Hypergeometric solutions to Schr\"odinger equations for the quantum Painlev\'e equations

We consider Schr\"odinger equations for the quantum Painlev\'e equations. We present hypergeometric solutions of the Schr\"odinger equations for the quantum Painlev\'e equations, as particular solutions. We also give a representation theoretic correspondence between Hamiltonians of the Schr\"odinger equations for the quantum Painlev\'e equations and those of the KZ equation or the confluent KZ equations.Comment: 17 pages; Journal of Mathematical Physics (Vol.52, Issue 8) 201

Population synthesis of DA white dwarfs: constraints on soft X-ray spectra evolution

Extending the population synthesis method to isolated young cooling white dwarfs we are able to confront our model assumptions with observations made in ROSAT All-Sky Survey (Fleming et al., 1996). This allows us to check model parameters such as evolution of spectra and separation of heavy elements in DA WD envelopes. It seems like X-ray spectrum temperature of these objects is given by the formula T_{X-ray} = min(T_eff, T_max). We have obtained DA WD's birth rate and upper limit of the X-ray spectrum temperature: DA birth rate $= 0.61\times 10^{-12}$ in cubic parsec per year and T_max = 41000 K. These values are in good correspondence with values obtained by other authors (Liebert et al., 2004; Wolff et al., 1996). From this fact we also conclude that our population synthesis method is applicable to the population of close-by isolated cooling white dwarfs as well as to the population of the isolated cooling neutron stars.Comment: 4 pages, 3 figures, conference "European White Dwarf Workshop, 2010", Tubingen, German

Vertical Structure of the Outer Accretion Disk in Persistent Low-Mass X-Ray Binaries

We have investigated the influence of X-ray irradiation on the vertical structure of the outer accretion disk in low-mass X-ray binaries by performing a self-consistent calculation of the vertical structure and X-ray radiation transfer in the disk. Penetrating deep into the disk, the field of scattered X-ray photons with energy $E\gtrsim10$\,keV exerts a significant influence on the vertical structure of the accretion disk at a distance $R\gtrsim10^{10}$\,cm from the neutron star. At a distance $R\sim10^{11}$\,cm, where the total surface density in the disk reaches $\Sigma_0\sim20$\,g\,cm$^{-2}$, X-ray heating affects all layers of an optically thick disk. The X-ray heating effect is enhanced significantly in the presence of an extended atmospheric layer with a temperature $T_{atm}\sim(2\div3)\times10^6$\,K above the accretion disk. We have derived simple analytic formulas for the disk heating by scattered X-ray photons using an approximate solution of the transfer equation by the Sobolev method. This approximation has a $\gtrsim10$\,% accuracy in the range of X-ray photon energies $E<20$\,keV.Comment: 19 pages, 8 figures, published in Astronomy Letter

Single - particle correlations in events with the total disintegration of nuclei

New experimental data on the behaviour of the single-particle two-dimensional correlation functions R versus Q (Q is the number of nucleons emitted from nuc- lei) and Ap (Ap is the mass of projectile nuclei) are presented in this paper. The interactions of protons, d, 4He and 12C nuclei with carbon nuclei (at a momentum of 4.2 A GeV/c) are considered.The values of R are obtained separately for pi minus mesons and protons.In so doing,the values of R are normalized so that -1=<R=<1.The value of R=0 corresponds to the case of the absence of corre- lations.It has been found that the Q- and Ap-dependence of R takes place only for weak correlations (R< 0.3).In the main (90 %),these correlations are con- nected with the variable pt and have a nonlinear character, that is the regi- ons with different characters of the Q-dependence of R are separated: there is a change of regimes in the Q-dependences of R.The correlations weaken with increasing Ap, and the variable R gets the least values of all the considered ones in 12CC interactions.Simultaneously with weakening the correlations in the region of large Q, the character of the Q-dependence of R changes.Comment: 17 pages, submitted to Phys. Rew.