(ELI-NP at Magurele - Pulse and Impulse of ELI) Extensive Light - PowerPoint PPT Presentation

(ELI-NP at Magurele - “Pulse and Impulse of ELI”) Extensive Light Investigations-ELI-apoma Laboratory 1) " Polaritonic pulse and coherent X- and gamma rays from Compton (Thomson) backscattering" (MA&MGan), J. Appl. Phys. 109 013307 (2011) (1-6) 2)”Dynamics of electron–positron pairs in a vacuum polarized by an external radiation field” (MA), Journal of Modern Optics, 58 611 (2011) 3)” Classical interaction of the electromagnetic radiation with two-level polarizable matter” (MA), Optik 123 193 (2012) 4)” Coherent polarization driven by external electromagnetic fields” (MA&MGan), Physics Letters A374 4848 (2010) 1

5)”Coupling of (ultra-) relativistic atomic nuclei with pho- tons” (MA&MGan), AIP Advances 3 112133 (2013) 6)”Propagation of electromagnetic pulses through the surface of dispersive bodies” (MA), Roum J. Phys. 58 1298 (2013) 7)” Giant dipole oscillations and ionization of heavy atoms by intense electromagnetic pulses” (MA), Roum. Reps. Phys. 67 837 (2015) 8)” Parametric resonance ” in molecular rotation spectra” (MA&LC), Chem. Phys. 472 262 (2016) 2

9)” Motion of an electric charge in laser fields ” (CM&MA), Roum. J. Phys. 62 117 (2017) 10)” Scattering of non-relativistic charges by electromagnetic radiation” (MA) Z. Naturforsch. A72 1173 (2017) 11)” Fast atom ionization in strong electromagnetic radiation” (MA) - 2017 12)”Electromagnetic-radiation effect on alpha decay ” (MA) - 2017 3

INSTITUTE of PHYSICS and NUCLEAR ENGINEERING Magurele-Bucharest Electromagnetic-Radiation Effect on alpha Decay M Apostol 2018 4

General In the previous Sem (Sem I) it was shown: -Bound charges in electric field (els in atoms, ions, molecules, at clstrs; ions in mols, at clstrs; protons, alpha particle in at nuclei) -Fire upon them an el field (static or oscill): - τ = a/c , a -dim bnd state; els: τ = 10 − 19 s , prtns: τ = 10 − 24 s -Very short times, ∆ E = ℏ /τ , els: 1 keV , prts: 100 MeV -Very high energy, no en levels! - indep of field strength! 5

Subsequently, Two courses : 1) If the field is low, it is accommodated, en levels, perturbation theory, adiabatic interaction , ionization by tunneling (low rate) 2) If the field is strong, different, fast ejection 3) How low? strong? 6

Static Electric Fields √ ∆ t = a/ ( qE ∆ t/m ) , ∆ t = ma/qE ≫ ℏ / ∆ E , ∆ E -level separation (∆ E ) 2 qEa ≪ ( ℏ 2 /ma 2 ) (cond for adiabatic interaction) For electrons: E ≪ 10 4 esu ( ≃ 10 6 V/cm ) ( ∆ t ≫ 10 − 15 s , qEa ≪ 0 . 1 eV )-very high For protons: extremely high For any static el field it is safe (and necessary) to work with pert theory, st states 7

Low Static Electric Fields -Class subject: Oppenheimer, Lanczos (1929), hydrogen atom -Polarization, Stark effect, Epstein, Schwarzschilld (1930) -El field brings a pot barrier, tunneling E 3 / 2 − w/t a ≃ 1 qEa ( ℏ 2 /ma 2)1 / 2 e t a E -binding energy ( t a -attempt time); note that exp is very small, due to the cond of low field above -Result valid for any charge in neutral bound-state 8

Important obs -Single-particle states in a mean field -Above considerations for high-energy charges -For deep-lying charges ∆ E ≃ ( ℏ 2 /ma 2 ) n , a → a/n , qEa ≪ ℏ 2 /ma 2 ! -Appreciable weakening of the condition! For deep states higher fields are “low”! -Separation between ’high” and “deep” state: atoms Z 2 / 3 , nuclei- closed shells 9

Oscillating Electric Fields -Laser radiation A = A 0 cos( ωt − kr ) ≃ A = A 0 cos ωt (finite motion, non-rel) ( E = − (1 /c ) ∂A/∂t ) - qE 0 /mω 2 ≪ a qE 0 ξ = mω 2 a ≪ 1 -note: qE 0 a ≪ ( ℏ ω ) 2 / ( ℏ 2 /ma 2 ) ! -For els: E 0 ≪ 10 4 esu (laser int I ≪ 10 11 w/cm 2 ), for protons: E 0 ≪ 10 2 esu ( I ≪ 10 7 w/cm 2 ) (opt laser ω = 10 15 s − 1 ); rather restrictive, compare with high-power lasers -(At the same time ξ ≪ 1 implies non-rel motion: qA 0 ≪ mc 2 (even lower, fine str)) 10

Low Oscillating Electric Fields -Class problem: Keldysh, Perelomov, Krainov (1960-1980) -Ionization rate (imaginary-time tunneling) ℏ ω ln 2 ω √ 2 m E b − E b w/t a ≃ 1 | q | E 0 e t a -Note that ξ ≪ 1 (low field cond) ensures w ≪ 1 (as required) (improper ext ∼ e − const/E 0 ) 11

High Oscillating Electric Fields It was shown in the previous Sem (Sem II): -Els: 10 4 < E 0 < 10 8 esu ( 10 11 < I < 10 18 w/cm 2 ) -Protons: 10 2 < E 0 < 10 11 esu ( 10 7 < I < 10 23 w/cm 2 ) -No stationary states, no en levels, no perturbation,... 12

-Solution: time evolution of the wavefunction -Fast ionization rate √ √ 1 τ ≃ ξ/πω = | q | E 0 /πma ≫ ω ( N = N 0 e − t/τ ) -Single-particle states, mean field (dont forget!); deep states! 13

Nucleus in electric field: -Protons: 10 2 < E 0 < 10 11 esu ( 10 7 < I < 10 24 w/cm 2 -Use fast ionization rate √ √ 1 τ ≃ ξ/πω = | q | E 0 /πma ≫ ω -However: electronic shell appreciably screes off the field E → ( ω 2 / Ω 2 ) E - Ω ≃ 10 16 Z ( s − 1 ) ( 30 Z ( eV ) ); reduction factor in E , 10 − 3 /Z 2 -ex: 10 11 esu ( I = 10 24 w/cm 2 ) → 10 4 esu ( I = 10 10 w/cm 2 ) 14

Nucleus in low oscillating field -Spontaneous proton (alpha) decay, V ( r ) pot barrier (Coulomb), E = E 0 sin ωt -Standard non-rel hamiltonian ( ) 2 1 p − q H s = + V ( r ) c A 2 m -Henneberger (Pauli, Fierz, Kramers) can transf, ψ = e iS ϕ , 1 2 mp 2 + � V ( r ) = V ( r − q E /mω 2 ) � � H = V ( r ) , iqA 2 q 0 S = ℏ mω 2 E 0 p sin ωt − 8 ℏ mc 2 ω (2 ωt + sin 2 ωt ) 15

Technical 1 V ( r ) ≃ Zq 2 /r ; no field, tunneling from r 1 = a to r 2 = Zq 2 / E r , E r radial energy of the charge; parameter ξ = qE 0 /mω 2 a ≪ 1 , field present � � a − q E /mω 2 � � � r 1 = � � and � r 2 = r 2 , where a = a r /r . Expand � r 1 in powers of ξ ( ) 1 − ξ sin ωt · cos θ + 1 2 ξ 2 sin 2 ωt · sin 2 θ r 1 = a + ... , � θ the angle r with E 0 16

Technical 2 Relevant factors in wavefunction ´ � r 2 iqE ( t ) ℏ mω 2 cos θ · ( p 2 − p 1 )+ i dr · p r ( r ) � ℏ r 1 e √ √ [ ] 2 m [ E − V ( r )] , p 1 , 2 = p r ( � ; p r ( r ) = r 1 , 2 ) = 2 m E − V ( � r 1 , 2 ) ( p 2 = 0 ) tunneling probability (transmission coefficient) w = e − γ , γ = − Aξ sin ωt · cos θ + B , ´ � A = 2 a | p 1 | r 2 qE 0 mω 2 a , B = 2 , ξ = r 1 dr | p r ( r ) | ℏ ℏ � √ √ | p 1 | = 2 m [ V ( � r 1 ) − E ] , | p r ( r ) | = 2 m [ V ( r ) − E ] 17

Technical 3 Expand A in powers of ξ , take the time average √ γ = − Zq 2 2 m Zq 2 /a − E ξ 2 cos 2 θ + B... 2 ℏ √ √ B = γ 0 − aξ 2 2 m ( Zq 2 /a − E ) + aξ 2 Zq 2 /a −E (3 Zq 2 / 2 a − E ) cos 2 θ 2 m 2 ℏ 2 ℏ γ 0 no field; finally, [ ] √ γ = γ 0 − aξ 2 1 − Zq 2 / 2 a − E Zq 2 /a − E cos 2 θ 2 m ( Zq 2 /a − E ) 2 ℏ 18

Technical 4 Total disintegration probability { [ ]} √ 1 + aξ 2 1 − Zq 2 / 2 a − E 2 m ( Zq 2 /a − E ) w 0 w tot ≃ tot 3( Zq 2 /a − E ) 2 ℏ (integrating over angle θ ), w 0 tot = e − γ 0 . Disintegration rate (1 /τ ) w tot , τ attempt time Exponent γ 0 , ( ) √ √ √ √ γ 0 = Zq 2 E a/Zq 2 − E a/Zq 2 1 − E a/Zq 2 2 m/ E arccos ℏ ( Zq 2 /a ≫ E ) ( ) √ √ γ 0 ≃ πZq 2 1 + 5 aξ 2 2 mZq 2 /a w 0 2 m/ E , w tot ≃ tot . 2 ℏ 12 ℏ 19

Technical 5 √ Geiger-Nuttall ln( w 0 tot /τ ) = − a 0 Z/ E + b 0 , a 0 and b 0 constants The only effect of the radiation is to modify the constant b 0 to √ b = b 0 + (5 aξ 2 / 12 ℏ ) 2 mZq 2 /a 20

Conclusion -Low field, charge accommodates in the field, adiabatically-introduced interaction; -Besides oscillating and emitting higher harmonics, charge may tunnel out from the bound state -Proton, alpha tunneling through the Coul barrier slightly en- hanced by radiation, -Second-order corrections, slight anisotropy 21

The Case of a Low Static Electric Field - Low static field is taken up in the energy levels (by pert calcs); -It is not available for the Henn tr anymore! -We do tunneling through ( ) V ( r ) = Zq 2 − q Er = Zq 2 1 − Er 2 Zq cos θ r r -Small parameter α = Er 2 2 /Zq = Eqr 2 / E ≪ 1 ( Z = 100 , E = 1 MeV , α = 10 − 4 E ≪ 1 ) -Finally, ( ) 1 + α 2 γ 2 w 0 0 w tot ≃ tot 108 22