ƊAURIN H₂, AN AUNA SHI ZUWA KILOHERTZ 175

Ƙwayar hydrogen, H₂ — proton biyu, electron biyu — ita ce ƙwaya mafi sauƙi mara caji. Fiye da ƙarni ɗaya, lambobinta biyu sun zama ma’aunin gwada ka’ida: makamashin ionization (ionization energy), makamashin da ake buƙata don cire electron ɗaya, da makamashin rabuwa (dissociation energy), makamashin da ake buƙata don raba ta zuwa atom biyu na hydrogen. Ioana Doran, Frédéric Merkt, Kjeld Eikema da abokan aiki 17 a ETH Zurich, VU Amsterdam da Université Paris-Saclay yanzu sun ba da dukansu da rashin tabbas da ya yi daidai da kilohertz 175.

Lissafin Bohr, lissafin Langmuir

A 1913, Bohr ya lissafa makamashin rabuwa ta hanyar faɗaɗa samfurinsa na atom ɗin hydrogen. Ya sami kusan 21,000 cm⁻¹ (ma’aunin da za a bayyana a ƙasa), kuma ya amince da shi har ya yi shakkar ƙimar gwaji ta Langmuir ta kusan 46,000, wadda aka samu ta “hanya ba kai tsaye ba” (indirect method). Gaskiya tana tsakaninsu: ƙarni ɗaya da ya wuce, auna-aunen sinadarai sun haɗu kusa da 36,750, da rashin tabbas na kusan kashi 5 zuwa 10%. Daga nan nazarin bakan haske (spectroscopy) da lissafi sun riƙa karɓar jagoranci bi da bi; zuwa 1995, Wolniewicz ya lissafa lambobi takwas na farko, 36,118.069.

Makamashi da aka ƙirga da hertz

Me ya sa kilohertz ga makamashi? Domin masu gwajin suna auna mitoci (frequencies): na hasken laser ko igiyoyin millimetre da ke sa ƙwayar ta yi tsalle daga matakin makamashi ɗaya zuwa wani. Kowane gibin makamashi ya yi daidai da mita ɗaya, don haka takardar tana bayyana makamashi a matsayin mitoci — “mitar ionization” kamar yadda ake faɗin makamashin ionization. Ɗayan ma’aunin, lambar igiya (wavenumber) a cm⁻¹, ita ce wannan mitar da aka raba da saurin haske: adadin igiyoyin haske a kowane centimetre. Da aka ba su gefe da gefe a cikin takardar, ma’aunan biyu suna ƙayyade farashin musaya: 1 cm⁻¹ kusan gigahertz 29.98 ne.

Makamashin rabuwar H₂ shi ne 36,118.069 6646 cm⁻¹, ko megahertz 1,082,792,488.30 — kusan hertz miliyan biliyan (dubu tiriliyan). A kan makamashin ionization, kHz 175 sun kai kashi 5 cikin biliyan ɗari, marubutan sun rubuta; a kan makamashin rabuwa, kusan kashi 1.6 cikin biliyan goma — kamar auna kilomita 1,000 cikin milimita 0.16.

Kewaye ta hanyar ion

Idan aka auna shi kai tsaye, makamashin rabuwa yana da wuyar kamawa: inda ƙwayar ta fara wargajewa, alamar tana hawa a hankali ne kawai. Saboda haka akwai kewaye. A cire electron daga H₂ (makamashin ionization ɗinta, Eᵢ), a raba ion ɗin da ya samu H₂⁺ zuwa proton da atom ɗin hydrogen, sannan a mayar da electron ga proton ɗin, wanda ke sakin makamashin ionization na atom ɗin hydrogen. Hanyoyin biyu suna farawa da ƙarewa a wuri ɗaya, don haka makamashinsu yana daidaita:

D₀(H₂) + Eᵢ(H) = Eᵢ(H₂) + D₀(H₂⁺)

inda D₀ shi ne makamashin rabuwa. Atom ɗin hydrogen da ion ɗin H₂⁺ kowanne yana da electron ɗaya kawai, kuma an san makamashinsu cikin kHz 6 da 18. Saboda haka komai ya dogara ne kan makamashin ionization na H₂: duk wani daidaito da aka samu a can yana wucewa kai tsaye zuwa D₀(H₂).

Matakai uku, birane biyu

A Amsterdam, photon biyu na hasken ultraviolet mai zurfi, a nanometre 201.7, suna ɗaga ƙwayar daga matakinta na ƙasa zuwa wani mataki mai ƙarin kuzari da ake kira EF. An auna mitar wannan tsallen ta hanyar spectroscopy ta Ramsey-comb: nau’i-nau’in bugun haske daga frequency comb — laser da ke fitar da jerin bugun haske masu tazara daidai — suna tayar da ƙwayar sau biyu, kuma tayarwar biyu suna tsoma baki da juna (interfere). Sakamako: kHz 2,972,885,517,077, cikin kHz 31 — fiye da ninki ɗari na daidaiton da aka samu a baya.

A Zurich, laser na ultraviolet yana kai ƙwayar daga EF zuwa matakan Rydberg (Rydberg states), inda electron ɗaya ke kewayawa can nesa, da ƙyar a ɗaure. Igiyoyin millimetre, daga GHz 110 zuwa 430, sai su haɗa waɗannan matakai da matakan Rydberg biyu na ma’auni waɗanda makamashin ɗaurinsu (makamashin da har yanzu ke riƙe da electron), kusan 48 da 28 cm⁻¹, aka san su cikin kHz 21 da 30 daga aikin baya. Da aka tara su a cikin haɗe-haɗe takwas, matakan suna ba da makamashin ionization da daidaito ninki biyar fiye da ƙimar da ta gabata.

Matakan makamashi na H₂ a matakinta na ƙasa (lanƙwasa ta ƙasa) da matakinta na EF (ta tsakiya), da na ion ɗin H₂⁺ (ta sama), a dubban cm⁻¹. Kibiyoyi masu launin violet, shuɗi da lemu su ne nau’ikan matakai uku da aka auna: ultraviolet mai zurfi, ultraviolet da igiyoyin millimetre. Kibiya mai ruwan hoda ita ce makamashin ionization; zagayen da ke dama yana mayar da shi makamashin rabuwa. — Hoto na 1, Doran et al. (2026), arXiv:2610.40359.

Me ya sa sigar hydrogen da ba ta da yawa

H₂ tana zuwa a sigogi biyu, ya danganta da yadda juyin (spin) proton ɗinta biyu ke haɗuwa: jimilla 0 a para-hydrogen, 1 a ortho-hydrogen. Mafi kyawun aunawa na baya ya yi amfani da ortho-hydrogen, wanda matakinsa na EF ke rabuwa zuwa ƙananan matakai masu kusa da juna — tsarin hyperfine (hyperfine structure) — waɗanda ba a iya rarrabe su ba kuma suka jawo kuskuren tsari (systematic error) fiye da kHz 200. Para-hydrogen ba ta da shi, amma ita ce ’yar tsiraru: kashi 25% na ƙwayoyin a cikin kwararar sanyi, idan aka kwatanta da 75% ortho. Kuma matakan Rydberg ɗinta suna da hargitsi da yawa da ba za a iya miƙa su daidai zuwa iyakar ionization ba — saboda haka kewayen ta hanyar igiyoyin millimetre.

Mafi kaifi fiye da ka’idar

Daga nan ƙungiyar ta daidaita tare tazarorin makamashi 45 da haɗin gwiwar ya auna a cikin shekaru. Makamashin ionization ya fito a 124,417.491 1573 cm⁻¹; an san makamashin biyu cikin kusan kHz 175. Mafi kyawun lissafi suna da rashin tabbas na kHz 780. Su biyun sun yi daidai, amma duk sabbin ƙimomin biyu, para da ortho, suna kusa da gefen sama na sandar kuskuren ka’idar.

Makamashin rabuwar H₂ da aka auna a debe mafi kyawun lissafi, wanda aka saita a sifili, a MHz: para-hydrogen da ruwan hoda, ortho-hydrogen da shuɗi, tsofaffin auna-aune a ƙasa. Layukan ɗigo suna nuna rashin tabbas na lissafin. — Hoto na 12, Doran et al. (2026), arXiv:2610.40359.

Lissafin suna ƙara gyare-gyare daga quantum electrodynamics, ka’idar kwantum ta haske da caji, mataki-mataki a cikin ƙarfin (powers) tsayayyen lambar tsari mai kyau (fine-structure constant) α. Har zuwa yanzu, matakai har zuwa α⁶ sun isa su yi daidai da gwaji ga H₂; mafi kyawun lissafi sun riga sun haɗa da babban sashen α⁷, kuma marubutan suna kiran cikakken lissafin gyaran α⁷ ga makamashin rabuwarta “abin da ake matuƙar buƙata”. A helium, ɗayan tsarin electron biyu da aka lissafa da irin wannan daidaito, ka’ida da gwaji sun saɓa da kHz 450 kan makamashin ionization na wani mataki mai ƙarin kuzari mai tsawon rai — ninki tara na haɗaɗɗen rashin tabbas ɗinsu — saboda dalilan da har yanzu ba a sani ba. A kHz 175, da zarar an lissafa gyaran α⁷, H₂ za ta iya gwada ko ka’idar tsarin electron biyu tana rasa wani abu.

Rufi ga sabon ilimin kimiyyar lissafi

Sigogin biyu suna ba da ƙarin gwaji ɗaya. Gibin da ke tsakanin makamashin ionization ɗinsu, 60.253 146 cm⁻¹, ya kamata ya yi daidai da bambancin makamashin juyawa da ka’ida ke lissafawa: 60.253 137 6 cm⁻¹. Sun yi daidai. Saboda haka duk wata gudummawa daga bayan Standard Model — ilimin kimiyyar lissafi da ke wajen tabbatacciyar ka’idar ƙwayoyi — da za ta bambanta sigogin biyu ta hanyar juyin tsakiyar atom ɗinsu daban-daban dole ta kasance ƙasa da kHz 540 (a matakin standard deviation ɗaya), iyakar da ta fi ta baya matsewa ninki uku.

Tun daga nazarce-nazarcen farko na shekarun 1910, marubutan sun ƙirga kusan matakan girma (orders of magnitude) tara na ingantawa a cikin wannan lamba ɗaya. Yanzu gwajin ne a gaba; kwatanta ta gaba tana jiran cikakken lissafin α⁷.