Energy-independent complex single PP-waves NNNN potential from Marchenko equation

We extend our previous results of solving the inverse problem of quantum scattering theory (Marchenko theory, fixed-$l$ inversion). In particular, we apply an isosceles triangular-pulse function set for the Marchenko equation input kernel expansion in a separable form. The separable form allows a reduction of the Marchenko equation to a system of linear equations for the output kernel expansion coefficients. We show that in the general case of a single partial wave, a linear expression of the input kernel is obtained in terms of the Fourier series coefficients of $q^{1-m}(1-S(q))$ functions in the finite range of the momentum $0\leq q\leq\pi/h$ [$S(q)$ is the scattering matrix, $l$ is the angular orbital momentum, $m=0,1,\dots,2l$]. Thus, we show that the partial $S$--matrix on the finite interval determines a potential function with $h$-step accuracy. The calculated partial potentials describe a partial $S$--matrix with the required accuracy. The partial $S$--matrix is unitary below the threshold of inelasticity and non--unitary (absorptive) above the threshold. We developed a procedure and applied it to partial-wave analysis (PWA) data of $NN$ elastic scattering up to 3 GeV. We show that energy-independent complex partial potentials describe these data for single $P$-waves.Comment: 7 pages, 6 figures. arXiv admin note: text overlap with arXiv:2112.1434

Carbon Detonation and Shock-Triggered Helium Burning in Neutron Star Superbursts

The strong degeneracy of the 12C ignition layer on an accreting neutron star results in a hydrodynamic thermonuclear runaway, in which the nuclear heating time becomes shorter than the local dynamical time. We model the resulting combustion wave during these superbursts as an upward propagating detonation. We solve the reactive fluid flow and show that the detonation propagates through the deepest layers of fuel and drives a shock wave that steepens as it travels upward into lower density material. The shock is sufficiently strong upon reaching the freshly accreted H/He layer that it triggers unstable 4He burning if the superburst occurs during the latter half of the regular Type I bursting cycle; this is likely the origin of the bright Type I precursor bursts observed at the onset of superbursts. The cooling of the outermost shock-heated layers produces a bright, ~0.1s, flash that precedes the Type I burst by a few seconds; this may be the origin of the spike seen at the burst onset in 4U 1820-30 and 4U 1636-54, the only two bursts observed with RXTE at high time resolution. The dominant products of the 12C detonation are 28Si, 32S, and 36Ar. Gupta et al. showed that a crust composed of such intermediate mass elements has a larger heat flux than one composed of iron-peak elements and helps bring the superburst ignition depth into better agreement with values inferred from observations.Comment: 11 pages, 11 figures, accepted to ApJ; discussion about onset of detonation discussed in new detail, including a new figur