetry of a general point group are calculated. The unitary transformations U(Γ_γΓ_ksΓ_k′s′, ρσ) from the Cartesian $\text{α}\text{?}{}_{\mathrm{\rho \sigma }}$ and spherical $\text{α}\text{?}{}_{\mathrm{Q}}{}^{\mathrm{K}}$ components, respectively, to the irreducible components $\text{α}\text{?}{}_{\mathrm{\gamma }}{}^{\mathrm{<mtext>\Gamma </mtext>}}\text{(}\text{Γ}{}_{\mathrm{ks}}\text{Γ}{}_{\mathrm{k\prime s\prime }}\text{)}$ for the 32 crystallographic point groups are collected in tables. As an example the unitary transformation U(Γ_γΓ_ksΓ_k′s′, ρσ) is used to discuss the behavior of the scattering tensor in a resonance Raman experiment. With the help of the general formalism the scattering tensor for electronic Raman transitions of transition metal ions is calculated. As an example the scattering tensors of electronic Raman transitions within the ⁵T₂ state of the high-spin trigonal distorted octahedral Fe²⁺ are calculated and the refinement of the selection rules is discussed.     

Evidence for a narrow peak in Ksoπ±π+π- at 2.6 gev in 12 gev/cpp interactions

We report the evidence for a narrow charged peak (5.5 s.d.), which we suggest calling the I, in the 6-prong-V⁰ topology of $\text{p}$p interactions at 12 GeV/c. The mass, widht and the product of cross section σ_I times the branching ratio BR into the final state (K_s^oτ±τ⁺τ^? are found to be: $\text{M}{}_{\mathrm{I}}\text{=2.60 ±}\text{0.01}\text{GeV}\text{/}\text{c}{}^2$, $\text{Γ}{}_{\mathrm{I}}\text{?}\text{0.018}\text{GeV}\text{/}\text{c}{}^2$, σ_I·BR≈20 μbarn     

Total width of the lowest T = 2 state in 24Mg

By analyzing thick-target excitation functions of the $\text{E}{}_{\mathrm{<mtext>p</mtext>}}\text{= 3906}\text{keV}{}^{23}\text{Na}\text{(}\text{p}\text{, γ)}$ resonance we have determined Γ_c.m ≦ 530⁺⁴⁰_?70 eV for the width of the lowest T = 2 state of ²⁴Mg. The beam energy resolution function was measured using a narrow ²⁷Al(p, γ) resonance at E_p = 3671 keV, for which we obtain Γ_c.m. = 180 ±50 eV.     

Interference effects in 12C(p, γ)13N and direct capture to unbound states

Excitation functions of the capture reaction ¹²C(p, γ₀)¹³N have been obtained at θ_γ = 0° and 90° and E_p = 150–2500 keV. The results can be explained if a direct radiative capture process, E1(s and d → p), to the ground state in ¹³N is included in the analysis in addition to the two well-known resonances in this beam energy range $\text{[E}{}_{\mathrm{p}}\text{= 457(}\text{1}\text{2}{}^{\mathrm{+}}\text{)}$ and 1699 $\text{(}\text{3}\text{2}{}^{\mathrm{?}}\text{) keV]}$. The direct capture component is enhanced through interference effects with the two resonance amplitudes. From the observed direct capture cross section, a spectroscopic factor of C²S(l = 1) = 0.49 ± 0.15 has been deduced for the $\text{1}\text{2}{}^{\mathrm{?}}$ ground state in ¹³N. Excitation functions for the reaction ${}^{12}\text{C(p,γ}{}_1\text{p}{}^1\text{)}{}^{12}\text{C}$ have been obtained at θ_γ = 0° and 90° and E_p = 610–2700 keV. Away from the 1699 keV resonance the capture γ-ray yield is dominated by the direct capture process E1 (p → s) to the $\text{2366 (}\text{1}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound state. Above E_p = 1 MeV, the observed excitation functions are well reproduced by the direct capture theory to unbound states (bremsstrahlung theory). Below E_p = 1 MeV, i.e., E_p → 457 keV, the theory diverges in contrast to observation. This discrepancy is well known in bremsstrahlung theory as the “infrared problem”. From the observed direct capture cross sections at $\text{E}{}_{\mathrm{p}}\text{? 1 MeV}$, a spectroscopic factor of C²S(l = 0) = 1.02 ± 0.15 has been found for the $\text{2366 (}\text{1}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound state. A search for direct capture transitions to the $\text{3512 (}\text{3}\text{2}{}^{\mathrm{?}}\text{)}$and $\text{3547 (}\text{5}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound states resulted in upper limits of C²S(l = 1) ≦ 0.5 and C²S(l = 2) ? 1.0, respectively. The results are compared with available stripping data as well as shell-model calculations. The astrophysical aspect of the ¹²C(p, γ₀)¹³N reaction also is discussed.     

Matthiessen's rule and its variation for cyclotron resonance width in two and three dimensions

Based on the proper connected diagram expansion, we calculated cyclotron resonance widths Γ_n associated with neighboring Landau states (n, n +1) for free electrons in interaction with more than one kind of impurities. In 3D usual Matthiessen's rule Γ_n=Γ⁽¹⁾_n+Γ⁽²⁾_n+…where Γ⁽ⁱ⁾_n represent widths calculated separately for each kind, is obtained. In 2D a new rule: is obtained.     

An experimental study of the form factor in the decay K+ → πoe+ν

The q² variation of the factor $\text{?}{}_{\mathrm{+}}\text{(q}{}^2\text{)}$ in the decay K⁺→π⁰e⁺ν has been studied using a sample of even detected in the CERN 1.1 m³ heavy-liquid bubble chamber. The data are consistent with a linear development $\text{?}{}_{\mathrm{+}}\text{(q}{}^2\text{)=?}{}_{\mathrm{+}}\text{(0) (1+λ}{}_{\mathrm{+}}\text{q/m}{}^2{}_{\mathrm{\pi }}\text{)}$ with λ₊=0.027±0.008.     

Measurement of the decay ϒ′→ϒπ+π−

We report the first observation of the decay $\text{?′→?π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{→}\text{l}{}^{\mathrm{+}}\text{l}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}$. The 7 events seen yield a branching ratio B(?′→?π⁺π^?)=(19±8)%. A consistent value of B=(26±13)% is obtained from the charged multiplicities of the ?′ and ? decays. Using these values we deduce Γ_tot(?′)=(31⁺¹⁰_?8) keV and B_ee(?′)=(1.8±0.5)%. Furthermore we estimate Γ(?′→gg?)=(10±5) keV in agreement with QCD predictions using vector gluons while one would expect 100 keV with scalar gluons.     

Decay of the mirror nuclide 45V

The β⁺ decay of ⁴⁵V $\text{(J}{}^{\mathrm{\pi }}\text{, T=}\text{7}\text{2}{}^{\mathrm{?}}\text{,}\text{1}\text{2}\text{)}$ has been observed. The half-life was found to be 539 ± 18 ms; in addition to the superallowed transition to the mirror state (⁴⁵Ti ground state), it exhibits a (4.3 ± 1.5)% allowed branch to the $\text{5}\text{2}{}^{\mathrm{?}}$ state at 40.1 keV in ⁴⁵Ti. Decay data for the complete $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ shell series of mirror nuclei are presented.     

Experimental results on J/ψ production by π±, K±, p and p incident on hydrogen at 39.5 GeV/c

J/ψ production at 40 GeV/c by π^±, K^±, p and $\text{p}$ incident on hydrogen has been studied and results compared with those obtained on tungsten in the same experiment. On hydrogen, J/ψ cross-section ratios relative to π^? have been measured to be (for $\text{x}{}_{\mathrm{<mtext>F</mtext>}}\text{> 0) σ(π}{}^{\mathrm{?}}\text{) : σ(π}{}^{\mathrm{+}}\text{) : σ(}\text{p}\text{) : σ(}\text{p}\text{) = 1 : (0.78 ± 0.09) : (0.83 ± 0.35) : (0.07 ± 0.04)}$. The suppression of the proton induced cross sections shows the importance of calence quark-antiquark fusiin J/ψ production at this energy (i.e. M_J²/_ψ/s=0.13).     

First determination of the proton electromagnetic form factors at the threshold of the time-like region

From the measurement of $\text{B}\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{=}\text{Γ(}\text{p}\text{p}\text{→}\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{)}\text{Γ}\text{p}\text{p}\text{→total}\text{= (3.2 ± 10}{}^{\mathrm{?7}}\text{)}$, obtained in an experiment at CERN with antiprotons at rest, a value of the proton electromagnetic form factors at the threshold of the time-like region is derived: |G_E| = |G_M| = 0.51 ± 0.08 at q² = -3.52 (GeV/c)².     

The hadronic cross section of electron-positron annihilation at 9.5 GeV and the ϒ and ϒ′ resonance parameters

The reaction e⁺e^?→ hadrons has been measured in the ? and ?′ region using the DASP detector at the DESY storage ring DORIS. The following final results are obtained: R_had(9.5 GeV)=3.73±0.16±0.28, Γ_ee(?)=(1.23 ± 0.08 ± 0.12) keV, B_μμ(?)=(3.2±1.3±0.3)%, $\text{Γ}{}_{\mathrm{<mtext>ee</mtext>}}\text{Γ}{}_{\mathrm{<mtext>had</mtext>}}\text{Γ}{}_{\mathrm{<mtext>tot</mtext>}}\text{(?′)=(0.55±0.11 ±0.06)}\text{keV}$, and M(?′)?M(?)=(556 ±10) MeV.     

Polarization spectroscopy of the E0g+-B0u+ band system of Br2

The E-B (0_g⁺-0_u⁺) band system of Br₂ has been investigated at Doppler-limited resolution using polarization labeling spectroscopy. Merged E state data for the three naturally occurring isotopes in the range v_E = 0–16, expressed in terms of the constants for ⁷⁹Br₂, are (in cm^?1) Y_0,0 = 49 777.962(54), Y_1,0 = 150.834(22), Y_2,0 = ?0.4182(28), Y_3,0 = 6.6(11) × 10^?4, Y_0,1 = 4.1876(28) × 10^?2, Y_1,1 = ?1.607(16) × 10^?4, and Y_0,2 = 1.39(39) × 10^?8. The bond distance is $\text{r}{}_{\mathrm{<mtext>e</mtext>}}\text{= 3.194}\text{A}\text{?}$, and the diabatic dissociation energy to $\text{Br}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_2\text{) +}\text{Br}{}^{\mathrm{?}}\text{(}{}^1\text{S}{}_0\text{)}\text{is 34 700 cm}{}^{\mathrm{?1}}$.     

Rotational constants of the E O+g state of I2 determined by polarization spectroscopy

The resonant 2-photon E(O⁺_g) ← B(O⁺_g) ← X(O⁺_g) transition of I₂ vapor has been studied by polarization spectroscopy, leading to a rotational analysis of the ν = 0–15 vibrational levels of the E state. The principal constants determined are $\text{B}{}_{\mathrm{e}}\text{= 19.9738(42) × 10}{}^{-3}\text{, α}{}_{\mathrm{e}}\text{= 5.602(84) × 10}{}^{-5}\text{, γ}{}_{\mathrm{e}}\text{= 1.02(41) × 10}{}^{-7}\text{, D}{}^{\mathrm{e}}{}_{\mathrm{J}}\text{= 3.040(74) × 10}{}^{-9}\text{cm}{}^{-1}\text{, and r}{}_{\mathrm{e}}\text{= 3.6470(5)}\text{A}\text{?}$.     

Hydrogen burning of 20Ne and 22Ne in stars

The ²⁰Ne(p, γ)²¹Na capture reaction has been studied in the energy range E_p = 0.37–2.10 MeV. Direct-capture transitions to the $\text{332 (}\text{5}\text{2}{}^{\mathrm{+}}\text{)}\text{and}\text{2425}\text{keV}\text{(}\text{1}\text{2}{}^{\mathrm{+}}\text{)}$ states have been found with spectroscopic factors of C²S(1d) = 0.77±0.13 and C²S(2s) = 0.90±0.12, respectively. The high-energy tail of the 2425 keV state, bound by 7 keV against proton decay, has also been observed in the above energy range as a subthreshold resonance. The excitation function for this tail is consistent with a single-level Breit-Wigner shape for a γ-width of Γ_γ = 0.31±0.07 eV at E_x = 2425 keV. The extrapolation of these data to stellar energies gives an astrophysical S-factor of S(0) = 3500 keV · b. Two new resonances at E_p = 384±5 and 417± 5 keV have been observed with strengths of ωγ = 0.11±0.02 and 0.06±0.01 meV, corresponding to the known states at and 2829 keV (presumably $\text{9}\text{2}{}^{\mathrm{+}}$), respectively. For the known E_p = 1830 keV resonance, a strength of ωγ = 1.0± 0.3 eV and a total width of Γ = 180± 15 keV were found. Branching ratios as well as transition strengths have been obtained for these three states. The Q-value for the ²⁰Ne(p, γ)²¹Na reaction (Q = 2432.3 ± 0.5 keV) as well as excitation energies for many low-lying states in ²¹Na have been measured. No evidence was found for the existence of the state reported at E_x = 4308±4 keV.In the case of ²²Ne(p, γ)²³Na, direct-capture transitions to six final bound states have been observed revealing sizeable spectroscopic factors for these states. The astrophysical S-factor extrapolated from these data to stellar energies, is S(0) = 67 ± 12 keV · b.The astrophysical as well as the nuclear structure aspects of the present results are discussed.     

Inclusive production of Ξ+ and Ξ− in K+ p interactions at 32 GeV/c

The inclusive production of $\text{Ξ}{}^{\mathrm{+}}$ and Ξ^? hyperons is investigated in K⁺ p interactions at 32 GeV/c. The production cross sections, 36.4±9 μb for the $\text{Ξ}{}^{\mathrm{+}}$ and 6.5±3 μb for the Ξ^?, are rising strongly with energy similarly to $\text{Λ}$ and Λ production in K⁺ p interactions. The $\text{Ξ}{}^{\mathrm{+}}$ are produced preferentially in the forward direction in the c.m.s., while the Ξ^? are produced dominantly backwards. The average transverse momenta and 〈p_T〉_Ξ^?=0.58±0.09 GeV/c.