Publicação
The polarizability of a confined atomic system: an application of the Dalgarno-Lewis method
| Resumo: | In this paper we give an application of the Dalgarno–Lewis method, the latter not usually taught in quantum mechanics courses. This is very unfortunate since this method allows one to bypass the sum over states appearing in the usual perturbation theory. In this context, and as an example, we study the effect of an external field, both static and frequency-dependent, on a model atom at fixed distance from a substrate. This can happen, for instance, when some organic molecule binds from one side to the substrate and from the other side to an atom or any other polarizable system. We model the polarizable atom by a short range potential, a Dirac-δ, and find that the existence of a bound state depends on the ratio of the effective 'nuclear charge' to the distance of the atom from the substrate. Using an asymptotic analysis, previously developed in the context of a single δ-function potential in an infinite medium, we determine the ionization rate and the Stark shift of our system. Using Dalgarno–Lewis theory we find an exact expression for the static and dynamic polarizabilities of our system valid to all distances. We show that the polarizability is extremely sensitive to the distance from the substrate, creating the possibility of using this quantity as a nanometric ruler. Furthermore, the line shape of the dynamic polarizability is also extremely sensitive to the distance from the substrate, thus providing another route to measure nanometric distances. The didactic value of the δ-function potential is widely accepted in teaching activities due to its simplicity, while still keeping the essential ingredients of a given problem. |
|---|---|
| Autores principais: | Antão, T. V. C. |
| Outros Autores: | Peres, N. M. R. |
| Assunto: | Dalgarno-Lewis Stark effect polarizability quantum mechanics |
| Ano: | 2021 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| _version_ | 1866876140199608320 |
|---|---|
| author | Antão, T. V. C. |
| author2 | Peres, N. M. R. |
| author2_role | author |
| author_facet | Antão, T. V. C. Peres, N. M. R. |
| author_role | author |
| contributor_name_str_mv | Universidade do Minho |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Antão, T. V. C.\"},{\"Person.name\":\"Peres, N. M. R.\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Universidade do Minho |
| datacite.creators.creator.creatorName.fl_str_mv | Antão, T. V. C. Peres, N. M. R. |
| datacite.date.Accepted.fl_str_mv | 2021-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2022-10-17T16:06:28Z |
| datacite.date.embargoed.fl_str_mv | 2022-10-17T16:06:28Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Dalgarno-Lewis Stark effect polarizability quantum mechanics |
| datacite.titles.title.fl_str_mv | The polarizability of a confined atomic system: an application of the Dalgarno-Lewis method |
| dc.contributor.none.fl_str_mv | Universidade do Minho |
| dc.creator.none.fl_str_mv | Antão, T. V. C. Peres, N. M. R. |
| dc.date.Accepted.fl_str_mv | 2021-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2022-10-17T16:06:28Z |
| dc.date.embargoed.fl_str_mv | 2022-10-17T16:06:28Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | https://hdl.handle.net/1822/80187 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | IOP Publishing Ltd |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Dalgarno-Lewis Stark effect polarizability quantum mechanics |
| dc.title.fl_str_mv | The polarizability of a confined atomic system: an application of the Dalgarno-Lewis method |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | In this paper we give an application of the Dalgarno–Lewis method, the latter not usually taught in quantum mechanics courses. This is very unfortunate since this method allows one to bypass the sum over states appearing in the usual perturbation theory. In this context, and as an example, we study the effect of an external field, both static and frequency-dependent, on a model atom at fixed distance from a substrate. This can happen, for instance, when some organic molecule binds from one side to the substrate and from the other side to an atom or any other polarizable system. We model the polarizable atom by a short range potential, a Dirac-δ, and find that the existence of a bound state depends on the ratio of the effective 'nuclear charge' to the distance of the atom from the substrate. Using an asymptotic analysis, previously developed in the context of a single δ-function potential in an infinite medium, we determine the ionization rate and the Stark shift of our system. Using Dalgarno–Lewis theory we find an exact expression for the static and dynamic polarizabilities of our system valid to all distances. We show that the polarizability is extremely sensitive to the distance from the substrate, creating the possibility of using this quantity as a nanometric ruler. Furthermore, the line shape of the dynamic polarizability is also extremely sensitive to the distance from the substrate, thus providing another route to measure nanometric distances. The didactic value of the δ-function potential is widely accepted in teaching activities due to its simplicity, while still keeping the essential ingredients of a given problem. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| fulltext.url.fl_str_mv | https://prod-dspace.uminho.pt/bitstreams/61a57601-84a7-40b6-9fec-141cd6df18ee/download |
| id | rum_79b7a125aa2d24f92b1fdd5a135aba9e |
| identifier.url.fl_str_mv | https://hdl.handle.net/1822/80187 |
| instacron_str | repositorium |
| institution | Universidade do Minho |
| instname_str | Universidade do Minho |
| language | eng |
| network_acronym_str | rum |
| network_name_str | RepositóriUM - Universidade do Minho |
| oai_identifier_str | oai:repositorium.uminho.pt:1822/80187 |
| organization_str_mv | urn:organizationAcronym:repositorium |
| person_str_mv | Antão, T. V. C. Peres, N. M. R. |
| publishDate | 2021 |
| publisher.none.fl_str_mv | IOP Publishing Ltd |
| reponame_str | RepositóriUM - Universidade do Minho |
| repository_id_str | urn:repositoryAcronym:rum |
| service_str_mv | urn:repositoryAcronym:rum |
| spelling | engIOP Publishing LtdporIn this paper we give an application of the Dalgarno–Lewis method, the latter not usually taught in quantum mechanics courses. This is very unfortunate since this method allows one to bypass the sum over states appearing in the usual perturbation theory. In this context, and as an example, we study the effect of an external field, both static and frequency-dependent, on a model atom at fixed distance from a substrate. This can happen, for instance, when some organic molecule binds from one side to the substrate and from the other side to an atom or any other polarizable system. We model the polarizable atom by a short range potential, a Dirac-δ, and find that the existence of a bound state depends on the ratio of the effective 'nuclear charge' to the distance of the atom from the substrate. Using an asymptotic analysis, previously developed in the context of a single δ-function potential in an infinite medium, we determine the ionization rate and the Stark shift of our system. Using Dalgarno–Lewis theory we find an exact expression for the static and dynamic polarizabilities of our system valid to all distances. We show that the polarizability is extremely sensitive to the distance from the substrate, creating the possibility of using this quantity as a nanometric ruler. Furthermore, the line shape of the dynamic polarizability is also extremely sensitive to the distance from the substrate, thus providing another route to measure nanometric distances. The didactic value of the δ-function potential is widely accepted in teaching activities due to its simplicity, while still keeping the essential ingredients of a given problem.application/pdfporThe polarizability of a confined atomic system: an application of the Dalgarno-Lewis methodAntão, T. V. C.Peres, N. M. R.HostingInstitutionOrganizationalUniversidade do Minhoe-mailmailto:repositorium@usdb.uminho.ptrepositorium@usdb.uminho.ptISSNIsPartOf0143-0807DOIIsPartOf10.1088/1361-6404/abfd242022-10-17T16:06:28Z20212021-01-01T00:00:00ZHandlehttps://hdl.handle.net/1822/80187http://purl.org/coar/access_right/c_abf2open accessDalgarno-LewisStark effectpolarizabilityquantum mechanics915242 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://prod-dspace.uminho.pt/bitstreams/61a57601-84a7-40b6-9fec-141cd6df18ee/download |
| spellingShingle | The polarizability of a confined atomic system: an application of the Dalgarno-Lewis method Antão, T. V. C. Dalgarno-Lewis Stark effect polarizability quantum mechanics |
| status | SINGLETON |
| subject.fl_str_mv | Dalgarno-Lewis Stark effect polarizability quantum mechanics |
| title | The polarizability of a confined atomic system: an application of the Dalgarno-Lewis method |
| title_full | The polarizability of a confined atomic system: an application of the Dalgarno-Lewis method |
| title_fullStr | The polarizability of a confined atomic system: an application of the Dalgarno-Lewis method |
| title_full_unstemmed | The polarizability of a confined atomic system: an application of the Dalgarno-Lewis method |
| title_short | The polarizability of a confined atomic system: an application of the Dalgarno-Lewis method |
| title_sort | The polarizability of a confined atomic system: an application of the Dalgarno-Lewis method |
| topic | Dalgarno-Lewis Stark effect polarizability quantum mechanics |
| topic_facet | Dalgarno-Lewis Stark effect polarizability quantum mechanics |
| url | https://hdl.handle.net/1822/80187 |
| visible | 1 |