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,$\text{V}{}^{\mathrm{+}}\text{∈L}{}^{\mathrm{p}}{}_{\mathrm{<mtext>loc</mtext>}}\text{(}\text{R}{}^{\mathrm{l}}\text{)}$, $\text{V}{}^{\mathrm{?}}\text{∈L}{}^{\mathrm{p}}\text{(}\text{R}{}^{\mathrm{l}}\text{)}$,$\text{p >}\text{l}\text{2}$.     

The quadrupole moments of the 5− states in 116Sn, 118Sn and 120Sn

The quadrupole interaction frequencies $\text{ω}{}_0\text{=}\text{3eQ}{}_1\text{V}{}_{\mathrm{zz}}\text{41(21-1)}\text{h}\text{?}$ in the 5^? state of ¹¹⁸Sn have been measured by time differential perturbed angular correlation technique in Sn, Sb and (95% Sn+5% Sb) environments. The ω₀ for ¹¹⁶Sn was determined in Sn environment only. With the help of the known electric field gradient ¹) of Sn in a Sn lattice the quadrupole moments have been deduced as $\text{Q(5}{}^{\mathrm{?}}\text{,}{}^{118}\text{Sn}\text{) = ±0.10(4) b}\text{and}\text{Q(5}{}^{\mathrm{?}}\text{,}{}^{116}\text{Sn}\text{) = ±0.165(60)}\text{b}$. These values together with the known²) quadrupole moment of the analogous 5^? state in ¹²⁰Sn are interpreted in terms of the pure single-particle model. The data exhibit the expected strong systematic variation of Q_I with the number of particles in the h_{$\text{11}\text{2}$}. subshell which is being filled with 1, 3 and 5 neutrons in ¹¹⁶Sn, ¹¹⁸Sn, and ¹²⁰Sn, respectively.     

Quadrupole moments of 81+ states in 92,94Mo

The ratio of the quadrupole moments of the 8₁⁺ states in ${}^{\mathrm{92,94}}\text{Mo}$ has been measured as $\text{Q(}{}^{94}\text{)}\text{Mo}\text{Q(}{}^{92}\text{Mo}\text{)}\text{= 1.48 ± 0.12}$ by means of the TD PAD method following the ${}^{\mathrm{90,92}}\text{Zr}\text{(α, 2}\text{n}\text{)}{}^{\mathrm{92,94}}\text{Mo}$ reactions on enriched Zr metal foils. This ratio is consistent with the effective charge ratio for the 8⁺ → 6⁺E2 transitions which demonstrates a prediction of the effective charge concept.     

Band contour analysis of compounds with pure isotopes: The E fundamentals of HC35Cl3

The vibration-rotation transitions for v = 1 ← 0 of NO (${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$) have been studied by using the technique of laser magnetic resonance spectroscopy. Five magnetic resonance lines are observed with three CO laser lines in the range from 1859 to 1886 cm^?1. From these, three zero-field transition frequencies, v = 1 ← 0; $\text{R(}\text{3}\text{2}\text{)}$, $\text{P(}\text{7}\text{2}\text{)}$, and $\text{P(}\text{9}\text{2}\text{)}$ are obtained with an accuracy of ±0.0007 cm^?1. The molecular constants which have been determined by borrowing centrifugal constants from a previous infrared work are $\text{B}{}_{02}{}^1\text{= 1.72004 ± 0.00006}\text{cm}{}^{\mathrm{?1}}$, $\text{B}{}_{12}{}^1\text{= 1.70212 ± 0.00010}\text{cm}{}^{\mathrm{?1}}$, and $\text{G(v = 1) ? G(v = 0) (}\text{for}{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{) = 1875.8470 ± 0.0007}\text{cm}{}^{\mathrm{?1}}$.     

Neutron diffraction measurement of the Debye-Walker factor of solid hcp 4He

The Debye-Waller factor of hcp ⁴He at molar volumes V_m of 12.06 and 15.72 cm³ has been measured by neutron diffraction techniques. It has been found that for scattering vectors $\text{Q ? 7}\text{A}\text{?}{}^{\mathrm{?1}}$ the Debye-Waller factor can be well represented by a simple Gaussian. The Debye temperatures, appropriate to the Debye-Waller factor, were found to be 99.73 K (V_m = 12.06 cm³) and 55.86 K (V_m = 15.72 cm³). No evidence was found of any forbidden reflections.     

Methyl barrier to internal rotation and quadrupole coupling constants in S-methylchlorothioformate

Internal rotation A-E splittings have been observed in the ground state for both ³⁵Cl and ³⁷Cl isotopic species of S-methylchlorothioformate. The values $\text{V}{}_3\text{(}{}^{35}\text{Cl}\text{) = 893 ± 20}$ and $\text{V}{}_3\text{(}{}^{37}\text{Cl) = 890 ± 20 cal/mole}$ have been obtained. The anaalysis of the hyperfine structure gave $\text{χ}{}_{\mathrm{aa}}\text{(}{}^{35}\text{Cl}\text{) = ?49.2}$, $\text{χ}{}_{\mathrm{bb}}\text{(}{}^{35}\text{Cl}\text{) = 22.4}$ and $\text{χ}{}_{\mathrm{aa}}\text{(}{}^{37}\text{Cl}\text{) = ?39.0}$, $\text{χ}{}_{\mathrm{bb}}\text{(}{}^{37}\text{Cl) = 18.3 MHz}$. Only the syn-conformation of the methyl group with respect to the carbonyl group has been observed. A partial r₀ structure is given.     

g-factors of 2.7 h 93Tc, 4.9 h 94Tc and 20 h 95Tc

The hyperfine splitting frequencies gμ_NB_H.F./h of 2.7 h ⁹³Tc $\text{(J}{}^{\mathrm{\pi }}\text{=}\text{9}\text{2}{}^{\mathrm{+}}\text{)}$, 4.9 h ⁹⁴Tc (J^π = 7⁺) and 20 h ⁹⁵Tc $\text{(J}{}^{\mathrm{\pi }}\text{=}\text{9}\text{2}{}^{\mathrm{+}}\text{)}$ as dilute impurities in Fe have been measured with NMR on oriented nuclei as 336.36(5) MHz, 175.11(1) MHz and 315.97(2) MHz, respectively. From the resonance shifts with an external magnetic field B₀ the hyperfine field of Tc$\text{Fe}$ has been determined as -317(5) kG. Taking this into account the nuclear g-factors are deduced as $\text{g(}{}^{93}\text{Tc}\text{) = 1.392(22), g(}{}^{94}\text{Tc}\text{) = 0.725(11)}\text{and}\text{g(}{}^{95}\text{Tc}\text{) = 1.308(21)}$.     

A new proof of the invariance principle in scattering theory

For free and interacting Hamiltonians, H₀ and H = H₀ + V(r) acting in L²(R³, dx) with V(r) a radial potential satisfying certain technical conditions, and for ? a real function on R with ?′ > 0 except on a discrete set, we prove that the Moller wave operators

exist and are independent of ?. The scattering operator

$\text{S = (Ω}{}^{\mathrm{+}}\text{)1Ω}{}^{\mathrm{?}}$

is shown to be unitary. Our proof utilizes time independent methods (eigenfunction expansions) and is effective in cases not previously analyzed, e.g. $\text{V(r) =}\text{sin}\text{r}\text{r}$ and many others.     

The nuclear magnetic moment of 71As and 72As

Nuclear magnetic resonance of oriented ⁷¹As and ⁷²As nuclei has been observed in an iron host lattice at low temperatures. The resonance frequencies are v_l = 174.96(10) MHz and 282.00(11) MHz respectively for zero external field. Using B_h.f.(FeAs) = 342.9(3) kG the g-factors of the two isotopes are derived as $\text{g(}{}^{71}\text{As}\text{) = (+)0.6694(7)}\text{and}\text{g(}{}^{72}\text{As) = (?)1.0789(11)}$. Combining nuclear orientation data with these results the spin of ⁷¹As has been confirmed as $\text{I =}\text{5}\text{2}$. The magnetic moments of the $\text{5}\text{2}{}^{\mathrm{?}}$ and 2^? states in the As isotopes are discussed in the framework of the shell model with configuration mixing.     

On the determination of α2F(ω) in metals by measuring I–V characteristics of “wide” (non-ballistic) point-contact junctions

For metals with small electron and phonon mean free paths (alloys, deformed or amorphous materials), there exists a possibility of determining α²F(ω) by measuring the V dependence of $\text{d}{}^2\text{I}\text{d}\text{V}{}^2$ or $\text{d}{}^3\text{I}\text{d}\text{V}{}^3$ of wide (d ? 10³ Å) point contacts (PC) and then inverting the linear equation relating these quantities to α²F(ω). The procedure is elaborated numerically and tested successfully for model electron-phonon interaction spectra.     

Resonances in the reaction 56Fe(p, γ)57Co

Resonances in the reaction ⁵⁶Fe(p, γ)⁵⁷Co have been surveyed over the energy range 1.2 ? E_p ? 1.5 MeV wherein the analogues of the ground state $\text{(J}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}^{\mathrm{?}}\text{, 0.014}\text{MeV}$ state $\text{(J}{}^{\mathrm{\pi }}\text{=}\text{3}\text{2}{}^{\mathrm{?}}\text{)}$ and 0.136 MeV state $\text{(J}{}^{\mathrm{\pi }}\text{=}\text{5}\text{2}{}^{\mathrm{?}}\text{)}$ of ⁵⁷Fe are expected to occur. Gamma-ray angular distributions have been used to establish resonance and bound-state spins, and decay schemes have been determined. The analogue resonances appear to be severely fragmented, however the density of resonances of a given spin correlates quite well with (³He, d) results and with the expected analogue-state positions.     

Beta-decay asymmetry and nuclear magnetic moment of 24Nam(T12 = 20 ms)

Polarized isomeric ${}^{24}\text{Na}{}^{\mathrm{m}}\text{(T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 20}\text{ms}\text{, I}{}^{\mathrm{\pi }}\text{= 1}{}^{\mathrm{+}}\text{)}$ nuclei were produced by capture of polarized thermal neutrons in a NaF single crystal at room temperature. The asymmetric β-decay radition of ²⁴Na^m was used to detect nuclear magnetic resonance signals yielding the magnetic moment $\text{|μ(}{}^{24}\text{Na}{}^{\mathrm{m}}\text{)| = 1.930 (3)}\text{n.m.}$ (uncorrected).     

Quadrupole moment of the β-emitter 17F

The quadrupole effect in the NMR of ${}^{17}\text{F}\text{(}\text{I}{}^{\mathrm{\pi }}\text{=}\text{5}\text{2}{}^{\mathrm{+}}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 66}\text{s}\text{)}$ in a MgF₂ single crystal has been investigated. Production and implantation of polarized ¹⁷F through the ¹⁶O(d, n) reaction and the resulting asymmetric β-decay were utilized. The quadrupole coupling constant is determined to be |eqQ/h| = 8.41 ± 0.24 MHz with η = 0.32 ± 0.02 at room temperature. No appreciable temperature dependence of eqQ is found from 77 K up to 770 K. Using previously known results, the following ratios of the quadrupole moments are obtained; $\text{|Q(}{}^{17}\text{F}\text{,}\text{5}\text{2}{}^{\mathrm{+}}\text{)| : |Q(}{}^{18}\text{F}{}^1\text{, 5}{}^{\mathrm{+}}\text{)| : |Q(}{}^{19}\text{F}{}^1\text{,}\text{5}\text{2}{}^{\mathrm{+}}\text{| : |Q(}{}^{20}\text{F}\text{, 2}{}^{\mathrm{+}}\text{)|= 1 : (1.33 ± 0.08) : (1.24 ± 0.06) : (0.69 ± 0.02)}$. The additivity relation of Q between ¹⁷F, ¹⁷O, and ¹⁸F1 is discussed.     

A study of valency changes of vanadium ions in Al2O3 by γ irradiation

The effect of γ irradiation at 300 K on the concentrations of vanadium ions V³⁺, V⁴⁺ and V²⁺ in Al₂O₃ has been studied quantitatively, using three techniques: optical absorption (V³⁺), low temperature thermal conductivity measurements (V⁴⁺) and EPR (V²⁺). Several single crystals of Al₂O₃ doped with vanadium in a large range of concentration $\text{(2.8 × 10}{}^{18}\text{? 1.3 × 10}{}^{20}\text{at.}\text{cm}{}^3\text{)}$ have been measured. The evolution of the respective concentrations by γ irradiation as a function of the total vanadium content C is quite different in the two regions $\text{C< 1.2 × 10}{}^{19}\text{at.}\text{cm}{}^3$ and C larger than this value. A consistent analysis of the results has nevertheless been achieved, leading to the determination of the absolute concentrations of the three ions in the as-received and γ irradiated states for all samples with $\text{C<4.2 × 10}{}^{19}\text{at.}\text{cm}{}^3$ (room temperature annealing is observed above this value). The concentrations of V⁴⁺ and V²⁺ ions are always small, but V⁴⁺ ions are more stable: they are present in the as-received state at a level of 1% of the total concentration and a maximum value of $\text{/}\text{?}\text{2.3 × 10}{}^{18}\text{at.}\text{cm}{}^3$ is observed in the γ irradiated state; on the other hand there are less than 4.7 × 10¹⁵V²⁺ ions per cm³ in the as-received state and the maximum value is only $\text{4.2 × 10}{}^{17}\text{at.}\text{cm}{}^3$. Charge transfer between V ions only is not sufficient to explain the experimental results and other defects must be involved in the γ irradiation effect.     

The bound states of weakly coupled long-range one-dimensional quantum hamiltonians

We study the small λ behavior of the ground state energy, E(λ), of the Hamiltonian $\text{?(}\text{d}{}^2\text{dx}{}^2\text{) + λV(x)}$. In particular, if V(x) ～ ?ax^?2 at infinity and if 69-1, we prove that $\text{(?E(λ))}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= ?[}\text{1}\text{2}\text{λ + aλ}{}^2\text{lnλ] ∫ dxV(x) + O(λ}{}^2\text{)}$.     

Nuclear spins of 186, 187, 188, 189, 189m Au

The nuclear spins of some neutron deficient gold isotopes have been measured using the atomic-beam magnetic resonance method. The following results have been obtained: ¹⁸⁶Au 10.7 min) I = 3, ${}^{187}\text{Au}\text{(8.5}\text{min}\text{) I =}\text{1}\text{2}$, ${}^{188}\text{Au}\text{(8.8}\text{min}\text{) I =}\text{1}\text{2}$, ${}^{189}\text{Au}\text{(28.3}\text{min}\text{) I =}\text{1}\text{2}$ and ${}^{\mathrm{<mtext>189</mtext><mtext>m</mtext>}}\text{Au}\text{(4.6}\text{min}\text{) I =}\text{11}\text{2}$. The spins of these typical transitional nuclei are discussed briefly in terms of various nuclear models.     

Determination of the isotopic shift of the first resonance line in Cs(I) spectrum for the isotopes 131Cs, 132Cs,and 136Cs

The isotope shifts of the resonance line $\text{λ = 8521}\text{A}\text{?}$ of ¹³¹Cs, ¹³²Cs, and ¹³⁶Cs with respect to ¹³³Cs were determined by a new scanning technique to be $\text{v}\text{?}\text{(}{}^{133}\text{Cs}\text{)-}\text{v}\text{?}\text{(}{}^{131}\text{Cs}\text{) = +1.70(40)}\text{mK}$, $\text{v}\text{?}\text{(}{}^{133}\text{Cs}\text{)-}\text{v}\text{?}\text{(}{}^{132}\text{Cs}\text{) = ?0.95(80)}\text{mK}$, $\text{v}\text{?}\text{(}{}^{136}\text{Cs}\text{)-}\text{v}\text{?}\text{(}{}^{133}\text{Cs}\text{) = ?4.0(3.0)}\text{mK}$. In accordance with results from other Cs isotopes and neighbouring elements they show the change 〈δr²〉 in the second radial moment of the nuclear charge distribution to be a factor of 5 to 10 smaller than expected from the model of uniform charge distribution. Integral isotope shifts over the isotopic chains of Xe, Cs, and Ba were analyzed in terms of collective models. Assuming an isotopic shift discrepancy of 0.5 for the nuclear volume shift it was possible to derive deformation parameters $\text{〈β}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ in quantitative agreement with those from B(E2) measurements.     

Mössbauer-effect studies of excited states of 155Gd, 156Gd and 157Gd

Mössbauer-effect studies yield the following nuclear parameters: In ¹⁵⁵Gd, Q(86)/Q(0) = 0.087 ± 0.006, Q(105)/Q(0) = 1.00 ± 0.03. In ${}^{156}\text{Gd}\text{, g(89) = 0.386 ± 0.004,}{}^{156}\text{Q(89)/}{}^{155}\text{Q(0) = ?1.51 ± 0.02.}\text{In}{}^{157}\text{Gd}\text{, Q(64)/Q(0) = 1.80 ± 0.03}\text{and}\text{g(64) = ?0.185 ± 0.005}$. The value of g(89) is in very good agreement with the theoretical value.     

The rotational analysis of the 1Π-X 1Σ+ system at 649.5 nanometers of zirconium oxide

A red-degraded band head, normally badly overlapped by the gamma system, $\text{A}{}^3\text{Φ}\text{- X′}{}^3\text{Δ}$, of zirconium oxide, appears in emission spectra of zirconium arcs and in absorption spectra of S-type stars and of frozen rare gas matrices containing zirconium. The emission band has been examined at high-resolution with the aid of separated zirconium isotopes. Identification of the band as 0-0 of a ${}^1\text{Π}\text{- X}{}^1\text{Σ}{}^{\mathrm{+}}$ system of zirconium oxide is confirmed by rotational analysis where the following constants (cm^?1) are obtained for ⁹⁰Zr¹⁶O:

$\text{B}{}_0\text{′(R,P) = 0.40142 D}{}_0\text{′(R,P) = 3.51 × 10}{}^{\mathrm{?7}}$

$\text{B}{}_0\text{′(Q) = 0.40166 D}{}_0\text{′(Q) =3.52 × 10}{}^{\mathrm{?7}}$

$\text{B}{}_0\text{″ = 0.42263 D}{}_0\text{″ =3.19 × 10}{}^{\mathrm{?7}}$

$\text{ν}{}_0\text{= 15383.81s}$

The Λ-type doubling in the ¹Π state and the question of whether $\text{X}{}^1\text{Σ}{}^{\mathrm{+}}$ or $\text{X′}{}^3\text{Δ}$ is the true ground state of ZrO are discussed.