{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T14:15:50Z","timestamp":1785507350677,"version":"3.56.0"},"reference-count":22,"publisher":"International Union of Crystallography (IUCr)","issue":"4","license":[{"start":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T00:00:00Z","timestamp":1781827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"},{"start":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T00:00:00Z","timestamp":1781827200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"}],"content-domain":{"domain":["iucr.org","wiley.com","iucrj.org"],"crossmark-restriction":true},"short-container-title":["J Synchrotron Rad","J Synchrotron Radiat"],"accepted":{"date-parts":[[2026,5,21]]},"published-print":{"date-parts":[[2026,7,1]]},"abstract":"<jats:p>Next-generation M\u00f6ssbauer spectroscopy at synchrotron and X-ray free-electron laser facilities demands rapid, accurate and polarization-aware modeling of nuclear hyperfine interactions. We present a unified analytical framework that provides exact, rotationally invariant expressions for resonance energies and transition probabilities in the presence of simultaneous magnetic dipole and electric quadrupole interactions. Unlike conventional approaches, our method avoids Hamiltonian diagonalization by expressing intensities entirely in terms of hyperfine invariants, enabling efficient global fitting and modeling of hyperfine-interaction distributions in complex materials. We further introduce a quantitative identifiability metric and demonstrate, via Monte Carlo sampling, that polarization control\u2014particularly orthogonal linear polarizations\u2014substantially improves hyperfine-parameter determination. This work offers a mathematically transparent and computationally efficient toolset for modern M\u00f6ssbauer spectroscopy, accelerating studies of iron-based compounds and magnetic, electronic and structural order under extreme conditions and at nanoscale geometries.<\/jats:p>","DOI":"10.1107\/s1600577526005357","type":"journal-article","created":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T12:43:25Z","timestamp":1781700205000},"page":"931-938","update-policy":"https:\/\/doi.org\/10.1107\/cm_01","source":"Crossref","is-referenced-by-count":0,"title":["A unified analytical framework for M\u00f6ssbauer synchrotron sources"],"prefix":"10.1107","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0930-3396","authenticated-orcid":true,"given":"Krzysztof R.","family":"Szyma\u0144ski","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01qaqcf60","id-type":"ROR","asserted-by":"publisher"}],"department":["Faculty of Physics"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"329","published-online":{"date-parts":[[2026,6,19]]},"reference":[{"key":"ye5085_bb909","doi-asserted-by":"crossref","first-page":"1764","DOI":"10.1103\/PhysRev.100.1764","volume":"100","author":"Brown","year":"1955","journal-title":"Phys. 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