ion-channeling in direct dm detectors · ion-channeling in direct dm detectors graciela gelmini -...

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 Crystalsrefer 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


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 (ViennaUniversity of Technology)-1995)



NaI crystal

.Si or Ge crystal .



Channeling effect observed in NaI (Tl) Altman et.al 1973



Channeling effect observed in NaI (Tl) Altman et.al 1973

Sintillation output of a monochromatic 10 MeV 16O

beam through NaI(Tl) scintillator

Left peak: Not channeled ions

Right peak: higher energy channeled ions



Channeling effect observed in NaI(Tl) Altman et.al 1973

Channeled ions produce morescintillation light(because they loose most oftheir energy via electronicstopping rather than nuclearstopping)



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 QI = 0.09 and QNa = 0.3

100 101 102 10310-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

MWIMP HGeVL

ΣΧpHp

bL

spin-independent CDMS I SiCDMS II Ge

XENON 10

Super-K

CoGeNT

TEXONO

CRESST I

DAMA H3Σ�90%Lwith channeling

DAMA H7Σ�5ΣLwith channeling

DAMA H3Σ�90%L

DAMA H7Σ�5ΣL

(Savage,Gelmini, Gondolo, Freese JCAP 0904:010,2009)



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...



Our calculation of the fraction of recoils that arechanneled 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

over a direction parallel to a row/plane (took just one)

0.00 0.05 0.10 0.15 0.200.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

DistanceHnmL

UHk

eVL

100 Channel, Si ions

aSiSi

Planar

Axial

• In the direction perpendicular the row or plane, the

“transverse energy” is conservedEperp = Eφ2

i + Ui

vperp = v sinφ ≃ vφ

and Eperp = Mv2perp/2



Axial and planar channelsρmin: min. distance of approach - ψ: angle far away from row or plane(Fig. from D. Gemmell 1974, Rev. Mod. Phys. 46, 129)

Eperp = Eφ2i + Ui

= U(ρmin)= Eψ2 + Umiddle

Umiddle: at middle of channel,

far from row/plane,

angle there is

ψ =

q

[U(ρmin)−Umiddle)]E

Channeling requiresρmin > ρcwhich amounts toψ ≤ ψc



Axial and planar channels can be understood as interference of Coulomb

shadow cones, ρmin > ρc and ψ < ψc

(Fig. from Hiroshi Kudo, 2001)



Channeling requires (Lindhard 1965, Morgan & Van Vliet 1971, Hobler 1995)

• Min. distance of approach to row or plane larger than a critical value:

ρmin > ρc(E,T ) =

√

ρ2c(E) + [c u1(T )]2

ρc(E): for perfect-rigid-lattice decreases with E

u1(T ): 1-dim. amplitude of thermal fluctuations

. (used Debye model) increases with T, e.g. in Si0 200 400 600 800

0.006

0.008

0.010

0.012

0.014

Crystal TemperatureHKL

HnmL

aSiSi

u1

c: found through data/simulations, 1 < c < 2

• Angle far from the row/plane smaller than a critical angle:

ψ ≤ ψc =√

[U(ρc)−U(rch)]E

If ρc(E, T ) ≥ the radius of thechannel rch = dch/2, ψc = 0:NO CHANNELING POSSIBLE



Si ion in Si crystal, c = 1 (i.e. rc → u1(T ) at high E)(Bozorgnia, Gelmiin, Gondolo 2010)

dach � 2

u1

Static lattice

293 K600 °C900 °C

40 mK

1 10 100 1000 1040.002

0.005

0.01

0.02

0.05

0.1

0.2

E HkeVL

r cHn

mL

<100> axial channel, Si ions, c=1

Static lattice

40 mK

293 K600 °C

900 °C

1 10 100 1000 1040.2

0.5

1.

2.

5.

E HkeVLΨ

cHd

egL




Si ion in Si crystal, c = 2 (i.e. rc → 2 u1(T ) at high E)(Bozorgnia, Gelmiin, Gondolo 2010)

dach � 2

2 u1

40 mK293 K600 °C900 °C

Static lattice

1 10 100 1000 1040.002

0.005

0.01

0.02

0.05

0.1

0.2

E HkeVL

r cHn

mL


Static lattice40 mK

293 K

600 °C

900 °C

1 10 100 1000 1040.2

0.5

1.

2.

5.

E HkeVLΨ

cHd

egL




Data B and P ion in Si crystal fitted with c = 2 (data from Hobler-1995)(Bozorgnia, Gelmiin, Gondolo 2010)

æ

æ

æ

æ

æ

æ

æ

æ

æ

<100>

{110}

{100}

0 100 200 300 400 500 6000.0

0.5

1.0

1.5

2.0

E HkeVL

ΨcHd

egL

B in Si, c1=c2=2

æ

æ

æ

æ

æ

æ

æ

æ

æ

<100>

{110}

{100}

0 100 200 300 400 500 6000.0

0.5

1.0

1.5

2.0

E HkeVL

ΨcHd

egL

P in Si,c1=c2=2



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)

ER (keV)

frac

tion

Iodine recoils

Sodium recoils

10-3

10-2

10-1

1

0 10 20 30 40 50 60



Reproduced DAMA calculations of channeled fractionWe used HEALPix (Hierarchical Equal Area iso Latitude Pixelisation)method to compute the integral over all directions. Dechanneling dueto Tl doping (only first interaction and no rechanneling)(Bozorgnia, Gelmiin, Gondolo 2010)

0 10 20 30 40 50 600.001

0.0050.01

0.050.1

0.51.

E HkeVL

Fra

ctio

n

Incident ions

NaDAMA

IDAMA

Na,dech

I,dech

Na

I



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! Collisionmay happen when nucleus is somewhat within the channel, with prob.

g(ρ) = ρ

u21e(−ρ

2/2u21) thus PCh =

∫

∞

ρi,mindrg(ρ) = e(−ρ

2i,min/2u

21)

and ρi,min is given by ρc (uncertainty in ρc is exponentiated in PCh)

• Recoiling nucleus leaves an empty lattice site.

Two main T effects: amplitude u1(T ) increases with T which increaseschannneling prob.- but rc also increases with T what decreases the prob.



Channeling probability of ions ejected from lattice sites: SiNo dechanneling included (Bozorgnia, Gelmiin, Gondolo 2010)

900 °C

600 °C

293 K

40 mK

5 10 50 100 50010001´10-42´10-4

5´10-40.0010.002

0.0050.01

E HkeVL

Fra

ctio

n

Si ions,c1=c2=1

40 mK

900 °C

600 °C 293 K

10 20 50 100200 50010000.0001

0.001

0.0005

0.00020.0003

0.00015

0.0015

0.0007

E HkeVL

Fra

ctio

n

Si ions,c1=c2=2

Upper bound (static lattice)

900 °C

600 °C

293 K40 mK

5 10 50 100 50010001´10-4

5´10-40.001

0.0050.01

E HkeVL

Fra

ctio

n

Si ions, Static lattice



Channeling probability of ions ejected from lattice sites: GeNo dechanneling included (Bozorgnia, Gelmiin, Gondolo 2010)

900 °C

600 °C293 K

40 mK

50 100 5001000 50001´10-42´10-4

5´10-40.0010.002

0.0050.01

E HkeVL

Fra

ctio

n

Ge ions,c1=c2=1

900 °C

600 °C293 K

40 mK

50 100 5001000 50000.0001

0.0005

0.0002

0.0003

0.00015

0.0007

E HkeVL

Fra

ctio

n

Ge ions,c1=c2=2

Upper bound (static lattice)

900 °C

600 °C

293 K

40 mK

50 100 5001000 50001´10-4

5´10-40.001

0.0050.01

E HkeVL

Fra

ctio

n

Ge ions, Static lattice



Channeling probability of ions ejected from lattice sites: NaI(Tl)Upper bound: T-dep. static lattice.

Righ: extreme dechanneling due to Tl, with no re-channeling considered.

(Bozorgnia, Gelmiin, Gondolo 2010)

Na, 600 °C

I, 600 °C

Na, 293 K

I, 293 K

Na, 77.2 K I, 77.2 K

1 10 100 1000 1041´10-4

5´10-40.001

0.0050.01

0.050.1

E HkeVL

Fra

ctio

n

Static lattice

Na, 600 °CI, 600 °C

Na, 293 K

I, 293 K

Na, 77.2 K I, 77.2 K

1 2 5 10 20 5010-8

10-6

10-4

0.01

E HkeVL

Fra

ctio

n

Static lattice, dechanneling



Channeling probability of ions ejected from lattice sites: NaI (Tl)More reasonable upper bounds at 20 K with lattice oscillations included

- Right: extreme dechanneling due to Tl with no re-channeling considered.

(Bozorgnia, Gelmiin, Gondolo 2010)

Na, c = 1

I, c = 1Na, c = 2

I, c = 2

1 10 100 1000 10410-5

10-4

0.001

0.01

E HkeVL

Fra

ctio

n

T=293 K

Na, c = 1

I, c = 1

Na, c = 2

I, c = 2

1 10 100 1000 10410-5

10-4

0.001

0.01

E HkeVL

Fra

ctio

n

T=293 K, dechanneling



Compatibility of DAMA/LIBRA with other experimentsThen (Savage, Gelmini, Gondolo, Freese JCAP 0904:010,2009)

100 101 102 10310-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

MWIMP HGeVL

ΣΧpHp

bL

spin-independent CDMS I SiCDMS II Ge

XENON 10

Super-K

CoGeNT

TEXONO

CRESST I

DAMA H3Σ�90%Lwith channeling

DAMA H7Σ�5ΣLwith channeling

DAMA H3Σ�90%L

DAMA H7Σ�5ΣL

and now (diff. at 7σ)(Savage,Gelmini, Gondolo 2010)



Compatibility of DAMA/LIBRA with other experimentsIf Leff extrapolated as a constant below 4 keVnr (band: how the 90%CL bound changes

with 1σ change in Leff)

(Savage,Gelmini, Gondolo 2010)



Compatibility of DAMA/LIBRA with other experimentsIf Leff extrapolated linearly to zero as E decreases below 4 keVnr (band: how the 90%CL

bound changes with 1σ change in Leff from Manzur (2010) data set)

(Savage, Gelmini, Gondolo 2010)



Conclusions:• The channeling of recoiling lattice ions and incident ions is different. The

effect of blocking is important to understand the channeling of recoilnuclei: the channeled fraction of recoils is smaller and it is stronglytemperature dependent (so it is negligible at mK).

• Channeling in crystaline detectors can lead to a daily modulation ofa WIMP signal, a DM signature without any background (Avignone,Creswell & Nussinov 2008) (with small amplitudes- but larger for halocomponents with small velocity dispersion)

• Analytic models give good qualitative results but need data/simulationsto get good quantitative results (not available or NaI).Montecarlo simulations may be needed to settle these issues (many areused in other applications of channeling).


ion-channeling in direct dm detectors · ion-channeling in direct dm detectors graciela gelmini -...

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