Vyrozhdennyi gaz

VYROZhDENNY' GAZ - gaz, v k-rom kvantovomehanich. vliyanie chastic drug na druga sushestvennym obrazom skazyvaetsya na ego fiz. sv-vah (davlenii, teploemkosti i t. d.). Vzaimnoe vliyanie obuslovleno tozhdestvennost'yu chastic. Zapolnenie chasticami kvantovyh sostoyanii zavisit ot nalichiya v dannyh sostoyaniyah drugih chastic togo zhe roda.

Effektami tozhdestvennosti chastic mozhno prenebrech', poka sr. rasstoyanie mezhdu nimi r ~ N^-1/3 namnogo prevyshaet dlinu volny de Broilya l = h/mv (m - massa chasticy, v - ee skorost', h - Planka postoyannaya, N - koncentraciya chastic). Pri gaz stanovitsya sil'no vyrozhdennym. Uslovie vyrozhdeniya vypolnyaetsya pri dostatochno nizkih temp-rah T (dlya ideal'nogo gaza ) i vysokoi koncentracii chastic.

Harakter vliyaniya tozhdestvennyh chastic drug na druga razlichen dlya chastic s celym (boze-gaz) i polucelym (fermi-gaz) spinom, poetomu razlichny i sv-va boze- i fermi-gazov. Dlya astrofiziki naibol'shii interes predstavlyayut vyrozhdennye fermi-gazy - elektronnyi V. g. i V. g. neitronov. Fermiony (chasticy s polucelym spinom) podchinyayutsya principu Pauli, soglasno k-romu v kazhdom kvantovom sostoyanii mozhet nahodit'sya odnovremenno ne bolee odnoi chasticy dannogo sorta. Chislo vozmozhnyh kvantovyh sostoyanii dlya fermi-chastic s abs. velichinoi impul'sa (r), lezhashei v intervale mezhdu r i r + dp, v ob'eme V ravno (2s + 1)4pp²dpV/h³, gde s - spin chasticy. U elektronov, protonov, neitronov spin s = ¹/₂, t. e. mnozhitel' (2s + 1), uchityvayushii orientaciyu spina chastic, raven 2. Pri ochen' nizkih temperaturah chasticy zapolnyayut vse sostoyaniya, vplot' do sostoyaniya s granichnym impul'som, zavisyashim ot ih koncentracii, p_F = (3/8p)^1/3hN^1/3. V sluchae nerelyativistskogo svobodnogo gaza sootvetstvuyushaya granichnaya energiya (energiya Fermi)

Temp-ra T~e_F/k 10^-11(m_e/m)N^2/3(K) naz. temperaturoi vyrozhdeniya (m_e - massa elektrona, k - Bol'cmana postoyannaya). Pri ochen' vysokih plotnostyah (r >10⁶ g/sm³) elektronnyi V. g. stanovitsya ul'trarelyativistskim: e_F = p_Fc >> m_ec².

Davlenie nerelyativistskogo vyrozhdennogo elektronnogo gaza r_e = 2,3^.10^-27N^5/3 din/sm², a ul'trarelyativistskogo r_e = 2,37^.10^-17N^4/3 din/sm². Imenno gradient davleniya V. g. elektronov uravnoveshivaet silu tyazhesti v belyh karlikah. V neitronnyh zvezdah etu rol' igraet gradient davleniya V. g. neitronov. Vyrozhdennyi nerelyativistskii gaz neitronov pri toi zhe koncentracii imeet davlenie v m_n/m_c 1839 raz men'she, chem V. g. elektronov.

Lit.: Landau L. D., Lifshic E. M., Statisticheskaya fizika, 3 izd., ch. 1, M., 1976.

(R.A. Syunyaev)