Ion-Channeling in Direct DM Detectors Graciela Gelmini - UCLA Based on work done with Nassim Bozorgnia and Paolo Gondolo GGI Florence, May 19, 2010

Graciela Gelmini-UCLA Channeling and Blocking Effects in Crystals refer to the orientation dependence of ion penetration in crystals. Channeling: Ions incident upon the crystal along symmetry axis and planes suffer a series of small-angle scattering that maintain them in the open“channels” and penetrate much further (ions do not get close to lattice sites) Blocking: Reduction of the flux of ions originating in lattice sites along symmetry axis and planes (“blocking dip”) (From D. Gemmell 1974, Rev. Mod. Phys. 46, 129) GGI Florence, May 19, 2010 1

Graciela Gelmini-UCLA Channeling and blocking in crystals is used in - studies of lattice disorder - ion implantation - to locate dopant and impurity atoms - studies of surfaces and interfaces - measurement of nuclear lifetimes - production of polarized beams... etc - channeling is to be avoided in ion implantation in Si to make circuits: good data at ∼ 100 ‘s keV (and analytic models by Gerhard Hobler (Vienna University of Technology)-1995) GGI Florence, May 19, 2010 2

Graciela Gelmini-UCLA NaI crystal . Si or Ge crystal . GGI Florence, May 19, 2010 3

Graciela Gelmini-UCLA Channeling effect observed in NaI (Tl) Altman et.al 1973 GGI Florence, May 19, 2010 4

Graciela Gelmini-UCLA Channeling effect observed in NaI (Tl) Altman et.al 1973 Sintillation output of a monochromatic 10 MeV 16 O beam through NaI(Tl) scintillator Left peak: Not channeled ions Right peak: higher energy channeled ions GGI Florence, May 19, 2010 5

Graciela Gelmini-UCLA Channeling effect observed in NaI(Tl) Altman et.al 1973 Channeled ions produce more scintillation light (because they loose most of their energy via electronic stopping rather than nuclear stopping) GGI Florence, May 19, 2010 6

Graciela Gelmini-UCLA Channeling effect in DM detection: The potential importance of the channeling effect for direct DM detection was first pointed out in stilbene crystals by H. Sekiya et al. (2003) and subsequently for NaI (Tl) by Drobyshevski (2007) and by the DAMA collaboration (2008). When ions recoiling after a collision with a WIMP move along crystal axes and planes, they give their energy to electrons, so Q = 1 instead of Q I = 0 . 09 and Q Na = 0 . 3 10 0 DAMA � 7 Σ � 5 Σ � 10 � 1 DAMA � 3 Σ � 90 � � 10 � 2 DAMA � 7 Σ � 5 Σ � with channeling DAMA � 3 Σ � 90 � � 10 � 3 with channeling Σ Χ p � pb � CRESST I 10 � 4 TEXONO 10 � 5 CoGeNT Super � K 10 � 6 XENON 10 10 � 7 spin � independent CDMS I Si CDMS II Ge 10 � 8 10 0 10 1 10 2 10 3 M WIMP � GeV � (Savage,Gelmini, Gondolo, Freese JCAP 0904:010,2009) GGI Florence, May 19, 2010 7

Graciela Gelmini-UCLA Daily-Modulation due to Channeling: H. Sekiya et al. (2003); Avignone, Creswick, Nussinov (2008) • The WIMP wind comes preferentially from one direction • When that direction is aligned with a channel, the scintillation or ionization output is larger • Earth’s rotation makes the WIMP wind change direction with respect to the crystal, which produces a daily modulation in the measured recoil energy (equivalent to a modulation of the quenching factor) This daily modulation would be a background free DM signature! Nassim Bosognia, Paolo Gondolo and I set out more than a year ago to do an analytic calculation to understand channeling and blocking for DM detection, and estimate daiy modulation amplitudes... GGI Florence, May 19, 2010 8

Graciela Gelmini-UCLA Our calculation of the fraction of recoils that are channeled as function of recoil energy and direction: • Use classical analytic models of the 60’s and 70’s, in particular Lindhard’s model (Lindhard 1965, Morgan & Van Vliet 1971, Dearnaley 1973, Gemmell 1974, Appleton & Foti 1977, Hobler 1995) • Continuum string and plane model, in which the screened Thomas-Fermi potential is averaged 100 Channel, Si ions 0.7 over a direction parallel to a row / plane (took just one) 0.6 Axial 0.5 Planar • In the direction perpendicular the row or plane, the U � keV � 0.4 a SiSi “transverse energy” is conserved 0.3 E perp = Eφ 2 i + U i 0.2 0.1 v perp = v sin φ ≃ vφ 0.0 0.00 0.05 0.10 0.15 0.20 and E perp = Mv 2 perp / 2 Distance � nm � GGI Florence, May 19, 2010 9

Graciela Gelmini-UCLA Axial and planar channels ρ min : min. distance of approach - ψ : angle far away from row or plane (Fig. from D. Gemmell 1974, Rev. Mod. Phys. 46, 129) E perp = Eφ 2 i + U i = U ( ρ min ) = Eψ 2 + U middle U middle : at middle of channel, far from row / plane, angle there is q [ U ( ρ min) − U middle) ] ψ = E Channeling requires ρ min > ρ c which amounts to ψ ≤ ψ c GGI Florence, May 19, 2010 10

Graciela Gelmini-UCLA Axial and planar channels can be understood as interference of Coulomb shadow cones, ρ min > ρ c and ψ < ψ c (Fig. from Hiroshi Kudo, 2001) GGI Florence, May 19, 2010 11

Graciela Gelmini-UCLA Channeling requires (Lindhard 1965, Morgan & Van Vliet 1971, Hobler 1995) • Min. distance of approach to row or plane larger than a critical value: � 0.014 c ( E ) + [ c u 1 ( T )] 2 ρ 2 ρ min > ρ c ( E, T ) = 0.012 ρ c ( E ) : for perfect-rigid-lattice decreases with E � nm � 0.010 u 1 ( T ) : 1-dim. amplitude of thermal fluctuations 0.008 u 1 a SiSi . (used Debye model) increases with T, e.g. in Si 0.006 0 200 400 600 800 c : found through data / simulations, 1 < c < 2 Crystal Temperature � K � • Angle far from the row / plane smaller than a critical angle: � [ U ( ρ c ) − U ( r ch )] ψ ≤ ψ c = E If ρ c ( E, T ) ≥ the radius of the channel r ch = d ch / 2 , ψ c = 0 : NO CHANNELING POSSIBLE GGI Florence, May 19, 2010 12

Graciela Gelmini-UCLA Si ion in Si crystal, c = 1 (i.e. r c → u 1 ( T ) at high E ) (Bozorgnia, Gelmiin, Gondolo 2010) � 100 � axial channel, Si ions, c � 1 � 100 � axial channel, Si ions, c � 1 0.2 d ach � 2 0.1 5. 40 mK 0.05 900 °C Static lattice 600 °C Ψ c � deg � r c � nm � 2. 293 K 40 mK 0.02 900 °C 1. 0.01 600 °C u 1 0.5 0.005 293 K Static lattice 0.002 0.2 10 4 10 4 1 10 100 1000 1 10 100 1000 E � keV � E � keV � GGI Florence, May 19, 2010 13

Graciela Gelmini-UCLA Si ion in Si crystal, c = 2 (i.e. r c → 2 u 1 ( T ) at high E ) (Bozorgnia, Gelmiin, Gondolo 2010) � 100 � axial channel, Si ions, c � 2 � 100 � axial channel, Si ions, c � 2 0.2 d ach � 2 0.1 5. 40 mK 900 °C 600 °C 293 K 0.05 Static lattice 40 mK Ψ c � deg � r c � nm � 2. 0.02 1. 2 u 1 900 °C 0.01 600 °C 0.5 0.005 293 K Static lattice 0.002 0.2 10 4 10 4 1 10 100 1000 1 10 100 1000 E � keV � E � keV � GGI Florence, May 19, 2010 14

Graciela Gelmini-UCLA Data B and P ion in Si crystal fitted with c = 2 (data from Hobler-1995) (Bozorgnia, Gelmiin, Gondolo 2010) B in Si, c 1 � c 2 � 2 P in Si, c 1 � c 2 � 2 2.0 2.0 <100> � � � 1.5 1.5 <100> � � Ψ c � deg � {110} Ψ c � deg � � � � 1.0 1.0 {110} {100} � � � � � � � � � 0.5 0.5 � {100} 0.0 0.0 0 100 200 300 400 500 600 0 100 200 300 400 500 600 E � keV � E � keV � GGI Florence, May 19, 2010 15

Graciela Gelmini-UCLA In NaI, no data or modeling available at low energies DAMA channeling fraction: Calculated as if ions start from the middle of the channel (DAMA- Eur. Phys. J. C 53, 205-2313, 2008) 1 -1 10 fraction Iodine recoils -2 10 Sodium recoils -3 10 0 10 20 30 40 50 60 E R (keV) GGI Florence, May 19, 2010 16

Graciela Gelmini-UCLA Reproduced DAMA calculations of channeled fraction We used HEALPix (Hierarchical Equal Area iso Latitude Pixelisation) method to compute the integral over all directions. Dechanneling due to Tl doping (only first interaction and no rechanneling) (Bozorgnia, Gelmiin, Gondolo 2010) Incident ions 1. 0.5 0.1 Fraction 0.05 I Na 0.01 I,dech 0.005 Na,dech I DAMA 0.001 Na DAMA 0 10 20 30 40 50 60 E � keV � GGI Florence, May 19, 2010 17

Graciela Gelmini-UCLA Channeling probability of ions ejected from lattice sites • Recoiling nuclei start at or close to lattice sites • Blocking effects are important • In a perfect lattice no recoil would be channeled (“rule of reversibility”) . • However, there are channeled recoils due to lattice vibrations! Collision may happen when nucleus is somewhat within the channel, with prob. � ∞ ρ i, min drg ( ρ ) = e ( − ρ 2 i, min / 2 u 2 1 e ( − ρ 2 / 2 u 2 1 ) thus P Ch = g ( ρ ) = ρ 1 ) u 2 and ρ i, min is given by ρ c (uncertainty in ρ c is exponentiated in P Ch ) • Recoiling nucleus leaves an empty lattice site. Two main T effects: amplitude u 1 ( T ) increases with T which increases channneling prob.- but r c also increases with T what decreases the prob. GGI Florence, May 19, 2010 18

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