Nonperturbative renormalization of the sine-Gordon/Coulomb gas system for β2<8π: A functional integral approach

A new method of analyzing the divergences of the sine-Gordon/Coulomb gas system is introduced. It is shown that for ²<8 all divergences may be eliminated by a nonperturbative renormalization of the ground-state energy.     

Power-law falloff in two-dimensional Coulomb gases at inverse temperature β>8π

We consider two-dimensional Coulomb gases (standard or hard-core) with activityz, and prove that for any >8 the two-point external charges correlation function exhibits the power-law falloff characteristic of the Kosterlitz-Thouless phase at sufficiently low activity.     

The evaluation of the branching ratios of the decays φ(1020)→2π<Superscript>+</Superscript>2π<Superscript>−</Superscript>π<Superscript>0</Superscript>, π<Superscript>+</Superscript>π<Superscript>−</Superscript>3π<Superscript>0</Superscript>

Combining the Okubo-Zweig-Iizuka rule in the decay φ→ρπ→π⁺π^?π⁰ with the ρ→4π decay amplitudes, we calculate the φ→2π⁺2π^?π⁰ and φ→π⁺π^?3π⁰ ones. The partial widths of the above φ decays are evaluated, and the excitation curves in e⁺e^? annihilation are obtained, assuming reasonable particular relations among the parameters characterizing the anomalous terms of the HLS Lagrangian. The evaluated branching ratios B_φ→π⁺_π^?_3π⁰ ≈ 2 × 10^?7 and B_φ→2π⁺_2π^?_π⁰ ≈ 7 × 10^?7 are such that, with the luminosity L=500 pb^?1 attained at DAΦNE φ factory, one may already possess about 1685 events of the decays φ→5π.     

Scheme of the β-decay of <Superscript>234</Superscript>Th

The scheme of the β-decay of ²³⁴Th is still not completely clear. Only the upper bound (10 keV) of the energy of the isomeric transition from level T_1/2 = 1.17 min of the ²³⁴Pa nucleus is known, and the correspondence between gamma quanta of several energies emitted in the β-decay of ²³⁴Th and specific nuclear levels of ²³⁴Pa has not been established. In this work, the isomeric transition energy of 2.6 ± 0.5 keV is determined via the γ-spectrometry of a ²³⁴Th source in γγ-coincidences, and a new ²³⁴Pa level populated in the β-decay of ²³⁴Th is introduced.     

Alternative method of calculating the eigenvalues of the transfer matrix of the τ<Subscript>2</Subscript> model for <Emphasis Type="Italic">N</Emphasis> = 2

It has been shown that the τ₂ (Baxter-Bazhanov-Stroganov) model for N = 2 with arbitrary parameters is a particular case of the generalized Ising model. The model satisfies the free-fermion condition, which enables one to solve it by the method of the auxiliary Grassmann field. Explicit expressions have been derived for the partition function on a finite-size lattice and eigenvalues of the transfer matrix. In this approach, in contrast to the functional relation method, there is no problem with the multiplicities of the eigenvalues of transfer matrix.     

Effective three-body interactions in the α-cluster model for the <Superscript>12</Superscript>C nucleus

Properties of the lowest 0⁺ states of ¹²C are calculated to study the role of three-body interactions in the α-cluster model. An additional short-range part of the local three-body potential is introduced to incorporate the effects beyond the α-cluster model. There is enough freedom in this potential to reproduce the experimental values of the ground-state and excited-state energies and the ground-state root-mean-square radius. The calculations reveal two principal choices of the two-body and three-body potentials. Firstly, one can adjust the potentials to obtain the width of the excited 0₂⁺ state and the monopole 0₂⁺↦0₁⁺ transition matrix element in good agreement with the experimental data. In this case, the three-body potential has strong short-range attraction supporting a narrow resonance above the 0₂⁺ state, the excited-state wave function contains a significant short-range component, and the excited-state root-mean-square radius is comparable to that of the ground state. Next, rejecting the solutions with an additional narrow resonance, one finds that the excited-state width and the monopole transition matrix element are insensitive to the choice of the potentials and both values exceed the experimental ones.     

Comparison of the π and Δ operator approximations for the two-dimensional t–J model

We compare the spectra of the new π operator of the SO(5) theory and the conventional Δ operator for the two-dimensional t–J model. We also calculate the weight transferred to the two-hole ground state from half-filling by these operators. We find that the spectra of these operators are quite similar and the weight for the π operator is smaller than the weight for the Δ operator. We argue that the two-dimensional t–J model does not have a good approximate SO(5) symmetry claimed in Ref. [1].     

Resonance states of the <Superscript>12</Superscript>С nucleus in the 3α model

A theoretical study of the 0⁺ resonance states of the ¹²С nucleus is performed using the 3α cluster model. Various phenomenological potentials are used to characterize the interaction between alpha particles. The results from calculations with different potentials are compared. The Schrödinger equation, transformed by means of complex rotation, is solved numerically using the finite element technique in order to determine the resonance energies. A set of new broad resonances is found.     

Spectrum of secondary electrons emitted during the nuclear β<Superscript>–</Superscript>-decay of the tritium atom

The depolarization of multiply scattered light in a disordered system of resonant dielectric Mie particles is studied. It is shown that the depolarization length of circularly polarized light under the first Kerker condition can be more than an order of magnitude larger than the transport length. Such a slow decay of circular polarization in a multiply scattering medium results in the enhancement of mesoscopic fluctuations of the transmission coefficient. The wavelength dependence of the variance of the transmission coefficient near the first Kerker point has a quasiresonant character. It is demonstrated that the second Kerker condition under which the forward scattering vanishes is satisfied with an increase in the refractive index. The depolarization lengths of circularly and linearly polarized light calculated for this case are minimal and almost coincide with the mean free path.     

Comparison of the Effects of Different <Superscript>19</Superscript>F <Emphasis Type="Italic">π</Emphasis> Pulses on the Sensitivity and Phaseability of the <Superscript>19</Superscript>F-<Superscript>13</Superscript>C HSQC

The ¹⁹F-¹³C heteronuclear single quantum coherence (HSQC) experiment is vital for the structural elucidation of polyfluorinated organic species, yet its sensitivity and phaseability are limited by difficulties in uniform excitation of the widely disperse ¹⁹F spectral window. Adiabatic pulses of different types have previously been employed to generate effective π pulses for inversion and refocussing, but a systematic comparison of various adiabatic and other inversion pulses has not been published. In this work, it was observed that the use of a broadband inversion pulse (BIP) during the t ₁ evolution period resulted in properly phaseable spectra for experiments optimized to detect ¹ J _CF, in contrast to CHIRP or WURST adiabatic pulses. For the INEPT and reverse-INEPT transfer segments of the HSQC, optimal sensitivity for resonances distant from the transmitter frequency was afforded by optimized universal rotation (BURBOP) or CHIRP pulses. In HSQC experiments with delays optimized for two-bond correlations, only the use of BURBOP pulses in INEPT and reverse-INEPT sequences afforded spectra cleanly phaseable across the F ₂ and F ₁ spectral windows. This observation is supported by off-resonance pulsed field gradient spin-echo experiments.     

Effect of the block-spin configuration on the location of βc in two-dimensional Ising modelsin two-dimensional Ising models

We consider the nearest neighbor Ising model on the 2D square lattice and divide the lattice into 2 by 2 blocks. Each block is assigned one spin value (1 or –1) and these block spin values are kept fixed. We then impose the majority rule and look at the effect on the phase transition that was present in the original unconstrained spin system. We find that for the checkerboard block-spin configuration, Monte Carlo simulations show that _c is close to 1, which, compared to the original nearest neighbor Ising _c = 0.44..., shows that the critical temperature has been reduced by more than one half. For none of the other 11 block-spin configurations that we have considered is there any indication of a phase transition in the constrained system of original spins.     

Spectroscopy of the <Stack><Subscript>Λ</Subscript><Superscript>7</Superscript></Stack>He nucleus in a three-cluster model

The _Λ ⁷ He hypernucleus is considered within the _Λ ⁵ He + n + n cluster model. The hyperon—nucleon interaction is described by a one-boson-exchange potential that is constructed on the basis of the NSC97f model. Phenomenological potentials are used to describe the αΛ and αN interactions. For the _Λ ⁵ Hen interaction, use is made of the folding-model potential. The calculations of the hyperon binding energy in the ground state of the _Λ ⁷ He hypernucleus on the basis of Faddeev equations in configuration space yield a result (5.35 MeV) that agrees well with preliminary experimental data (5.4 MeV). The problem of calculating the hyperon binding energy within the three-body approach is discussed. In calculating the energy spectrum of _Λ ⁷ He, use is made of a version of the method of analytic continuation in the coupling constant. Low-lying excited states of this nucleus can be classified as an analog of the corresponding states of the ⁶He nucleus with allowance for the clustering of the _Λ ⁵ He+n+n system in the ⁶He(J ^π)+Λ(s) form.     

Study of supersolidity in the two-dimensional Hubbard–Holstein model

We derive an effective Hamiltonian for the two-dimensional Hubbard–Holstein model in the regimes of strong electron–electron and strong electron–phonon interactions by using a nonperturbative approach. In the parameter region where the system manifests the existence of a correlated singlet phase, the effective Hamiltonian transforms to a t₁ ? V ₁ ? V ₂ ? V ₃ Hamiltonian for hard-core-bosons on a checkerboard lattice. We employ quantum Monte Carlo simulations, involving stochastic-series-expansion technique, to obtain the ground state phase diagram. At filling 1∕8, as the strength of off-site repulsion increases, the system undergoes a first-order transition from a superfluid to a diagonal striped solid with ordering wavevector \(\vec{Q}\) = (π∕4, 3π∕4) or (π∕4, 5π∕4). Unlike the one-dimensional situation, our results in the two-dimensional case reveal a supersolid phase (corresponding to the diagonal striped solid) around filling 1∕8 and at large off-site repulsions. Furthermore, for small off-site repulsions, we witness a valence bond solid at one-fourth filling and tiny phase-separated regions at slightly higher fillings.     

Fine structure of the strength function for the β<Superscript>+</Superscript>/EC decay of the <Superscript>160<Emphasis Type="Italic">m</Emphasis></Superscript>Ho (5.02 h) isomer

The strength function for the β⁺/EC decay of the deformed nucleus of the ^160m Ho (5.02 h) isomer is obtained from the experimental data, The fine structure of the strength function S _β(E) is analyzed. It has a pronounced resonance structure for Gamow-Teller transitions and is found to exhibit a resonance structure for first-forbidden transitions. It is shown that for some excitation energies of the 160Dy daughter nucleus the probability of first-forbidden β⁺/EC transitions in the decay of the ^160m Ho isomer is comparable with the probability of Gamow-Teller β⁺/EC transitions.     

Shell model calculations for the allowed Gamow-Teller β-decays of light nuclei

The allowed Gamow-Teller β-decay information of Li,Be,B,C,and N isotopes under the frame work of nuclear shell model is calculated herein.Theoretical results of Q values,half-lives,excitation energies,log ft values,branching fractions,and β-delayed proton/neutron emission probabilities are tabulated and compared with experimental data.The deviations from the observations are also analyzed.The 11Be nucleus is well known for its anomaly ground state Jπ=1/2+.Thus,we compared the theoretical energy levels with the experimental data and the agreements for low excitation states are consistent.The quenching factor is also evaluated and discussed.