Radiative muon capture for N = Z nuclei

The commonly used elementary hamiltonian of radiative muon capture has been confirmed, while the alternative Hwang-Primakoff approach is shown not to be gauge invariant.In the inclusive process on N = Z nuclei, the closure approximation is avoided by using a realistic nuclear excitation spectrum.The study is exemplified by a detailed application to ⁴⁰Ca. Predictions are given for the high-energy photon spectrum, circular polarization and asymmetry with respect to the muon polarization for various values of the pseudoscalar coupling constant g_p. A semi-quantitative agreement is found with the data on the spectrum; more precise experiments are necessary to determine g_p.     

SU(N) invariant non-linear σ models

Two series of SU(N) invariant non-linear σ models are constructed using exceptional orbits of the adjoint representation of SU(N). Each of these models possesses infinitely many local as well as non-local conserved charges.     

Magnetic lenses performance with fields of the form B(Z)∝Z

Performance of magnetic lenses with fields of the form B(z)∝Zⁿ was studied. To compare the performance of different objective lenses the results are presented in W. Tretner's [Existenzbereiche rotations symmetrischer Elektronenlinsen, Optik 16 (1959) 155-184] form.     

The large-N phase transition in the U(N) chiral models

We prove the existence of a large-N phase transition in the d = 2 chiral model and calculate via strong-coupling methods the phase-transition point. The critical coupling constant is 0.324. We also treat the chiral model chains (equivalent to the gauge model on polyhedrons) and our approximate calculations come very close to the exact results for the solvable cases.     

Non-planar diagrams in the large N limit of U(N) and SU(N) lattice gauge theories

It is shown that the limit as N → ∞ with g²N fixed of the strong coupling expansion for the vacuum expectation values of a U(N) or SU(N) lattice gauge theory is not given by a sum of planar diagrams. This contradicts a result claimed by De Wit and 't Hooft.     

等时性质量谱仪中N=Z核质量测量的方法探索

N=Z核的质量数据对于研究rp-和νp-过程至关重要。此外,N=Z原子核的质量数据将会帮助我们解决与核结构有关的许多关键问题。结合碎片分离器的等时性质谱仪（Isochronous mass spectrometry,IMS）是十分快速有效而且高分辨的质量测量工具。由于N=Z核的m/q值非常接近,目前国际上的储存环质量谱仪CSRe/IMP和ESR/GSI还无法实现对N=Z核运用飞行时间谱进行鉴别,因而无法对它们进行质量测量。在日本理化学研究所的仁科加速器中心新建了专用的等时性质谱仪（IMS）,即稀有放射性同位素储存环"Rare-RI Ring"（R3）,以确定短寿命的放射性原子核的质量,其目标质量相对精度为10-6。R3质谱仪与高分辨的碎片分离器BigRIPS的组合,运用束流线的高分辨的离子鉴别,使得R3上的IMS方法对N=Z核进行质量测量成为可能。本文设计了专用的等时性束流光学设置,模拟了124Xe的主束经过碎裂反应产生的N=Z核在束流线中穿过各焦平面的径迹、能量、速度等信息,同时检验了这些次级束在环内的飞行时间相对于动量的变化关系。模拟的结果表明:当储存环的等时性光学设置在某一个N=Z核时,所有其它N=Z核在环内的回旋时间也与动量弥散无关,说明了这些核也满足等时性条件。基于N=Z核的这种等时性的特点,本文对R3上刻度N=Z核的方法也进行了讨论。     

Comparing O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions to SU(N) gauge theories in 3 + 1 dimensions

We have computed the scale breaking Λ parameters of the euclidean and hamiltonian formulations of the lattice regulated O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions in terms of the Λ_PV parameters of the Pauli-Villars regulated continuum models. Using lattice perturbation theory, the renormalized mass gap has been determined in terms of Λ_PV for each model. These results are compared to analogous calculations in SU(N) gauge theories.     

Total muon capture rates for N = Z nuclei in the 1p shell

The approach to total muon capture rates by means of sum rule techniques is applied systematically to 1p shell nuclei. Explicit calculations involve ground-state wave functions extracted from Cohen-Kurath effective interactions. For the double commutator expectation value we use a form of the potential consistent with the effective interaction and the giant dipole resonance energy.Results are given for N = Z nuclei, studying the minimal sensitivity with the parameter of the improved closure approach. The manifestations of SU(4) breaking are quantitatively shown. Within the uncertainties of the model the rates thus obtained compare reasonably well with experiment.     

N = 1 superspace formulation of N = 2 and N = 4 super-Yang-Mills models with central charge

The component models of N = 2 and N = 4 supersymmetric Yang-Mills theories of Sohnius, Stelle and West are reformulated in terms of N = 1 superfields. The non-supersymmetric constraints are supersymmetrized generalizing the linear multiplet in the presence of the non-abelian gauge superfield and (in the N = 4 case) a doublet of chiral superfields. The extended supersymmetry transformations preserving constraints are explicitly given in terms of N = 1 superfields. We are able to introduce the constraints back into the lagrangian using superfield Lagrange multipliers. The on-shell equivalence of this formulation with the formulation of Fayet with one (for N = 2) and three (for N = 4) chiral superfields is shown. The abelian N = 2 model is worked out to show the connection between full superspace treatment and the N = 1 superfield formulation.     

The phase structure of SU(N)/Z(N) lattice gauge theories

The phase structure of pure SU(N)/Z(N) lattice gauge theories in four dimensions is discussed. The presence of ZN monopoles plausibly leads to a phase transition. A Monte Carlo simulation of SO(3) shows the presence of a very strong, may be first order, phase transition.     

Chiral symmetry,the 1/N expansion and the SU(N) thirring model

In the two-dimensional SU(N) Thirring model, the 1/N expansion seems to predict spontaneous breaking of the continuous chiral symmetry. This is impossible in two-dimensions. Reasoning along the lines of Berezinski, Kosterlitz and Thouless for the two-dimensional XY model, we argue that, in fact, rather than showing long-range order, $\text{〈}\text{ψ}\text{ψ(x)}\text{ψ}\text{ψ(0)〉}$ vanishes in this model as |x|^?1/N at large |x|. The 1/N expansion is, in fact, a rather good guide to the properties of this model.     

Mass gap and universality for euclidean O(N) and CPN−1 models

From a suitably defined correlation function we evaluate the strong coupling expansion for the mass gap of an euclidean version of the O(N) models in 2D. Good agreement is found for N = 0, 1 and 2 with the known values of the critical temperature and for N ? 3 with the continuum mass gap as evaluated in an hamiltonian approach. Another test of universality based on the use of an asymmetric lattice also yields good results. An analogous discussion for the CP^N?1 models is performed.     

A study of the critical behavior of the O(N) linear and nonlinear σ models

A study of the large N behavior of both the O(N) linear and nonlinear σ models is presented. The purpose is to investigate the relationship between the disordered (ordered) phase of the linear and nonlinear sigma models. Utilizing operator product expansions and stability analyses, it is shown that for 2 ≤ d < 4, it is the dimensionless renormalized quartic coupling and $\text{λ}{}^1$ is the IR fixed point) limit of the linear σ model which yields the nonlinear σ model. It is also shown that stable large N linear σ models with λ < 0 (σ is the bare quartic coupling) can exist (at least in the context of no tachyonic states being present). A criteria valid for all dimensionalities d, less than four, is derived which determines when λ < 0 models are tachyonic free. Arguments are given showing that the d = 4 large N linear (for λ > 0) and nonlinear models are trivial. This result (i.e., triviality) is well known but only for one and two component models. Interestingly enough, the λ < 0, d = 4 linear σ model remains nontrivial and tachyonic free.     

Duality relations and equivalences for models with O(N) and cubic symmetry

Formal expression for high-temperature series are derived for models with O(N) and cubic symmetry, with a special form of nearest neighbor interactions on the honeycomb lattice. By deriving low-temperature series for a class of generalized solid-on-solid and cubic models, a duality relation is established. Equivalences between cubic and SOS type models are also found. In the large-N limit, the series reduce to those of the hard hexagon model.     

Nonconvergence of the 1/N expansion for SU(N) gauge fields on a lattice

We present specific examples that demonstrate the non-convergence of the 1/N expansion for the lattice theory of SU(N) gauge fields.     

Duality for Z(N) gauge theories

The duality properties of simple Z(N) gauge theories are discussed. For N ? 4 we find self duality in four dimensions and we give the transition points. For N > 4 these systems are not self dual. Also, the order parameter is discussed. The general Z(N) gauge theory is found to be self dual for all N.     

Gaussian fluctuations to U(N) and SU(N) lattice gauge theories in the mean field approximation

The mean field can be considered as a classical solution of an appropriately reformulated version of lattice gauge theories. Axial gauge fixing renders it stable. The quadratic forms for the fluctuations in the gaussian approximation are analyzed. The gaussian correction to the mean field free energy is expressed for all U(N) and SU(N) in terms of structure functions that are explicitly calculated for U(N), SU(∞, and SU(∞) numerical calculations are performed for the phase transition point, its latent heat, and some correlation lengths that are characteristic for this kind of mean field approach.     

U(N) invariance in extended supergravity

U(N) invariance of previously established extended supergravity theories (O(1), O(2), O(3)) is shown to be also compatible with the O(4) theory at the first non-trivial order in the Newton constant. If U(4) invariance remains true to all orders the non-polynomial feature of this theory is enormously simplified. As an example we determine, to all orders, the non-polynomial correction to the spin-1 kinetic term using some of the constraints of supersymmetry.     

On-shell O(N) supergravity in superspace

We show that general considerations of the properties of free on-shell O(N) superfield strengths lead directly to linearized on-shell O(N) supergravity. We consequently obtain a formulation of the fully non-linear on-shell theories in which all fields are contained in the covariant derivatives.     

Electric dipole transitions for La I (Z=57)

Wavelengths, weighted oscillator strengths and transition probabilities for electric dipole (E1) transitions for some excited levels in neutral lanthanum (La I, Z=57) have been calculated using the multiconfiguration Hartree-Fock (MCHF) method within the framework of Breit-Pauli relativistic corrections. Results obtained have been compared with other calculations and experiments. A discussion of these calculations for La I in this study has also been given in view of the MCHF method.