Kernel solutions of the Kostant operator on eight-dimensional quotient spaces

After introducing the generators and irreducible representations of the ${\rm su}(5)$ and ${\rm so}(6)$ Lie algebras in terms of the Schwinger's scillators, the general kernel solutions of the Kostant operators on eight-dimensional quotient spaces ${\rm su}(5)/{\rm su}(4)\times {\rm u}(1)$ and ${\rm so}(6)/{\rm so}(4)\times {\rm so}(2)$ are derived in terms of the diagonal subalgebras ${\rm su}(4)\times {\rm u}(1)$ and ${\rm so}(4)\times {\rm so}(2)$, respectively.Comment: 13 pages. Typos correcte

Continuation of Direct Products of Distributions

If, in some problems, one has to deal with the ``product'' of distributions $\rm f_i$ (also called generalized functions) $\rm\bar T = \Pi^m_{i=1} f_i$, this product has a priori no definite meaning as a functional $(\rm \bar T, \phi)$ for $\rm\phi \in S$. But if $\rm x^{\kappa +1} \Pi^m_{i=1} f_i$ exists, whatever the associativity is between some powers $\rm r_i$ of $\rm x$ ($\rm r_i \in \Bbb N, \sum_i r_i\leq \kappa +1, r_i \geq 0$) and the various $\rm f_i$, then a continuation of the linear functional $\rm \bar T$ from $\rm M$ onto $\rm S^{(N)}$ for some $\rm N$ is shown to exist in such a way that $\rm x^{\kappa +1} \bar T$ is defined unambiguously, and $\rm (\bar T, \phi), \phi \in S$, significant, though not unique.Comment: 3 pages, late

16O+16O^{16}{\rm O} + ^{16}{\rm O} nature of the superdeformed band of 32S^{32}{\rm S} and the evolution of the molecular structure

The relation between the superdeformed band of $^{32}{\rm S}$ and $^{16}{\rm O} + ^{16}{\rm O}$ molecular bands is studied by the deformed-base antisymmetrized molecular dynamics with the Gogny D1S force. It is found that the obtained superdeformed band members of $^{32}{\rm S}$ have considerable amount of the $^{16}{\rm O} + ^{16}{\rm O}$ component. Above the superdeformed band, we have obtained two excited rotational bands which have more prominent character of the $^{16}{\rm O} + ^{16}{\rm O}$ molecular band. These three rotational bands are regarded as a series of $^{16}{\rm O} + ^{16}{\rm O}$ molecular bands which were predicted by using the unique $^{16}{\rm O}$ -$^{16}{\rm O}$ optical potentil. As the excitation energy and principal quantum number of the relative motion increase, the $^{16}{\rm O} + ^{16}{\rm O}$ cluster structure becomes more prominent but at the same time, the band members are fragmented into several states

Enhanced Kondo Effect in an Electron System Dynamically Coupled with Local Optical Phonon

We discuss Kondo behavior of a conduction electron system coupled with local optical phonon by analyzing the Anderson-Holstein model with the use of a numerical renormalization group (NRG) method. There appear three typical regions due to the balance between Coulomb interaction $U_{\rm ee}$ and phonon-mediated attraction $U_{\rm ph}$. For $U_{\rm ee}>U_{\rm ph}$, we observe the standard Kondo effect concerning spin degree of freedom. Since the Coulomb interaction is effectively reduced as $U_{\rm ee}-U_{\rm ph}$, the Kondo temperature $T_{\rm K}$ is increased when $U_{\rm ph}$ is increased. On the other hand, for $U_{\rm ee}<U_{\rm ph}$, there occurs the Kondo effect concerning charge degree of freedom, since vacant and double occupied states play roles of pseudo-spins. Note that in this case, $T_{\rm K}$ is decreased with the increase of $U_{\rm ph}$. Namely, $T_{\rm K}$ should be maximized for $U_{\rm ee} \approx U_{\rm ph}$. Then, we analyze in detail the Kondo behavior at $U_{\rm ee}=U_{\rm ph}$, which is found to be explained by the polaron Anderson model with reduced hybridization of polaron and residual repulsive interaction among polarons. By comparing the NRG results of the polaron Anderson model with those of the original Anderson-Holstein model, we clarify the Kondo behavior in the competing region of $U_{\rm ee} \approx U_{\rm ph}$.Comment: 8 pages, 8 figure

Fundamental Plane of Black Hole Activity in Quiescent Regime

A correlation among the radio luminosity ($L_{\rm R}$), X-ray luminosity ($L_{\rm X}$), and black hole mass ($M_{\rm BH}$) in active galactic nuclei (AGNs) and black hole binaries is known to exist and is called the "Fundamental Plane" of black hole activity. Yuan & Cui (2005) predicts that the radio/X-ray correlation index, $\xi_{\rm X}$, changes from $\xi_{\rm X}\approx 0.6$ to $\xi_{\rm X}\approx 1.2-1.3$ when $L_{\rm X}/L_{\rm Edd}$ decreases below a critical value $\sim 10^{-6}$. While many works favor such a change, there are also several works claiming the opposite. In this paper, we gather from literature a largest quiescent AGN (defined as $L_{\rm X}/L_{\rm Edd} < 10^{-6}$) sample to date, consisting of $75$ sources. We find that these quiescent AGNs follow a $\xi_{\rm X}\approx 1.23$ radio/X-ray relationship, in excellent agreement with the Yuan \& Cui prediction. The reason for the discrepancy between the present result and some previous works is that their samples contain not only quiescent sources but also "normal" ones (i.e., $L_{\rm X}/L_{\rm Edd} > 10^{-6}$). In this case, the quiescent sources will mix up with those normal ones in $L_{\rm R}$ and $L_{\rm X}$. The value of $\xi_{\rm X}$ will then be between $0.6$ and $\sim1.3$, with the exact value being determined by the sample composition, i.e., the fraction of the quiescent and normal sources. Based on this result, we propose that a more physical way to study the Fundamental Plane is to replace $L_{\rm R}$ and $L_{\rm X}$ with $L_{\rm R}/L_{\rm Edd}$ and $L_{\rm X}/L_{\rm Edd}$, respectively.Comment: 11 pages, 7 figures, accepted for publication in The Astrophysical Journa

Analysing powers for the reaction n⃗p→ppπ−\vec{\rm n} {\rm p} \to {\rm p} {\rm p} \pi^{-} and for np elastic scattering from 270 to 570 MeV

The analysing power of the reaction ${\rm n}{\rm p} \to {\rm p}{\rm p} \pi^{-}$ for neutron energies between threshold and 570 MeV has been determined using a transversely polarised neutron beam at PSI. The reaction has been studied in a kinematically complete measurement using a time-of-flight spectrometer with large acceptance. Analysing powers have been determined as a function of the c.m. pion angle in different regions of the proton-proton invariant mass. They are compared to other data from the reactions ${\rm n}{\rm p} \to {\rm p}{\rm p} \pi^{-}$ and ${{\rm p}{\rm p} \to {\rm p}{\rm p} \pi^{0}}$. The np elastic scattering analysing power was determined as a by-product of the measurements.Comment: 12 pages, 6 figures, subitted to EPJ-

Plateau of the Magnetization Curve of the S=1/2 Ferromagnetic-Ferromagnetic-Antiferromagnetic Spin Chain

I analytically study the plateau of the magnetization curve at $M/M_{\rm S} = 1/3$ (where $M_{\rm S}$ is the saturation magnetization) of the one-dimensional $S=1/2$ trimerized Heisenberg spin system with ferromagnetic ($J_{\rm F}$)-ferromagnetic ($J_{\rm F}$)-antiferromagnetic ($J_{\rm A}$) interactions at $T=0$. I use the bosonization technique for the fermion representation of the spin Hamiltonian through the Jordan-Wigner transformation. The plateau appears when $\gamma \equiv J_{\rm F}/J_{\rm A} \allowbreak < \gamma_{\rm C}$, and vanishes when $\gamma > \gamma_{\rm C}$, where the critical value $\gamma_{\rm C}$ is estimated as $\gamma_{\rm C} = 5 \sim 6$. The behavior of the width of the plateau near $\gamma_{\rm C}$ is of the Kosterlitz-Thouless type. The present theory well explains the numerical result by Hida.Comment: 7 pages, Plain Tex, 4 figures on reques