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 evidence so-called shadow poles in theory for ${}^{134}$Xe. number and location depends upon how one continues operators complex wave numbers. also establish new pole sections, called $w\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}w\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}d$ $m\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}e$ $p\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}z\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n$, which can be Doppler-broadened analytically. This averaging sections over thermal motion target atoms is crucial as it ensures stability many reactors; yet, computing major bottleneck. windowed multipole their uncertainty stored computed breakthrough performance.