Binding energies of λλ hypernuclei and the λλ interaction

The binding energies of the ΛΛ hypernuclei ¹⁰_ΛΛBe and ⁶_ΛΛHe are calculated variationally with a 2α + 2Λ and with an α + 2Λ model, respectively. For ¹⁰_ΛΛBe the integrations were made with Monte Carlo techniques while for ⁶_ΛΛHe direct numerical methods were used. A wide range of phenomenological ΛΛ potentials based on meson-exchange models was considered. An approximately universal linear relation between the calculated values of $\text{B}{}_{\mathrm{\Lambda \Lambda }}\text{(}{}^{10}{}_{\mathrm{\Lambda \Lambda }}\text{Be}\text{)}$ and of $\text{B}{}_{\mathrm{\Lambda \Lambda }}\text{(}{}^6{}_{\mathrm{\Lambda \Lambda }}\text{He}\text{)}$ is obtained. For the experimental value of $\text{B}{}_{\mathrm{\Lambda \Lambda }}\text{(}{}^{10}{}_{\mathrm{\Lambda \Lambda }}\text{Be}\text{) = 17.7 ± 0.1}\text{MeV}$ this relation predicts a much too small value of $\text{B}{}_{\mathrm{\Lambda \Lambda }}\text{(}{}^6{}_{\mathrm{\Lambda \Lambda }}\text{He}\text{)}$, well below the lower limit of the quoted experimental value of 10.9 ± 0.6 MeV. For ΛΛ potentials with repulsive cores the relations, for a given $\text{B}{}_{\mathrm{\Lambda \Lambda }}\text{(}{}^{10}{}_{\mathrm{\Lambda \Lambda }}\text{Be}\text{)}$, between the low-energy ΛΛ scattering parameters a, r₀ and the intrinsic range b are both approximately universal and independent of the detailed potential shape. For the experimental value of $\text{B}{}_{\mathrm{\Lambda \Lambda }}\text{(}{}^{10}{}_{\mathrm{\Lambda \Lambda }}\text{Be}\text{)}$ the preferred values are 2.5 ? ?a ? 3.5 fm, 2.6 ? r₀ ? 3.1 fm. The large and negative values of a correspond to conditions not too far from a bound ¹S₀ ΛΛ state and could indicate a 6-quark dibaryon state with the same quantum numbers and above the ΛΛ threshold.     

The j-dependence of the (19F, 16O) reaction

The total angular momentum transfer (j) dependence was studied for orbital angular momentum transfers l = 1, 2, and 3 in the (¹⁹F, ¹⁶O) reactions on ^{28, 30}Si and ⁶⁰Ni. In contrast to the strong j-dependence for the l = 2 transitions to ^{31, 33}P states, no distinct j-dependence was found for the l = 1 and l = 3 transitions to ⁶³Cu states. Previously reported results for the ${}^{28}\text{Si}\text{(}{}^{19}\text{F}\text{,}{}^{16}\text{O)}{}^{31}\text{P}$ reaction were re-analyzed using optical-potential sets which fit the elastic-scattering data for both the entrance and exit channels. Results of DWBA calculations without use of spin-orbit potentials were found to be out of phase with the data for all l-transfers and the j-dependence could not be reproduced. Both of these problems were alleviated by including spin-orbit forces in the optical potentials. However, a good fit to the ²⁸Si(¹⁹F, ¹⁶O)³¹P data was obtained only if the optical potentials that fit the elastic scattering data were modified for the exit channel.     

Spin-flip and resistivity scattering of conduction electrons due to metallic impurities dissolved in lithium and sodium

We analyse the impurity induced scattering cross sections with (σ_sf) or without (σ_r) spin-flip, for conduction electrons in lithium and sodium. We show that the experimental values of $\text{σ}{}_{\mathrm{sf}}\text{σ}{}_{\mathrm{r}}$, are approximately equal to the Elliott parameter $\text{(}\text{λ}\text{Δ}\text{)}{}^2$ (λ is the spin-orbit splitting of an impurity state (A) close to the impurity conduction band (C), and Δ is the energy separation between (C) and (A). We conclude that the Elliott calculation is valid not only for a spin-independent scattering potential, but also for the perturbation due to heavy impurities (strong spin-orbit coupling) dissolved in light metals (weak spin-orbit coupling).     

The analyzing power for neutron scattering from 9Be at 9 to 17 MeV

Time-of-flight techniques were used to measure the analyzing power for the scattering of neutrons from ⁹Be at energies from 9 to 17 MeV. Because of the high nuclear density of beryllium, particular attention was paid to finite-geometry and multiple-scattering effects. For representing the data, an unusual method of Legendre-coefficient analysis was used to establish the smooth energy dependence of both the cross section σ(θ) and the analyzing power A_y(θ). Spherical optical-model calculations were able to describe the σ(θ) and A_y(θ) data simultaneously, but only after the introduction of an imaginary spin-orbit potential W_s.o.(r). The geometry of the W_s.o.(r) term was found to be the same as that of the surface-peaked imaginary central potential. Coupledchannels calculations using a quadrupole-deformed rotational model built on the $\text{3}\text{2}{}^{\mathrm{?}}$ ground state were able to describe inelastic scattering to the $\text{5}\text{2}{}^{\mathrm{?}}$ and $\text{7}\text{2}{}^{\mathrm{?}}$ excited states, but also required a W_s.o.r potential.     

Elastic scattering of 119 MeV 3He particles and energy and mass-number dependence of optical potential parameters

The elastic scattering of 119 MeV ³He particles by ¹²C, ²⁷Al, ^58,60,62,64Ni, ⁵⁹Co, ^90,92Zr and ⁸⁹Y has been investigated over a wide angular range in order to study the mass-number dependence of the optical potential and odd-even differences in the elastic scattering. The elastic scattering cross sections have been analyzed in terms of the optimal model. The data, except for ¹²C, ²⁷Al and ⁵⁹Co, were fitted with r_R = 1.21 fm, a_R = 0.76 fm and r_I = 1.17 fm, fixed at the average values. The following formulae were obtained for the three remaining parameters by combining with the energy dependence of the parameters (90–120 MeV) obtained previously:

$\text{V=111.4?0.173E+}\text{Z}\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{+14.9}\text{N?Z}\text{A}\text{(}\text{MeV}\text{)}$

$\text{W}{}_{\mathrm{<mtext>D</mtext>}}\text{=24.8?0.028E (}\text{MeV}\text{)}$

,

$\text{a}{}_{\mathrm{I}}\text{=0.754+0.78}\text{N?Z}\text{A}\text{(}\text{fm}\text{)}$

The depths of the valleys of the angular distribution in the case of ${}^{59}\text{Co}\text{(I =}\text{7}\text{2}\text{)}$ are considerably shallower than those for Ni isotopes, while the depths in the case of ${}^{89}\text{Y}\text{(I =}\text{1}\text{2}\text{)}$ are nearly the same as those for Zr isotopes. Thus it may be concluded that the odd-even differences are attributed to the scattering from the quadrupole moment of the odd-A nucleus (if $\text{I >}\text{1}\text{2}$).     

Three-nucleon results for separable potentials modelled on the Reid soft-core potential

Using a solution to the inverse scattering problem we have generated phase-equivalent separable potentials in the ${}^1\text{S}{}_0$ and ${}^3\text{S}{}_1\text{?}{}^3\text{D}{}_1$ states, which have nearly the same singlet UPA form factors and deuteron parameters (E_D, P_D, Q_D, A_S and $\text{A}{}_{\mathrm{D}}\text{A}{}_{\mathrm{S}}$) as the Reid soft-core potential. We compare our results for the binding energy of the triton and the neutron-deuteron doublet scattering length with the corresponding values for the Reid soft-core potential.     

3Σu−-3Σu+ coupling in the O2B3Σu− predissociation

The role of $\text{B}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{-2}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ spin-orbit mixing in the O₂ Schumann-Runge predissociation is investigated. The $\text{2}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ state is found to cross the $\text{B}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}$ state near 2.0 Å with an interaction matrix element of approximately 55 cm^?1. This state contributes to the widths of the Bv ≥ 6 levels, but introduces only small level shift perturbations. When the partial widths due to the ${}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{-}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ interaction are added to the previously calculated widths due to the ⁵Π_u, ³Π_u, and ¹Π_u states, reasonable agreement is obtained with experimental measurements on O¹⁶O¹⁶ and O¹⁸O¹⁸. The possibility of non-Lorentzian line profiles and the dependence of the width on rotational quantum number is investigated. The approximation of the spin-orbit matrix element by its value at the crossing point is shown to be a good approximation for calculating the second difference perturbations.     

Phase-shift analysis of d-α elastic scattering between 3 and 43 MeV

Phase shifts for the d-α elastic scattering have been extracted from differential cross sections and the vector and tensor analyzing powers of ${}^4\text{He(}\text{d}\text{, d)}{}^4$He scattering in the energy range from 3 to 43 MeV. The analysis includes spin-orbit splitting, mixing of states and absorption to reaction channels. A new parametrization of two-channel scattering matrices is given and compared. Excellent fits have been obtained with a new phase-shift code ONEZERO, which is capable of taking into account all degrees of freedom in strong interactions. The Argand-plot method has been used for resonance analysis of the excited ⁶Li system. Five new broad T = 0 resonances above 15 MeV deuteron energy have been found in ⁶Li, corresponding to D₃, F₂, F₃, G₃ and G₄ resonant states. Problems from phase-shift ambiguities are pointed out.     

Predissociation of the Schumann-Runge bands of O2

The predissociation line broadening in the Schumann-Runge bands of O₂ is interpreted through an ab initio calculation of the pertinent repulsive potential energy curves and spin-orbit matrix elements. The ab initio results provide an overall qualitative picture of the predissociation which is further refined through a detailed comparison of calculated level shifts and widths with experimental data. The position of the dominant repulsive curve is also deduced by a deperturbation of the level shift in the second vibrational difference. The predissociation is dominated by the ⁵Π_u state crossing the $\text{B}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}$ state around 1.875 Å with a spin-orbit matrix element of 65 cm^?1. The ¹Π_u and ³Π_u states have small spin-orbit matrix elements and play only minor roles in the predissociation. The calculated and experimental widths are in good agreement for low and high vibrational levels. The apparent experimental widths between v = 5 and 11 are shown to be inconsistent with the theoretical analysis, the difference probably being due to line blending.     

Double folding model analysis of 7Li scattering

Elastic scattering angular distributions have been measured for the scattering of ⁷Li by ⁴⁴Ca, ⁵⁶Fe and ^{58, 60}Ni at $\text{E(}{}^7\text{Li}\text{) = 34}\text{MeV}$. These data are well described by the optical model using volume Woods-Saxon potentials. These and previously measured ⁷Li scattering data also have been analyzed with a double-folding real potential which employs the nucleon-nucleon potential of Bertsch et al. The overall best fit to the experimental data down to σ/σ_R ~ 10^?3 is obtained when the DF potential is multiplied by approximately 0.6. However, the best fit for the peripheral data alone (σ/σ_R ～ 10^?1 is obtained without any renonnalization.     

The interaction of 33 MeV polarised helions with 30Si

Distributions of cross sections and analysing powers have been measured over the range ～ 14°–100° c.m. for the $\text{(}{}^3\text{H}\text{,}{}^3\text{He), (}{}^3\text{H}\text{,}{}^4\text{He), (}{}^{\mathrm{<mtext>3</mtext><mtext>H</mtext>}}\text{,}{}^2\text{H)}$ reactions at 33.4 MeV incident e using a ～ 95 % enriched ³⁰Si target. Phenomenological optical-model analyses of the elastic-scattering data have been carried out. A DWBA analysis of the inelastic-scattering data for the 2.24 MeV (2⁺) and 5.49 MeV (3^?) states of ³⁰Si has yielded values of the deformation β₂ and β₃. The j-dependence of the analysing powers for the (³He, ⁴He) and (³He, ²H) reactions has identified the 6.71 MeV level of ²⁹Si as a $\text{5}\text{2}{}^{\mathrm{+}}$ state, and a level near 9.5 MeV in ³¹P as a possible $\text{7}\text{2}{}^{\mathrm{?}}$ state. Spectroscopic factors for ten states in ²⁹Si and seven states in ³¹P have been deduced and are compared with other work. The extent to which the data defines the ³He spin-orbit potential is discussed.     

The (α, α), (α, α′) and (α, 3He) reactions on 12C at 139 MeV

The nucleus ¹²C was bombarded with 139 MeV α-particles to study the characteristics of the elastic, inelastic, and (α, ³He) reactions. An optical model analysis of the elastic data yielded a unique family of Woods-Saxon potential parameters with central real well depth V ≈ 108 MeV, and volume integral $\text{J}\text{4A}\text{≈ 353}\text{MeV}\text{·}\text{fm}{}^3$. By comparing the present results with those of other studies above 100 MeV, we find that the real part of the α-nucleus interaction decreases with increasing energy; the fractional decrease with energy is roughly one-half that observed for proton potentials. Using the optical potential parameters derived from the elastic scattering, first-order DWBA calculations with complex first-derivative form factors reproduced the inelastic scattering data to the 4.44 MeV (2⁺) and 9.64 MeV (3^?) states of ¹²C. For the 0⁺ state at 7.65 MeV it was necessary to employ a real, second-derivative form factor to fit the data. The deformation lengths β_lR_m and deformations β_l obtained in this and other experiments are summarized and compared. DWBA calculations using microscopic model form factors were also performed for the 2⁺ and 3^? states using the wave functions of Gillet and Vinh Mau. These reproduced the shapes and relative magnitudes of the differential cross sections. We also fit the shape of the 0⁺ differential cross section using a microscopic form factor which contains a node, which is similar to that occurring in the collective model second-derivative form factor. In the ($\text{α,}{}^3\text{He}$) reaction the differential cross sections to the ground state ($\text{1}\text{2}{}^{\mathrm{?}}$) and the 3.85 MeV ($\text{5}\text{2}{}^{\mathrm{+}}$) state in ¹³C could not be reproduced by zero-range local DWBA stripping calculations; it was necessary to employ finite-range and non-local corrections in the local-energy approximation. This DWBA analysis is notable in that unambiguous optical potentials were available for both entrance and exit channels. The ground state spectroscopic factor is in agreement with the prediction of Cohen and Kurath, while the relative spectroscopic factors agree fairly well with the rather few existing measurements of this kind.     

Elastic electron scattering from the magnetization distribution of 27Al

Cross sections have been measured for the scattering of electrons through 180° from Mg, Al and Si targets in the energy range 35 to 95 MeV. Scattering from the magnetization distribution of ²⁷Al is observed as the difference of the scattering from ²⁷Al and from the neighbouring doubly even nuclei Mg and Si. Corrections have been applied for differences in instrumental effects and in rms charge radii. Theoretical magnetic cross sections have been computed with a single-particle wave function and with a shell-model wave function involving configuration mixing. If the distorted-wave Born approximation is used, good agreement with experiment is obtained. In both cases the best fit to the data yields a value of the oscillator range parameter b = 1.71 ± 0.06 fm. Using the q-dependence of the single-particle model a value $\text{Ω = 18.7 ± 3.5 μ}{}_{\mathrm{<mtext>N</mtext>}}\text{·}\text{fm}{}^2$ for the magnetic octupole moment of ²⁷Al is found. The present low-energy (E < 100 MeV) data are in good agreement with the results obtained from the scattering of high-energy (E = 500 MeV) electrons from ²⁷Al through “normal” angles.     

Reorientational motion of the OH− ion in cubic sodium hydroxide

The rotational motion of the OH^? ion was studied in cubic NaOH at 575 K with quasielastic incoherent neutron scattering. The data are compared to two simple models yielding values for the radius of rotation R, the translational mean square displacement 〈u²〉_H, the rotational jump rate τ^?1 and the rotational diffusion coefficient D_R. The following parameter values are obtained: (a) rotational jump model: $\text{R = 0.95}\text{A}\text{?}$, $\text{〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.052}\text{A}\text{?}{}^2\text{, τ}{}^{\mathrm{?1}}\text{= 2}\text{meV}$, (b) rotational diffusion model: $\text{R = 0.99}\text{A}\text{?}\text{, 〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.046}\text{A}\text{?}{}^2\text{, D}{}_{\mathrm{R}}\text{= 0.72}\text{meV}$.     

Magnetic elastic electron scattering from 3Be and 13C

Elastic scattering through 180° from ⁹Be, ¹²C and ¹³C targets has been observed for electrons of 35 to 90 MeV. Magnetic scattering cross sections for ⁹Be and ¹³C have been obtained by subtracting charge scattering as deduced from the scattering from the spin-zero nucleus ¹²C. Theoretical shell model predictions for the magnetic cross sections are derived for (1s)⁴(1p)^A?4 configurations and various coupling schemes. Both harmonic oscillator and Woods-Saxon radial wave functions are used. A comparison of our results with magnetic cross sections calculated in DWBA yields magnetic rms radii $\text{〈r}{}^2\text{〉}{}_{\mathrm{<mtext>M</mtext>}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 3.2 ± 0.3}\text{fm}$ and $\text{〈r}{}^2\text{〉}{}_{\mathrm{<mtext>M</mtext>}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 3.3 ± 0.3}\text{fm}$ for ⁹Be and ¹³C. For ¹³C a combined flt to our low-q data and to earlier high-q data, yields $\text{〈r}{}^2\text{〉}{}_{\mathrm{<mtext>M</mtext>}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 3.4 ± 0.1}\text{fm}$ and a strong preference for intermediate coupling (IC) wave functions. Magnetic dipole scattering from ⁹Be is also close to the IC prediction, as deduced from a fit to our data and earlier high-q data. The fitted value of the octupole moment $\text{Ω = 5±1 μ}{}_{\mathrm{<mtext>N</mtext><mtext>fm</mtext>}}{}^1$ can only be explained by a deformation of the average nuclear potential. The radial size $\text{〈r}{}^2\text{〉}{}_{\mathrm{<mtext>1</mtext><mtext>p</mtext>}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 2.85 ± 0.05}\text{fm}$ for the 1p radial wave function is in agreement with both the ⁹Be and ¹³C data.     

Photoluminescence of the A2Π-X2Σ+ system of the yttrium oxide molecule

A cw dye laser, tunable in the region 570–620 nm, has been used to excite photoluminescence in the A²Π-X²Σ⁺ system of the YO molecule. Two methods have been used to obtain spectra. They are (i) photoluminescence and (ii) spectrally selective excitation spectroscopy. The latter maintains the simplicity of photoluminescence, but has higher resolution. The spectra obtained at medium resolution (～0.05 nm) have been surveyed and the identification of transitions has been outlined. A method was devised in which known lower state constants were used in calculating approximate upper state constants whenever the laser simultaneously excited coincident rotational transitions in the same band. From these calculations, an approximate value of α′_e was calculated which was found to be close to, but slightly larger than values previously computed from the Pekeris formula. Many examples of collisional transfer were observed. In particular, maximum transfer from ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ to ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ was always observed to involve an increase of one unit in the vibrational quantum number. No transfer was observed between opposite parity components of Λ doublets, in spite of their closeness in energy, indicating that the symmetry of the electronic eigenfunctions was unaffected by collisions. Reanalysis of previous high resolution data has shown that, when the contribution of Λ-doubling parameters to the separation of the ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ states is taken into account, the value of the spin-orbit coupling constant, A, changes significantly. It was also found necessary to include the constant, A_D, to account for the effect of centrifugal distortion on the spin-orbit interaction.     

Analyzing power measurements for n-p scattering between 13.5 and 16.9 MeV

The analyzing power A_γ(θ) for neutron-proton scattering has been measured for θ = 90°(c.m.) from 13.5 to 16.9 MeV and from θ = 50° to 145°(c.m.) at 16.9 MeV. Extensive Monte Carlo calculations have been made to correct for multiple scattering effects. Overall uncertainties are about ± 0.002. All the A_γ(θ) data, but primarily those at 16.9 MeV, disagree with predictons based on the phase-shift sets which have been derived previously by way of global analyses of nucleon-nucleon scattering data. Data for the product σ(θ)A_γ(θ) have been fitted with an expansion of the form (sin θ)($\text{a}{}_0\text{+ a}{}_1\text{cos}\text{θ + a}{}_2\text{cos}{}^2\text{θ)}$. For the first time the need for a non-zero a₂ has been illustrated for energies below 20 MeV. This parameter is shown to be related to the nucleon-nucleon F-state spin-orbit phase parameter. In addition, the P, D, and F spin-orbit phase parameter values derived from the present data differ significantly from the ones based on the Yale-IV and Liver-more-X global analyses. The derived D and F spin-orbit phase parameters also differ from those obtained in the recent analysis of nucleon-nucleon scattering data by Arndt et al.