1. An alternative description of electron screening Matej Lipoglavšek Jožef Stefan Institute, Ljubljana, Slovenia Instit ut "Jož ef Stefa n" Russbach, March 2016

2. Nuclear Reactions at Low Energies 7 Li(p,α) 4 He Cross Section C. Rolfs and R.W.Kavanagh, Nucl. Phys. A455 (1986) 179. Due to Coulomb repulsion the cross section σ for charged particle induced nuclear reactions drops rapidly with decreasing beam energy. where η=Z 1 Z 2 e 2 /4πε 0 ħ(2E/μ) 1/2 is the Sommerfeld parameter. Exponential (Gamow) factor approximates barrier penetration probability.

3. Electron Screening E + U e = E eff U e = Z 1 Z 2 e 2 /4   R a Potential V(r ) RnRn EcEc 0 RaRa r electron cloud Bohr radius nuclear radius Cross section increases at low energies when the interacting nuclei are not bare. Enhancement factor where U e is the screeening potential. H. J. Assenbaum, K. Langanke and C. Rolfs, Z. Phys. A 327 (1987) 461. 305 citations (Web of Science, March 2016).

4. Previous Results 1 for d(d,p)t reaction from F. Raiola et al., Eur. Phys. J. A19 (2004) 283.

5. Previous Results 2 J. Kasagi, Prog. Theo. Phys. Suppl. 154 (2004) 365. for the d(d,p)t reaction U e =310±30 eV @ 7% H/Pd => concentration dependence

6. Previous Results 3 for d(d,p)t reaction from K. Czerski et al., J. Phys. G 35 (2008) 014012. for zirconium metal U e =319±3 eV

7. Previous Results 4 PdLi 1% : U e = 3.7 ± 0.3 keV Li metal:U e = 1.18 ± 0.06 keV Li 2 WO 4 : U e = 237 +133 eV S(E)=0.055+0.21E-0.31E 2 [MeV b] J. Cruz et al., Phys. Lett. B 624 (2005) 181; J. Phys. G 35 (2008) 014004. -77

8. Previous Results 5 L. Lamia et al., Astron. Astrophys. 541, A158 (2012). 7 Li(p,α) 4 He reaction U e = 425 ± 60 eV in Li metal Adiabatic limit: U e = 240 eV Trojan horse method → bare S factor S(E)=0.053+0.213E-0.336E 2 [MeV b]

9. Measurements @ JSI target beam X-ray detector Ge detector neutron detector beam current Pb absorber

10. Measurements @ JSI 2 MV Tandem van de Graaf accelerator

11. Electron screening in implanted metals Results: TargetU e [keV]Stoichiometry Ni4.1 ± 1.00.041±0.003 Zn2.4 ± 1.00.68±0.05 Pd2.3 ± 0.50.296±0.007 Pt2.8 ± 1.30.24±0.02 Inverse kinematics: 1 H( 7 Li,α) 4 He

12. Comparison to previous results Target Reaction U e [keV] 7 Li+p p+ 7 Li d+d Ni4.1 ± 1.00.38 ± 0.04 Zn2.4 ± 1.00.48 ± 0.05 Pd2.3 ± 0.53.7 ± 0.30.80 ± 0.09 Pt2.8 ± 1.30.67 ± 0.05 Target Stoichiometry 7 Li+p d+d Ni0.040.13 Zn0.680.13 Pd0.2960.03 Pt0.240.06 d+d F. Raiola et al., Eur. Phys. J. A19 (2004) 283. p+ 7 Li J. Cruz et al., Phys. Lett. B 624 (2005) 181. 7 Li+p J. Vesic et al., Eur. Phys. J. A50 (2014) 153.

13. Thick targets TargetU e [keV]Stoichiometry Graphite10.3 ± 0.40.059±0.003 Pd3.6 ± 0.70.21±0.01 TiH3.9 ± 0.41.03±0.04 W5.9 ± 0.90.042±0.003 Adiabatic limit: U e = 0.24 keV 1 H( 7 Li,α) 4 He

14. Thin targets and resonances C. Iliadis, Nuclear Physics of Stars, Wiley-VCH, Weinheim, (2007) p. 341. Breit Wigner resonance cross section Infinitely thick target yield of narrow resonance Integral over the resonance

15. The 19 F(p,αγ) 16 O reaction K. Spyrou et al., Z. Phys. A 357 (1997) 283; Eur. Phys. J. A 7 (2000) 79.

16. Fluorine results A. Cvetinović, PhD Thesis, University of Ljubljana (2015).

17. The 11 B(p,αα) 4 He reaction H. W. Becker et al., Z. Phys., A 327, 341 (1987).

18. Results Target Reaction U e [keV] 7 Li+p 11 B+p 19 F+p adiabatic0.240.682.19 Graphite10.3 ± 0.432 ± 4115 ± 8 Pd3.6 ± 0.78.0 ± 1.963 ± 6 TiH3.9 ± 0.46.7 ± 1.862 ± 6 W5.9 ± 0.9 -75 ± 15 Graphite/ adiabatic 42.9 ± 1.747.1 ± 5.952.5 ± 3.6 A. Cvetinović, Phys. Rev. C 92 (2015) 065801. Answer to the Ultimate Question of Life, the Universe, and Everything D. Adams, The Hitchhiker's Guide to the Galaxy, Harmony books, New York (1979).

19. Crystal symmetry fcc (Pd) small screening large screening Hexagonal Graphite

20. Enhancement factor C – fraction of protons on dislocated sites TargetC Enhancement factor 11 B exp. 11 B calc. 19 F exp. 19 F calc. TiH0.28±0.021.3 ± 0.11.6 ± 0.13.6 ± 0.43.1 ± 0.4 Pd0.28±0.041.4 ± 0.11.6 ± 0.13.7 ± 0.43.1 ± 0.4 W0.51±0.05 -2.1 ± 0.24.5 ± 1.54.9 ± 0.6

21. Hydrogen molecular ion

23. Enhancement factor K – fraction of electrons remaining between the reactants until the reaction τ – lifetime of the capturing state; TargetK Enhancement factor 11 B exp. 11 B calc. 19 F exp. 19 F calc. graphite(1.0±0.1)10 -2 3.1 ± 0.43.1 ± 0.38.7 ± 1.09.1 ± 0.9 We are now planning experiments to show that electrons are really involved

24. Conclusions We are hopefully getting closer to understanding some aspects of electron screening. The largest electron screening was so far measured in tungsten (metal) and graphite (not a metal). The size of electron screening potential is almost two orders of magnitude above theoretical predictions. The size of the effect is not proportional to Z. Different screening potentials are due to different proportions of target nuclei on active and inactive sites. For stellar plasma we really need to understand what happens in the laboratory experiments. Thanks to: Jelena Vesić, Aleksandra Cvetinović,