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The pseudogap phase is identified with the $d$-charge-density wave ($d$-CDW) phase in this model. Using the small electron-phonon coupling constant $\\lambda_d \\sim 0.02$ obtained previously in LDA calculations in YBa$_2$Cu$_3$O$_7$, $\\alpha^{\\ast}$ is negative but negligible small whereas $\\alpha$ increases from about 0.03 at optimal doping to values around 1 at small dopings in a"},"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":"0908.1911","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2009-08-13T14:47:21Z","cross_cats_sorted":[],"title_canon_sha256":"a02a826cfc99ae22deeb58064f3fe8b4ec7b46fa5b20fa6fa75738b9b6d51307","abstract_canon_sha256":"78b0cc626e04af5d0dfa555fbe576d9da354f32945fac4f491191b96960fc2e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:12:34.547869Z","signature_b64":"Xz9SiWm+zIr3eLkn73tMff0ZpFcGfshHmelROc4jqvvB88++dKPSTUE5S1kd1H8Ddp3J/A/wsJJJ775dNpLTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb90f91da4951d2ba81e73bb5840f595c3aa02c3ccfb0531f26b500c6c0a973f","last_reissued_at":"2026-05-18T02:12:34.547228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:12:34.547228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large isotope effect on $T_c$ in cuprates despite of a small electron-phonon coupling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.supr-con","authors_text":"Andr\\'es Greco, Roland Zeyher","submitted_at":"2009-08-13T14:47:21Z","abstract_excerpt":"We calculate the isotope coefficients $\\alpha$ and $\\alpha^\\ast$ for the superconducting critical temperature $T_c$ and the pseudogap temperature $T^\\ast$ in a mean-field treatment of the t-J model including phonons. 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