Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields

Transcription

1 Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields Victor G Bezchastnov victor@tcpciuni-heidelbergde Theoretische Chemie Physikalisch-Chemisches Institut Universität Heidelberg INF 229, D Heidelberg, Germany Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p1/21

2 Ion Cyclotron Frequency Ω = QB/M Acomplexioninastationaryanduniformmagneticfieldcanexhibita varietyofcyclotronfrequenciesasaresultofthecouplingofcmtothe internal structure The effects of the coupling are important when Ω is not negligible compared to the binding energy ε for the infinitely heavy ion Negative( magnetically induced) ions: laboratory field strengths VG Bezchastnov, P Schmelcher and LS Cederbaum, Phys Rev A, 2007, 75, Positiveions(He + ):astrophysicallystrongfields GG Pavlov and VG Bezchastnov, Ap J Lett, 2005, 635, L61 Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p2/21

3 Landau Levels, Cyclotron Transition Energies and Oscillator Strengths Landau levels E N = E N=0 + N Ω N = 0, 1, 2, Selection rules N N ± 1 N x ± iy N ± 1 Absorption N N + 1: Transitionenergies Ω N = E N+1 E N = Ω Oscillatorstrengths F N = (Q 2 /M)(2N + 1) Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p3/21

4 Atomic Ions: Quantum States with CM Motion Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p4/21

5 Atomic Ions: Hamiltonian and Integrals of Motion H = 1 2M ( P cm Q 2 B R cm) 2 + H rel + W H rel = 1 2M 0 W = α M α 1 = 1 Q M [ (p i + 1 ) ] 2 2 α 1 B r i i [ B ( ) 2 1 M ( P cm Q )] 2 B R cm i i r i,, α 2 = 1 Q M 2, α = 1 + Q M ( p i 1 2 α 2 B r i ) 2 + V, K = P cm + Q 2 B R cm K 2 = B(2N 0 + 1) N 0 = 0, 1, 2, L = P cm R cm + J = N 0 + L i p i r i L z = (Q/ Q )L L = 0, ±1, ±2, Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p5/21

6 Perturbation Analysis Incorporating the integrals of motion: E = E sj s = 0, 1,, J = σs, σs + 1,, σ = Q/ Q NocouplingtoCM(W = 0): Energies E sj = ε s + Ω(J σs), Ω = B/M Ioncyclotronabsorption sj s, J + 1 Transitionenergies Ω J = Ω Oscillatorstrengths F J = (Q 2 /M)(2J + s + 1) Including coupling: Energies E sj = E s, s + Ω eff (J σs), Ω eff = B/M eff E s, s > ε s, Ω eff < Ω Ioncyclotronabsorption sj s, J + 1 Transitionenergies ω J = (M/M eff ) Ω Oscillatorstrengths f J = (M/M eff ) 3 F J Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p6/21

7 Field-Induced Formation of Bound Anions BoundstatesoftheHamiltonian H rel formtheinfinitemanifold JE Avron, IW Herbst and B Simon, Commun Math Phys, 1981, 79, 529 Electron affinities binding energies of neutrals Exchange effects are not important z B r L extra electron guiding center A neutral atom is a static attractive center r c V (r) = α/(2r 4 ) The excess electron is confined in the plane transverse to the magnetic field l z isanintegralofmotion Bindingofanextraelectroncanbetreatedas a1dproblem,forthemotionoftheguiding centerr c alongthemagneticfield neutral atom Theelectroncanbeattachedwithdifferent l z = infinitemanifoldof bound states Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p7/21

8 Magnetically Induced Anions: Static and Beyond Bindingenergiesfor H rel :analyticalestimates l z = s, s = 0, 1, 2, I s = V s(z)dz < 0 = ε s = µi 2 s/2 Asaresult: ε 0 = 031 α 2 B 2, s = 0, ε s = α 2 B 3 δ 2 s, s = 1, 2,, δ 1 = 1, δ s = [1 (15/s)]δ s 1, s = 2, 3, ImpactofthecouplingtoCM(M Xe = , α Xe = 2729) ( ) ε 0 α 2 Ω = 237 M Xe 103 α Xe M ( ) ε 1 α 2 Ω = 039 M Xe α Xe M ( B 100 T B 100 T, ) 2 Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p8/21

9 Moving Anions: Quantum States Including coupling: E sj = E s, s + Ω eff (J + s) Ω eff = B/M eff s = 1, B = 100T atom ε s,mhz Ω,MHz Xe Mg Hg s = 0, B = 10T atom ε s,mhz Ω,MHz Ar Be Xe s=1, B=100 T: s=0,b=10t: Mg Hg Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p9/21

10 Moving Anions: Cyclotron Transitions Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p10/21

11 Cs at B = 100T Ω = 115MHz ε 1 = 9960MHz ε 2 = 623MHz ε 3 = 156MHz Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p11/21

12 He + (Z = 2)at B = T(γ = 2000) Strong field regime: γ = B/ T 1 Tightly-bound states: ε 0 Z 2 Ry [ ln(γ/z 2 ) ] 2 Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p12/21

13 He + (Z = 2)at B = G(γ = 2000) Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p13/21

14 He + (Z = 2)at B = G(γ = 2000) Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p14/21

15 He + (Z = 2)at B = G(γ = 2000) Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p15/21

16 He + (Z = 2)at B = G(γ = 2000) Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p16/21

17 He + (Z = 2)at B = G(γ = 2000) Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p17/21

18 He + (Z = 2)at B = G(γ = 10000) Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p18/21

19 He + atmagnetar-scalefields X-ray-dim isolated neutron stars sjν-states ν = 0 tightly-bound ν = 1, 2, H-like Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p19/21

20 He + atmagnetar-scalefields Broadabsorptionfeaturesat03-05keV Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p20/21

21 Conclusions Bound-ion cyclotron transitions are an interesting area of research For negative magnetically induced ions they directly relate to detecting that these ions do exist Forpositive(egHe + )ionsatsuperstrongmagneticfieldstheycanbe relevant for interpretation of the radiation from isolated neutron stars (eg magnetars) Magnetic Binding and Cyclotron Transitions of the Ions: Applications to Laboratory and Astrophysically Strong Magnetic Fields p21/21