Separation of variables in the generalized 4th Appelrot class

We consider the analogue of the 4th Appelrot class of motions of the Kowalevski top for the case of two constant force fields. The trajectories of this family fill the four-dimensional surface O^4 in the six-dimensional phase space. The constants of three first integrals in involution restricted to this surface fill one of the sheets of the bifurcation diagram in R^3. We point out the pair of partial integrals to obtain the explicit parametric equations of this sheet. The induced system on O^4 is shown to be Hamiltonian with two degrees of freedom having the thin set of points where the induced symplectic structure degenerates. The region of existence of motions in terms of the integral constants is found. We provide the separation of variables on O^4 and the algebraic formulae for the initial phase variables.Comment: LaTex, 16 pages, 1 figur

Electronic energy relaxation and transition frequency jumps of single molecules at 30 mK

Transition frequency jumps for single terrylene molecules in a polyethylene matrix caused by resonant laser irradiation are investigated at 30 mK. These jumps are not accompanied by substantial sample heating. A model for the effect is: proposed, based on the interaction of tunneling two-level systems (TLSs) surrounding the single molecule with high-energy nonthermal phonons emitted by the molecule during electronic energy relaxation. The radius of the effective interaction volume is estimated to be r(m) approximate to 12.5 nm, and the interaction cross section for nonequilibrium phonon -TLS scattering is estimated as similar to 10(-22) cm(-2)

Fragmentation channels of relativistic 7^7Be nuclei in peripheral interactions

Nuclei of $^7$Li were accelerated at the JINR Nuclotron. After the charge-exchange reaction involving these nuclei at an external target a second $^7$Be beam of energy 1.23A GeV was formed. This beam was used to expose photo-emulsion chambers. The mean free path for inelastic $^7$Be interactions in emulsion $\lambda$=14.0$\pm$0.8 cm coincides within the errors with those for $^6$Li and $^7$Li nuclei. More than 10% of the $^7$Be events are associated with the peripheral interactions in which the total charge of the relativistic fragments is equal to the charge of the $^7$Be and in which charged mesons are not produced. An unusual ratio of the isotopes is revealed in the composition of the doubly charged $^7$Be fragments: the number of $^3$He fragments is twice as large as that of $^4$He fragments. In 50% of peripheral interactions, a $^7$Be nucleus decays to two doubly charged fragments. The present paper gives the channels of the $^7$Be fragmentation to charged fragments. In 50% of events, the $^7$Be fragmentation proceeds only to charged fragments involving no emission of neutrons. Of them, the $^3$He+$^4$He channel dominates, the $^4$He+d+p and $^6$Li+pchannels constitute 10% each. Two events involving no emission of neutrons are registered in the 3-body $^3$He+t+p and $^3$He+d+d channels. The mean free path for the coherent dissociation of relativistic $^7$Be nuclei to $^3$He+$^4$He is 7$\pm$1 m. The particular features of the relativistic $^7$Be fragmentation in such peripheral interactions are explained by the $^3$He+$^4$He 2-cluster structure of the $^7$Be nucleus.Comment: 10 pages, 3 figures, 3 tables, conference: Conference on Physics of Fundamental Interactions, Moscow, Russia, 5-9 Dec 200

Topology of energy surfaces and existence of transversal Poincar\'e sections

Two questions on the topology of compact energy surfaces of natural two degrees of freedom Hamiltonian systems in a magnetic field are discussed. We show that the topology of this 3-manifold (if it is not a unit tangent bundle) is uniquely determined by the Euler characteristic of the accessible region in configuration space. In this class of 3-manifolds for most cases there does not exist a transverse and complete Poincar\'e section. We show that there are topological obstacles for its existence such that only in the cases of $S^1\times S^2$ and $T^3$ such a Poincar\'e section can exist.Comment: 10 pages, LaTe

Measurement of hadron cross sections with the SND detector

New results on exclusive hadron production in $e^+e^-$ annihilation obtained in experiments with the SND detector at the VEPP-2M and VEPP-2000 $e^+e^-$ colliders are presented.Comment: 4 pages, 4 figures, presented at the 14th International Workshop on Meson Production, Properties and Interaction (MESON 2016), Cracow, Poland, 2nd - 7th June 201

Exposure of Nuclear Track Emulsion to a Mixed Beam of Relativistic 12^{12}N, 10^{10}C, and 7^7Be Nuclei

A nuclear track emulsion was exposed to a mixed beam of relativistic $^{12}$N, $^{10}$C, and $^7$Be nuclei having a momentum of 2 GeV/$c$ per nucleon. The beam was formed upon charge exchange processes involving $^{12}$C primary nuclei and their fragmentation. An analysis indicates that $^{10}$C nuclei are dominant in the beam and that $^{12}$N nuclei are present in it. The charge topology of relativistic fragments in the coherent dissociation of these nuclei is presented.Comment: ISSN 1063-7788, Pleiades Publishing, Ltd., 201

Topology of "white" stars in relativistic fragmentation of light nuclei

In the present paper, experimental observations of the multifragmentation processes of light relativistic nuclei carried out by means of emulsions are reviewed. Events of the type of "white" stars in which the dissociation of relativistic nuclei is not accompanied by the production of mesons and the target-nucleus fragments are considered. A distinctive feature of the charge topology in the dissociation of the Ne, Mg, Si, and S nuclei is an almost total suppression of the binary splitting of nuclei to fragments with charges higher than 2. The growth of the nuclear fragmentation degree is revealed in an increase in the multiplicity of singly and doubly charged fragments with decreasing charge of the non-excited part of the fragmenting nucleus. The processes of dissociation of stable Li, Be, B, C, N, and O isotopes to charged fragments were used to study special features of the formation of systems consisting of the lightest $\alpha$, d, and t nuclei. Clustering in form of the $^3$He nucleus can be detected in "white" stars via the dissociation of neutron-deficient Be, B, C, and N isotopes.Comment: 20 pages, 3 figures, 9 tables, conference: Conference on Physics of Fundamental Interactions, Moscow, Russia, 1-5 Mar 2004.(Author's translation