1,287 research outputs found
Energy-independent complex single -waves potential from Marchenko equation
We extend our previous results of solving the inverse problem of quantum
scattering theory (Marchenko theory, fixed- 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 functions in the
finite range of the momentum [ is the scattering
matrix, is the angular orbital momentum, ]. Thus, we show
that the partial --matrix on the finite interval determines a potential
function with -step accuracy. The calculated partial potentials describe a
partial --matrix with the required accuracy. The partial --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 elastic scattering up to 3 GeV. We show that
energy-independent complex partial potentials describe these data for single
-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
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