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If $a$ is the characteristic size of the particle, $\\lambda$ is the wavelength, $a<<\\lambda$ and $\\zeta$ is the boundary impedance of $D$, $[N,[E,N]]=\\zeta [N,H]$ on $S$, where $S$ is the surface of the particle, $N$ is the unit outer normal to $S$, and $E$, $H$ is the EM field, then the scattered field is $E_{sc}=[\\nabla g(x,x_1), Q]$. Here $g(x,y)=\\frac{e^{ik|x-y|}}{4\\pi |x-y|}$, $k$ is the wave number, $x_1\\in D$ is an arbitrary point, and $Q=-\\frac{\\zeta |S"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1503.00639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-03-02T17:51:46Z","cross_cats_sorted":[],"title_canon_sha256":"8314f2001e2cd807ae2295add917dc5a7854721e8f34f51aac73bbe5c24fe227","abstract_canon_sha256":"932243390ac61fa8d6f07380531541c02eb29147a76f4f6ae48d88c311540bb1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:49.614263Z","signature_b64":"o8WUUNQjFTJk8tEDlWKDDa3K6S+TUw65radOeTBXICLPbnvhS48PsmBR/H6z5U31JCL29Z7+7hIVhuLFGSttBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95e2e715bc59fb78c6bdc1a6cc145ddccd1e9670d628097598fc5a1744edd622","last_reissued_at":"2026-05-18T02:25:49.613717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:49.613717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scattering of electromagnetic waves by small impedance particles of an arbitrary shape","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Alexander G. Ramm","submitted_at":"2015-03-02T17:51:46Z","abstract_excerpt":"An explicit formula is derived for the electromagnetic (EM) field scattered by one small impedance particle $D$ of an arbitrary shape. If $a$ is the characteristic size of the particle, $\\lambda$ is the wavelength, $a<<\\lambda$ and $\\zeta$ is the boundary impedance of $D$, $[N,[E,N]]=\\zeta [N,H]$ on $S$, where $S$ is the surface of the particle, $N$ is the unit outer normal to $S$, and $E$, $H$ is the EM field, then the scattered field is $E_{sc}=[\\nabla g(x,x_1), Q]$. 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