Universal description of the rotational-vibrational spectrum of three particles with zero-range interactions

A comprehensive universal description of the rotational-vibrational spectrum for two identical particles of mass $m$ and the third particle of the mass $m_1$ in the zero-range limit of the interaction between different particles is given for arbitrary values of the mass ratio $m/m_1$ and the total angular momentum $L$. If the two-body scattering length is positive, a number of vibrational states is finite for $L_c(m/m_1) \le L \le L_b(m/m_1)$, zero for $L>L_b(m/m_1)$, and infinite for $L<L_c(m/m_1)$. If the two-body scattering length is negative, a number of states is either zero for $L \ge L_c(m/m_1)$ or infinite for $L<L_c(m/m_1)$. For a finite number of vibrational states, all the binding energies are described by the universal function $\epsilon_{LN}(m/m_1) = {\cal E}(\xi, \eta)$, where $\xi=\displaystyle\frac{N-1/2}{\sqrt{L(L + 1)}}$, $\eta=\displaystyle\sqrt{\frac{m}{m_1 L (L + 1)}}$,and $N$ is the vibrational quantum number. This scaling dependence is in agreement with the numerical calculations for $L > 2$ and only slightly deviates from those for $L = 1, 2$. The universal description implies that the critical values $L_c(m/m_1)$ and $L_b(m/m_1)$ increase as $0.401 \sqrt{m/m_1}$ and $0.563 \sqrt{m/m_1}$, respectively, while a number of vibrational states for $L \ge L_c(m/m_1)$ is within the range $N \le N_{max} \approx 1.1 \sqrt{L(L+1)}+1/2$

Three-body problem for ultracold atoms in quasi-one-dimensional traps

We study the three-body problem for both fermionic and bosonic cold atom gases in a parabolic transverse trap of lengthscale $a_\perp$. For this quasi-one-dimensional (1D) problem, there is a two-body bound state (dimer) for any sign of the 3D scattering length $a$, and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths, $a_{ad}$ and $b_{ad}$. In the tightly bound `dimer limit', $a_\perp/a\to\infty$, we find $b_{ad}=0$, and $a_{ad}$ is linked to the 3D atom-dimer scattering length. In the weakly bound `BCS limit', $a_\perp/a\to-\infty$, a connection to the Bethe Ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is non-universal: $a_{ad}$ and $b_{ad}$ depend both on $a_\perp/a$ and on a parameter $R^*$ related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.Comment: 20 pages, 6 figures, accepted for publication in PRA, appendix on the derivation of an integral formula for the Hurvitz zeta functio

Hip replacement in case of false joint of the femoral neck with a high dislocation of the hip and severe stiffness soft tissue component. A case from practice

The results of the treatment of the patient A., 57 years of age, with a diagnosis of post-traumatic pseudarthrosis of neck of right femur. Combined contracture of the hip joint, shortening of the right lower extremity 6.5 santimeters, local osteoporosis. In the process of treatment the patient was applied the llizarov apparatus to equalize the limb length, by gradual distraction dosed daily for 39 days. The second stage, 3 days after removal of the llizarov apparatus, made a total hip replacement. After 1 year achieved anatomical and functional result of treatment is maintained.Приведены результаты лечения пациента А., 57 лет, с диагнозом: посттравматический псевдоартроз шейки правой бедренной кости, болевой синдром, комбинированная контрактура тазобедренного сустава, относительное укорочение правой нижней конечности 6,5 сантиметров, локальный остеопороз. В процессе лечения больному был наложен аппарат Илизарова для уравнивания длины конечностей посредством постепенной дозированной дистракции сутки в течение 39 дней. Вторым этапом, через 3 дня после демонтажа аппарата Илизарова, выполнено тотальное эндопротезирование правого тазобедренного сустава. Через 1 год достигнутый анатомо-функциональный результат лечения сохраняется

Exclusive semileptonic and nonleptonic decays of the Bc meson

We study exclusive nonleptonic and semileptonic decays of the Bc-meson within a relativistic constituent quark model previously developed by us. For the nonleptonic decays we use the factorizing approximation. We update our model parameters by using new experimental data for the mass and the lifetime of the Bc meson and the leptonic decay constants of the D-meson. We calculate the branching ratios for a large set of exclusive nonleptonic and semileptonic decays of the $B_c$ meson and compare our results with the results of other studies. As a guide for further experimental exploration we provide explicit formulas for the full angular decay distributions in the cascade decays Bc^- => J/psi(=> l^+l^-) + rho^-(=> pi^- pi^0) and Bc^- => J/psi(=> l^+l^-) + W^-(off-shell)(=> l^- + nubar).Comment: 19 pages, 2 figure

Ultra-low energy scattering of a He atom off a He dimer

We present a new, mathematically rigorous, method suitable for bound state and scattering processes calculations for various three atomic or molecular systems where the underlying forces are of a hard-core nature. We employed this method to calculate the binding energies and the ultra-low energy scattering phase shifts below as well as above the break-up threshold for the three He-atom system. The method is proved to be highly successful and suitable for solving the three-body bound state and scattering problem in configuration space and thus it paves the way to study various three-atomic systems, and to calculate important quantities such as the cross-sections, recombination rates etc.Comment: LaTeX, RevTeX and amssymb styles, 7 pages (25 Kb), 3 table

Borromean Binding of Three or Four Bosons

We estimate the ratio $R=g_{3}/g_{2}$ of the critical coupling constants $g_{2}$ and $g_{3}$ which are required to achieve binding of 2 or 3 bosons, respectively, with a short-range interaction, and examine how this ratio depends on the shape of the potential. Simple monotonous potentials give $R\simeq 0.8$. A wide repulsive core pushes this ratio close to R=1. On the other hand, for an attractive well protected by an external repulsive barrier, the ratio approaches the rigorous lower bound $R=2/3$. We also present results for N=4 bosons, sketch the extension to $N>4$, and discuss various consequences.Comment: 12 pages, RevTeX, 5 Figures in tex include

Photon distribution amplitudes and light-cone wave functions in chiral quark models

The leading- and higher-twist distribution amplitudes and light-cone wave functions of real and virtual photons are analyzed in chiral quark models. The calculations are performed in the nonlocal quark model based on the instanton picture of QCD vacuum, as well as in the spectral quark model and the Nambu--Jona-Lasinio model with the Pauli-Villars regulator, which both treat interaction of quarks with external fields locally. We find that in all considered models the leading-twist distribution amplitudes of the real photon defined at the quark-model momentum scale are constant or remarkably close to the constant in the $x$ variable, thus are far from the asymptotic limit form. The QCD evolution to higher momentum scales is necessary and we carry it out at the leading order of the perturbative theory for the leading-twist amplitudes. We provide estimates for the magnetic susceptibility of the quark condensate $\chi_m$ and the coupling $f_{3\gamma}$, which in the nonlocal model turn out to be close to the estimates from QCD sum rules. We find the higher-twist distribution amplitudes at the quark model scale and compare them to the Wandzura-Wilczek estimates. In addition, in the spectral model we evaluate the distribution amplitudes and light-cone wave functions of the $\rho$-meson.Comment: 24 pages, 15 figure

Experience in Utilization of Phylogenetic Analysis for Epidemiological Investigation of HIV Infection Case

Objective of the study was to investigate a criminal case of infection with HIV, applying molecular-genetic analysis of blood plasma samples from an estimated source of an infection and the recipient for evaluation of probability of epidemiological connection between them. Materials and methods. The study involved genotyping and phylogenetic analysis of nucleotide sequences of HIV-1 variants, isolated from patients in the investigated group and the control one (19 nucleotide sequences of the HIV-1 from the patients living in the Saratov region, and 15 nucleotide sequences from GenBank). Genotyping was performed using the commercial ViroSeq HIV-1 Genotyping System. The sub-typing of HIV-1 strains was carried out on-line, through the COMET HIV-1/2 and HCV and REGA HIV-1 Sybtyping Tool programs. Phylogenetic analysis of nucleotide sequences was carried out by Mega software, version 5.2. Phylogenetic trees were constructed; nucleotide distances were calculated by Kimura method (bootstrap level 1000). Results and conclusions. Virus variants, isolated from the studied samples, were defined as HIV-1 A subtype. Performed phylogenetic analysis showed that nucleotide sequences of the studied samples authentically grouped on the phylogenetic tree, forming a common cluster, which mismatched that of control group. Calculation of the genetic distance testifies that the genetic relation between the samples within the investigated group is higher, than between the same samples and those of the control group. Thus, by means of phylogenetic analysis it is shown that the strains received from an estimated source of infection and the recipient are genetically closer to each other, than to the strains from the group of comparison. In this regard, it is possible to claim with a big share of confidence that probability of epidemiological connection between them exists

On The Universality Class Of Little String Theories

We propose that Little String Theories in six dimensions are quasilocal quantum field theories. Such field theories obey a modification of Wightman axioms which allows Wightman functions (i.e. vacuum expectation values of products of fundamental fields) to grow exponentially in momentum space. Wightman functions of quasilocal fields in x-space violate microlocality at short distances. With additional assumptions about the ultraviolet behavior of quasilocal fields, one can define approximately local observables associated to big enough compact regions. The minimum size of such a region can be interpreted as the minimum distance which observables can probe. We argue that for Little String Theories this distance is of order {\sqrt N}/M_s.Comment: 25 pages, late