On the spontaneous origin of newtons constant

We speculate on a modification of Einstein's equations at distances related to the Planck length $\text{(G}{}_{\mathrm{N}}\text{)}\text{1}\text{2}\text{(}\text{h}\text{?}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(c)}{}^{\mathrm{<mtext>-3</mtext><mtext>2</mtext>}}\text{= l}{}_{\mathrm{Pl}}\text{= 1.61 X 10}{}^{-33}$ cm, m_Pl = ?c^-1 (l_Pl)^-1 = 2.18 X 10^-5 g = 1.22 X 10¹⁹ GeV. The Planck mass arises spontaneously through the coupling of gravity to a system of scalar fields, in a scale invariant way.The same scalars generate all masses of leptons, quarks and vector bosons responsible for the matter interactions in the limit of weak gravitational fields.     

Magnetic moments of (νi132)−n isomers in neutron-deficient lead isotopes

The magnetic moments of the 12⁺ isomers in ^{192, 196, 198, 200, 206}Pb and of the $\text{33}\text{2}{}^{\mathrm{+}}$ isomer in ²⁰⁵Pb have been measured using the PAD technique. The results for the g-factors are: g(192) = ?0.173(2), g(196) = ?0.1600(15), g(198) = ?0.1552(15), g(200) = ?0.1512(15), g(206) = ?0.1496(18), and g(205) = ?0.148(5). As all states have a rather pure $\text{(νi}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?n}}$ configuration, the values reflect directly the $\text{νi}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ orbital. They show a decrease towards the more neutron-deficient isotopes attributed to the reduced core polarisation as a result of decreasing occupation of the $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron shell. The measured systematics are discussed regarding core polarisation, mesonic corrections, and small admixtures of core-excited states to the $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ wave function.     

The g-factor difference for the 61+ and 88+ states in 210Po

The difference in g-factors for the 6₁⁺ and 8₁⁺$\text{(πh}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}{}^2\text{)}$ states in ²¹⁰Po has been measured as $\text{(g}{}_6\text{? g}{}_8\text{)}\text{g}{}_8\text{= 2.0 ± 0.7\%}$. This result represents a small violation of additivity. A value of g₈ = 0.909 ± 0.011, independent of g₆, was also obtained.     

On the order of levels in charmonium

We prove a theorem concerning the energies of the 2S and 3D states in a potential $\text{V(r) =}\text{?g}{}^2\text{r}\text{+ V}{}_{\mathrm{<mtext>c</mtext>}}\text{(r)}$, where V_c is a non-singular confining potential. If $\text{(}\text{d}\text{d}\text{r)}{}^3\text{(r}{}^2\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{)}$ is positive, then the 3D state lies above the 2S state, provided

$\text{d}\text{d}\text{r}\text{1}\text{r}\text{d}\text{d}\text{r}\text{2V}{}_{\mathrm{<mtext>c</mtext>}}\text{+r}\text{d}\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{d}\text{r}\text{< 0, ?}{}_{\mathrm{r}}\text{>0.}$

For V_c = r^α, this corresponds to 0 < α < 2.     

Neutron-proton shell model multiplets in 88Y and 90Y from a study of the (α, nγ) reaction

The non-selective nature of the (α, nγ) reaction has been used to complement information from charged-particle reactions on the level structure of ⁸⁸Y and ⁹⁰Y. The γ-ray spectra were recorded with a 25 cm³ Ge(Li) detector at 90° to the beam using primarily targets of ⁸⁵Rb₂CO₃ and ⁸⁷Rb₂CO₃ and α-particle energies of 11.8, 12.2 and 13.0 MeV. The resulting transitions were accommodated in level schemes that involved primarily the following shell model configurations: $\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}$, $\text{(π}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}\text{(ν}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^1$, $\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}$, $\text{(π}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}\text{(ν}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}$ in ⁸⁸Y and $\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}{}^1$, $\text{π}\text{g}\text{(}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}{}^1$,$\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2)</mtext>}}\text{)}{}^1$ in ⁹⁰Y.     

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 $\text{B}{}_{\mathrm{e}}\text{= 19.9738(42) × 10}{}^{-3}\text{, α}{}_{\mathrm{e}}\text{= 5.602(84) × 10}{}^{-5}\text{, γ}{}_{\mathrm{e}}\text{= 1.02(41) × 10}{}^{-7}\text{, D}{}^{\mathrm{e}}{}_{\mathrm{J}}\text{= 3.040(74) × 10}{}^{-9}\text{cm}{}^{-1}\text{, and r}{}_{\mathrm{e}}\text{= 3.6470(5)}\text{A}\text{?}$.     

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 $\text{(σ2p)}{}^2\text{(π2p)}{}^3\text{(π}{}^1\text{2p)}{}^2$.     

Absorption spectra of Ni2+ in (NH4)2Mg(SO4)2·6H2O and Co2+ in Na2Zn(SO4)2·4H2O

Optical absorption spectra of Ni²⁺ in (NH₄)₂Mg(SO₄)₂·6H₂O and Co²⁺ in Na₂Zn(SO₄)₂·4H₂O single crystals have been studied at room and liquid nitrogen temperatures. From the nature and position of the observed bands, a successful interpretation could be made assuming octahedral symmetry for both the ions in the crystals. The splitting observed for ${}^3\text{T}{}_{\mathrm{1g}}\text{(F)}$ band in Ni²⁺ and ${}^4\text{T}{}_{\mathrm{2g}}\text{(F)}$ band in Co²⁺ at liquid nitrogen temperature have been explained as due to spin-orbit interaction. The extra band observed at 16,325 cm^-1 in the case of Ni²⁺ at low temperature has been interpreted to be the superposition of vibrational mode of SO^2-₄ radical on ${}^3\text{T}{}_{\mathrm{1g}}\text{(F)}$ band. The observed band positions in both the crystals have been fitted with four parameters B, C, Dq and ζ.     

Some properties of heavy lepton families

The simplest four-quark SU(2) ? U(1) models with an anomally-free heavy lepton sector can have two charged heavy leptons and one or two neutral leprons. Such models also explain the rise in R (the ratio of hadronic to muon pair production in e⁺e^? collisions). We study some consequences of different choices of leptonic numbers for L₁ and L₂. In particular, we derive, the leptonic decay width when several final-stae leptons are massive; the cross section for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{L}{}_1\text{L}{}_2$ production; the branching ratio for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{L}{}_2\text{L}{}_2\text{→}\text{e}\text{3μ+}\text{missing energy}$.     

Leptonic nonet in SUL (3) × SUR (3)

A left-right symmetric SU_L(3) × SU_R(3) gauge model with leptons in the ($\text{3}\text{, 3) + (3,}\text{3}$) representation is presented. The SU^I_L(2)×U(1) subgroup is practically the WS + GIM model for $\text{sin}{}^2\text{?}{}_{\mathrm{<mtext>W</mtext>}}\text{≈}\text{3}\text{8}$, with additional currents involving heavy leptons. μ→eγ is naturally suppressed and a new kind of $\text{ν}{}_{\mathrm{<mtext>e</mtext>}}\text{?}\text{ν}{}_{\mathrm{\mu }}$ oscillations is possible. τ and 3_μ events can be related to one leptonic triplet. The model is naturally imbedded in exceptional groups.     

Classical integrable finite-dimensional systems related to Lie algebras

During the last few years many dynamical systems have been identified, that are completely integrable or even such to allow an explicit solution of the equations of motion. Some of these systems have the form of classical one-dimensional many-body problems with pair interactions; others are more general. All of them are related to Lie algebras, and in all known cases the property of integrability results from the presence of higher (hidden) symmetries. This review presents from a general and universal viewpoint the results obtained in this field during the last few years. Besides it contains some new results both of physical and mathematical interest.The main focus is on the one-dimensional models of n particles interacting pairwise via potentials V(q) = g²ν(q) of the following 5 types: $\text{ν}{}_{\mathrm{<mtext>I</mtext>}}\text{(q)=q}{}^{\mathrm{?2}}\text{, ν}{}_{\mathrm{<mtext>II</mtext>}}\text{(q)=a}{}^{\mathrm{?2}}\text{sinh}{}^2\text{(aq), ν}{}_{\mathrm{<mtext>III</mtext>}}\text{(q)=a}{}^2\text{/}\text{sin}\text{2(aq), ν}{}_{\mathrm{<mtext>IV</mtext>}}\text{=a}{}^2\text{P}\text{(aq), , ν}{}_{\mathrm{<mtext>V</mtext>}}\text{(q)=q}{}^{\mathrm{?2}}\text{+ω}{}^2\text{q}{}^2$. Here $\text{P}$(q) is the Weierstrass function, so that the first 3 cases are merely subcases of the fourth. The system characterized by the Toda nearest-neighbor potential, g_j²exp[-a(q_j?q_j+1)], is moreover considered. Various generalizations of these models, naturally suggested by their association with Lie algebras, are also treated.     

Electronic spectra and vibronic coupling of pyrazine

The absorption and fluorescence spectra of pyrazine have been observed in vapor, solution and crystal, and the vibrational structures have been analyzed in detail. The fluorescence spectrum consists of long progressions of the nontotally symmetric vibration ν₅(b_2g), and the absorption spectrum contains also the progression of the corresponding excited state vibration ν′₅(b_2g. However, the pattern of the latter progression is unusual because of the highly anharmonic nature of the potential of the ¹B^3u state, which may be expressed by a functional form containing a quadratic term in the normal coordinate. All the experimental results suggest that the known vibronic interaction between the ${}^1\text{B}{}_{\mathrm{3u}}\text{(n,π}{}^1\text{)}$ state and the ${}^1\text{B}{}_{\mathrm{1u}}\text{(π, π}{}^1\text{)}$ state through the vibration ν₂(b_2g) is strong. The vibronic coupling and the potential of the ¹B_3u state were found to be very sensitive to solvent.     

On the oscillatory modes of quarks in baryons

The color bond structure of a quark-antiquark system is extended, in the long-range approximation, self-consistently to the baryonic three-quark bond structure for SU(3)_c and generally to the N-quark bond structure for SU(N)_c. The universal (N-independent) mass square eigenvalues for massless quarks are

$\text{M}{}^2\text{=(H}{}_{\mathrm{N}}\text{)}{}^2\text{?2m}{}_{\mathrm{\rho }}{}^2\text{∑}\text{α=1}\text{3N?3}\text{ν}{}_{\mathrm{\alpha }}\text{+}\text{constant}\text{, ν}{}_{\mathrm{\alpha }}\text{=0,1,2,…}$

.     

On the electronic spectrum of the Mo2 molecule observed after flash photolysis of Mo(CO)6

Absorption and emission spectra of Mo₂ were investigated using flash photolysis of the Mo(CO)₆ molecule. Tentative vibrational and rotational analyses of the ⁹⁸Mo₂ spectra were performed. For the ground state, ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ type was proposed with ω_e = 477.1 cm^?1, $\text{r}{}_{\mathrm{e}}\text{= 1.929}\text{A}\text{?}$, and D₀(Mo₂) = 95 ± 15 kcal mole^?1. The results were compared with theoretical calculations for Mo₂ and experimental results for Cr₂ obtained previously. It seems reasonable that the transition metal diatomic molecules of this type have a high bond order.     

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.     

Irreducible gauge theory of a consolidated Salam-Weinberg model

We derive the Salam-Weinberg model by gauging an internal simple supergroup $\text{SU}\text{(}\text{2}\text{1}\text{)}$. The theory uniquely assigns the correct SU(2)_L ? U(1) eigenvalues for all leptons, fixes θ_W = 30°, generates the W^±_σ, Z⁰_σ and A_σ together with the Higgs-Goldstone $\text{I}{}_{\mathrm{<mtext>L</mtext>}}\text{=}\text{1}\text{2}$ scalar multiplets as gauge fields, and imposes the standard spontaneous breakdown of SU(2)_L ? U(1). The masses of intermediate bosons and fermions are directly generated by $\text{SU}\text{(}\text{2}\text{1}\text{)}$ universality, which also fixes the Higgs field coupling.     

Lorentz contracted geometrical model

The model assumes that when two high energy particles collide each behaves as a geometrical object which has a Gaussian density and is spherically symmetric except for the Lorentz-contraction in the incident direction. Folding the two spatial distribution together we obtain the slope (b) of the elastic diffraction peak in terms of the c.m. velocities (β_i and β_j) and the sizes (A_i and A_j) of the two incident particles. These sizes are assumed to have the experimental s-dependence of σ_tot ∝ πA² for each reaction. The combined s-dependence of the σ_tot's and the β's gives the s-dependence of the elastic slope $\text{b}{}_{\mathrm{ij}}\text{(s) =}\text{1}\text{2}\text{(A}{}_{\mathrm{i}}{}^2\text{β}{}_{\mathrm{i}}{}^2\text{+ A}{}_{\mathrm{j}}{}^2\text{β}{}_{\mathrm{j}}{}^2\text{)}\text{σ}{}^{\mathrm{ij}}{}_{\mathrm{<mtext>tot</mtext>}}\text{(s)}\text{σ}{}^{\mathrm{ij}}{}_{\mathrm{<mtext>tot</mtext>}}\text{(∞)}$. This formula agrees with the experimental slope for p-p, $\text{p}$-p, K⁺-p, K^?-p and π^±-p elastic scattering from 3 to 1500 GeV/c, with only 3 parameters: A_π² = 6.1, A_K² = 3.3 and A_p² = 10.5 (GeV/c)^?2.     

Predissociation and Λ-doubling in the even-parity Rydberg states of the nitrogen molecule

Predissociations in the y¹Π_g and $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ Rydberg states of N₂ (configurations $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{4pσ}$ and $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{3pπ}$, respectively) and their likely causes, are discussed. Peaking of rotational intensity at unusually low J values, without sharp breaking off, is interpreted as due to case c^? or case cⁱ predissociation. Λ doubling in the y state, attributed to interactions with the $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state and with another, ¹Σ⁺, state of the same electron configuration as x, is analyzed. From this analysis the location of the (unobserved) ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ state, here labeled x′, is obtained. It is concluded that the predissociation in the Π⁺ levels of the y state is an indirect one mediated by the interaction with x′ coupled with predissociation of x′ by a ${}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state dissociating to ${}^4\text{S +}{}^2\text{P}$ atoms: combined, however, with perturbation of the y state by the k¹Π_g Rydberg state (configuration $\text{3σ}{}_{\mathrm{g}}{}^{\mathrm{?1}}\text{4dπ}$), whose Π⁺ levels are completely predissociated.     

O(18) revived: Splitting the spinor

We propose an O(18) theory which is perturbatively unifiable and which accounts for the absence of right-handed families in the low-energy world. The theory predicts a fourth left-handed family as well as four right-handed families at energies near the weak scale. It also implies the existence of eight light neutrinos, all of which contribute to the width of the Z⁰. Cosmological arguments suggest that four of these neutrinos should have masses between 2 and 35 GeV, and that the other four should be much lighter. They also suggest the existence of a doubly charged scalar φ⁺⁺ and a singly charged scalar φ⁺. Dramatic signatures include the production of four right-handed charged leptons and eight right-handed quarks, $\text{Z}{}^0\text{→ v′}{}_{\mathrm{<mtext>R</mtext>}}\text{+}\text{v}\text{′}{}_{\mathrm{<mtext>R</mtext>}}\text{→ v}{}_{\mathrm{<mtext>R</mtext>}}\text{γ +\_}\text{v}{}_{\mathrm{<mtext>R</mtext>}}\text{γ}$, and e⁺e^? → φ⁺⁺ + φ^??. The lightest right-handed charged quark should be surprinsingly long-lived $\text{(τ?10}{}^{\mathrm{?2}}\text{sec}\text{)}$ for a particle of mass ? 100 GeV.