242 research outputs found
Critical phenomena in gravitational collapse of Husain-Martinez-Nunez scalar field
We construct analytical models to study the critical phenomena in
gravitational collapse of the Husain-Martinez-Nunez massless scalar field. We
first use the cut-and-paste technique to match the conformally flat solution
( ) onto an outgoing Vaidya solution. To guarantee the continuity of the
metric and the extrinsic curvature, we prove that the two solutions must be
joined at a null hypersurface and the metric function in Vaidya spacetime must
satisfy some constraints. We find that the mass of the black hole in the
resulting spacetime takes the form , where the
critical exponent is equal to . For the case , we show
that the scalar field must be joined onto two pieces of Vaidya spacetimes to
avoid a naked singularity. We also derive the power-law mass formula with
. Compared with previous analytical models constructed from a
different scalar field with continuous self-similarity, we obtain the same
value of . However, we show that the solution with is not
self-similar. Therefore, we provide a rare example that a scalar field without
self-similarity also possesses the features of critical collapse.Comment: 14 pages, 6 figure
Residue cross sections of Ti-induced fusion reactions based on the two-step model
Ti-induced fusion reactions to synthesize superheavy elements are
studied systematically with the two-step model developed recently, where fusion
process is divided into approaching phase and formation phase. Furthermore, the
residue cross sections for different neutron evaporation channels are evaluated
with the statistical evaporation model. In general, the calculated cross
sections are much smaller than that of Ca-induced fusion reactions, but
the results are within the detection capability of experimental facilities
nowadays. The maximum calculated residue cross section for producing superheavy
element is in the reaction Ti+Bk in channels with
pb at = 37.0 MeV.Comment: 6 pages, 7 figure
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