Interacting boson-fermion model of collective states I,the Spin (6) limit

We discuss in detail one of the three possible spinor symmetries of the interacting boson-fermion model. This symmetry, Spin (6), arises when the bosons have SO(6) symmetry and the fermions occupy a single particle orbital with $\text{j =}\text{1}\text{2}$. We derive, within the framework of the Spin (6) symmetry, closed expressions for energies, electromagnetic (EO, M1, E2) transition rates, static moments and (one and two) nucleon transfer reaction intensities.     

Polarization spectroscopy of ICl: The D′, a and a′ states

Three previously-unanalyzed states of ICl are reported, an ion-pair state D′(Ω =2) which converges to the limit I⁺(P₂+ Cl^-(S_o), and two shallow states a(Ω = 1) and a′(Ω = 0⁺) both of which converge to the ground states of separated atoms I(P_{$\text{3}\text{2}$}) + Cl(P_{$\text{3}\text{2}$}). The a(0⁺) state is responsible for the well-known interruption of the B(0⁺) state above υ_B = 3. Spectroscopic constants are given for the D′ and a′ states.     

Coulomb excitation of 115Sn

Coulomb excitation of the nucleus ¹¹⁵Sn was studied with beams of ⁴He and ¹⁶O. Level energies, spins, mean-lives and B(E2) and B(M1) transition probabilities were obtained. Spin $\text{3}\text{2}$⁺ states were observed at 497.35 and 1280.08 keV and spin $\text{5}\text{2}$⁺ states were observed at 986.54 and 1416.78 keV. A state of 612.79 keV was observed to be indirectly excited by decay of the Coulomb excited states. Eleven B(E2) values and nine B(M1) values were obtained for the transitions between the low-lying states. In contrast to previous particle transfer results which suggested a clear distinction between shell-model and collective $\text{3}\text{2}$⁺ and $\text{5}\text{2}$⁺ states, our results suggest the collective strength is shared by the two $\text{3}\text{2}$⁺ and two $\text{5}\text{2}$⁺ states.     

Exact Fermi energy,susceptibilities, and their singularities for an electron gas in a uniform magnetic field at T = 0 °K

Exact analysis is presented to derive the magnetic response functions and their singularities of free-electron gas in a uniform magnetic field of arbitrary strength at T = 0 °K. The newly defined functions, Λ_μ(s) = ∑₀^[s])(s ? n)^μ of $\text{μ =}\text{?1}\text{2}\text{,}\text{1}\text{2}\text{,}\text{3}\text{2}$, are employed to obtain the Fermi energy, magnetization, and susceptibility as functions of B. It is revealed that the spin susceptibility is composed of two parts, χ_s1 and χ_s2, where χ_s2 is purely oscillatory diamagnetic. A graphical method of finding the Fermi energy ?_F(B) as a function of B has been obtained. The system is shown to become totally one-dimensional electron gas in the field B greater than $\text{B}{}_{\mathrm{\downarrow }}\text{= (2ηn)}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$ and the total energy satisfies $\text{E}{}_{\mathrm{t}}\text{=}\text{1}\text{3}\text{?}{}_{\mathrm{F}}\text{(B)N}$. The obvious extension of the present theory to the Bloch electrons on the ellipsoidal constant energy surface is also discussed.     

Microwave optical double resonance and continuous wave dye laser excitation spectroscopy of NO2: Rotational assignment of the K = 0−4 subbands of the 593 nm band

A rotational assignment of approximately 80 lines with K_a′ = 0, 1, 2, 3, and 4 has been made of the 593 nm ${}^2\text{A}{}_1\text{→}{}^2\text{B}{}_2$ band of NO₂ using cw dye laser excitation and microwave optical double-resonance spectroscopy. Rotational constants for the ²B₂ state were obtained as A = 8.52 cm^?1, B = 0.458 cm^?1, and C = 0.388 cm^?1. Spin splittings for the K_a′ = 0 excited state levels fit a simple symmetric top formula and give $\text{(?}{}_{\mathrm{bb}}\text{+ ?}{}_{\mathrm{cc}}\text{)}\text{2}\text{= ?0.0483}\text{cm}{}^{\mathrm{?1}}$. Spin splittings for K_a′ = 1 (N′ even) are irregular and are shown to change sign between N′ = 6 and 8. Assuming that the large inertial defect of 4.66 amu Ų arises solely from A, a structure for the ²B₂ state is obtained which gives $\text{r}\text{(NO) = 1.35}\text{A}\text{?}$ and an ONO angle of 105°. Alternatively, weighting the three rotational constants equally gives $\text{r = 1.29}\text{A}\text{?}$ and θ = 118°.     

Does the enhancement mechanism work in non-leptonic decays of heavy pseudoscalar mesons with new flavors (b and t)?

We show that the enhancement mechanism proposed for non-leptonic decays of charmed mesons (D⁰, F⁺) is still important for decays of pseudoscalar mesons with b flavor, while its effect is small for mesons with t flavor. For the semi-leptonic branching ratios of B^? (b$\text{u}$), B⁰(b$\text{d}$) and B_S⁰(b$\text{s}$) we predict BR (B^? → evX ～' 9%, BR(B⁰ → evX) ～' BR(B_s⁰ → evX) ～' 5%. We can also derive the enhancement of the branching ratios of uncharmed final states in B decays, i.e. $\text{BR}\text{(}\text{B}{}^{\mathrm{?}}\text{→}\text{X}{}_{\mathrm{<mtext>s</mtext><mtext>u</mtext>}}\text{)}$ ～' 20 %, $\text{BR}\text{(}\text{B}{}^0\text{→}\text{X}{}_{\mathrm{<mtext>s</mtext><mtext>d</mtext>}}\text{)}$ ≈ 10%, where $\text{X}{}_{\mathrm{<mtext>s</mtext><mtext>u</mtext><mtext>(</mtext><mtext>s</mtext><mtext>d</mtext><mtext>)</mtext>}}$ = $\text{K}$π + ... + $\text{K}$K$\text{K}$ + ... .     

Effect of the frustration to the ground state energy and entropy of the spin-glass in the random bond Ising model on the square lattice

The energies and the entropies of the spin-glass state and the paramagnetic state at T = 0 of the random-bond Ising mixture of the ferromagnetic bond (concentration p) and the antiferromagnetic bond (concentration 1 ? p) on the square lattice are calculated by the method of the square approximation in the simple version. A self-consistent relation that the partial trace of the normalized density matrix of the square cluster is equal to that of the vertex ($\text{tr}\text{(}{}_{\mathrm{jkl}}\text{?}\text{?}{}^{\mathrm{(4)}}\text{(i,j,k,l) =}\text{?}\text{?}{}^{\mathrm{(1)}}\text{(i)}$) leads to an integral equation for the distribution function of the effective fields, and it is solved exactly at T = 0. The symmetric solution of the integral equation contains the paramagnetic state and two spin-glass states, SG1 and SG2. The energies and the entropies of these states are obtained as functions of the concentration p. The values of the energies per spin at $\text{p =}\text{1}\text{2}$ are -0.75|E_F|, -0.72746|E_F|, -0.72543|E_F|, and correspond to a minimum, a saddle point, and a maximum, respectively, and the values of the entropies are 0, 0.082886k_B, and 0.054457k_B, respectively. The present results are compared with those of the pair approximation and discussed.     

Observed and calculated interactions between valence states of the NO molecule

No perturbation between two valence states of NO has ever been identified, although many valence-Rydberg and several Rydberg-Rydberg perturbations have been extensively studied. The first valence-valence crossing to be experimentally documented for NO is reported here and occurs between the ¹⁵N¹⁸O B²Π (v = 18) and B′²Δ (v = 1) levels. No level shifts larger than the detection limit of 0.1 cm^?1 are observed at the crossings near $\text{J = 6.5 [B}{}^2\text{Π}\text{(F}{}_1\text{) ～ B′}{}^2\text{Δ}\text{(F}{}_2\text{)]}$ and $\text{J = 12.5 [B}{}^2\text{Π}\text{(F}{}_1\text{) ～ B′}{}^2\text{Δ}\text{(F}{}_1\text{)]}$; two crossings involving higher rotational levels could not be examined. Semi-empirical calculations of spin-orbit and Coriolis perturbation matrix elements indicate that although the electronic part of the $\text{B}{}^2\text{Π}\text{～ B′}{}^2\text{Δ}$ interaction is large, a small vibrational factor renders the ¹⁵N¹⁸O B (v = 18) ? B′ (v = 1) perturbation unobservable. Semi-empirical estimates are given for all perturbation matrix elements of the operators $\text{Σ}{}_{\mathrm{i}}\text{a}\text{?}{}_{\mathrm{i}}\text{l}{}_{\mathrm{i}}\text{·s}{}_{\mathrm{i}}$ and $\text{B(L}{}_{\mathrm{\pm }}\text{S}{}_{\mathrm{?}}\text{? J}{}_{\mathrm{\pm }}\text{L}{}_{\mathrm{?}}\text{)}$ which connect states belonging to the configurations $\text{(σ2p)}{}^2\text{(π2p)}{}^4\text{(π}{}^1\text{2p)}$, $\text{(σ2p)(π2p)}{}^4\text{(π}{}^1\text{2p)}{}^2$, and $\text{(σ2p)}{}^2\text{(π2p)}{}^3\text{(π}{}^1\text{2p)}{}^2$.     

Group theoretical aspects ofU B(6) ⊗U F(20) symmetry limits of IBFM related to theU B(5) andO B(6) limits of IBM

TheU ^B(6)⊗U ^F(20) Bose-Fermi dynamical symmetry of interacting boson-fermion model arises when the odd nucleon occupies single particle orbits withj=1/2, 3/2, 5/2, and 7/2. The subgroup structures ofU ^B(6)⊗U ^F(20) related to theU ^B(5) andO ^B(6) limits of sdIBM (U ^B(6)) are analysed. Broadly speaking,U ^B(6)⊗U ^F(20) admitsU ^BF(5)⊗U _s ^F (4), Spin^BF(5)⊗U _k ^F (5) andU ^BF(5)⊗U _s ^F (2) limits withU ^B(5) core and Spin^BF(6),O ^BF(5)⊗U _s ^F (4), Spin^BF(6)⊗U _k ^F (5) andO ^BF(6)⊗U _s ^F (2) limits withO ^B(6) core respectively. For each of these seven symmetry limits, group chains, quantum numbers labelling the basis states, generators and Casimir operators for the various subgroups and energy formulas are given. Recoupling coefficients (reduced Wigner coefficients) for constructing wavefunctions of low-lying states are tabulated and these will allow (together with sdIBMU ^B(5) andO ^B(6) limit results) one to calculateB(E2)’s,B(M1)’s, one and two nucleon transfer strengths etc. in the seven symmetry limits. Experimental examples for theU ^B(6)⊗U ^F(20) symmetry limits are briefly discussed.     

Thermochemistry of azide salts and the azide ion using direct minimisation equations to obtain the lattice energy of the univalent azide salts

The opportunity to test a new equation for the computation of the lattice energy and at the same time examine a disparity in the literature data for the enthalpy of formation of the azide ion, $\text{ΔH}{}^{\mathrm{\theta }}{}_{\mathrm{?}}\text{(}\text{N}{}_3{}^{\mathrm{?}}\text{) (}\text{g}\text{)}$ was the motivation for this study. The results confirm our earlier calculation and show the new equation to be reliable. Thermodynamic data produced in the study take values: $\text{ΔH}{}^{\mathrm{\theta }}{}_{\mathrm{?}}\text{(}\text{N}{}_3{}^{\mathrm{?}}\text{)(}\text{g}\text{) = 144}\text{kJ mor}{}^{\mathrm{?1}}$ΔH^θ_hyd(N₃^?) = ?315 KJ mol^?1 or ΔH^θ_hyd(N₃^?) = ?295 KJ mol^?1U_POT(NaN₃) = 732 kJ mol^?1U_POT(KN₃) = 659 kJ mol^?1U_POT(RbN₃) = 637 kJ mol^?1U_POT(CsN₃) = 612 kJ mol^?1U_POT(TIN₃) = 689 kJ mol^?1. The lattice energies of azides whose enthalpies of formation are documented have been calculated as well as the enthalpy of formation of the azide radical.     

Proton scattering at 1 GeV

The physics of 1-GeV proton scattering on nuclei is discussed in the light of recent calculations, and compared to the Gatchina, Los Alamos, and Saclay data. The impulse approximation (including spin-orbit effects and correlations) is reviewed, and comparison is made with other theories such as the Glauber model and the low-energy optical model. This discussion is addressed to specialists as well as nonspecialists in the field. The neutron distribution is extracted from the data and a detailed comparison is made with other determinations of this distribution and with the Hartree-Fock predictions. The neutron radii are seen to be generally larger than the proton radii. Within a given shell, they increase at a much slower rate ($\text{～A}{}^{\mathrm{<mtext>1</mtext><mtext>8</mtext>}}$) than the $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ rule. Except possibly for ²⁰⁸Pb, they are consistent with the Hartree-Fock predictions, but not with the values obtained from Coulomb energies. The study of inelastic scattering to collective states allows the extraction of neutron transition densities, and in particular the analog B(N, L) of the electromagnetic transition rates B(E, L) one usually considers for the protons. Neutron excitations are seen to be stronger by 20 to 40 % than proton excitation, exceeding the $\text{N}\text{Z}$ prediction of the collective model. Spin effects lead only to small changes in the cross section, but to a measurable analyzing power. The unnatural parity excitations of the lowest 2^? (T = 0) state of ¹⁶O and the 1⁺ (T = 1) state of ¹²C show that the spin-spin and tensor terms of the nucleon-nucleon amplitude are sizable. Their relative magnitudes are seen to be crucial for explaining the observed cross sections.     

The cosmic microwave background and the hadron era of the early universe: A possible connection

A cosmological model is constructed which is a Friedman model, but with a finite ultimate temperature (T_F). A plausible argument is presented which suggests that the existence of T_F and the cosmic microwave background restricts the form of the hadronic level density:

, where A, B = constants. In our model, $\text{B =}\text{7}\text{2}\text{?}\text{3}\text{s}\text{,}\text{where}\text{s =}\text{positive}$ integer. The case $\text{s = 3 (B =}\text{5}\text{2}\text{)}$ is the well-known Hagedorn model; the Frautschi model corresponds to s = 6 (B = 3); the cases $\text{s = 1 (B =}\text{1}\text{2}\text{)}$ and s = 2 (B = 2) have not been considered before now. For each value of $\text{B <}\text{7}\text{2}$, the model gives the temperature (T_γ0) of the microwave background as a function of A, T_F and ?₀ (the present energy density of the universe). Two fascinating results then emerge: first, all estimates of T_γ0 favor a low density Friedman universe (?0 = 10^?31g/cm³), which rules out a universe with positive curvature; second, for ?₀ = 10^?31gr/cm³ the best estimate of T_γ0 (?3K) occurs for the Hagedorn model.     

On the asymptotic behaviour of the mass operator near the Fermi energy

By taking due account of momentum conservation, it is shown that, when ω is near the Fermi energy ω_F, the imaginary part of the mass operator $\text{M(}\text{k}\text{, ω)}$ for an infinite Fermi system behaves like (ω ? ω_F)^p(k) where the exponent p(k) ? 2 depends on the interval in which $\text{|}\text{k}\text{|}$ is lying. In particular, the commonly asserted quadratic behaviour (ω ? ω_F² is shown to be true only for $\text{|}\text{k}\text{| ? 3k}{}_{\mathrm{<mtext>F</mtext>}}$. It is explicity assumed that the Fermi system admits a perturbative type treatment.     

On the optimality of axiomatic constraints for π0π0 scattering: The case of the lower bounds

We construct a nine-parameter family of π⁰π⁰ → π⁰π⁰ amplitudes F(s, t) such that (i) all the analyticity and unitarity conditions used in the derivation bounds are satisfied; (ii) F(s, t) can assume negative values in the unphysical region. Within this set, we minimize the values of $\text{F(}\text{4}\text{3}\text{,}\text{4}\text{3}\text{)}$ and of the scattering length a⁰⁰ = F(4, 0). Our best results are $\text{F(}\text{4}\text{4}\text{,}\text{4}\text{3}\text{) = -1.69}\text{and}\text{α}{}^{00}\text{= -0.88}$, whereas the best present lowers bounds are $\text{F(}\text{4}\text{3}\text{,}\text{4}\text{3}\text{) > -8.2}\text{and}\text{α}{}^{00}\text{> -1.65}$.     

The microwave spectrum,structure, and quadrupole coupling constants of boron chloride difluoride,BCIF2

The microwave spectrum of boron chloride difluoride, BClF₂, has been investigated in the region 26.5–40.0 GHz. R-branch transitions belonging to the isotopic species ¹¹B³⁵Cl¹⁹F₂, ¹¹B³⁷Cl¹⁹F₂, and ¹⁰B³⁵Cl¹⁹F₂ have been observed and the derived rotational constants yield the following ground-state structural parameters: $\text{r}{}^0\text{(BF) = 1.315 ± 0.006}\text{A}\text{?}$, $\text{r}{}^{\mathrm{s}}\text{(BCl) = 1.728 ± 0.009}\text{A}\text{?}$, < FBF = 118.1 ± 0.5°. The ground-state rotational constants of the most abundant species ¹¹B³⁵Cl¹⁹F₂ are: A₀ = 10 449.32 ± 0.13, B₀ = 4705.811 ± 0.020, C₀ = 3239.702 ± 0.026 MHz, Δ_JK = 8.9 ± 1.7, and Δ_J = 1.86 ± 0.48 KHz. The asymmetry parameter κ = ?0.593291 and the inertial defect δ⁰ = 0.2361 amu Ų which is consistent with that expected for this type of molecule if planar. The ³⁵Cl quadrupole coupling constants for ¹¹B³⁵Cl¹⁹F₂ are χ_aa = ?42.8 ± 1.0, χ_bb = 30.2 ± 1.5, χ_cc = 12.6 ± 1.5 MHz with the asymmetry parameter η = 0.41.     

Phase transition in the lattice gross-neveu model

The confining properties of the leading logarithm approximation to the effective lagrangian $\text{L}\text{= F}{}^2\text{/2g}{}^2\text{(t)}$ [ with g(t) a running coupling function of t = log(F²/μ⁴)] are seen to disappear when the second and the third approximations of the β-function power series expansion are considered.     

EPR lineshape in ethylenediammonium chloromanganate (II), [C2H10N2] [MnCl4]

The EPR line shape has been measured on a single crystal of ethylene diammonium chloromanganate (II) as a function of field orientation with respect to the expected two dimensional network of manganese ions. The angular variation of the linewidth may be described by the expression δH= α + β(3 cos²δ ? 1)² with α = 20 and β = 4, and the lineshape may be described by I(H ? H₀) ? F [exp (? At ? Bt ln ($\text{t}\text{t}{}_0\text{)]}$ (where F refers to the Fourier transform of the bracketed function) with $\text{|}\text{B}\text{A}\text{| = 1.9 ± 0.8}$.     

The microwave spectrum of C-fluorophosphaethyne FCP: Structure determination,dipole moment,and vibration-rotation data

The microwave spectrum of the new linear triatomic molecule C-fluorophosphaethyne FCP which is produced when CF₃PH₂ vapor passes over solid KOH at room temperature and ca. 20 μmHg pressure has been studied. Transitions belonging to the two isotopic variants ¹⁹F¹²C³¹P and ¹⁹F¹³C³¹P have been analyzed and the resulting structural data are $\text{r(}\text{FC}\text{) = 1.285 ± 0.005}\text{A}\text{?}$ and $\text{r(}\text{CP}\text{) = 1.541 ± 0.005}\text{A}\text{?}$. The study has yielded the following spectroscopic parameters for ¹⁹F¹²C³¹P: B₀ = 5257.80 ± 0.03 MHz, α₂ = ?11.95 ± 0.05 MHz, q₂ = 4.478 ± 0.002 MHz, and μ = 0.279 ± 0.001 Debye.     

Rotational analyses and vibrational assignments of the 463- and 474-nm bands of NO2

The excitation spectrum of NO₂ was investigated in the blue region by using a Nd:YAG laser-pumped dye laser. The 463- and 474-nm bands of the ²B₂-²A₁ system were identified and analyzed using the simplification that occurs if the excitation spectrum is monitored at particular wavelengths. Band origins and rotational constants were obtained. Vibrational assignments have been given to these bands by comparing the Franck-Condon Factors calculated for the ²B₂-²A₁ system with the fluorescence intensities of bands going to different vibrational levels of the ground state. The vibrational assignments and molecular constants obtained in this work are (v′₁, v′₂, v′₃) = (3, 11, 0)ν₀(K′ = 0) = 21584.1, $\text{B}\text{= 0.405}$, and $\text{∥}\text{?}\text{′∥ = 0.05}\text{cm}{}^{\mathrm{?1}}$ for the 463-nm band; and (v′₁, v′₂, v′₃) = (2, 12, 0), ν₀(K′ = 1) = 21104.9, $\text{B}\text{= 0.408}$, and $\text{∥}\text{?}\text{′∥ = 0.03}\text{cm}{}^{\mathrm{?1}}$ for the 474-nm band.     

Magnetic structure of the canted 1D-antiferromagnet NaBaFe2F9

NaBaFe₂F₉ crystallizes with the Ba₂CoFeF₉ structural type (space group P2₁/n, Z = 4). In this structure, infinite cis double [M₂F₉]^3? chains of corner sharing octahedra are isolated one from each other by sodium and barium ions. At 4.5 K, the cell parameters (Å) are found to be: a = 7.3236(3), b = 17.4525(7), c = 5.4586(2), β = 91.840(3)°. Antiferromagnetic interactions dominate but, below T_N ? 19 K, a parasitic ferromagnetic component appears with σ_r(4.5K) = 0.03(1) μ_B·mole^?.The magnetic structure (C_xF_yC_z mode) was foreseen by the macroscopic theory of Bertaut and established from neutron powder diffraction. Using the Rietveld profile refinement method, the 4.5 K spectrum was analysed at $\text{λ =}\text{1.909}\text{A}\text{?}\text{(R}{}_{\mathrm{<mtext>Profile</mtext>}}\text{=}\text{0.093}\text{, R}{}_{\mathrm{<mtext>Nucl</mtext>}}\text{=}\text{0.053}\text{, R}{}_{\mathrm{<mtext>Mag</mtext>}}\text{=}\text{0.126}\text{)}$ and the 4.5–35K difference spectrum at $\text{λ =}\text{2.518}\text{A}\text{?}\text{(R}{}_{\mathrm{<mtext>Mag</mtext>}}\text{=}\text{0.049}\text{, R}{}_{\mathrm{<mtext>Profile</mtext>}}\text{=}\text{0.092}\text{)}$. The magnetic moments on two Fe³⁺ sites, lie mainly in the (0 1 0) plane, approximately at 45° from the a- and c-axes. They form a pseudo G-type antiferromagnetic arrangement (μ(Fe1) = 3.60(4) μ_B;μ(Fe2) = 3.61(6)μ_B).