Band spectrum of manganese oxide (MnO)

New measurements of the wavelengths of the band heads of MnO spectrum have been made. In all 57 band heads, including 15 hitherto unrecorded ones, have been measured. The equation representing the wave-number of a band head has been modified as,

$$\begin{gathered} v = 17949 \cdot 19 + \{ 762 \cdot 75(v' + \tfrac{1}{2}) - 9 \cdot 60(v' + \tfrac{1}{2})^2 + 0 \cdot 06(v' + \tfrac{1}{2})^3 \} \hfill \\ - \{ 839 \cdot 55(v'' + \tfrac{1}{2}) - 4 \cdot 79(v'' + \tfrac{1}{2})^2 \} \hfill \\ \end{gathered} $$     

The band spectrum of PO: Two new doublet systems in the ultraviolet

The band spectrum of PO was excited in a high frequency discharge from a 1/2 kW oscillator working at a frequency of 30 to 40 Mc/sec. A new doublet system of bands degraded to red designated asC′?X ² Π _r occuring in the region λ 2200–λ 2900 was observed and analyzed. The following vibrational quantum formula was derived for the inner heads (R ₁ andQ ₂)

$$\begin{gathered} v = ^{43854 \cdot 5} + 825 \cdot 8(\upsilon ' + \tfrac{1}{2}) - 6 \cdot 44(\upsilon ' + \tfrac{1}{2})^2 \hfill \\ ^{43631 \cdot 4} - 1232 \cdot 6(\upsilon '' + \tfrac{1}{2}) - 6 \cdot 48(\upsilon '' + \tfrac{1}{2})^2 . \hfill \\ \end{gathered}$$     

Vibrational analysis of the (B 2 П→X 2 П) system of NS

A few red degraded bands attributable to NS have been reported earlier byFowler andBarker, Dressler andBarrow et al, and they occur in the same region (2300 to 2700 Å) as the bands of the known systems (C ² ∑ ⁺?X ² П) and (A ² Δ?X ² П). Measurements made on the heads of some of these weak bands ledBarrow et al. to believe that these bands may form a system analogous to theβ-system of NO and be due to a² П-² П transition. The spectrum of NS has now been studied in a little more detail by means of an uncondensed discharge through dry nitrogen and sulphur vapour in the presence of argon and thirty three bands belonging to this system have been recorded in the region 2280 to 2760 Å. It has been found possible to represent the band heads by means of the equation

$$^v {\text{head}} {\text{ = }} \left. {_{43182 \cdot 5}^{{\text{43311}} \cdot {\text{5}}} } \right\}_{ - [1219 \cdot 20(v'' + \tfrac{1}{2}) - 7 \cdot 48(v'' + \tfrac{1}{2})^2 ].}^{ + [761 \cdot 04(v' + \tfrac{1}{2}) - 5 \cdot 10(v' + \tfrac{1}{2})^2 ]}$$     

Half-life measurements in59Co,141Pr and227Ac

The half-lives of the 1291.6 keV level in⁵⁹Co, 145.43 keV level in¹⁴¹Pr and 27.35 keV level in²²⁷Ac have been measured using leading edge and zero-crossover timing techniques. The decay curves analysed by moments, Laplace transform and slope methods gave the following half-life values: $$\begin{gathered} T_{\tfrac{1}{2}} (1291.6 keV level in {}^{59}Co) = (0.538 \pm 0.004) ns \hfill \\ T_{\tfrac{1}{2}} (145.43 keV level in {}^{141}\Pr ) = (1.82 \pm 0.04) ns \hfill \\ T_{\tfrac{1}{2}} (27.35 keV level in {}^{227}Ac) = (41.0 \pm 1.1) ns. \hfill \\ \end{gathered} $$ From the measured half-lives, the reduced transition probabilitiesB(M1)↓,B(E2)↓ for gamma transitions de-exciting the above mentioned levels in⁵⁹Co and¹⁴¹Pr are determined and compared with single particle, intermediate coupling and Sorensen estimates. In²²⁷Ac, absolute transition probability for the 27.35 keV transition is determined and compared with single particle and Nilsson estimates.     

The nonlocal tensor operatorS 12 N (ρ, ρ′)

The extension of the tensor potentialS ₁₂ V _T (r) to the case of a nonlocal interaction is shown to be $$\begin{gathered} V_T (r{\text{,}}r'{\text{) = }}S_{12}^N F(r,r') \hfill \\ {\text{ = }}\tfrac{{\text{1}}}{{\text{2}}}[9(\rho \cdot \rho '{\text{)(}}\sigma _1 \cdot \rho \sigma _2 \cdot \rho '{\text{ + }}\sigma _1 \cdot \rho '\sigma _2 \cdot \rho {\text{)}} - 2(\sigma _1 \cdot \sigma _2 )]F(r,r'), \hfill \\ \end{gathered}$$ where ρ=r/r. This potential has the necessary invariance properties provided thatF(r, r′)=F(r′, r). With this potential andF(r, r′) taken to have a rank-one separable form, the behaviour of the model-deuteron radius with respect to the strength of the tensor nonlocality is investigated. It is found that the model radius decreases as the tensor nonlocality becomes more attractive. This is consistent with recent work which considers only central nonlocality.     

Gleichzeitige Messung von Hyperfeinstruktur,Starkeffekt und Zeemaneffekt des133Cs19F mit einer Molekülstrahl-Resonanzapparatur

An electric molecular beam resonance spectrometer has been used to measure simultaneously the Zeeman- and Stark-effect splitting of the hyperfine structure of¹³³Cs¹⁹F. Electric four pole lenses served as focusing and refocusing fields of the spectrometer. A homogenous magnetic field (Zeeman field) was superimposed to the electric field (Stark field) in the transition region of the apparatus. Electrically induced (Δ m _J =±1)-transitions have been measured in theJ=1 rotational state, υ=0, 1 vibrational state. The obtained quantities are: The electric dipolmomentμ _el of the molecule for υ=0, 1; the rotational magnetic dipolmomentμ _J for υ=0, 1; the anisotropy of the magnetic shielding (σ _⊥-σ‖) by the electrons of both nuclei as well as the anisotropy of the molecular susceptibility (ξ _⊥-ξ‖), the spin rotational interaction constantsc _Cs andc _F, the scalar and the tensor part of the nuclear dipol-dipol interaction, the quadrupol interactioneqQ for υ=0, 1. The numerical values are:

$$\begin{gathered} \mu _{el} \left( {\upsilon = 0} \right) = 73878\left( 3 \right)deb \hfill \\ \mu _{el} \left( {\upsilon = 1} \right) - \mu _{el} \left( {\upsilon = 0} \right) = 0.07229\left( {12} \right)deb \hfill \\ \mu _J /J\left( {\upsilon = 0} \right) = - 34.966\left( {13} \right) \cdot 10^{ - 6} \mu _B \hfill \\ \mu _J /J\left( {\upsilon = 1} \right) = - 34.823\left( {26} \right) \cdot 10^{ - 6} \mu _B \hfill \\ \left( {\sigma _ \bot - \sigma _\parallel } \right)_{Cs} = - 1.71\left( {21} \right) \cdot 10^{ - 4} \hfill \\ \left( {\sigma _ \bot - \sigma _\parallel } \right)_F = - 5.016\left( {15} \right) \cdot 10^{ - 4} \hfill \\ \left( {\xi _ \bot - \xi _\parallel } \right) = 14.7\left( {60} \right) \cdot 10^{ - 30} erg/Gau\beta ^2 \hfill \\ c_{cs} /h = 0.638\left( {20} \right)kHz \hfill \\ c_F /h = 14.94\left( 6 \right)kHz \hfill \\ d_T /h = 0.94\left( 4 \right)kHz \hfill \\ \left| {d_s /h} \right|< 5kHz \hfill \\ eqQ/h\left( {\upsilon = 0} \right) = 1238.3\left( 6 \right) kHz \hfill \\ eqQ/h\left( {\upsilon = 1} \right) = 1224\left( 5 \right) kHz \hfill \\ \end{gathered} $$     

More corrections to the sixth-order anomalous magnetic moment of the muon

The contribution to the sixth-order muon anomaly from second-order electron vacuum polarization is determined analytically to orderm _e/m _μ. The result, including the contributions from graphs containing proper and improper fourth-order electron vacuum polarization subgraphs, is $$\begin{gathered} \left( {\frac{\alpha }{\pi }} \right)^3 \left\{ {\frac{2}{9}\log ^2 } \right.\frac{{m_\mu }}{{m_e }} + \left[ {\frac{{31}}{{27}}} \right. + \frac{{\pi ^2 }}{9} - \frac{2}{3}\pi ^2 \log 2 \hfill \\ \left. { + \zeta \left( 3 \right)} \right]\log \frac{{m_\mu }}{{m_e }} + \left[ {\frac{{1075}}{{216}}} \right. - \frac{{25}}{{18}}\pi ^2 + \frac{{5\pi ^2 }}{3}\log 2 \hfill \\ \left. { - 3\zeta \left( 3 \right) + \frac{{11}}{{216}}\pi ^4 - \frac{2}{9}\pi ^2 \log ^2 2 - \frac{1}{9}log^4 2 - \frac{8}{3}a_4 } \right] \hfill \\ + \left[ {\frac{{3199}}{{1080}}\pi ^2 - \frac{{16}}{9}\pi ^2 \log 2 - \frac{{13}}{8}\pi ^3 } \right]\left. {\frac{{m_e }}{{m_\mu }}} \right\} \hfill \\ \end{gathered} $$ . To obtain the total sixth-order contribution toa _μ?a _e, one must add the light-by-light contribution to the above expression.     

Gleichzeitige Messung von Hyperfeinstruktur,Stark-Effekt und Zeeman-Effekt des39K19F mit einer Molekülstrahlresonanzapparatur

An electric Molecular-Beam-Resonance-Spectrometer has been used to measure simultanously the Zeeman- and Stark-effect splitting of the hyperfine structure of³⁹K¹⁹ F. Electric four pole lenses served as focusing and refocusing fields of the spectrometer. A homogenous magnetic field (Zeeman field) was superimposed to the electric field (Stark field) in the transition region of the apparatus. The observed (Δm _J =±1)-transitions were induced electrically. Completely resolved spectra of KF in theJ=1 rotational state have been measured. The obtained quantities are: The electric dipolmomentμ _e l of the molecul forv=0,1 and 2; the rotational magnetic dipolmomentμ _J forv=0,1; the difference of the magnetic shielding (σ_⊥ ? σ_∥) by the electrons of both nuclei as well as the difference of the molecular susceptibility (ξ_⊥ ? ξ_∥). The numerical values are

$$\begin{array}{*{20}c} {\mu _{e1} = 8,585(4)deb,} \\ {\frac{{(\mu _{e1} )_{\upsilon = 1} }}{{(\mu _{e1} )_{\upsilon = 0} }} = 1,0080,} \\ {{{\mu _J } \mathord{\left/ {\vphantom {{\mu _J } J}} \right. \kern-\nulldelimiterspace} J} = ( - )2352(10) \cdot 10^{ - 6} \mu _B ,} \\ {(\sigma _ \bot - \sigma _\parallel )F = ( - )2,19(9) \cdot 10^{ - 4} ,} \\ {(\sigma _ \bot - \sigma _\parallel )K = ( - )12(9) \cdot 10^{ - 4} ,} \\ {(\xi _ \bot - \xi _\parallel ) = 3 (1) \cdot 10^{ - 30} {{erg} \mathord{\left/ {\vphantom {{erg} {Gau\beta ^2 }}} \right. \kern-\nulldelimiterspace} {Gau\beta ^2 }}} \\ \end{array} $$     

Gleichzeitige Messung von Hyperfeinstruktur,Starkeffekt und Zeemaneffekt des23Na19F mit einer Molekülstrahl-Resonanzapparatur

An electric molecular beam resonance spectrometer has been used to measure simultaneously the Zeeman- and Stark-effect splitting of the hyperfine structure of²³Na¹⁹F. Electric four pole lenses served as focusing and refocusing fields of the spectrometer. A homogenous magnetic field (Zeeman field) was superimposed to the electric field (Stark field) in the transition region of the apparatus. The observed (Δm _J=±1)-transitions were induced electrically. Completely resolved spectra of NaF in theJ=1 rotational state have been measured in several vibrational states. The obtained quantities are: The electric dipolmomentμ _el of the molecule forv=0, 1 and 2, the rotational magnetic dipolmomentμ _J forv=0, 1, the difference of the magnetic shielding (σ _⊥-σ _‖) by the electrons of both nuclei as well as the difference of the molecular susceptibility (ξ _⊥-ξ _‖), the spin rotational constantsc _F andc _Na, the scalar and the tensor part of the molecular spin-spin interaction, the quadrupol interactione q Q forv=0, 1 and 2. The numerical values are

$$\begin{gathered} \mu _{\mathfrak{e}1} = 8,152(6) deb \hfill \\ \frac{{\mu _{\mathfrak{e}1} (v = 1)}}{{\mu _{\mathfrak{e}1} (v = 0)}} = 1,007985 (7) \hfill \\ \frac{{\mu _{\mathfrak{e}1} (v = 2)}}{{\mu _{\mathfrak{e}1} (v = 1)}} = 1,00798 (5) \hfill \\ \mu _J = - 2,89(3)10^{ - 6} \mu _B \hfill \\ \frac{{\mu _J (v = 0)}}{{\mu _J (v = 1)}} = 1,020 (13) \hfill \\ (\sigma _ \bot - \sigma _\parallel )_{Na} = - 51(12) \cdot 10^{ - 5} \hfill \\ (\sigma _ \bot - \sigma _\parallel )_F = - 51(12) \cdot 10^{ - 6} \hfill \\ (\xi _ \bot - \xi _\parallel ) = - 1,59(120)10^{ - 30} erg/Gau\beta ^2 \hfill \\ {}^CNa/^h = 1,7 (2)kHz \hfill \\ {}^CF/^h = 2,2 (2)kHz \hfill \\ {}^dT/^h = 3,7 (2)kHz \hfill \\ {}^dS/^h = 0,2 (2)kHz \hfill \\ eq Q/h = - 8,4393 (19)MHz \hfill \\ \frac{{eq Q(v = 0)}}{{eq Q(v = 1)}} = 1,0134 (2) \hfill \\ \frac{{eq Q(v = 1)}}{{eq Q(v = 2)}} = 1,0135 (2) \hfill \\ \end{gathered} $$     

An expansion of Hartree-Fock and correlation energies,relativistic corrections and the dipole matrix element in the powers of of 1/Z

Feynman diagrammatic technique was used for the calculation of Hartree-Fock and correlation energies, relativistic corrections, dipole matrix element. The whole energy of atomic system was defined as a polen-electron Green function. Breit operator was used for the calculation of relativistic corrections. The Feynman diagrammatic technique was developed for 〈H_B>. Analytical expressions for the contributions from diagrams were received. The calculations were carried out for the terms of such configurations as 1s² 2sⁿ¹ 2pⁿ² (2 ≧n₁≧ 0, 6≧ n₂ ≧ 0). Numerical results are presented for the energies of the terms in the form $$E = E_0 Z^2 + \Delta {\rm E}_2 + \frac{1}{Z}\Delta {\rm E}_3 + \frac{{\alpha ^2 }}{4}(E_0^r + \Delta {\rm E}_1^r Z^3 )$$ and for fine structure of the terms in the form $$\begin{gathered} \left\langle {1s^2 2s^{n_1 } 2p^{n_2 } LSJ|H_B |1s^2 2s^{n_1 \prime } 2p^{n_2 \prime } L\prime S\prime J} \right\rangle = \hfill \\ = ( - 1)^{\alpha + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 1} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 [E^{(0)} (Z - B) + \varepsilon _{co} ] + \hfill \\ + ( - 1)^{L + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 2} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 \varepsilon _{cc} . \hfill \\ \end{gathered} $$ Dipole matrix elements are necessary for calculations of oscillator strengths and transition probabilities. For dipole matrix elements two members of expansion by 1/Z have been obtained. Numerical results were presented in the form P(a,a′) = a/Z(1+τ/Z).     

On the similarity solution of evolution equation u t =H(x,t, u,u x,u xx , ...)

Let $$\begin{gathered} u^* = u + \in \eta (x,{\text{ }}t,{\text{ }}u), \hfill \\ \hfill \\ \hfill \\ x^* = x + \in \xi (x, t, u{\text{),}} \hfill \\ \hfill \\ \hfill \\ {\text{t}}^{\text{*}} = {\text{ }}t + \in \tau {\text{(}}x,{\text{ }}t,{\text{ }}u), \hfill \\ \end{gathered}$$ be an infinitesimal invariant transformation of the evolution equation u _t =H(x,t,u,?u/?x,...,? ⁿ :u/?x ⁿ . In this paper we give an explicit expression for \(\eta ^{X^i }\) in the ‘determining equation’ $$\eta ^T = \sum\limits_{i = 1}^n {{\text{ }}\eta ^{X^i } {\text{ }}\frac{{\partial H}}{{\partial u_i }} + \eta \frac{{\partial H}}{{\partial u_{} }} + \xi \frac{{\partial H}}{{\partial x}} + \tau } \frac{{\partial H}}{{\partial t}},$$ where u _i =? ⁱ u/?x ⁱ . By using this expression we derive a set of equations with η, ξ, τ as unknown functions and discuss in detail the cases of heat and KdV equations.     

Detection of a hexadecapole interaction in the atomic ground state3 H 6 of167Er

Using the atomic beam magnetic resonance method, precision measurements of the hyperfine structure and Zeeman interactions have been performed in the ground state 4f ¹²6s ^{2 3} H ₆ of¹⁶⁷Er. The experimental data were analyzed using an effective operator parametrized in the space of states of the ground state multiplet. It yielded eight effective hyperfine structure and Zeeman interaction constants which served to calculate the seven hyperfine separations of the ground state. The results are: $$\begin{gathered} 2F 2F' v_{FF'} (MHz) \hfill \\ 5 7 - 354.371 9409 (27) \hfill \\ 7 9 - 2{\text{78}}{\text{.231}} {\text{8263(14)}} \hfill \\ {\text{9}} 11 - 69.050 7785 (4) \hfill \\ 11 13 + 302.735 3731(12) \hfill \\ 13 15 + 866.691 3871(10) \hfill \\ 15 17 + 1,652.383 5154 (6) \hfill \\ 17 19 + 2,689.380 8050(10) \hfill \\ \end{gathered}$$ From the effective Zeeman interaction constants it was possible to determine an improvedg _I -value, uncorrected for atomic diamagnetism: $$ g_I = + 0.086 775 (19) \cdot 10^{ - 3}$$ Furthermore a hexadecapole interaction corresponding to a diagonal hexadecapole interaction constant $$A_4 = - 16 (10) Hz$$ could be established which is of the order of magnitude expected from Coulomb excitation experiments as well as theoretical calculations.     

Determination of heavy quark non-perturbative parametersfrom spectral moments in semileptonic B decays

Moments of the hadronic invariant mass and of the lepton energy spectra in semileptonic B decays have been determined with the data recorded by the DELPHI detector at LEP. From measurements of the inclusive b-hadron semileptonic decays, and imposing constraints from other measurements on b- and c-quark masses, the first three moments of the lepton energy distribution and of the hadronic mass distribution, have been used to determine parameters which enter into the extraction of |V_cb| from the measurement of the inclusive b-hadron semileptonic decay width. The values obtained in the kinetic scheme are: and include corrections at order 1/m_b³. Using these results, and present measurements of the inclusive semileptonic decay partial width of b-hadrons at LEP, an accurate determination of |V_cb| is obtained: Received: 26 April 2005, Revised: 16 September 2005, Published online: 16 November 2005     

Three-loop on-shell charge renormalization without integration:\Lambda _{QED}^{\overline {MS} } to four loops

Using algebraic methods, we find the three-loop relation between the bare and physical couplings of one-flavourD-dimensional QED, in terms of Γ functions and a singleF ₃₂ series, whose expansion nearD=4 is obtained, by wreath-product transformations, to the order required for five-loop calculations. Taking the limitD→4, we find that the \(\overline {MS} \) coupling \(\bar \alpha (\mu )\) satisfies the boundary condition $$\begin{gathered} \frac{{\bar \alpha (m)}}{\pi } = \frac{\alpha }{\pi } + \frac{{15}}{{16}}\frac{{\alpha ^3 }}{{\pi ^3 }} + \left\{ {\frac{{11}}{{96}}\zeta (3) - \frac{1}{3}\pi ^2 \log 2} \right. \hfill \\ \left. { + \frac{{23}}{{72}}\pi ^2 - \frac{{4867}}{{5184}}} \right\}\frac{{\alpha ^4 }}{{\pi ^4 }} + \mathcal{O}(\alpha ^5 ), \hfill \\ \end{gathered} $$ wherem is the physical lepton mass and α is the physical fine structure constant. Combining this new result for the finite part of three-loop on-shell charge renormalization with the recently revised four-loop term in the \(\overline {MS} \) β-function, we obtain $$\begin{gathered} \Lambda _{QED}^{\overline {MS} } \approx \frac{{me^{3\pi /2\alpha } }}{{(3\pi /\alpha )^{9/8} }}\left( {1 - \frac{{175}}{{64}}\frac{\alpha }{\pi } + \left\{ { - \frac{{63}}{{64}}\zeta (3)} \right.} \right. \hfill \\ \left. { + \frac{1}{2}\pi ^2 \log 2 - \frac{{23}}{{48}}\pi ^2 + \frac{{492473}}{{73728}}} \right\}\left. {\frac{{\alpha ^2 }}{{\pi ^2 }}} \right), \hfill \\ \end{gathered} $$ at the four-loop level of one-flavour QED.     

Messung des gR-Faktors des 2+-Rotationsniveaus von Dy160 nach der Spinrotationsmethode und Bestimmung der Multipolmischungen mehrerer γ-Übergänge im Zerfall des Tb160

A differential measurement of the spin rotation of Dy¹⁶⁰ in the 2+ rotational state was performed by using liquid sources of TbCl₃ solved in 3M HCl and applying an external magnetic field of 33 500 Gauss. No change of the Larmor precession frequency could be detected within the first 10·10^?9 s. It is concluded that the ground state of the electronic shell of Dy⁺⁺⁺ is reached in 6·10^?10 s after theβ-decay of Tb¹⁶⁰. The valueg _R=+0.364±0.011 was derived using 〈r^?3〉_eff=8.92 a. u. for the 4f-shell of Dy⁺⁺⁺. A comparison with the result ofCohen who studied the Mössbauer-effect in Fe₂Dy shows that the value of 〈r^?3〉_eff must be 10% larger in this compound. A measurement of the effective magnetic field at the position of the nucleus in a source of terbium metal was performed for different temperatures. It revealed a temperature dependence which is very similar to the paramagnetic susceptibility χ(T). We observed a strong attenuation ofγ γ-angular correlations in the 2+ rotational state. For liquid sources of TbCl₃ solved in 3M HCl the following attenuation parameters were measured:

$$\begin{gathered} \lambda _2 = (0.122 \pm 0.013) \cdot 10^9 {\text{s}}^{ - {\text{1}}} , \hfill \\ \lambda _4 = (0.235 \pm 0.024) \cdot 10^9 {\text{s}}^{ - {\text{1}}} . \hfill \\ \end{gathered}$$     

Electromagnetic moment investigation of two short-lived isomeric states in118Sb

Two short-lived isomeric states in¹¹⁸Sb have been investigated by the¹¹⁸Sn(p, n),¹¹⁸Sn(d, 2n) and¹¹⁵In(α, n) reactions. The TDPAD method on solid and liquid metallic targets was used to measure the electromagnetic moments of these states. The results of the experiments are: $$\begin{gathered} T_{1/2} = 13.4{\text{ }}(3){\text{ }}ns I^\pi = 3^ - {\text{ }}g = - 1.254(31){\text{ }}|Q| = 0.25{\text{ }}(5){\text{ }}b, \hfill \\ T_{1/2} = 22.8{\text{ }}(4){\text{ }}ns I^\pi = 7^ + {\text{ }}g = + 0.680(18){\text{ }}|Q| > 1.4{\text{ }}b. \hfill \\ \end{gathered}$$ Pure \([\pi 2d_{5/2} \otimes v1h_{1{\text{ }}1/2} ]_{3 - }\) and \([\pi 1g_{9/2}^{ - 1} \otimes v2d_{5/2}^{ - 1} ]_{7 + }\) configurations have been established for the two isomeric states. An experimental evidence concerning the participation of the 1g ₉ ^2/?1 proton shell-model intruder excitation into the positive parity low-lying level structure of the odd-odd¹¹⁸Sb nucleus was obtained.     

Asymptotic behavior of Mayer cluster sums for the one-dimensional Ising model

The properties of the high-field polynomialsL _n (u) for the one-dimensional spin 1/2 Ising model are investigated. [The polynomialsL _n (u) are essentially lattice gas analogues of the Mayer cluster integralsb _n (T) for a continuum gas.] It is shown thatu ^?1 L _n (u) can be expressed in terms of a shifted Jacobi polynomial of degreen?1. From this result it follows thatu ^?1 L _n (u); n=1, 2,... is a set of orthogonal polynomials in the interval (0, 1) with a weight functionω(u)=u, andu ^?1 L _n (u) hasn?1 simple zerosu _n (v); v=1, 2,...,n?1 which all lie in the interval 0<u<1. Next the detailed behavior ofL _n (u) asn→∞ is studied. In particular, various asymptotic expansions forL _n (u) are derived which areuniformly valid in the intervalsu<0, 0<u<1, andu>1. These expansions are then used to analyze the asymptotic properties of the zeros {u _n (v); v=1, 2,...,n?1}. It is found that $$\begin{array}{*{20}c} {u_n (v) \sim \tfrac{1}{4}({{j_{1,v} } \mathord{\left/ {\vphantom {{j_{1,v} } n}} \right. \kern-\nulldelimiterspace} n})^2 [1 - ({{j_{1,v}^2 } \mathord{\left/ {\vphantom {{j_{1,v}^2 } {12}}} \right. \kern-\nulldelimiterspace} {12}})n^{ - 1} + ({{j_{1,v}^2 } \mathord{\left/ {\vphantom {{j_{1,v}^2 } {700)( - 3 + 2j_{1,v}^2 )n^{ - 4} }}} \right. \kern-\nulldelimiterspace} {700)( - 3 + 2j_{1,v}^2 )n^{ - 4} }}} \\ { + ({{j_{1,v}^2 } \mathord{\left/ {\vphantom {{j_{1,v}^2 } {20160)(40 + 4j_{1,v}^2 - j_{1,v}^4 }}} \right. \kern-\nulldelimiterspace} {20160)(40 + 4j_{1,v}^2 - j_{1,v}^4 }})n^{ - 6} + \cdot \cdot \cdot ]} \\ {u_n (n - v) \sim 1 - ({{j_{0,v}^2 } \mathord{\left/ {\vphantom {{j_{0,v}^2 } 4}} \right. \kern-\nulldelimiterspace} 4})n^{ - 2} + ({{j_{0,v}^2 } \mathord{\left/ {\vphantom {{j_{0,v}^2 } {48)( - 2 + j_{0,v}^2 )n^{ - 4} }}} \right. \kern-\nulldelimiterspace} {48)( - 2 + j_{0,v}^2 )n^{ - 4} }}} \\ { + ({{j_{0,v}^2 } \mathord{\left/ {\vphantom {{j_{0,v}^2 } {2880)(2 + 9j_{0,v}^2 - 2j_{0,v}^4 )n^{ - 6} + \cdot \cdot \cdot }}} \right. \kern-\nulldelimiterspace} {2880)(2 + 9j_{0,v}^2 - 2j_{0,v}^4 )n^{ - 6} + \cdot \cdot \cdot }}} \\ \end{array} $$ asn→∞v fixed, wherej _k,v denotes thevth zero of the Bessel functionJ _k(^z)     

Half-life measurements of the 86.6 keV level in233Pa and 59.6 keV level in237Np

The half-lives of the 86.6 keV level in²³³Pa and the 59.6 keV level in²³⁷Np have been measured. A silicon surface barrier alpha detector and a NaI(Tl) gammadetector were used. The decay time spectrum of alpha-gamma coincidences obtained from a start-stop type of time-to-pulse height converter was recorded on a 2048-channel analyser. Analysis of the data gave the following half-life values: $$\begin{gathered} T_{\frac{1}{2}} :^{233} Pa (86.6 keV level) = (37.4 \pm 0.4) ns \hfill \\ T_{\frac{1}{2}} :^{237} Np (59.6 keV level) = (66.7 \pm 0.7) ns \hfill \\ \end{gathered}$$ . Using the experimental levelT _1/2's, partial gamma-ray half-lives have been calculated for the 86.6- and the 29.6-keV transitions (from the 86.6 keV level) in²³³Pa and the 59.6- and the 26.36-keV transitions (from the 59.6 keV level) in²³⁷Np. The results are compared with the single particle and the Nilsson estimates.     

Nuclear orientation of105Rh and95Tc in iron

The temperature-dependent anisotropy of γ-rays following the decay of oriented⁹⁵Tc and¹⁰⁵Rh nuclei was studied with a Ge(Li) detector. Mixing coefficients of some γ-and preceding β-transitions, the spins of two intermediate levels, and the magnetic hyperfine splitting of the⁹⁵Tc and¹⁰⁵Rh ground states in an Fe host were measured. From the known hyperfine fields the following magnetic moments were deduced: $$\begin{gathered} \mu \left( {^{105} Rh,\tfrac{{7 + }}{2}} \right) = 4.34\left( {12} \right) n.m.; \hfill \\ \mu \left( {^{95} Tc,\tfrac{{9 + }}{2}} \right) = 5.82\left( {12} \right)n.m. \hfill \\ \end{gathered}$$      

Superconductive superheating field for finiteκ

We have calculated analytically the superheating fieldH _sh for bulk superconductors, correct to second order in. We find , which agrees well with numerical computations for<0.5. The surface order parameter is , and the penetration depth is .