3275:
1400:
2988:
3270:{\displaystyle \omega =2\pi \,f={\frac {1}{\,J\,\sin {\phi }\,}}\,\left|{\frac {\,{\rm {{d}\,\mathbf {J} \,}}}{\,{\rm {{d}\,t\,}}}}\right|={\frac {\,\left|\mathbf {T} \right|\,}{\,J\,\sin {\phi }\,}}={\frac {\,\left|\mathbf {m} \times \mathbf {B} \right|\,}{\,J\,\sin {\phi }\,}}={\frac {\,m\,B\sin {\phi }\,}{\,J\,\sin {\phi }\,}}={\frac {\,m\,B\,}{J}}=\gamma \,B~.}
106:
body rotating about an axis of symmetry. According to the laws of classical physics, it has both a magnetic dipole moment due to the movement of charge and an angular momentum due to the movement of mass arising from its rotation. It can be shown that as long as its charge and mass density and flow
2749:
of a gyroscope. The earth's gravitational attraction applies a force or torque to the gyroscope in the vertical direction, and the angular momentum vector along the axis of the gyroscope rotates slowly about a vertical line through the pivot. In the place of the gyroscope imagine a sphere spinning
511:
1539:
373:. While an electron's spin is sometimes visualized as a literal rotation about an axis, it cannot be attributed to mass distributed identically to the charge. The above classical relation does not hold, giving the wrong result by the absolute value of the electron's
844:
943:
359:
2524:
392:
2604:
613:
1426:, which gives rise to a gyromagnetic ratio as above. The ratio is conventionally written in terms of the proton mass and charge, even for neutrons and for other nuclei, for the sake of simplicity and consistency. The formula is:
2874:
2335:
3334:
1670:
729:
722:
1432:
2740:
848:
1275:
2750:
around the axis and with its center on the pivot of the gyroscope, and along the axis of the gyroscope two oppositely directed vectors both originated in the center of the sphere, upwards
2202:
198:
The derivation of this relation is as follows. It suffices to demonstrate this for an infinitesimally narrow circular ring within the body, as the general result then follows from an
146:
2635:
1707:
1814:
1571:
2934:
2461:
3827:
2980:
2898:
2824:
2662:
2412:
535:
2795:
2770:
2684:
2434:
2374:
2290:
2268:
1768:
1604:
3401:, the resonance frequency of an ionized plasma being under the influence of a static finite magnetic field, when we superimpose a high frequency electromagnetic field.
2956:
2640:
The model of the spinning electron we use in the derivation has an evident analogy with a gyroscope. For any rotating body the rate of change of the angular momentum
633:
240:
2466:
2337:
The identity of the functional form of the stationary electric and magnetic fields has led to defining the magnitude of the magnetic dipole moment equally well as
193:
171:
2529:
2830:
3458:
2295:
3453:
661:
506:{\displaystyle \gamma _{\mathrm {e} }={\frac {-e}{2m_{\mathrm {e} }}}\,|g_{\mathrm {e} }|={\frac {g_{\mathrm {e} }\mu _{\mathrm {B} }}{\hbar }}\,,}
3651:
3283:
1735:
Most common nuclei such as H and C have positive gyromagnetic ratios. Approximate values for some common nuclei are given in the table below.
1616:
1534:{\displaystyle \gamma _{\text{n}}={\frac {e}{\,2m_{\text{p}}\,}}\,g_{\rm {n}}=g_{\rm {n}}\,{\frac {\,\mu _{\mathrm {N} }\,}{\hbar }}~,}
1363:
100:
2692:
2248:
The derivation of this relation is as follows: First we must prove that the torque resulting from subjecting a magnetic moment
4047:
3585:
puts a positive sign on the quantity; however, to be consistent with the formulas in this article, a negative sign is put on
1728:, which is simply the product of the gyromagnetic ratio with the magnetic field strength. With this phenomenon, the sign of
1407:, determines the sense of precession. While the magnetic moments (the black arrows) are oriented the same for both cases of
3691:
4152:
1068:
839:{\displaystyle \gamma _{\mathrm {e} }=\mathrm {-1.760\,859\,630\,23(53)\times 10^{11}\,rad{\cdot }s^{-1}{\cdot }T^{-1}} }
2382:
of an electric dipole: The magnetic dipole can be represented by a needle of a compass with fictitious magnetic charges
3889:
3860:
3951:
3922:
3705:
3663:
3467:
969:
Since a gyromagnetic factor equal to 2 follows from Dirac's equation, it is a frequent misconception to think that a
647:
2163:
1318:
976:
2 is a consequence of relativity; it is not. The factor 2 can be obtained from the linearization of both the
938:{\displaystyle {\frac {\gamma _{\mathrm {e} }}{2\pi }}=\mathrm {-28\,024.951\,4242(85)\,MHz{\cdot }T^{-1}} .}
113:
3658:. Poincaré Seminar. Progress in Mathematical Physics. Vol. 30. Paris, FR: BirkhÀuser (published 2003).
2609:
1675:
3791:
1775:
1547:
2903:
3669:
2439:
1717:
1713:
3795:
2961:
2879:
2800:
2643:
3434:
2385:
1023:
981:
3471:
999:
of the minimal coupling and of the fact of having the same order of derivatives for space and time.
2775:
1411:, the precession is in opposite directions. Spin and magnetic moment are in the same direction for
655:
2753:
2667:
2417:
2340:
2273:
2251:
4147:
3881:
1746:
1580:
636:
977:
3914:
2939:
1308:
957:
354:{\displaystyle \mu =IA={\frac {qv}{2\pi r}}\,\pi r^{2}={\frac {q}{2m}}\,mvr={\frac {q}{2m}}L~.}
2519:{\displaystyle \,{\boldsymbol {\mathrm {T} }}=q_{\rm {m}}(\mathbf {d} \times \mathbf {B} )\,.}
529:
The gyromagnetic ratio due to electron spin is twice that due to the orbiting of an electron.
3731:
factors of the spin 1/2 particles in the (1/2-1/2-1/2) triad of the four-vector spinor,
618:
3906:
3338:
This relationship also explains an apparent contradiction between the two equivalent terms,
4048:"Tritium Solid State NMR Spectroscopy at PNNL for Evaluation of Hydrogen Storage Materials"
3757:
3530:
3410:
3508:
8:
3396:
2599:{\displaystyle \,q_{\rm {m}}\mathbf {d} =I\pi r^{2}{\hat {\mathbf {d} }}=\mathbf {m} \,,}
2121:
Any free system with a constant gyromagnetic ratio, such as a rigid system of charges, a
176:
154:
4086:
4025:
3761:
3534:
608:{\displaystyle g_{\mathrm {e} }=-2\left(1+{\frac {\alpha }{\,2\pi \,}}+\cdots \right)~,}
3773:
3747:
3554:
3520:
1607:
989:
970:
374:
77:
3985:
3632:
1720:(MRI). These procedures rely on the fact that bulk magnetization due to nuclear spins
369:
An isolated electron has an angular momentum and a magnetic moment resulting from its
4064:
4003:
3947:
3918:
3907:
3885:
3856:
3777:
3701:
3659:
3558:
3546:
3463:
3371:
2869:{\displaystyle {\frac {\,\operatorname {d} \mathbf {J} \,}{\,\operatorname {d} t\,}}}
2116:
4126:
4109:
3967:
3420:
4121:
4110:"Explorations of Magnetic Properties of Noble Gases: The Past, Present, and Future"
3765:
3614:
3572:
3542:
3538:
3363:
1725:
1574:
107:
are distributed identically and rotationally symmetric, its gyromagnetic ratio is
40:
4157:
3697:
3429:
3347:
2330:{\displaystyle \,{\boldsymbol {\mathrm {T} }}=\mathbf {m} \times \mathbf {B} \,.}
2139:
103:
36:
3415:
3389:
3355:
2130:
2122:
1019:
370:
3769:
3724:
Delgado Acosta, E.G.; Banda GuzmĂĄn, V.M.; Kirchbach, M. (2015). "Gyromagnetic
3395:
The angular precession frequency has an important physical meaning: It is the
4141:
523:
88:
2982:
and the vertical. Hence the angular velocity of the rotation of the spin is
3550:
2233:
1423:
58:
3625:
3507:
Fan, X.; Myers, T. G.; Sukra, B. A. D.; Gabrielse, G. (13 February 2023).
964:
3329:{\displaystyle f={\frac {\gamma }{\,2\pi \,}}\,B~.\quad {\text{q.e.d.}}}
3674:
2746:
2143:
2040:
3607:
3943:
2147:
1983:
1948:
1882:
996:
1732:
determines the sense (clockwise vs counterclockwise) of precession.
3904:
3752:
3723:
3525:
2126:
1399:
1307:
stand for the
Lorentz group generators in the Dirac space, and the
199:
66:
1665:{\displaystyle \,{\frac {\gamma _{n}}{\,2\pi \,g_{\rm {n}}\,}}\,,}
1895:
1721:
62:
20:
3565:
3838:
1821:
1419:
985:
717:{\displaystyle g_{\mathrm {e} }=-2.002\,319\,304\,361\,18(27).}
72:
The term "gyromagnetic ratio" is often used as a synonym for a
54:
3652:"The anomalous magnetic moments of the electron and the muon"
2229:
2154:
44:
32:
3989:
3971:
3832:
3636:
3618:
3582:
3576:
654:-factor is known to twelve decimal places by measuring the
87:-factor only differs from the gyromagnetic ratio in being
3604:
Also note that the units of radians are added for clarity.
3346:
ratio: whereas it is a ratio of a magnetic property (i.e.
2735:{\displaystyle {\frac {d\mathbf {J} }{dt}}=\mathbf {T} ~.}
1391:
and consequently to behave as a truly quadratic fermion.
1018:
particles which cannot be described by the linear gauged
2876:
represents the linear velocity of the pike of the arrow
995:
is found to be equal to 2; Therefore, the factor 2 is a
639:. Here the small corrections to the relativistic result
2414:
on the two poles and vector distance between the poles
646:
come from the quantum field theory calculations of the
50:
3937:
3654:. In Duplantier, Bertrand; Rivasseau, Vincent (eds.).
3506:
1366:. This particle has been shown to be characterized by
965:
Gyromagnetic factor not as a consequence of relativity
234:. Then the magnitude of the magnetic dipole moment is
3798:
3286:
2991:
2964:
2942:
2906:
2882:
2833:
2803:
2778:
2756:
2695:
2670:
2646:
2612:
2532:
2469:
2442:
2420:
2388:
2343:
2298:
2276:
2254:
2166:
1778:
1749:
1678:
1619:
1583:
1550:
1435:
1071:
851:
732:
664:
621:
538:
395:
243:
179:
157:
116:
31:
in other disciplines) of a particle or system is the
3869:
2463:
By classical mechanics the torque on this needle is
1712:
The gyromagnetic ratio of a nucleus plays a role in
532:
In the framework of relativistic quantum mechanics,
3459:
Quantities, Units and
Symbols in Physical Chemistry
2436:under the influence of the magnetic field of earth
1270:{\displaystyle \left\;\psi \;=\;0~,\quad g\neq 2~.}
3913:. San Diego, CA: Elsevier Academic Press. p.
3821:
3719:
3717:
3328:
3269:
2974:
2950:
2928:
2892:
2868:
2818:
2797:Replace the gravity with a magnetic flux density
2789:
2764:
2734:
2678:
2656:
2629:
2598:
2518:
2455:
2428:
2406:
2368:
2329:
2284:
2262:
2196:
2138:(measured in teslas) that is not aligned with its
1808:
1762:
1701:
1664:
1598:
1565:
1533:
1269:
937:
838:
716:
627:
607:
505:
353:
187:
165:
140:
3875:
3454:International Union of Pure and Applied Chemistry
1613:of the nucleon or nucleus in question. The ratio
4139:
3905:Bernstein, M.A.; King, K.F.; Zhou, X.J. (2004).
2376:, or in the following way, imitating the moment
94:
3844:
3714:
2157:), that is proportional to the external field:
1321:. An example for such a particle, is the spin
4087:"shielded helion gyromagnetic ratio in MHz/T"
4026:"shielded proton gyromagnetic ratio in MHz/T"
3509:"Measurement of the Electron Magnetic Moment"
3850:
2197:{\displaystyle f={\frac {\gamma }{2\pi }}B.}
988:is obtained and for both linearizations the
984:(which leads to Dirac's). In both cases a 4-
955:are in excellent agreement with theory; see
61:(rad⋅s⋅T) or, equivalently, the
16:Ratio of magnetic moment to angular momentum
3491:
364:
3597:
3462:, 2nd edition, Oxford: Blackwell Science.
1241:
1237:
1233:
4125:
3751:
3740:International Journal of Modern Physics E
3524:
3310:
3306:
3299:
3257:
3244:
3240:
3236:
3226:
3214:
3210:
3207:
3192:
3188:
3178:
3166:
3162:
3159:
3135:
3125:
3113:
3109:
3106:
3092:
3076:
3072:
3064:
3059:
3053:
3045:
3037:
3033:
3021:
3017:
3004:
2971:
2965:
2947:
2943:
2922:
2907:
2889:
2883:
2862:
2852:
2849:
2837:
2804:
2653:
2647:
2592:
2533:
2512:
2470:
2449:
2443:
2323:
2299:
1724:in a magnetic field at a rate called the
1658:
1654:
1641:
1634:
1620:
1518:
1505:
1501:
1473:
1469:
1455:
1364:representation space of the Lorentz group
1227:
1200:
1186:
1182:
1178:
1171:
1149:
1145:
1123:
1107:
1103:
1093:
1077:
903:
890:
886:
789:
763:
759:
755:
698:
694:
690:
686:
584:
577:
499:
440:
314:
282:
4107:
1398:
43:, and it is often denoted by the symbol
3938:Weast, R.C.; Astle, M.J., eds. (1982).
3689:
3589:here. Indeed, many references say that
2243:
141:{\displaystyle \gamma ={\frac {q}{2m}}}
4140:
3649:
3633:"electron gyromagnetic ratio in MHz/T"
3986:"proton gyromagnetic ratio over 2 pi"
3643:
2630:{\displaystyle {\hat {\mathbf {d} }}}
1702:{\displaystyle \mu _{\mathrm {N} }/h}
4065:"shielded helion gyromagnetic ratio"
4004:"shielded proton gyromagnetic ratio"
3486:Physics for Scientists and Engineers
3483:
2236:(Hz/T), are often quoted instead of
2110:
1403:The sign of the gyromagnetic ratio,
1809:{\displaystyle \gamma _{n}/(2\pi )}
1566:{\displaystyle \mu _{\mathrm {N} }}
726:The electron gyromagnetic ratio is
13:
3805:
3693:Quantum Mechanics: An introduction
3690:Greiner, Walter (4 October 2000).
3073:
3068:
3049:
2929:{\displaystyle \,J\sin {\phi }\,,}
2853:
2838:
2540:
2487:
2398:
1685:
1648:
1590:
1557:
1512:
1495:
1480:
1422:, neutrons, and many nuclei carry
1130:
1084:
919:
910:
907:
904:
860:
823:
805:
796:
793:
790:
739:
671:
545:
487:
475:
452:
431:
402:
76:but closely related quantity, the
14:
4169:
3940:Handbook of Chemistry and Physics
3738:, irreducibility and linearity".
2606:so the desired formula comes up.
2456:{\displaystyle \,\mathbf {B} \,.}
1709:, is 7.622593285(47) MHz/T.
1520:
494:
3822:{\displaystyle \mu _{\rm {N}}/h}
3650:Knecht, Marc (12 October 2002).
3150:
3142:
3098:
3055:
2975:{\displaystyle \,\mathbf {J} \,}
2967:
2893:{\displaystyle \,\mathbf {J} \,}
2885:
2845:
2819:{\displaystyle \,\mathbf {B} ~.}
2806:
2780:
2758:
2722:
2703:
2672:
2657:{\displaystyle \,\mathbf {J} \,}
2649:
2617:
2588:
2574:
2547:
2505:
2497:
2473:
2445:
2422:
2319:
2311:
2302:
2278:
2256:
1394:
648:anomalous magnetic dipole moment
4127:10.3390/magnetochemistry6040065
4101:
4079:
4057:
4040:
4018:
3996:
3978:
3960:
3931:
3909:Handbook of MRI Pulse Sequences
3898:
3784:
3600:Electron Paramagnetic Resonance
3320:
2900:along a circle whose radius is
2407:{\displaystyle \pm q_{\rm {m}}}
1251:
4108:Makulski, Wlodzimierz (2020).
3683:
3596:for an electron; for example,
3543:10.1103/PhysRevLett.130.071801
3500:
3492:Tipler, P.A.; Llewellyn, R.A.
3476:
3447:
2621:
2578:
2509:
2493:
1803:
1794:
1319:electromagnetic four-potential
900:
894:
773:
767:
708:
702:
459:
442:
202:. Suppose the ring has radius
1:
3855:. John Wiley & Sons Ltd.
3615:"electron gyromagnetic ratio"
3573:"electron gyromagnetic ratio"
3488:(3rd ed.). p. 1017;
3440:
2790:{\displaystyle \mathbf {m} .}
2637:is the unit distance vector.
2129:, when placed in an external
658:in a one-electron cyclotron:
95:For a classical rotating body
27:(also sometimes known as the
3792:"Nuclear magneton in MHz/T:
3496:(4th ed.). p. 309.
3372:angular precession frequency
2765:{\displaystyle \mathbf {J} }
2679:{\displaystyle \mathbf {T} }
2429:{\displaystyle \mathbf {d} }
2369:{\displaystyle m=I\pi r^{2}}
2285:{\displaystyle \mathbf {B} }
2263:{\displaystyle \mathbf {m} }
7:
3968:"proton gyromagnetic ratio"
3404:
3398:angular cyclotron frequency
2207:For this reason, values of
1763:{\displaystyle \gamma _{n}}
1599:{\displaystyle g_{\rm {n}}}
10:
4174:
4153:Nuclear magnetic resonance
3876:Palmer, Arthur G. (2007).
3598:Weil & Bolton (2007).
2664:equals the applied torque
2114:
1718:magnetic resonance imaging
1714:nuclear magnetic resonance
3770:10.1142/S0218301315500603
3710:– via Google Books.
3435:Proton gyromagnetic ratio
3362:, "turn") property (i.e.
3359:
2951:{\displaystyle \,\phi \,}
2526:But as previously stated
3927:– via archive.org.
3878:Protein NMR Spectroscopy
1415:> 0 (as for protons).
656:electron magnetic moment
365:For an isolated electron
3882:Elsevier Academic Press
3513:Physical Review Letters
2745:Note as an example the
637:fine-structure constant
628:{\displaystyle \alpha }
224:, and angular momentum
3823:
3370:, a ratio between the
3330:
3271:
2976:
2952:
2930:
2894:
2870:
2820:
2791:
2766:
2736:
2680:
2658:
2631:
2600:
2520:
2457:
2430:
2408:
2370:
2331:
2286:
2264:
2198:
1810:
1764:
1703:
1666:
1600:
1567:
1535:
1416:
1309:electromagnetic tensor
1271:
958:Precision tests of QED
939:
840:
718:
629:
609:
507:
355:
189:
167:
142:
3851:Levitt, M.H. (2008).
3824:
3656:Poincaré Seminar 2002
3602:. Wiley. p. 578.
3331:
3272:
2977:
2958:is the angle between
2953:
2931:
2895:
2871:
2821:
2792:
2767:
2737:
2681:
2659:
2632:
2601:
2521:
2458:
2431:
2409:
2371:
2332:
2287:
2265:
2199:
1811:
1765:
1704:
1667:
1601:
1568:
1536:
1402:
1272:
1024:KleinâGordon equation
982:KleinâGordon equation
980:and the relativistic
940:
841:
719:
630:
610:
508:
356:
190:
168:
143:
3841:-recommended values)
3796:
3411:Charge-to-mass ratio
3284:
2989:
2962:
2940:
2904:
2880:
2831:
2801:
2776:
2754:
2693:
2668:
2644:
2610:
2530:
2467:
2440:
2418:
2386:
2341:
2296:
2274:
2270:to a magnetic field
2252:
2244:Heuristic derivation
2164:
1776:
1747:
1676:
1617:
1581:
1548:
1433:
1311:respectively, while
1069:
978:Schrödinger equation
849:
730:
662:
619:
536:
393:
241:
177:
155:
114:
3762:2015IJMPE..2450060D
3679:on 15 October 2005.
3535:2023PhRvL.130g1801F
3472:Electronic version.
1062:term according to,
1022:satisfy the gauged
380:, which is denoted
188:{\displaystyle {m}}
166:{\displaystyle {q}}
3942:. Boca Raton, FL:
3819:
3482:For example, see:
3354:(rotational, from
3326:
3267:
2972:
2948:
2926:
2890:
2866:
2816:
2787:
2762:
2732:
2676:
2654:
2627:
2596:
2516:
2453:
2426:
2404:
2366:
2327:
2282:
2260:
2194:
1806:
1760:
1699:
1662:
1596:
1563:
1531:
1417:
1337:companion to spin
1267:
935:
836:
714:
625:
605:
503:
351:
185:
173:is its charge and
163:
138:
29:magnetogyric ratio
25:gyromagnetic ratio
3324:
3316:
3308:
3263:
3249:
3228:
3180:
3127:
3080:
3035:
2864:
2812:
2728:
2716:
2624:
2581:
2186:
2117:Larmor precession
2111:Larmor precession
2108:
2107:
1656:
1527:
1523:
1471:
1466:
1443:
1263:
1247:
1184:
874:
601:
586:
497:
438:
347:
340:
312:
280:
136:
4165:
4132:
4131:
4129:
4114:Magnetochemistry
4105:
4099:
4098:
4096:
4094:
4083:
4077:
4076:
4074:
4072:
4061:
4055:
4054:
4053:. November 2015.
4052:
4044:
4038:
4037:
4035:
4033:
4022:
4016:
4015:
4013:
4011:
4000:
3994:
3993:
3982:
3976:
3975:
3964:
3958:
3957:
3935:
3929:
3928:
3912:
3902:
3896:
3895:
3873:
3867:
3866:
3848:
3842:
3836:
3828:
3826:
3825:
3820:
3815:
3810:
3809:
3808:
3788:
3782:
3781:
3755:
3737:
3727:
3721:
3712:
3711:
3687:
3681:
3680:
3678:
3668:. Archived from
3647:
3641:
3640:
3629:
3623:
3622:
3611:
3605:
3603:
3595:
3593:
3588:
3580:
3569:
3563:
3562:
3528:
3504:
3498:
3497:
3489:
3480:
3474:
3451:
3424:
3387:
3368:at the same time
3364:angular momentum
3361:
3335:
3333:
3332:
3327:
3325:
3322:
3314:
3309:
3307:
3294:
3276:
3274:
3273:
3268:
3261:
3250:
3245:
3234:
3229:
3227:
3225:
3208:
3206:
3186:
3181:
3179:
3177:
3160:
3158:
3154:
3153:
3145:
3133:
3128:
3126:
3124:
3107:
3105:
3101:
3090:
3085:
3081:
3079:
3078:
3077:
3071:
3062:
3061:
3060:
3058:
3052:
3043:
3036:
3034:
3032:
3012:
2981:
2979:
2978:
2973:
2970:
2957:
2955:
2954:
2949:
2935:
2933:
2932:
2927:
2921:
2899:
2897:
2896:
2891:
2888:
2875:
2873:
2872:
2867:
2865:
2863:
2850:
2848:
2835:
2825:
2823:
2822:
2817:
2810:
2809:
2796:
2794:
2793:
2788:
2783:
2771:
2769:
2768:
2763:
2761:
2741:
2739:
2738:
2733:
2726:
2725:
2717:
2715:
2707:
2706:
2697:
2685:
2683:
2682:
2677:
2675:
2663:
2661:
2660:
2655:
2652:
2636:
2634:
2633:
2628:
2626:
2625:
2620:
2615:
2605:
2603:
2602:
2597:
2591:
2583:
2582:
2577:
2572:
2569:
2568:
2550:
2545:
2544:
2543:
2525:
2523:
2522:
2517:
2508:
2500:
2492:
2491:
2490:
2477:
2476:
2462:
2460:
2459:
2454:
2448:
2435:
2433:
2432:
2427:
2425:
2413:
2411:
2410:
2405:
2403:
2402:
2401:
2380:
2375:
2373:
2372:
2367:
2365:
2364:
2336:
2334:
2333:
2328:
2322:
2314:
2306:
2305:
2291:
2289:
2288:
2283:
2281:
2269:
2267:
2266:
2261:
2259:
2239:
2227:
2225:
2224:
2223:
2218:
2215:
2214:
2203:
2201:
2200:
2195:
2187:
2185:
2174:
2152:
2136:
2104:
2102:
2095:
2093:
1932:
1930:
1927:
1920:
1918:
1915:
1877:
1875:
1872:
1865:
1863:
1847:
1845:
1842:
1835:
1833:
1830:
1815:
1813:
1812:
1807:
1793:
1788:
1787:
1769:
1767:
1766:
1761:
1759:
1758:
1738:
1737:
1731:
1726:Larmor frequency
1708:
1706:
1705:
1700:
1695:
1690:
1689:
1688:
1671:
1669:
1668:
1663:
1657:
1655:
1653:
1652:
1651:
1632:
1631:
1622:
1610:
1605:
1603:
1602:
1597:
1595:
1594:
1593:
1575:nuclear magneton
1572:
1570:
1569:
1564:
1562:
1561:
1560:
1540:
1538:
1537:
1532:
1525:
1524:
1519:
1517:
1516:
1515:
1503:
1500:
1499:
1498:
1485:
1484:
1483:
1472:
1470:
1468:
1467:
1464:
1450:
1445:
1444:
1441:
1414:
1410:
1406:
1390:
1389:
1387:
1386:
1383:
1380:
1376:
1370:
1362:
1352:
1350:
1349:
1346:
1343:
1336:
1334:
1333:
1330:
1327:
1316:
1306:
1300:
1296:
1294:
1293:
1290:
1287:
1276:
1274:
1273:
1268:
1261:
1245:
1232:
1228:
1226:
1225:
1213:
1212:
1199:
1198:
1185:
1183:
1173:
1164:
1160:
1159:
1158:
1138:
1137:
1122:
1118:
1117:
1116:
1092:
1091:
1061:
1060:
1048:
1046:
1045:
1042:
1039:
1030:
1026:extended by the
1017:
1015:
1014:
1011:
1008:
992:
973:
954:
950:
944:
942:
941:
936:
931:
930:
929:
917:
875:
873:
865:
864:
863:
853:
845:
843:
842:
837:
835:
834:
833:
821:
816:
815:
803:
788:
787:
744:
743:
742:
723:
721:
720:
715:
676:
675:
674:
653:
645:
634:
632:
631:
626:
614:
612:
611:
606:
599:
598:
594:
587:
585:
572:
550:
549:
548:
521:
512:
510:
509:
504:
498:
493:
492:
491:
490:
480:
479:
478:
467:
462:
457:
456:
455:
445:
439:
437:
436:
435:
434:
420:
412:
407:
406:
405:
388:
377:
360:
358:
357:
352:
345:
341:
339:
328:
313:
311:
300:
295:
294:
281:
279:
268:
260:
233:
223:
219:
215:
205:
194:
192:
191:
186:
184:
172:
170:
169:
164:
162:
147:
145:
144:
139:
137:
135:
124:
86:
80:
47:
41:angular momentum
4173:
4172:
4168:
4167:
4166:
4164:
4163:
4162:
4138:
4137:
4136:
4135:
4106:
4102:
4092:
4090:
4085:
4084:
4080:
4070:
4068:
4063:
4062:
4058:
4050:
4046:
4045:
4041:
4031:
4029:
4024:
4023:
4019:
4009:
4007:
4002:
4001:
3997:
3984:
3983:
3979:
3966:
3965:
3961:
3954:
3946:. p. E66.
3936:
3932:
3925:
3903:
3899:
3892:
3874:
3870:
3863:
3849:
3845:
3811:
3804:
3803:
3799:
3797:
3794:
3793:
3790:
3789:
3785:
3736:
3732:
3730:
3725:
3722:
3715:
3708:
3698:Springer Verlag
3688:
3684:
3672:
3666:
3648:
3644:
3631:
3630:
3626:
3613:
3612:
3608:
3591:
3590:
3586:
3571:
3570:
3566:
3505:
3501:
3484:Giancoli, D.C.
3481:
3477:
3452:
3448:
3443:
3430:Larmor equation
3422:
3407:
3379:
3366:), it is also,
3321:
3298:
3293:
3285:
3282:
3281:
3235:
3233:
3221:
3209:
3202:
3187:
3185:
3173:
3161:
3149:
3141:
3140:
3136:
3134:
3132:
3120:
3108:
3097:
3093:
3091:
3089:
3067:
3066:
3065:
3063:
3054:
3048:
3047:
3046:
3044:
3042:
3038:
3028:
3016:
3011:
2990:
2987:
2986:
2966:
2963:
2960:
2959:
2941:
2938:
2937:
2917:
2905:
2902:
2901:
2884:
2881:
2878:
2877:
2851:
2844:
2836:
2834:
2832:
2829:
2828:
2805:
2802:
2799:
2798:
2779:
2777:
2774:
2773:
2757:
2755:
2752:
2751:
2721:
2708:
2702:
2698:
2696:
2694:
2691:
2690:
2671:
2669:
2666:
2665:
2648:
2645:
2642:
2641:
2616:
2614:
2613:
2611:
2608:
2607:
2587:
2573:
2571:
2570:
2564:
2560:
2546:
2539:
2538:
2534:
2531:
2528:
2527:
2504:
2496:
2486:
2485:
2481:
2472:
2471:
2468:
2465:
2464:
2444:
2441:
2438:
2437:
2421:
2419:
2416:
2415:
2397:
2396:
2392:
2387:
2384:
2383:
2378:
2360:
2356:
2342:
2339:
2338:
2318:
2310:
2301:
2300:
2297:
2294:
2293:
2277:
2275:
2272:
2271:
2255:
2253:
2250:
2249:
2246:
2237:
2221:
2219:
2216:
2212:
2211:
2210:
2208:
2178:
2173:
2165:
2162:
2161:
2150:
2140:magnetic moment
2134:
2119:
2113:
2100:
2098:
2091:
2089:
1928:
1925:
1923:
1916:
1913:
1911:
1873:
1870:
1868:
1861:
1859:
1855:
1843:
1840:
1838:
1831:
1828:
1826:
1789:
1783:
1779:
1777:
1774:
1773:
1754:
1750:
1748:
1745:
1744:
1729:
1691:
1684:
1683:
1679:
1677:
1674:
1673:
1647:
1646:
1642:
1633:
1627:
1623:
1621:
1618:
1615:
1614:
1608:
1589:
1588:
1584:
1582:
1579:
1578:
1556:
1555:
1551:
1549:
1546:
1545:
1511:
1510:
1506:
1504:
1502:
1494:
1493:
1489:
1479:
1478:
1474:
1463:
1459:
1454:
1449:
1440:
1436:
1434:
1431:
1430:
1412:
1408:
1404:
1397:
1384:
1381:
1378:
1377:
1374:
1372:
1368:
1367:
1354:
1347:
1344:
1341:
1340:
1338:
1331:
1328:
1325:
1324:
1322:
1312:
1302:
1291:
1288:
1285:
1284:
1282:
1281:
1221:
1217:
1205:
1201:
1191:
1187:
1177:
1172:
1154:
1150:
1133:
1129:
1128:
1124:
1112:
1108:
1087:
1083:
1082:
1078:
1076:
1072:
1070:
1067:
1066:
1059:
1043:
1040:
1035:
1034:
1032:
1031:
1028:
1027:
1012:
1009:
1006:
1005:
1003:
990:
971:
967:
952:
948:
922:
918:
913:
879:
866:
859:
858:
854:
852:
850:
847:
846:
826:
822:
817:
808:
804:
799:
783:
779:
748:
738:
737:
733:
731:
728:
727:
670:
669:
665:
663:
660:
659:
651:
650:. The electron
640:
620:
617:
616:
576:
571:
564:
560:
544:
543:
539:
537:
534:
533:
520:
514:
486:
485:
481:
474:
473:
469:
468:
466:
458:
451:
450:
446:
441:
430:
429:
425:
421:
413:
411:
401:
400:
396:
394:
391:
390:
387:
381:
375:
367:
332:
327:
304:
299:
290:
286:
269:
261:
259:
242:
239:
238:
225:
221:
217:
207:
203:
180:
178:
175:
174:
158:
156:
153:
152:
128:
123:
115:
112:
111:
97:
84:
78:
57:per second per
45:
37:magnetic moment
17:
12:
11:
5:
4171:
4161:
4160:
4155:
4150:
4148:Atomic physics
4134:
4133:
4100:
4078:
4056:
4039:
4017:
3995:
3977:
3959:
3952:
3930:
3923:
3897:
3891:978-0121644918
3890:
3868:
3862:978-0470511176
3861:
3843:
3818:
3814:
3807:
3802:
3783:
3746:(7): 1550060.
3734:
3728:
3713:
3706:
3682:
3664:
3642:
3624:
3606:
3564:
3499:
3494:Modern Physics
3475:
3470:. p. 21.
3445:
3444:
3442:
3439:
3438:
3437:
3432:
3427:
3418:
3416:Chemical shift
3413:
3406:
3403:
3390:magnetic field
3319:
3313:
3305:
3302:
3297:
3292:
3289:
3280:Consequently,
3278:
3277:
3266:
3260:
3256:
3253:
3248:
3243:
3239:
3232:
3224:
3220:
3217:
3213:
3205:
3201:
3198:
3195:
3191:
3184:
3176:
3172:
3169:
3165:
3157:
3152:
3148:
3144:
3139:
3131:
3123:
3119:
3116:
3112:
3104:
3100:
3096:
3088:
3084:
3075:
3070:
3057:
3051:
3041:
3031:
3027:
3024:
3020:
3015:
3010:
3007:
3003:
3000:
2997:
2994:
2969:
2946:
2925:
2920:
2916:
2913:
2910:
2887:
2861:
2858:
2855:
2847:
2843:
2840:
2815:
2808:
2786:
2782:
2772:and downwards
2760:
2743:
2742:
2731:
2724:
2720:
2714:
2711:
2705:
2701:
2674:
2651:
2623:
2619:
2595:
2590:
2586:
2580:
2576:
2567:
2563:
2559:
2556:
2553:
2549:
2542:
2537:
2515:
2511:
2507:
2503:
2499:
2495:
2489:
2484:
2480:
2475:
2452:
2447:
2424:
2400:
2395:
2391:
2363:
2359:
2355:
2352:
2349:
2346:
2326:
2321:
2317:
2313:
2309:
2304:
2280:
2258:
2245:
2242:
2228:, in units of
2205:
2204:
2193:
2190:
2184:
2181:
2177:
2172:
2169:
2131:magnetic field
2115:Main article:
2112:
2109:
2106:
2105:
2096:
2087:
2083:
2082:
2079:
2076:
2072:
2071:
2068:
2065:
2061:
2060:
2057:
2054:
2050:
2049:
2046:
2043:
2037:
2036:
2033:
2030:
2026:
2025:
2022:
2019:
2015:
2014:
2011:
2008:
2004:
2003:
2000:
1997:
1993:
1992:
1989:
1986:
1980:
1979:
1976:
1973:
1969:
1968:
1965:
1962:
1958:
1957:
1954:
1951:
1945:
1944:
1941:
1938:
1934:
1933:
1921:
1909:
1905:
1904:
1901:
1898:
1892:
1891:
1888:
1885:
1879:
1878:
1866:
1857:
1853:
1849:
1848:
1836:
1824:
1818:
1817:
1805:
1802:
1799:
1796:
1792:
1786:
1782:
1771:
1757:
1753:
1742:
1698:
1694:
1687:
1682:
1661:
1650:
1645:
1640:
1637:
1630:
1626:
1592:
1587:
1559:
1554:
1542:
1541:
1530:
1522:
1514:
1509:
1497:
1492:
1488:
1482:
1477:
1462:
1458:
1453:
1448:
1439:
1396:
1393:
1278:
1277:
1266:
1260:
1257:
1254:
1250:
1244:
1240:
1236:
1231:
1224:
1220:
1216:
1211:
1208:
1204:
1197:
1194:
1190:
1181:
1176:
1170:
1167:
1163:
1157:
1153:
1148:
1144:
1141:
1136:
1132:
1127:
1121:
1115:
1111:
1106:
1102:
1099:
1096:
1090:
1086:
1081:
1075:
1055:
1020:Dirac equation
1002:Physical spin
966:
963:
934:
928:
925:
921:
916:
912:
909:
906:
902:
899:
896:
893:
889:
885:
882:
878:
872:
869:
862:
857:
832:
829:
825:
820:
814:
811:
807:
802:
798:
795:
792:
786:
782:
778:
775:
772:
769:
766:
762:
758:
754:
751:
747:
741:
736:
713:
710:
707:
704:
701:
697:
693:
689:
685:
682:
679:
673:
668:
624:
604:
597:
593:
590:
583:
580:
575:
570:
567:
563:
559:
556:
553:
547:
542:
518:
502:
496:
489:
484:
477:
472:
465:
461:
454:
449:
444:
433:
428:
424:
419:
416:
410:
404:
399:
385:
366:
363:
362:
361:
350:
344:
338:
335:
331:
326:
323:
320:
317:
310:
307:
303:
298:
293:
289:
285:
278:
275:
272:
267:
264:
258:
255:
252:
249:
246:
183:
161:
149:
148:
134:
131:
127:
122:
119:
96:
93:
69:(C⋅kg).
15:
9:
6:
4:
3:
2:
4170:
4159:
4156:
4154:
4151:
4149:
4146:
4145:
4143:
4128:
4123:
4119:
4115:
4111:
4104:
4088:
4082:
4066:
4060:
4049:
4043:
4027:
4021:
4005:
3999:
3991:
3987:
3981:
3973:
3969:
3963:
3955:
3953:0-8493-0463-6
3949:
3945:
3941:
3934:
3926:
3924:0-12-092861-2
3920:
3916:
3911:
3910:
3901:
3893:
3887:
3883:
3879:
3872:
3864:
3858:
3854:
3853:Spin Dynamics
3847:
3840:
3834:
3830:
3816:
3812:
3800:
3787:
3779:
3775:
3771:
3767:
3763:
3759:
3754:
3749:
3745:
3741:
3720:
3718:
3709:
3707:9783540674580
3703:
3699:
3695:
3694:
3686:
3676:
3671:
3667:
3665:3-7643-0579-7
3661:
3657:
3653:
3646:
3638:
3634:
3628:
3620:
3616:
3610:
3601:
3584:
3578:
3574:
3568:
3560:
3556:
3552:
3548:
3544:
3540:
3536:
3532:
3527:
3522:
3519:(7): 071801.
3518:
3514:
3510:
3503:
3495:
3487:
3479:
3473:
3469:
3468:0-632-03583-8
3465:
3461:
3460:
3455:
3450:
3446:
3436:
3433:
3431:
3428:
3426:
3419:
3417:
3414:
3412:
3409:
3408:
3402:
3400:
3399:
3393:
3391:
3386:
3382:
3377:
3373:
3369:
3365:
3357:
3353:
3349:
3348:dipole moment
3345:
3342:ratio versus
3341:
3336:
3317:
3311:
3303:
3300:
3295:
3290:
3287:
3264:
3258:
3254:
3251:
3246:
3241:
3237:
3230:
3222:
3218:
3215:
3211:
3203:
3199:
3196:
3193:
3189:
3182:
3174:
3170:
3167:
3163:
3155:
3146:
3137:
3129:
3121:
3117:
3114:
3110:
3102:
3094:
3086:
3082:
3039:
3029:
3025:
3022:
3018:
3013:
3008:
3005:
3001:
2998:
2995:
2992:
2985:
2984:
2983:
2944:
2923:
2918:
2914:
2911:
2908:
2859:
2856:
2841:
2826:
2813:
2784:
2748:
2729:
2718:
2712:
2709:
2699:
2689:
2688:
2687:
2638:
2593:
2584:
2565:
2561:
2557:
2554:
2551:
2535:
2513:
2501:
2482:
2478:
2450:
2393:
2389:
2381:
2361:
2357:
2353:
2350:
2347:
2344:
2324:
2315:
2307:
2241:
2235:
2231:
2191:
2188:
2182:
2179:
2175:
2170:
2167:
2160:
2159:
2158:
2156:
2153:(measured in
2149:
2145:
2141:
2137:
2132:
2128:
2124:
2118:
2097:
2088:
2085:
2084:
2080:
2077:
2074:
2073:
2069:
2066:
2063:
2062:
2058:
2055:
2052:
2051:
2047:
2044:
2042:
2039:
2038:
2034:
2031:
2028:
2027:
2023:
2020:
2017:
2016:
2012:
2009:
2006:
2005:
2001:
1998:
1995:
1994:
1990:
1987:
1985:
1982:
1981:
1977:
1974:
1971:
1970:
1966:
1963:
1960:
1959:
1955:
1952:
1950:
1947:
1946:
1942:
1939:
1936:
1935:
1922:
1910:
1907:
1906:
1902:
1899:
1897:
1894:
1893:
1889:
1886:
1884:
1881:
1880:
1867:
1858:
1851:
1850:
1837:
1825:
1823:
1820:
1819:
1800:
1797:
1790:
1784:
1780:
1772:
1770:(10 radâ
sâ
T)
1755:
1751:
1743:
1740:
1739:
1736:
1733:
1727:
1723:
1719:
1715:
1710:
1696:
1692:
1680:
1659:
1643:
1638:
1635:
1628:
1624:
1612:
1585:
1576:
1552:
1528:
1507:
1490:
1486:
1475:
1460:
1456:
1451:
1446:
1437:
1429:
1428:
1427:
1425:
1421:
1401:
1395:For a nucleus
1392:
1365:
1361:
1357:
1320:
1315:
1310:
1305:
1299:
1264:
1258:
1255:
1252:
1248:
1242:
1238:
1234:
1229:
1222:
1218:
1214:
1209:
1206:
1202:
1195:
1192:
1188:
1179:
1174:
1168:
1165:
1161:
1155:
1151:
1146:
1142:
1139:
1134:
1125:
1119:
1113:
1109:
1104:
1100:
1097:
1094:
1088:
1079:
1073:
1065:
1064:
1063:
1058:
1054:
1051:
1038:
1025:
1021:
1000:
998:
994:
987:
983:
979:
975:
962:
961:for details.
960:
959:
947:The electron
945:
932:
926:
923:
914:
897:
891:
887:
883:
880:
876:
870:
867:
855:
830:
827:
818:
812:
809:
800:
784:
780:
776:
770:
764:
760:
756:
752:
749:
745:
734:
724:
711:
705:
699:
695:
691:
687:
683:
680:
677:
666:
657:
649:
643:
638:
622:
602:
595:
591:
588:
581:
578:
573:
568:
565:
561:
557:
554:
551:
540:
530:
527:
525:
524:Bohr magneton
517:
500:
482:
470:
463:
447:
426:
422:
417:
414:
408:
397:
384:
379:
372:
348:
342:
336:
333:
329:
324:
321:
318:
315:
308:
305:
301:
296:
291:
287:
283:
276:
273:
270:
265:
262:
256:
253:
250:
247:
244:
237:
236:
235:
232:
228:
214:
210:
201:
196:
195:is its mass.
181:
159:
132:
129:
125:
120:
117:
110:
109:
108:
105:
102:
101:nonconductive
92:
90:
89:dimensionless
82:
75:
70:
68:
64:
60:
56:
52:
49:, gamma. Its
48:
42:
38:
34:
30:
26:
22:
4117:
4113:
4103:
4091:. Retrieved
4081:
4069:. Retrieved
4059:
4042:
4030:. Retrieved
4020:
4008:. Retrieved
3998:
3980:
3962:
3939:
3933:
3908:
3900:
3877:
3871:
3852:
3846:
3786:
3743:
3739:
3692:
3685:
3670:the original
3655:
3645:
3627:
3609:
3599:
3567:
3516:
3512:
3502:
3493:
3485:
3478:
3457:
3449:
3397:
3394:
3384:
3380:
3375:
3367:
3351:
3344:magnetogyric
3343:
3340:gyromagnetic
3339:
3337:
3279:
2827:
2744:
2639:
2377:
2247:
2206:
2133:
2120:
1734:
1711:
1543:
1424:nuclear spin
1418:
1359:
1355:
1313:
1303:
1297:
1279:
1056:
1052:
1049:
1036:
1001:
968:
956:
951:-factor and
946:
725:
641:
531:
528:
515:
382:
368:
230:
226:
212:
208:
197:
150:
98:
73:
71:
53:unit is the
28:
24:
18:
4089:. NIST 2022
4067:. NIST 2022
4028:. NIST 2022
4006:. NIST 2022
997:consequence
200:integration
99:Consider a
4142:Categories
3753:1507.03640
3675:PostScript
3581:Note that
3526:2209.13084
3441:References
3378:property)
2747:precession
1716:(NMR) and
4120:(4): 65.
3944:CRC Press
3801:μ
3778:119303031
3559:123962197
3374:(another
3304:π
3296:γ
3255:γ
3223:ϕ
3219:
3204:ϕ
3200:
3175:ϕ
3171:
3147:×
3122:ϕ
3118:
3030:ϕ
3026:
3002:π
2993:ω
2945:ϕ
2919:ϕ
2915:
2857:
2842:
2622:^
2579:^
2558:π
2502:×
2390:±
2354:π
2316:×
2183:π
2176:γ
2148:frequency
1900:285.3508
1801:π
1781:γ
1752:γ
1681:μ
1672:equal to
1639:π
1625:γ
1553:μ
1521:ℏ
1508:μ
1438:γ
1256:≠
1235:ψ
1210:ν
1207:μ
1196:ν
1193:μ
1189:σ
1156:μ
1135:μ
1131:∂
1114:μ
1089:μ
1085:∂
924:−
915:⋅
881:−
871:π
856:γ
828:−
819:⋅
810:−
801:⋅
777:×
750:−
735:γ
681:−
623:α
592:⋯
582:π
574:α
555:−
495:ℏ
483:μ
415:−
398:γ
284:π
274:π
245:μ
220:, charge
118:γ
74:different
3837:(citing
3551:36867820
3490:or see:
3456:(1993).
3405:See also
3388:and the
2127:electron
2125:, or an
2045:108.291
2032:â53.190
1999:251.815
1988:â36.264
1975:â27.116
1956:10.7084
1953:67.2828
1940:103.962
1912:â203.789
1816:(MHzâ
T)
1741:Nucleus
1373:â
67:kilogram
3992:. 2022.
3974:. 2022.
3835:. 2014.
3758:Bibcode
3594:< 0
3531:Bibcode
3425:-factor
3350:) to a
2226:
2209:
2144:precess
2142:, will
2123:nucleus
2099:â11.776
2090:â73.995
2078:16.767
2070:11.319
2067:71.118
2048:17.235
2035:â8.465
2024:11.103
2021:69.763
2013:11.262
2010:70.761
2002:40.078
1991:â5.772
1978:â4.316
1964:19.331
1943:16.546
1924:â32.434
1903:45.415
1887:41.065
1860:267.515
1852:H (in H
1827:267.522
1722:precess
1611:-factor
1606:is the
1573:is the
1420:Protons
1388:
1353:in the
1351:
1339:
1335:
1323:
1317:is the
1295:
1283:
1047:
1033:
1016:
1004:
993:-factor
974:-factor
888:024.951
635:is the
522:is the
378:-factor
216:, mass
206:, area
104:charged
81:-factor
63:coulomb
39:to its
35:of its
21:physics
4158:Ratios
4093:9 July
4071:9 July
4032:19 May
4010:19 May
3950:
3921:
3888:
3859:
3839:CODATA
3776:
3704:
3662:
3557:
3549:
3466:
3421:Landé
3323:q.e.d.
3315:
3262:
2936:where
2811:
2727:
2081:2.669
2059:1.382
2056:8.681
1967:3.077
1890:6.536
1869:42.576
1839:42.577
1577:, and
1544:where
1526:
1280:Here,
1262:
1246:
986:spinor
615:where
600:
513:where
346:
151:where
83:. The
55:radian
23:, the
4051:(PDF)
3774:S2CID
3748:arXiv
3555:S2CID
3521:arXiv
3376:gyric
3360:ÎłÏÏÎżÏ
3356:Greek
3352:gyric
2292:is
2234:tesla
2230:hertz
2155:hertz
2146:at a
753:1.760
684:2.002
59:tesla
33:ratio
4095:2024
4073:2024
4034:2021
4012:2021
3990:NIST
3972:NIST
3948:ISBN
3919:ISBN
3886:ISBN
3857:ISBN
3833:NIST
3702:ISBN
3660:ISBN
3637:NIST
3619:NIST
3583:NIST
3577:NIST
3547:PMID
3464:ISBN
2232:per
2101:7338
1931:(28)
1919:(18)
1876:(17)
1864:(11)
1862:3194
1846:(18)
1834:(11)
1301:and
892:4242
371:spin
65:per
4122:doi
3915:960
3766:doi
3539:doi
3517:130
3383:= 2
3216:sin
3197:sin
3168:sin
3115:sin
3023:sin
2912:sin
2103:(3)
2094:(2)
2092:401
2086:Xe
2075:Zn
2064:Cu
2053:Fe
2029:Si
2018:Al
2007:Na
1937:Li
1929:033
1926:100
1914:460
1908:He
1871:385
1856:O)
1844:461
1841:478
1829:187
761:630
757:859
696:361
692:304
688:319
644:= 2
231:mvr
19:In
4144::
4116:.
4112:.
3988:.
3970:.
3917:.
3884:.
3880:.
3831:.
3772:.
3764:.
3756:.
3744:24
3742:.
3716:^
3700:.
3696:.
3635:.
3617:.
3575:.
3553:.
3545:.
3537:.
3529:.
3515:.
3511:.
3392:.
3385:Ïf
3358::
2686::
2240:.
1996:F
1972:N
1961:N
1917:78
1874:43
1832:08
1371:=
1358:â
1057:ΌΜ
898:85
884:28
785:11
781:10
771:53
765:23
706:27
700:18
526:.
389::
229:=
213:Ïr
211:=
91:.
51:SI
4130:.
4124::
4118:6
4097:.
4075:.
4036:.
4014:.
3956:.
3894:.
3865:.
3829:"
3817:h
3813:/
3806:N
3780:.
3768::
3760::
3750::
3735:Ό
3733:Ï
3729:s
3726:g
3677:)
3673:(
3639:.
3621:.
3592:Îł
3587:Îł
3579:.
3561:.
3541::
3533::
3523::
3423:g
3381:Ï
3318:.
3312:B
3301:2
3291:=
3288:f
3265:.
3259:B
3252:=
3247:J
3242:B
3238:m
3231:=
3212:J
3194:B
3190:m
3183:=
3164:J
3156:|
3151:B
3143:m
3138:|
3130:=
3111:J
3103:|
3099:T
3095:|
3087:=
3083:|
3074:t
3069:d
3056:J
3050:d
3040:|
3019:J
3014:1
3009:=
3006:f
2999:2
2996:=
2968:J
2924:,
2909:J
2886:J
2860:t
2854:d
2846:J
2839:d
2814:.
2807:B
2785:.
2781:m
2759:J
2730:.
2723:T
2719:=
2713:t
2710:d
2704:J
2700:d
2673:T
2650:J
2618:d
2594:,
2589:m
2585:=
2575:d
2566:2
2562:r
2555:I
2552:=
2548:d
2541:m
2536:q
2514:.
2510:)
2506:B
2498:d
2494:(
2488:m
2483:q
2479:=
2474:T
2451:.
2446:B
2423:d
2399:m
2394:q
2379:p
2362:2
2358:r
2351:I
2348:=
2345:m
2325:.
2320:B
2312:m
2308:=
2303:T
2279:B
2257:m
2238:Îł
2222:Ï
2220:2
2217:/
2213:Îł
2192:.
2189:B
2180:2
2171:=
2168:f
2151:f
2135:B
2041:P
1984:O
1949:C
1896:H
1883:H
1854:2
1822:H
1804:)
1798:2
1795:(
1791:/
1785:n
1756:n
1730:Îł
1697:h
1693:/
1686:N
1660:,
1649:n
1644:g
1636:2
1629:n
1609:g
1591:n
1586:g
1558:N
1529:,
1513:N
1496:n
1491:g
1487:=
1481:n
1476:g
1465:p
1461:m
1457:2
1452:e
1447:=
1442:n
1413:Îł
1409:Îł
1405:Îł
1385:3
1382:/
1379:2
1375:+
1369:g
1360:D
1356:D
1348:2
1345:/
1342:3
1332:2
1329:/
1326:1
1314:A
1304:F
1298:Ï
1292:2
1289:/
1286:1
1265:.
1259:2
1253:g
1249:,
1243:0
1239:=
1230:]
1223:2
1219:m
1215:+
1203:F
1180:4
1175:e
1169:g
1166:+
1162:)
1152:A
1147:e
1143:i
1140:+
1126:(
1120:)
1110:A
1105:e
1101:i
1098:+
1095:u
1080:(
1074:[
1053:F
1050:Ï
1044:4
1041:/
1037:e
1029:g
1013:2
1010:/
1007:1
991:g
972:g
953:Îł
949:g
933:.
927:1
920:T
911:z
908:H
905:M
901:)
895:(
877:=
868:2
861:e
831:1
824:T
813:1
806:s
797:d
794:a
791:r
774:)
768:(
746:=
740:e
712:.
709:)
703:(
678:=
672:e
667:g
652:g
642:g
603:,
596:)
589:+
579:2
569:+
566:1
562:(
558:2
552:=
546:e
541:g
519:B
516:Ό
501:,
488:B
476:e
471:g
464:=
460:|
453:e
448:g
443:|
432:e
427:m
423:2
418:e
409:=
403:e
386:e
383:g
376:g
349:.
343:L
337:m
334:2
330:q
325:=
322:r
319:v
316:m
309:m
306:2
302:q
297:=
292:2
288:r
277:r
271:2
266:v
263:q
257:=
254:A
251:I
248:=
227:L
222:q
218:m
209:A
204:r
182:m
160:q
133:m
130:2
126:q
121:=
85:g
79:g
46:Îł
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