Relativistic Electron-Positron Plasma Screening In Astrophysical Environments

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1 in Weak and the In Astrophysical Environments Enhancements to Weak and Intermediate 1,, A. Baha Balantekin, T. Kajino,4 1 Western Michigan University, National Astronomical Observatory of Japan, University of Wisconsin 4 University of Tokyo 15 September 16

2 in Weak and the 1 in Weak Outline and 4 the 5

3 Review: in Weak and the V (r) = Z 1Z e + r Ũ(r) Γ 1 σ(e U )de E 1/ e E/kT Assume constant electron background. Salpeter approximation assumes constant energy shift. [Clayton (196)]

4 Review: in Weak and the V (r) = Z 1Z e + Ũ(r) r Γ 1 E 1/ e E/kT σ(e U )de Assume constant electron background. Salpeter approximation assumes constant energy shift. Approximate turning-point (fm) vs particle energy in screened and unscreened case.(c+c) Energy shift changes classical turning point in a Coulomb potential.

5 in Weak and the Weak Salpeter Approximation Shift in energy changes classical turning point. E C kt V (r) scr V (r)e r/λ D Γ scr e U /kt Γ ( ) 1/ T λ D = 4πe n i (Z i + Z i )Y i Debye-Huckel : Poisson Equation to first order. NOTE: Corrections to the ion-sphere model may result in potential shifts a few percent. σv scr = f σv = e U /T σv [ Z1 Z e ] f = exp λ D T Review: Weak Regimes Strong Ion-Sphere E C kt [ U (Z 1 + Z ) 5/ Z 5/ 1 Z 5/ ] ρ T M 1 Ions approach a lattice-like configuration. log(t) [K] Weak Strong log(ρ) [g/cm ]

6 in Weak and the π λ D of reaction rates using e e + plasmas. Schwinger-Dyson equation for photon propagator. = e [ ] dpp 1 µ e (E µ)/t e (E+µ)/T + 1 potential at close range VC scr (r λ D ) VC bare Z 1Z e λ D = V bare C E High Temperature Limit E (T m e ) = Z 1Z e ] 1/ [µ + π π T σ(e) σ(e + E )

7 in Weak and the (kev) E e + e plasma T.5-1 MeV Electron number density modified by pair production T (MeV) T (MeV) Energy shift could be important for low-lying resonances. Z 1 =, Z = 4 (kev) E (fm) λ D <σv> scr /<σv> unsc Z µ = MeV µ =.1 MeV µ =. MeV µ =. MeV µ =.4 MeV T (MeV) T=1 MeV, µ= Z [Famiano, Balantekin, & Kajino (16)] 5

8 in Weak and the λ D (fm) 4 1 log(ρ)=6 1 1 log(ρ)=7 log(ρ)= log(ρ)=9 log(ρ)= T 9 classical and relativistic Debye lengths. Assume C+C plasma. Debye Length: ) 1/ ( T λ D = 4πe nξ ξ = ( ) i Z i + Z i Yi Effects Example: Neutral 1 C log(t) [K] Weak Strong log(ρ) [g/cm ] Approximate Regimes Strong screening: ions locked into a lattice. Wigner-Seitz spheres. Ion-sphere approximation.

9 in Weak and the λ D (fm) 4 1 log(ρ)=6 1 1 log(ρ)=7 log(ρ)= log(ρ)=9 log(ρ)= T 9 classical and relativistic Debye lengths. Assume C+C plasma. Debye Length: ) 1/ ( T λ D = 4πe nξ ξ = ( ) i Z i + Z i Yi Effects Example: Neutral 1 C log(t) [K] r-process Weak SNIa Strong log(ρ) [g/cm ] Where might relativistic screening be appropriate? How the intermediate screening region is handled can be quite important.

10 in Weak and the λ D (fm) 4 1 log(ρ)=6 1 1 log(ρ)=7 log(ρ)= log(ρ)=9 log(ρ)= T 9 classical and relativistic Debye lengths. Assume C+C plasma. Debye Length: ) 1/ ( T λ D = 4πe nξ ξ = ( ) i Z i + Z i Yi Effects Example: Neutral 1 C log(t) [K] r-process 15 M Weak core SNIa Strong WD Ignition< log(ρ) [g/cm ] For WD ignition we will need quantum plasma physics.

11 in Weak and the (fm) λ D 4 1 log(ρ)=6 1 1 log(ρ)=7 log(ρ)= log(ρ)=9 log(ρ)= T 9 classical and relativistic Debye lengths. Assume C+C plasma. Debye Length: ) 1/ ( T λ D = 4πe nξ ξ = ( ) i Z i + Z i Yi Effects Example: Neutral 1 C log(t) [K] r-process 15 M Weak core SNIa Strong WD Ignition< log(ρ) [g/cm ] For WD ignition we will need quantum plasma physics.

12 in Weak and the Note the 7 Be 1 C branch. Could a resonance here be significant? [Broggini et al. (1), Hammache et al. (1)] for 1 - X/X p d t n He 4 He 6 Li 7 Li Be Time (s) X X X scr X bare X bare Very small effects Low Z More massive nuclei not produced until T.5 MeV

13 Resonances in 7 Be+ He in Weak and the ) o E σ(e+e -E/T exp 5 1 E R =.75 MeV E R =.5 MeV E R =.1 MeV =1. MeV E R E R =-.5 MeV E R =.5 MeV E (MeV) 6 1 T=1 MeV Resonances 5 kev ruled out [Hammache et al. (1)]. TRRs including resonances are small in this regime. <σv>] [N 1 A Shifts in resonances indicated above. Possible effect for sub-threshold resonances. log E R = MeV E R =. MeV E R =.4 MeV E R =.6 MeV E R =. MeV E R = 1. MeV Non-Resonant TRR T (MeV)

14 in Weak and the Y e PRELIMINARY Astrophysical Sites Where Could Be Important Ye:t Unscreened/Default Effects t (s) r-process screening effects x-ray burst frequency changes x-ray burst light curve changes More work to follow L/L L/L exp(log_l):t*.15e7 Unscreened time (s) 6 4 Unscreened time (s) x-ray bursts light curves [PRELIMINARY].

15 in Weak and the Explored relativistic plasma effects in. Continuing to work on dynamics in: r-process WD x-ray bursts Massive stellar cores One really has to be careful in the intermediate screening region. Work supported by NSF PHY-1446 and PHY-164 and NAOJ Visiting Professorship

16 in Weak and Clayton, D.D., Principles of Stellar Evolution and Nucleosynthesis, The University of Chicago Press 196 Broggini et al., JCAP 6, (1) Famiano, M.A., Balantekin, B., & Kajino, T., Phys. Rev. C 9, 454 (16) Hammache, F. et al., Phys. Rev. D, 6 (1) the