Pion Production via Proton Synchrotron Radiation in Strong Magnetic Fields in Relativistic Quantum Approach

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1 Po Producto va Proto Sychrotro Radato Strog Magtc Flds Rlatvstc Quatum Approach Partcl Productos TV Ergy Rgo Collaborators Toshtaka Kajo Myog-K Chou Grad. J. MATHEWS Tomoyuk Maruyama BRS. Nho Uvrsty NaO, Japa Sosl Uv., Korad Uv. o Notr Dom, USA T.Maruyama t al., Phys. Rv. D91, (2015). Phys. Ltt.. B757, 125 ( 2016). 1

2 1 Itroducto 2 Sot Gamma Rpatr (SGR), Aomalous Xray pulsar (AXP) Magtar G surac G sd B.C.Duca & C.Thompso ApJL 92, L9 (1992) S.Mrghtt, A&AR 15, 225 (2008) Obsrvato o γ-ray Study od Magtar Structur

3 γ- ray Radato Proto s acclrat up to 1GV~1TV Sychtotro Radato Mso Prod (Str. > El.Mag.) All Thors ar Sm-Classcal V.L.Gzburg t al., UsFN 87, 65, ARA&A, 297 (65) G.F. Zharkov, Sov. J. Nucl. Phys., 1, 1714 (65) V. Brzsky, t al., Phys. Ltt. B 51, 261 (95) A. Tokushta ad T. Kajo, ApJ. 525, L117 (99). T.Kajo t al., ApJ 782, 70 (2014) May Assumpto ad Approxs. Mom.-Dst. caot b calculatd Quatum Calulatos. Exact Imormato

4 4 2 Formulato Rlatvstc Quatum Approach Magtc Fld : Drac Equato Aomalous Mag. Momt Tsor-Typ Ma-Fld [ ], γ γ σ σ σ z z z = = = Σ ( ) N p N z T M B s M s P E κ =

5 Dcay Wdth o p to p + p 0 5 N tracto PV couplg Q = (, Q, Q ) = q B 0 T z H ( x) : Hrmt Polyomal L m ( x) : Assocatd Lagurr Polyomlal

6 Rsults o 0 Producto Dcay Wdth E = 1GV, B = G χ χ = B p / mn = Prod. Domat B κ = 17.2 MV, p B = 2m N 28. MV max + s + 1 = 50 2 = 45 or or s s = 1 = + 1 s + 1 o AM max + = 47 2

7 Trasto Strgths btw two Ladau Lvls = 45 wth AMM wthout AMM -1 -> +1 small Ladau-lvl drc

8 Trasto Strgth 2

9 Vry Larg AMM Ects p p + 0 Ergy Momtum Cosrvato s ot satsd th r kmatcs Mag. Fld.+AMM Tsor Typ Ma-Fld s = -1 (rpulsv), s = +1 (attractv) Lvl Itrval o Trasto s = -1 s = +1 Smallr Itrvals Ehacs Trasto Strgth s = +1 s = -1 Largr Itrvals Rducs Trasto StrgthV Small Shts - mak Larg chag o Trasto Strgth

10 4 Ralstc Systm Po Producto Domat Ergy Rgo χ = B p / mn B = G Ladau Numbr : Actual calculatos ar almost mpossbl Problm : HO ovrlap tgral It s possbl to mak a Lortz Trasportato alog z-drcto Sm-Classcal Thory Scalg, Dp. Oly o χ

11 Cotrbuto at Fxd Fal Ladau Numbr cl AMM χ = M N RL B = M N No AMM Scalg Law Fucto o χ, ( )/ Prdcto Rsults 10 4 Rsults ー 1 (B ~ G) Hug Ects o AMM rma v B ~ G

12 Small χ Largr Scalg Total Dcay Wdth Scalg Rlato (All Sm-Classal Thorys Show) Varabls B,, 2 Varabls χ = BE /m N, ( )/ Pak posto ( ) / 0.

13 Adabatc Lmt ( ) 1 - Classcal: Sm ,,, << + = + = N N m m m m m m Rlatv Momtum btw Fal Proto ad Po s Zro, Sam Vlocty

14 Agular Dstrbuto at p z = 0 d I dq = d Γ dq p Δq z dp. o I Icdt Ergy Adabatc Lmt Norrow Agular Dtsr. Γ(, ; P z δ = 0) ( Q ) Lortz Tras. alog z-drcto z

15 Agular Dstrbuto o Po Lumocty d I dq = d Γ dq p χ = 0.07 wh >> 1, q T // p // p Sam Polar Agl Wdth s vry small m qz = m + m q T N m = m + m N p z B 2 adabatc lmt

16 Proto Dcay Wdth >> 1 p z = 0 Lortz Trasormato p z 0 Scalg Rsults wth, ~ 10 4 Rsults wth Sm-Classcal Approxmato assum - << has mass Ths Assumpyo s wrog 16 ( ) ( ) ), ( 1 ) 0, ( 0 z p z p q q dq s p d δ δ Γ = = Γ ( ) ), ( 1 ), ( 0 Γ = Γ z z p T z p p q q dq s p d δ δ N m m m + >

17 Total Dcay Wdth Sm-Classcal A.Tokushta ad T. Kajo, ApJ. 525, L117 (99).

18 Lumocty-Dstrbuto o Emttd Photos p p γ Avrag ovr Ital Proto Agl Dstrbuto s Sphrcal

19 Total Dcay Wdth Γ(, χ; Pz = 0) Sm-Classcal A.Tokushta ad T. Kajo, ApJ. 525, L117 (99). Γ(, χ; P = z dp.o 0)

20 5 Summary 20 l 0 msso rom Proto Trasto btw two Ladau Lvls, ~ 10 5 B ~ G AMM ct Dccay wdths bcom tms largr l Scalg Law, prdctd by th Sm-Classcal thory Varabls B,, 2 Varabls χ = BE /m N, ( )/ B ~ G B ~ G (Magtar) Rsults wth, ~ 10 4 Rsults wth l Agular Dst θ θ θ dγ p (, pz ) α δ qz pz dq l Po Ergs ar dstrbutd Broad Rgo > m N m + m Sm-Classcal Approx. - <<

21 Th Rsults com rom HO ovrlap Itgral It s a ucto o Q T ad vry rapdly chag wh, >> 1 Grally Othr Partcl Productos Magtc Structur sd Magtars

22 HO Ovrlap Itgral

23 I PS-couplg Γ(, ) dos ot satsy Scalg Rlato