Paper Citation Record · LEDGER

Angular Geometry of Atomic Multipole Transitions

As of 20 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2510.07451.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2510.07451 v4

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T11:03:00.169437Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

40 of 40 outbound references displayed

verified exact1
verified fuzzy0
unresolved39
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 05df168b-a7c2-44fe-96af-66716b3002d9 · outbound

This paper cites whereρ⊥k, which could be written in the helicity basis (Appendix B) asρ=x ′ ˆ e′ x′ +y ′ ˆ e′ y′.

Angular Geometry of Atomic Multipole Transitions whereρ⊥k, which could be written in the helicity basis (Appendix B) asρ=x ′ ˆ e′ x′ +y ′ ˆ e′ y′

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:55.035208Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0410a172-bd62-44d6-9c88-d28ba64b9ec8 · outbound

This paper cites On the one hand, a transverse displacement of a Gaus- sian beam will reduce the intensity at the atom, which 8 will suppress the resonant Rabi frequency in most geome- tries.

Angular Geometry of Atomic Multipole Transitions On the one hand, a transverse displacement of a Gaus- sian beam will reduce the intensity at the atom, which 8 will suppress the resonant Rabi frequency in most geome- tries

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:55.130414Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e7c8b91-203a-492c-9ca3-9cd79099ed2e · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:55.216762Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cebe0295-e9da-4cef-aa65-1432ad9ad4cd · outbound

This paper cites For example, even for a centered Gaussian beam, a ∆M= 0 cannot be driven on anE2 transition if ˆk⊥ˆ ez for any polarization (Fig.

Angular Geometry of Atomic Multipole Transitions For example, even for a centered Gaussian beam, a ∆M= 0 cannot be driven on anE2 transition if ˆk⊥ˆ ez for any polarization (Fig

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:55.334788Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8235ac4a-eb3a-4f66-baf2-5378ac6fe9de · outbound

This paper cites , whereL (α) k [x] is a generalized Laguerre polynomial and φρ ≡arctan(y ′/x′).

Angular Geometry of Atomic Multipole Transitions , whereL (α) k [x] is a generalized Laguerre polynomial and φρ ≡arctan(y ′/x′)

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:55.495682Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a75032e-24db-49db-bdfb-4db371e8bd30 · outbound

This paper cites orbit” and “spin.

Angular Geometry of Atomic Multipole Transitions orbit” and “spin

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:55.679006Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d443eb32-e7ae-4ff1-a68f-370cbfe62736 · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:55.841341Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d2729398-dc02-414e-80fb-b89c60644311 · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:55.927268Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aca2d3dc-d0f0-4446-87f7-d76dc8b15ed0 · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:56.082882Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b66e8c5-8bdd-454d-9a91-5dd0c4af996d · outbound

This paper cites Weissbluth,Atoms and Molecules(Academic Press, 1978).

Angular Geometry of Atomic Multipole Transitions Weissbluth,Atoms and Molecules(Academic Press, 1978)

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:56.201040Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 554c1df8-0882-4fb4-9381-798bd6afe106 · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:56.310483Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1d8f0410-fe66-41de-a50e-a641efa6fa3a · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:56.417356Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dfc6b099-f86e-44e3-b7ed-4fb9df46df6e · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:56.601758Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 82c330a8-0068-4155-ab5a-444c0af7c280 · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:56.763976Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 966712c0-b185-46a3-9829-f2a18d14d4b1 · outbound

This paper cites Roberts, P.

Angular Geometry of Atomic Multipole Transitions Roberts, P

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:56.900439Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 31ee7c93-5d07-4aee-95d6-2a75052e7a49 · outbound

This paper cites Huntemann, M.

Angular Geometry of Atomic Multipole Transitions Huntemann, M

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:57.091326Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2f35cb6d-4fd1-4046-892f-46c8f050bda0 · outbound

This paper cites Tofful, C.

Angular Geometry of Atomic Multipole Transitions Tofful, C

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:57.220519Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d5eae60e-c4b5-49d5-8448-85a340012db5 · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:57.400437Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca25b31b-47b4-49ae-8054-088bee6d3b2e · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:57.490130Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4aaa8076-4dd0-4b4f-811e-a53505edb082 · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:57.651565Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 205040c9-18b8-40b1-a509-4ccdd9e9a1ef · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:57.782667Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a3668b6-1e3e-4aa7-a37d-9cc51edee166 · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:57.854445Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 528c893a-56b5-4395-bcc5-e62dc3c0ccea · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:57.915185Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a3de5306-98fb-401a-8dcd-1874ff0217cf · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:58.080359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4fe4165f-0c35-4b1e-9459-0a7f704e8f68 · outbound

This paper cites Rosales-Guzm´ an, B.

Angular Geometry of Atomic Multipole Transitions Rosales-Guzm´ an, B

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:58.274011Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9715428f-ecef-48ec-aabc-77e591eb85be · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:58.459695Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 05d826d6-0abe-4085-9654-60a55a321fad · outbound

This paper cites Hasegawa, R.

Angular Geometry of Atomic Multipole Transitions Hasegawa, R

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:58.690929Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d3db7c2b-c01f-490e-89f0-43a509782c49 · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:58.902732Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b9641fb-bf50-4b03-91b1-99a942d5b6e1 · outbound

This paper cites Luis, Coherence, polarization, and entanglement for classical light fields, Optics Communications282, 3665 (2009).

Angular Geometry of Atomic Multipole Transitions Luis, Coherence, polarization, and entanglement for classical light fields, Optics Communications282, 3665 (2009)

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:58.998503Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 92977df5-8283-4a26-8f9d-73b2b4eb118d · outbound

This paper cites Chen and W.

Angular Geometry of Atomic Multipole Transitions Chen and W

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:59.126707Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 173d773e-68f3-452e-af28-875acfbb29d6 · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:59.220454Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3386879f-efb7-4b1b-8b23-74a196e464aa · outbound

This paper cites Qian and J.

Angular Geometry of Atomic Multipole Transitions Qian and J

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:59.339247Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d66fa6c5-a4f9-4448-a680-273ffdd9321a · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:59.542732Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 848a1371-88d5-4201-baa7-d71db4923229 · outbound

This paper cites Karimi and R.

Angular Geometry of Atomic Multipole Transitions Karimi and R

Reference 34

Resolution: verified exact; doi, observed 2026-08-04T11:04:43.021399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 31378ca7-ed5d-4435-a9f0-db1f5c0987a4 · outbound

This paper cites T¨ oppel, A.

Angular Geometry of Atomic Multipole Transitions T¨ oppel, A

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:59.708292Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e6d1e56-8883-456a-adea-fc238158b6e9 · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:59.788647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2513166f-98f8-4125-a46e-a104a07767df · outbound

This paper cites Hecht,Optics, 3rd ed.

Angular Geometry of Atomic Multipole Transitions Hecht,Optics, 3rd ed

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:59.884919Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bd5cfa7e-a44d-4ed5-9f50-bc3dbcaf7e90 · outbound

This paper cites Yariv,Optical Electronics in Modern Communications (Oxford University Press, 1997).

Angular Geometry of Atomic Multipole Transitions Yariv,Optical Electronics in Modern Communications (Oxford University Press, 1997)

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-04T11:02:59.976243Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 66ea82fa-0596-423c-ac67-a7b112c5bedc · outbound

This paper cites an unresolved cited work.

Angular Geometry of Atomic Multipole Transitions Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-04T11:03:00.068464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d3b8b025-2240-4c54-8744-11f93c740d84 · outbound

This paper cites iˆφ(ϑk, φk) 2p sin(ϑk) YK,p(ϑk, φk) + ˆϑ(ϑk, φk) p K(K+ 1)−p(p+ 1)Y K,p+1(ϑk, φk)e −iφk − p K(K+ 1)−p(p−1)Y K,p−1(ϑk, φk)e iφk # (A11) Y(0) K,p(ϑk, φk) =− 1 2 p K(K+ 1).

Angular Geometry of Atomic Multipole Transitions iˆφ(ϑk, φk) 2p sin(ϑk) YK,p(ϑk, φk) + ˆϑ(ϑk, φk) p K(K+ 1)−p(p+ 1)Y K,p+1(ϑk, φk)e −iφk − p K(K+ 1)−p(p−1)Y K,p−1(ϑk, φk)e iφk # (A11) Y(0) K,p(ϑk, φk) =− 1 2 p K(K+ 1)

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-04T11:03:00.169437Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.