142:, the composite particle must be modeled as a sphere of negative rather than positive electric charge for the interpretation of electron scattering experiments. In these cases, the square of the charge radius of the particle is defined to be negative, with the same absolute value with units of length squared equal to the positive squared charge radius that it would have had if it was identical in all other respects but each quark in the particle had the opposite electric charge (with the charge radius itself having a value that is an imaginary number with units of length). It is customary when charge radius takes an imaginary numbered value to report the negative valued square of the charge radius, rather than the charge radius itself, for a particle.
149:. The heuristic explanation for why the squared charge radius of a neutron is negative, despite its overall neutral electric charge, is that this is the case because its negatively charged down quarks are, on average, located in the outer part of the neutron, while its positively charged up quark is, on average, located towards the center of the neutron. This asymmetric distribution of charge within the particle gives rise to a small negative squared charge radius for the particle as a whole. But, this is only the simplest of a variety of theoretical models, some of which are more elaborate, that are used to explain this property of a neutron.
326:
988:
Antognini, A.; Nez, F.; Schuhmann, K.; Amaro, F. D.; Biraben, F.; Cardoso, J. M. R.; Covita, D. S.; Dax, A.; Dhawan, S.; Diepold, M.; Fernandes, L. M. P.; Giesen, A.; Gouvea, A. L.; Graf, T.; Hänsch, T. W.; Indelicato, P.; Julien, L.; Kao, C. -Y.; Knowles, P.; Kottmann, F.; Le Bigot, E. -O.; Liu, Y.
71:
of the nucleus imagine a fairly uniform density of nucleons, theoretically giving a more recognizable surface to a nucleus than an atom, the latter being composed of highly diffuse electron clouds with density gradually reducing away from the centre. For individual protons and neutrons or small
594:
See, e.g., J. Byrne, "The mean square charge radius of the neutron", Neutron News Vol. 5, Issue 4, pg. 15-17 (1994) (comparing different theoretical explanations for the neutron's observed negative squared charge radius to the data) DOI:10.1080/10448639408217664
180:
989:-W.; Lopes, J. A. M.; Ludhova, L.; Monteiro, C. M. B.; Mulhauser, F.; Nebel, T.; Rabinowitz, P.; Dos Santos, J. M. F.; Schaller, L. A. (2013). "Proton Structure from the Measurement of 2S-2P Transition Frequencies of Muonic Hydrogen".
394:
foil, with some of the particles being scattered through angles of more than 90°, that is coming back to the same side of the foil as the α-source. Rutherford put an upper limit on the radius of the gold nucleus of 34
503:
recommended values for the proton and deuteron root-mean-square charge radii. Furthermore, spectroscopic measurements can be made both with regular hydrogen (consisting of a proton and an electron) or
95:
Fundamentally important are realizable experimental procedures to measure some aspect of size, whatever that may mean in the quantum realm of atoms and nuclei. Foremost, the nucleus can be
321:{\displaystyle R_{\rm {d}}={\sqrt {r_{\rm {d}}^{2}+{\frac {3}{4}}\left({\frac {m_{\rm {e}}}{m_{\rm {d}}}}\right)^{2}\left({\frac {\lambda _{\rm {C}}}{2\pi }}\right)^{2}}},}
715:
92:. It could be difficult to decide whether to include the surrounding Yukawa meson field as part of the proton or nucleon size or to regard it as a separate entity.
1148:
1119:
938:
707:
511:
consisting of a proton and a negative muon). An inconsistency between proton charge radius measurements made using different techniques was known as the
766:
484:: the nonzero size of the nucleus causes a shift in the electronic energy levels which shows up as a change in the frequency of the
569:
Charge Radius and a CP Violating
Asymmetry Together with a Search for CP Violating E1 Direct Photon Emission in the Rare Decay
365:
103:
experiments: the electrons "see" a range of cross-sections, for which a mean can be taken. The qualification of "rms" (
1189:
585:(determining that the neutral kaon has a negative mean squared charge radius of -0.077 ± 0.007(stat) ± 0.011(syst)fm).
1179:
174:
in an electromagnetic field and which is appropriate for treating spectroscopic data. The two radii are related by
946:
171:
51:
by the nucleus. Relative changes in the mean squared nuclear charge distribution can be precisely measured with
1184:
383:
493:
108:
489:
72:
nuclei, the concepts of size and boundary can be less clear. A single nucleon needs to be regarded as a "
608:
1063:
998:
955:
911:
868:
775:
724:
665:
620:
512:
89:
465:
100:
52:
63:
The problem of defining a radius for the atomic nucleus has some similarity to that of defining a
1087:
1032:
884:
858:
681:
655:
442:
353:
85:
596:
138:. In the case of an anti-matter baryon (e.g. an anti-proton), and some particles with zero net
1079:
1024:
803:
379:
73:
68:
646:
Friar, J. L.; Martorell, J.; Sprung, D. W. L. (1997), "Nuclear sizes and the isotope shift",
1071:
1014:
1006:
971:
963:
919:
876:
815:
783:
740:
732:
673:
628:
104:
96:
23:
156:
and higher nuclei, it is conventional to distinguish between the scattering charge radius,
504:
139:
111:, proportional to the square of the radius, which is determining for electron scattering.
84:, and a so-called "sea" of quark-antiquark pairs. Also, the nucleon is surrounded by its
1067:
1002:
959:
915:
872:
779:
728:
669:
624:
1174:
806:(1911), "The Scattering of α and β Particles by Matter and the Structure of the Atom",
761:
375:
29:
923:
1168:
1091:
1051:
888:
485:
387:
77:
64:
685:
880:
461:
1036:
1140:
1111:
757:
508:
403:
371:
1075:
819:
632:
396:
37:
677:
460:
Modern direct measurements are based on precision measurements of the atomic
1010:
967:
481:
402:
Later studies found an empirical relation between the charge radius and the
1083:
1028:
788:
170:, which includes the Darwin–Foldy term to account for the behaviour of the
902:
Sick, Ingo; Trautmann, Dirk (1998), "On the rms radius of the deuteron",
477:
473:
153:
48:
1052:"How big is the proton? Particle-size puzzle leaps closer to resolution"
863:
660:
581:", Phys. Rev. Lett. 96:101801 (2006) DOI: 10.1103/PhysRevLett.96.101801
1019:
939:"CODATA recommended values of the fundamental physical constants: 2002"
708:"CODATA recommended values of the fundamental physical constants: 1998"
582:
146:
123:
499:
Both scattering data and spectroscopic data are used to determine the
736:
500:
469:
145:
The best known particle with a negative squared charge radius is the
119:
115:
33:
163:(obtained from scattering data), and the bound-state charge radius,
345:
are the masses of the electron and the deuteron respectively while
135:
81:
43:
445:
of the proton. This gives a charge radius for the gold nucleus (
391:
131:
127:
114:
This definition of charge radius is often applied to composite
597:
https://www.tandfonline.com/doi/abs/10.1080/10448639408217664
356:
of the electron. For the proton, the two radii are the same.
370:
The first estimate of a nuclear charge radius was made by
99:
as a sphere of positive charge for the interpretation of
515:, but more recent measurements show consistent results.
468:. There is most interest in knowing the charge radii of
1145:
The NIST Reference on
Constants, Units, and Uncertainty
1116:
The NIST Reference on
Constants, Units, and Uncertainty
476:, as these can be compared with the spectrum of atomic
386:, UK. The famous experiment involved the scattering of
849:
Sick, Ingo (2003), "On the rms-radius of the proton",
764:(1909), "On a Diffuse Reflection of the α-Particles",
67:; neither has well defined boundaries. However, basic
183:
565:See, e.g., Abouzaid, et al., "A Measurement of the
320:
1141:"2022 CODATA Value: deuteron rms charge radius"
716:Journal of Physical and Chemical Reference Data
464:in hydrogen and deuterium, and measurements of
1112:"2022 CODATA Value: proton rms charge radius"
833:Blatt, John M.; Weisskopf, Victor F. (1952),
441:of 1.2–1.5 fm can be interpreted as the
36:distribution. The proton radius is about one
8:
701:
699:
697:
695:
47:. It can be measured by the scattering of
1018:
937:Mohr, Peter J.; Taylor, Barry N. (2005).
862:
787:
706:Mohr, Peter J.; Taylor, Barry N. (1999).
659:
307:
286:
285:
279:
268:
255:
254:
243:
242:
236:
221:
212:
206:
205:
199:
189:
188:
182:
611:(1958), "Neutron–Electron Interaction",
558:
7:
583:https://arxiv.org/abs/hep-ex/0508010
382:at the Physical Laboratories of the
134:, that are made up of more than one
16:Measure of the size of atomic nuclei
518:The CODATA recommended values are:
107:) arises because it is the nuclear
767:Proceedings of the Royal Society A
287:
256:
244:
207:
190:
14:
837:, New York: Wiley, pp. 14–16
466:scattering of electrons by nuclei
378:in 1909, under the direction of
28:is a measure of the size of an
881:10.1016/j.physletb.2003.09.092
1:
924:10.1016/S0375-9474(98)00334-0
434:where the empirical constant
1050:Castelvecchi (2019-11-07).
835:Theoretical Nuclear Physics
1206:
1076:10.1038/d41586-019-03432-4
363:
65:radius for the entire atom
947:Reviews of Modern Physics
820:10.1080/14786440508637080
633:10.1103/RevModPhys.30.471
488:. Such comparisons are a
452:) of about 7.69 fm.
366:Geiger–Marsden experiment
172:anomalous magnetic moment
678:10.1103/PhysRevA.56.4579
384:University of Manchester
1011:10.1126/science.1230016
968:10.1103/RevModPhys.77.1
494:quantum electrodynamics
789:10.1098/rspa.1909.0054
410:, for heavier nuclei (
322:
323:
513:proton radius puzzle
181:
90:strong nuclear force
88:responsible for the
1068:2019Natur.575..269C
1003:2013Sci...339..417A
960:2005RvMP...77....1M
916:1998NuPhA.637..559S
873:2003PhLB..576...62S
780:1909RSPSA..82..495G
729:1999JPCRD..28.1713M
670:1997PhRvA..56.4579F
625:1958RvMP...30..471F
456:Modern measurements
217:
101:electron scattering
53:atomic spectroscopy
32:, particularly the
1190:Physical constants
443:Compton wavelength
354:Compton wavelength
318:
201:
69:liquid drop models
1180:Nuclear chemistry
1062:(7782): 269–270.
997:(6118): 417–420.
380:Ernest Rutherford
313:
301:
262:
229:
86:Yukawa pion field
1197:
1160:
1159:
1157:
1156:
1137:
1131:
1130:
1128:
1127:
1108:
1102:
1101:
1099:
1098:
1047:
1041:
1040:
1022:
985:
979:
978:
976:
970:. Archived from
943:
934:
928:
926:
899:
893:
891:
866:
846:
840:
838:
830:
824:
822:
800:
794:
792:
791:
774:(557): 495–500,
754:
748:
747:
745:
739:. Archived from
737:10.1063/1.556049
723:(6): 1713–1852.
712:
703:
690:
688:
663:
643:
637:
635:
605:
599:
592:
586:
580:
563:
549:
546:
544:
540:
532:
529:
527:
451:
414: > 20):
327:
325:
324:
319:
314:
312:
311:
306:
302:
300:
292:
291:
290:
280:
273:
272:
267:
263:
261:
260:
259:
249:
248:
247:
237:
230:
222:
216:
211:
210:
200:
195:
194:
193:
105:root mean square
46:
1205:
1204:
1200:
1199:
1198:
1196:
1195:
1194:
1185:Nuclear physics
1165:
1164:
1163:
1154:
1152:
1139:
1138:
1134:
1125:
1123:
1110:
1109:
1105:
1096:
1094:
1049:
1048:
1044:
987:
986:
982:
974:
941:
936:
935:
931:
901:
900:
896:
864:nucl-ex/0310008
848:
847:
843:
832:
831:
827:
814:(125): 669–88,
802:
801:
797:
756:
755:
751:
743:
710:
705:
704:
693:
661:nucl-th/9707016
645:
644:
640:
613:Rev. Mod. Phys.
607:
606:
602:
593:
589:
578:
570:
564:
560:
556:
547:
542:
538:
536:
530:
525:
523:
505:muonic hydrogen
458:
446:
440:
427:
368:
362:
351:
344:
337:
293:
281:
275:
274:
250:
238:
232:
231:
184:
179:
178:
169:
162:
140:electric charge
76:" bag of three
61:
41:
17:
12:
11:
5:
1203:
1201:
1193:
1192:
1187:
1182:
1177:
1167:
1166:
1162:
1161:
1132:
1103:
1042:
980:
977:on 2017-10-01.
929:
894:
857:(1–2): 62–67,
841:
825:
810:, 6th Series,
804:Rutherford, E.
795:
749:
746:on 2017-10-01.
691:
654:(6): 4579–86,
638:
600:
587:
574:
557:
555:
552:
551:
550:
533:
486:spectral lines
457:
454:
438:
432:
431:
425:
376:Ernest Marsden
364:Main article:
361:
358:
349:
342:
335:
329:
328:
317:
310:
305:
299:
296:
289:
284:
278:
271:
266:
258:
253:
246:
241:
235:
228:
225:
220:
215:
209:
204:
198:
192:
187:
167:
160:
78:valence quarks
74:color confined
60:
57:
30:atomic nucleus
15:
13:
10:
9:
6:
4:
3:
2:
1202:
1191:
1188:
1186:
1183:
1181:
1178:
1176:
1173:
1172:
1170:
1150:
1146:
1142:
1136:
1133:
1121:
1117:
1113:
1107:
1104:
1093:
1089:
1085:
1081:
1077:
1073:
1069:
1065:
1061:
1057:
1053:
1046:
1043:
1038:
1034:
1030:
1026:
1021:
1016:
1012:
1008:
1004:
1000:
996:
992:
984:
981:
973:
969:
965:
961:
957:
953:
949:
948:
940:
933:
930:
925:
921:
917:
913:
910:(4): 559–75,
909:
905:
904:Nucl. Phys. A
898:
895:
890:
886:
882:
878:
874:
870:
865:
860:
856:
852:
851:Phys. Lett. B
845:
842:
836:
829:
826:
821:
817:
813:
809:
805:
799:
796:
790:
785:
781:
777:
773:
769:
768:
763:
759:
753:
750:
742:
738:
734:
730:
726:
722:
718:
717:
709:
702:
700:
698:
696:
692:
687:
683:
679:
675:
671:
667:
662:
657:
653:
649:
642:
639:
634:
630:
626:
622:
619:(2): 471–81,
618:
614:
610:
604:
601:
598:
591:
588:
584:
577:
573:
568:
562:
559:
553:
534:
521:
520:
519:
516:
514:
510:
506:
502:
497:
495:
491:
487:
483:
479:
475:
471:
467:
463:
462:energy levels
455:
453:
449:
444:
437:
430:
424:
420:
417:
416:
415:
413:
409:
405:
400:
398:
393:
389:
385:
381:
377:
373:
367:
359:
357:
355:
348:
341:
334:
315:
308:
303:
297:
294:
282:
276:
269:
264:
251:
239:
233:
226:
223:
218:
213:
202:
196:
185:
177:
176:
175:
173:
166:
159:
155:
150:
148:
143:
141:
137:
133:
129:
125:
121:
117:
112:
110:
109:cross-section
106:
102:
98:
93:
91:
87:
83:
79:
75:
70:
66:
58:
56:
54:
50:
45:
39:
35:
31:
27:
26:charge radius
25:
19:
1153:. Retrieved
1144:
1135:
1124:. Retrieved
1115:
1106:
1095:. Retrieved
1059:
1055:
1045:
994:
990:
983:
972:the original
954:(1): 1–107.
951:
945:
932:
907:
903:
897:
854:
850:
844:
834:
828:
811:
807:
798:
771:
765:
752:
741:the original
720:
714:
651:
648:Phys. Rev. A
647:
641:
616:
612:
609:Foldy, L. L.
603:
590:
575:
571:
566:
561:
517:
498:
459:
447:
435:
433:
428:
422:
418:
411:
407:
401:
369:
346:
339:
332:
330:
164:
157:
151:
144:
113:
94:
62:
22:
20:
18:
1020:10316/79993
762:Marsden, E.
509:exotic atom
404:mass number
397:femtometres
388:α-particles
372:Hans Geiger
1169:Categories
1155:2024-05-18
1151:. May 2024
1126:2024-05-18
1122:. May 2024
1097:2021-11-04
808:Phil. Mag.
758:Geiger, H.
554:References
535:deuteron:
524:8.4075(64)
118:such as a
80:, binding
59:Definition
38:femtometre
1092:207938065
889:119339313
545:10 m
528:10 m
482:deuterium
474:deuterons
298:π
283:λ
154:deuterons
49:electrons
1084:31719693
1029:23349284
686:16441189
522:proton:
478:hydrogen
42:10
1064:Bibcode
999:Bibcode
991:Science
956:Bibcode
912:Bibcode
869:Bibcode
776:Bibcode
725:Bibcode
666:Bibcode
621:Bibcode
548:
531:
496:(QED).
470:protons
360:History
352:is the
147:neutron
124:neutron
116:hadrons
97:modeled
1090:
1082:
1056:Nature
1037:346658
1035:
1027:
887:
684:
579:→ ππee
501:CODATA
331:where
120:proton
82:gluons
34:proton
1175:Radii
1088:S2CID
1033:S2CID
975:(PDF)
942:(PDF)
885:S2CID
859:arXiv
744:(PDF)
711:(PDF)
682:S2CID
656:arXiv
537:2.127
450:= 197
136:quark
130:, or
44:metre
1149:NIST
1120:NIST
1080:PMID
1025:PMID
541:(27)
507:(an
490:test
480:and
472:and
392:gold
374:and
338:and
152:For
132:kaon
128:pion
21:The
1072:doi
1060:575
1015:hdl
1007:doi
995:339
964:doi
920:doi
908:637
877:doi
855:576
816:doi
784:doi
733:doi
674:doi
629:doi
492:of
390:by
24:rms
1171::
1147:.
1143:.
1118:.
1114:.
1086:.
1078:.
1070:.
1058:.
1054:.
1031:.
1023:.
1013:.
1005:.
993:.
962:.
952:77
950:.
944:.
918:,
906:,
883:,
875:,
867:,
853:,
812:21
782:,
772:82
770:,
760:;
731:.
721:28
719:.
713:.
694:^
680:,
672:,
664:,
652:56
650:,
627:,
617:30
615:,
539:78
421:≈
406:,
399:.
126:,
122:,
55:.
40:=
1158:.
1129:.
1100:.
1074::
1066::
1039:.
1017::
1009::
1001::
966::
958::
927:.
922::
914::
892:.
879::
871::
861::
839:.
823:.
818::
793:.
786::
778::
735::
727::
689:.
676::
668::
658::
636:.
631::
623::
576:L
572:K
567:K
543:×
526:×
448:A
439:0
436:r
429:A
426:0
423:r
419:R
412:A
408:A
350:C
347:λ
343:d
340:m
336:e
333:m
316:,
309:2
304:)
295:2
288:C
277:(
270:2
265:)
257:d
252:m
245:e
240:m
234:(
227:4
224:3
219:+
214:2
208:d
203:r
197:=
191:d
186:R
168:d
165:R
161:d
158:r
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