Experimental investigations of the nuclear level density by using heavy ion reactions

The transition of the level density parameter a _off from the low excitation energy value a _off=A/8 MeV⁻¹ to the Fermi gas value a _FG ∼ A/15 MeV⁻¹ was discovered a few years ago studying particle spectra evaporated from hot compound systems of A∼ 160. A number of experiments have been recently performed to confirm the earlier findings and extend the investigation to other mass regions and to higher excitation energies. Furthermore, precision coincidence experiments have been done in the lead region in which evaporation residues are tagged by low energy gammarays. Those experiments open the possibility of a detailed study of the level densities in nuclei where the shell effects are important.     

On weak compactness of bounded sets in Banach and locally convex spaces

We investigate the compactness of one class of bounded subsets in Banach and locally convex spaces. We obtain a generalization of the Banach-Alaoglu theorem to a class of subsets that are not polars of convex balanced neighborhoods of zero. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp 731–739, June. 2000.     

Studies of chiral symmetry breaking in SU(2) lattice gauge theory

We study chiral symmetry breaking (_χSB) in SU(2) lattice gauge theory with quarks in the $\text{l =}\text{1}\text{2}\text{, l = 1, l =}\text{3}\text{2}$, and l = 2 representations of the color group. We perform Monte Carlo evaluations of $\text{〈}\text{ψ}\text{ψ〉}$ in the quenched approximation and extract the relevant length scales for _χSB. We revise a previous estimate for the ratio between the chiral symmetry restoration temperatures for fundamental and adjoint quarks and obtain $\text{T}{}_{\mathrm{l\; =\; 1}}\text{/T}{}_{\mathrm{l}}\text{=}\text{1}\text{2}\text{～ 8}$. Our results for the higher representations, $\text{l =}\text{3}\text{2}\text{and}\text{l = 2}$, are consistent with Casimir scaling and give C₂g_mom² ～ 4. Many aspects of our calculational method are explained in detail. The issues discussed include the relation between _χSB in the quenched approximation and the spectrum of the Dirac operator, the flavor symmetries of euclidean staggered fermions, estimates of finite-size effects and the reliability of m → 0 extrapolations on finite lattices.     

Comparison of recent massive muon pair data with the asymptotically free parton model

We present calculations of vW₂ and of massive muon pair production cross sections in the kinematic ranges of recent experiments. These calculations test the asymptotically free parton model and excellent agreement with the data is found. Estimates of the transverse momentum 〈q_⊥〉_μμ expected in massive dimuon experiments are made. For s = 750 GeV² and M_μμ ≈ 10 GeV, we predict 〈q_⊥〉_μμ ≈ 1.4 GeV/c.     

The renormalization group and the ϵ expansion

The modern formulation of the renormalization group is explained for both critical phenomena in classical statistical mechanics and quantum field theory. The expansion in ? = 4?d is explained [d is the dimension of space (statistical mechanics) or space-time (quantum field theory)]. The emphasis is on principles, not particular applications. Sections 1–8 provide a self-contained introduction at a fairly elementary level to the statistical mechanical theory. No background is required except for some prior experience with diagrams. In particular, a diagrammatic approximation to an exact renormalization group equation is presented in sections 4 and 5; sections 6–8 include the approximate renormalization group recursion formula and the Feyman graph method for calculating exponents. Sections 10–13 go deeper into renormalization group theory (section 9 presents a calculation of anomalous dimensions). The equivalence of quantum field theory and classical statistical mechanics near the critical point is established in section 10; sections 11–13 concern problems common to both subjects. Specific field theoretic references assume some background in quantum field theory. An exact renormalization group equation is presented in section 11; sections 12 and 13 concern fundamental topological questions.