G-omil (fizika)

G -omil (shuningdek, g qiymati deb ataladi) atom, zarracha yoki yadroning magnit momentini va burchak momentini tavsiflovchi o'lchamsiz kattalikdir. Bu mohiyatan proportsionallik konstantasi bo'lib, zarrachaning turli kuzatilgan magnit momentlari m ni ularning burchak momentum kvant raqamlari va magnit moment birligi (uni o'lchamsiz qilish uchun), odatda Bor magnitoni yoki yadro magnitoni bilan bog'laydi.

Ushbu maqola Mirzo Ulug'bek nomidagi O'zbekisto Milliy Universiteti Fizika fakulteti talabasi Do'stmuhamedova Shahzoda tomonidan wikita'lim loyihasi doirasida ingliz tilidan tarjima qilindi.

Ta'rif

Dirak zarrasi

Hech qanday ichki tuzilishga ega bo'lmagan (Dirak zarrasi) zaryadlangan, spin-1/2 zarraning spin magnit momenti ^[1] bilan berilgan. ${\boldsymbol {\mu }}=g{e \over 2m}\mathbf {S} ,$ ${\boldsymbol {\mu }}=g{e \over 2m}\mathbf {S} ,$ Bu yerda $\mu$ - zarrachaning spin magnit momenti, g - zarrachaning g - omili, e - elementar zaryad, m - zarrachaning massasi va S - zarrachaning spin burchak momenti (Dirak zarralari uchun ħ/2).

Barion yoki yadro

Protonlar, neytronlar, yadrolar va boshqa kompozit barion zarralar spinidan kelib chiqadigan magnit momentlarga ega (spin ham, magnit moment ham nolga teng bo'lishi mumkin, bu holda g -omil aniqlanmagan). An'anaviy ravishda, bog'langan g -omillar yadro magnitoni yordamida aniqlanadi va shuning uchun Dirak zarrasi kabi zarracha massasidan emas, balki protonning massasidan bilvosita foydalaniladi. Ushbu konventsiyada ishlatiladigan formula

${\boldsymbol {\mu }}=g{\mu _{\text{N}} \over \hbar }{\mathbf {I} }=g{e \over 2m_{\text{p}}}\mathbf {I} ,$ ${\boldsymbol {\mu }}=g{\mu _{\text{N}} \over \hbar }{\mathbf {I} }=g{e \over 2m_{\text{p}}}\mathbf {I} ,$ bu yerda $\mu$ - nuklon yoki yadroning spini natijasida hosil bo'lgan magnit momenti, g - samarali g -omil, I - spin burchak impulsi, $\mu$ _N - yadro magnitoni, e - elementar zaryad va m _p - protonning qolgan qismi. massa.

Hisoblash

Elektron g -omillar

Elektron bilan bog'liq uchta magnit moment mavjud: biri uning spin burchak momentidan, biri orbital burchak momentidan va ikkinchisi umumiy burchak momentidan (bu ikki komponentning kvant-mexanik yig'indisi). Ushbu uch momentga mos keladigan uchta turli g -faktor:

Elektron spin g -omil

Ulardan eng ma'lum bo'lgan elektron spin g-omil (ko'pincha oddiygina elektron g-omil deb ataladi), g _e, tomonidan aniqlanadi.

{\boldsymbol {\mu }}_{\text{s}}=g_{\text{e}}{\mu _{\text{B}} \over \hbar }\mathbf {S}

Bu yerda $\mu$ _{s -} elektronning spini natijasida hosil bo'lgan magnit moment, S - uning spin burchak momenti va $\mu _{\text{B}}=e\hbar /2m_{\text{e}}$ Bor magnitoni hisoblanadi. Atom fizikasida elektronning spin g - faktori ko'pincha g _e ning mutlaq qiymati yoki manfiyligi sifatida aniqlanadi:

g_{\text{s}}=|g_{\text{e}}|=-g_{\text{e}}.

Keyin magnit momentning z -komponenti bo'ladi

\mu _{\text{z}}=-g_{\text{s}}\mu _{\text{B}}m_{\text{s}}

g _s qiymati taxminan 2,002319 ga teng va favqulodda aniqlik bilan ma'lum. ^[2]^[3] Uning aniq ikkita emasligi sababi anomal magnit dipol momentini kvant elektrodinamika hisobi bilan izohlanadi. ^[4] Spin g faktori siklotronning magnit maydonidagi erkin elektron uchun spin chastotasi bilan bog'liq:

\nu _{\text{s}}={\frac {g}{2}}\nu _{\text{c}}

Elektron orbital g -omil

Ikkinchidan, elektron orbital g-omil g _L bilan aniqlanadi

{\boldsymbol {\mu }}_{L}=-g_{L}{\mu _{\mathrm {B} } \over \hbar }\mathbf {L} ,

Bu yerda $\mu$ _{L -} elektronning orbital burchak impulsi natijasida hosil bo'lgan magnit moment, L - uning orbital burchak momenti va $\mu$ _B - Bor magnitoni . Cheksiz massali yadro uchun g _L ning qiymati klassik magnitogirik nisbatning kelib chiqishiga o'xshash kvant-mexanik argumentga ko'ra aynan bittaga teng. Magnit kvant soni m _l bo'lgan orbitaldagi elektron uchun orbital burchak momentining z -komponenti.

\mu _{\text{z}}=-g_{L}\mu _{\text{B}}m_{\text{l}}

g _L = 1 bo'lgani uchun - $\mu$ _B m _l

Cheklangan massali yadro uchun samarali g qiymati mavjud ^[5]

g_{L}=1-{\frac {1}{M}}

bu yerda M - yadro massasining elektron massasiga nisbati.

Umumiy burchak momenti (Landé) g -faktor

Uchinchidan, Lande g-omil g _J tomonidan aniqlanadi

|{\boldsymbol {\mu _{\text{J}}}}|=g_{J}{\mu _{\text{B}} \over \hbar }|\mathbf {J} |

Bu yerda $\mu$ _{J -} elektronning spin va orbital burchak momentumidan kelib chiqadigan umumiy magnit moment, J = L + S - uning umumiy burchak momenti va $\mu$ _B - Bor magnitoni . g _J qiymati g _L va g _s ga kvant-mexanik argument bilan bog'liq; Landé g -faktor maqolasiga qarang. $\mu$ _J va J vektorlari kollinear emas, shuning uchun faqat ularning kattaliklarini solishtirish mumkin.

Muon g - faktor

Agar supersimmetriya tabiatda amalga oshirilsa, yangi zarrachalarni o'z ichiga olgan halqa diagrammalari tufayli muonning g -2 ga tuzatishlar bo'ladi. Etakchi tuzatishlar orasida bu yerda tasvirlanganlar mavjud: neytral va smuon halqasi, chargino va muon sneutrino halqasi. Bu g -2 ga hissa qo'shishi mumkin bo'lgan "standart modeldan tashqari" fizikaga misoldir.

Myuon, xuddi elektron kabi, tenglama bilan berilgan spin bilan bog'liq bo'lgan g -omilga ega

{\boldsymbol {\mu }}=g{e \over 2m_{\mu }}\mathbf {S} ,

bu yerda $\mu$ - muonning spini natijasida hosil bo'lgan magnit moment, S - spin burchak momenti, m $\mu$ - muon massasi.

Myuon g -omilning elektron g -omil bilan mutlaqo bir xil emasligi asosan kvant elektrodinamiği va uning anomal magnit dipol momentini hisoblashi bilan izohlanadi. Ikki qiymat o'rtasidagi deyarli barcha kichik farqlar (uning 99,96%) og'ir zarrachalar diagrammalarining yaxshi tushunilgan etishmasligi bilan bog'liq bo'lib, ular magnit dipol maydonini ifodalovchi fotonning emissiya ehtimoliga hissa qo'shadi, ular muonlar uchun mavjud. QED nazariyasida elektronlar emas. Bular butunlay zarralar orasidagi massa farqining natijasidir.

Biroq, elektronlar va muonlar uchun g -omillar o'rtasidagi barcha farqlar standart model tomonidan aniq tushuntirilmagan. Muon g -omil, nazariy jihatdan, standart modeldan tashqari fizikaga ta'sir qilishi mumkin, shuning uchun u juda aniq o'lchangan, xususan , Brukxaven milliy laboratoriyasida . 2006 yil noyabr oyida E821 hamkorlik yakuniy hisobotida, 7000200233184160000♠2.0023318416(13) 7000200233183620000♠2.00233183620(86) ni tashkil qiladi. ^[6] Bu 3,4 standart og'ishlar farqi bo'lib, standart Model fizikasidan tashqari ta'sir ko'rsatishi mumkinligini ko'rsatadi. Brookhaven myuon saqlash halqasi Fermilabga ko'chirildi, u yerda Muon g -2 tajribasi undan muon g - faktorini aniqroq o'lchash uchun foydalandi. 2021-yil 7-aprelda Fermilab Muon g −2 hamkorligi muon magnit anomaliyasining yangi o‘lchovini taqdim etdi va chop etdi. ^[7] Brookhaven va Fermilab o'lchovlari birlashtirilganda, yangi jahon o'rtacha ko'rsatkichi nazariya prognozidan 4,2 standart og'ish bilan farq qiladi.

O'lchangan g - faktor qiymatlari

NIST CODATA tavsiya etilgan g faktor qiymatlari ^[9]
Zarracha	Belgi	g -omil	Nisbiy standart noaniqlik
elektron	g _e	−2.002319 304 362 56 (35)	1.7× 10 -13
muon - (tajriba-Brookhaven-2006)	g _m	−2.002331 8418 (13)	6.3× 10 -10
muon - (tajriba-Fermilab-2021)	g _m	−2.002 331 8408(11)	5,4 × 10 ^-10
muon - (eksperiment-dunyo o'rtacha-2021)	g _m	−2.002 331 8 4121 (82)	4,1 × 10 ^-10
muon - (nazariya - iyun 2020)	g _m	−2.002 331 8 3620 (86)	4,3 × 10 ^-10
neytron	g _n	2999617391455000000♠−3.82608545(90)	6993239999999999999♠2.4×10⁻⁷ ^[8]
proton	g _p	+ 5.585694 6893 (16)	2.9× 10 -10

Elektron g -omil fizikada eng aniq o'lchanadigan qiymatlardan biridir.

Shuningdek qarang

Anomal magnit dipol momenti
Elektron magnit momenti
Lande g faktori

Eslatmalar va havolalar

↑ Povh, Bogdan. Particles and Nuclei, 2013-04-17. ISBN 978-3-662-05023-1.
↑ Gabrielse, Gerald; Hanneke, David (October 2006). "Precision pins down the electron's magnetism". CERN Courier 46 (8): 35–37. Archived from the original on 2006-10-18. https://web.archive.org/web/20061018223513/http://www.cerncourier.com/main/article/46/8/20. Qaraldi: 2007-05-27. G-omil (fizika)]]
↑ Odom, B.; Hanneke, D.; d’Urso, B.; Gabrielse, G. (2006). "New measurement of the electron magnetic moment using a one-electron quantum cyclotron". Physical Review Letters 97 (3): 030801. doi:10.1103/PhysRevLett.97.030801. PMID 16907490.
↑ Brodsky, S; Franke, V; Hiller, J; McCartor, G; Paston, S; Prokhvatilov, E (2004). "A nonperturbative calculation of the electron's magnetic moment". Nuclear Physics B 703 (1–2): 333–362. doi:10.1016/j.nuclphysb.2004.10.027.
↑ Lamb, Willis E. (1952-01-15). "Fine Structure of the Hydrogen Atom. III". Physical Review 85 (2): 259–276. doi:10.1103/PhysRev.85.259. PMID 17775407.
↑ Hagiwara, K.; Martin, A. D.; Nomura, Daisuke; Teubner, T. (2007). "Improved predictions for g−2 of the muon and α_QED(M²_Z)". Physics Letters B 649 (2–3): 173–179. doi:10.1016/j.physletb.2007.04.012.
↑ B. Abi (7 April 2021). "Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm". Physical Review Letters 126 (14): 141801. doi:10.1103/PhysRevLett.126.141801. ISSN 0031-9007. PMID 33891447.
↑ „CODATA Value: neutron g factor“. NIST. Qaraldi: 2017-yil 5-noyabr.
↑ „CODATA values of the fundamental constants“. NIST.

Qo'shimcha o'qish

CODATA tavsiyalari 2006

Havolalar

Media related to G-factor (physics) at Wikimedia Commons
Gwinner, Gerald; Silwal, Roshani (June 2022). "Tiny isotopic difference tests standard model of particle physics" (en). Nature 606 (7914): 467–468. doi:10.1038/d41586-022-01569-3. PMID 35705815. https://www.nature.com/articles/d41586-022-01569-3.

[1] Povh, Bogdan. Particles and Nuclei, 2013-04-17. ISBN 978-3-662-05023-1.

[2] Gabrielse, Gerald; Hanneke, David (October 2006). "Precision pins down the electron's magnetism". CERN Courier 46 (8): 35–37. Archived from the original on 2006-10-18. https://web.archive.org/web/20061018223513/http://www.cerncourier.com/main/article/46/8/20. Qaraldi: 2007-05-27. G-omil (fizika)]]

[3] Odom, B.; Hanneke, D.; d’Urso, B.; Gabrielse, G. (2006). "New measurement of the electron magnetic moment using a one-electron quantum cyclotron". Physical Review Letters 97 (3): 030801. doi:10.1103/PhysRevLett.97.030801. PMID 16907490.

[4] Brodsky, S; Franke, V; Hiller, J; McCartor, G; Paston, S; Prokhvatilov, E (2004). "A nonperturbative calculation of the electron's magnetic moment". Nuclear Physics B 703 (1–2): 333–362. doi:10.1016/j.nuclphysb.2004.10.027.

[5] Lamb, Willis E. (1952-01-15). "Fine Structure of the Hydrogen Atom. III". Physical Review 85 (2): 259–276. doi:10.1103/PhysRev.85.259. PMID 17775407.

[6] Hagiwara, K.; Martin, A. D.; Nomura, Daisuke; Teubner, T. (2007). "Improved predictions for g−2 of the muon and α_QED(M²_Z)". Physics Letters B 649 (2–3): 173–179. doi:10.1016/j.physletb.2007.04.012.

[7] B. Abi (7 April 2021). "Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm". Physical Review Letters 126 (14): 141801. doi:10.1103/PhysRevLett.126.141801. ISSN 0031-9007. PMID 33891447.

[8] „CODATA Value: neutron g factor“. NIST. Qaraldi: 2017-yil 5-noyabr.

[9] „CODATA values of the fundamental constants“. NIST.

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