Shadow poles in the alternative parametrization of R-matrix theory

As a trilogy, this first paper along with the authors' two companion articles introduces alternate approaches to standard $R$-matrix parametrization of nuclear cross sections. The authors present first evidence of so-called shadow poles in $R$-matrix theory for ${}^{134}$Xe. The number and location of shadow poles depends upon how one continues the $R$-matrix operators to complex wave numbers. The authors also establish a new pole parametrization of $R$-matrix cross sections, called the $w\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}w\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}d$ $m\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}e$ $p\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}z\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n$, which can be Doppler-broadened analytically. This averaging of cross sections over the thermal motion of target atoms is crucial as it ensures the stability of many nuclear reactors; yet, computing it is a major bottleneck. Doppler-broadened windowed multipole cross sections and their uncertainty can be stored and computed with breakthrough performance.