Atomic enhancements in the detection of weakly interacting particles

Volume 168B, number 1,2

PHYSICS LETTERS

27 February 1986

ATOMIC ENHANCEMENTS IN T H E D E T E C T I O N O F W E A K L Y I N T E R A C T I N G P A R T I C L E S Savas D I M O P O U L O S ~. G l e n n D. S T A R K M A N

:

t'hrsws Department, Stanford Untt'ersit)', Stanford. ('A 94305, USA

and Bryan W. LY'N'N ~ Stanford l, mear Accelerator Center. Theory Group, Stanford. CA 94305. USA

Received 23 November 1985

Proposed bolometric and supercolloidal detectors can measure energy depositions of the order of atomic energies. At these energies, atomic bound state effects lead to great enhancements in the detection of weakly interacting particles. As an example, we show that solar axions could give event rates 10~-106 times larger than published neutrino detector design capabilities. Thus, relatively small detectors nught see solar axions.

I n t r o d u c t i o n . There are arguments in both theoretical elementary particle physics and astrophysics for the proliferation o f neutral weakly interacting particles. On the theoretical side, gauge theories suggest the existence o f many new particles: neutrinos, axions [ 1] ~t, etc. Experimentally, astronomical observations suggest that the mass of the universe is dominated by dark matter which might be made of neutral weakly interacting particles. Because these particles tend to interact so weakly, we must rely on some enhancement mechanisms to detect them. For example, one suggested enhancement mechanism for detecting neutrinos relies on their coherent nuclear scattering [ 3 - 7 ] ; this works well for neutrinos if the momentum transfers involved are less than 100 MeV. Until now, detectors for weakly interacting particles, such as neutrinos, have been limited by high minimum energy deposition thresholds. However, re-

i Work supported by National Science Foundation Grant PHY 83-10654. A.P. Sloan Foundation Fellow. 2 National Science and Engineering Research Council (Canada).Postgraduate Scholar. Work supported by DOE contract DE-AC03-76SFO0515. ,1 Other axion detectors have been proposed in ref. [2].

cent progress in experimental techniques [4,6] has made feasible the measurement o f energy depositions as small as atomic energies using supercolloidal and bolometric detectors. In this paper, we show that, at these energies, atomic bound state effects lead to great enhancements ( ~ 1 0 6 ) in the detection rates o f weakly interacting particles. As a simple example we work out the ionization of atoms by axions. In ref. [8], we consider similar enhancements for neutrino detection. Atomic enhancements are quite familiar. A wellknown example is the photoelectric effect, shown in fig. 1. The photoelectric cross section per unit mass of, for example, silicon is 234 times larger than that o f hydrogen around I keV photon energies. This is because silicon has electrons with binding energies of 1 keV; similar enhancements occur in any atom with keV electron binding energies. Enhancements similar to those in the photoelectric effect occur for the ionization of atoms by absorption of axions. We call this process, depicted in fig. 2, the axioelectric effect or axionization. We expect such effects to be large for solar axions because their energy is comparable to atomic energies. We show that the 145

PHYSICS LETTERS

Volume 168B, number 1,2

Oaxioelectric --~ [3( 2 X~)2 / 321raem l (meco/F 2)

Photoelectric Effect for H. C, $i, Pb i 10 8

I .... ""-~-- . . . . . .

I

.......

X Ophotoeleetric ,

.'.' /

\\

i

x

\ \ \

L

\\

.3 o~ \

\ ,

O 1

05 1 PHOTON ENERGY(KeV)

\

5

10

Fig. 1. Photoionization cross section per kg for II (dots), C (dot-dashes), Si (dashes) and Pb (solid). Note that for a photon energy of 1 keV there is an enhancement of about 103 for Si relative to H. Further, for both Si and Pb, the cross seetion for smaller photon energies is enhanced by a factor of ~104 relative to large photon energies due to atomic effects. rate of axionization could be five to six orders of magnitude larger than the published design capabilities of planned bolometric and supercolloidal neutrino detectors [4,6].

The axioelectric effect. The axioelectric effect is directly analogous to the photoelectric effect; a boson is absorbed by a bound electron which is then ejected from the atom. Neglecting Coulomb effects for the outgoing electron, and considering axion energies •~ m e,

(2)

Here a is the axion rid& N0f(th~i! (1)-i-s s-till~t~tectfor the axionization of S-state electrons when Coulomb effects are included for the outgoing electron. Lower bounds on F come from the following sources: (a) If the solar axion luminosity does not exceed the photon luminosity then F > 1.65 X 107 GeV [I 1, 121. (b) If axion emission is not the dominant energy loss mechanism of red giants then F > 4 × 107 GeV [11] *2 Furthermore, cosmological arguments give an upper bound o f F < 1012 GeV [ 15]. In this paper we shall assume F = 4 × 107 GeV, but it must be remembered that the event rate goes like F - 4 .

Event rates. For F = 4 × 107 GeV, the axionization event rates in various elements can be obtained by multiplying Oaxio(O~) of fig. 3 with the solar axion flux calculated with solar temperature T = 1 keV (fig. 4). In fig. 5 we plot the events per kg per day against the incoming axion energy. From these figures we see that the major contribution to the event rate comes from a narrow band between 1 keV and 10 keV. This is because the solar axion flux peaks there. In fig. 6 we plot the total number of events per kg per day as a function of the minimum experimentally observable incoming axion energy CCmin,

X

L

tron

"E 1011

bound electron

Fig. 2. The axioelectric effect. 146

(1)

where 2X e is a constant of order unity [9,10] which we take for now to be 1, and F is defined by the axion- electron interaction lagrangian

L = 2X'e(me/F) a ei75 e .

10 5

27 February 1986

*2 More restrictive lower bounds of F > 6 × 10a - 3 × 109 GeV have been obtained in ref. [13] from limits on axion cooling of X-ray pulsars. However, these calculations neglect possible internal and external heat sources and a s s u m e that the observed X-ray spectra are thermal and neglect the possibilities of nonthermal magnetospheric emission and internal heat sources; their results must therefore be considered speculative. Furthermore, note that the upper bound on the luminosities of the weB-known X-ray sources SN 1006, Tyeho and Cast is below the predictions of the standard cooling model [14]. This suggests additional cooling mechanisms for X-ray sources including, possibly, axion emission.

Volume 168B, number 1,2

PHYSICS LETTERS

A x i o e l e c t r i c Effect for 11. C. Si, t°b "I 10-17

J

. . . .\. . . .

Axion Event Rate for H, C. Si, Pb

I

.....

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27 February 1986

ix

A

)

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%)

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~. ,.=,

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--

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, \ ',,\

i0-19

\ 1

3

........

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10-20

I

..............

05 1 AXION E N E R G Y ( K e V )

0A

5

1. . . .

[ N u m b e r o f e v e n t s per day per kg] = [ N u m b e r o f a t o m s per kg]

(3)

Oaxio(W)0(6o) d c o ,

~min

,01t)

~ -

,

.~,

1017

5

r

w h e r e 0(co) is the solar axion flux [11,12]. In fig. 7 we plot the total events per kilogram per day for C~min = 1 keV for several e l e m e n t s spanning the periodic table. N o t e that the total e v e n t rate per kilogram per day is fairly c o n s t a n t f o r Z > 10. This is p r o b a b l y because the n u m b e r o f e l e c t r o n s c o n t r i b u t ing to the a x i o n i z a t i o n or p h o t o i o n i z a t i o n cross section at a few keV grows a p p r o x i m a t e l y linearly with Z, f o r Z > 10, while the n u m b e r o f a t o m s in a kilogram goes roughly as Z -1 .

:. , -, , : : -

\

................. lO 1

.

.

.

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,\

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.......

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i0

Total Axion Events vs '~;'mm ?1, C, $1, l'b

,-,-r-r] ............

L

ea

05 I AXION E N E R G Y ( K e V )

Fig. 5. Solar axion events per kg per day for H (dots), C (dotdashes), Si (dashes) and Pb (solid).

Solar Axiorl l,'lux •]

,,'

I

Ol

Fig. 3. Axionization cross section per kg for it (dots), C (dot-dashes), Si (dashes), and Pb (solid). Note again that for axion energies of 1 keV there is an enhancement of about 103 for Si relative to H, and that the cross section at low energies is enhanced relative to the cross section at high energies b y - ~ 1 0 4 .

X /

.... [

I0

4 L.._,

~

~ '''10

Fig. 4. The flux of solar axions on earth for solar temperature T = 1 keV. The dashed line comes from the Primakoff effect and the dotted from bremsstrahlung. The solid line is the total axion flux.

,

io-~

~_. l............ 01

I

...........

05 1 MINIMUM AXION E N E R G Y W m m ( ~ e ~ )

5

t:

'iN 10

Fig. 6. Integrated axion events per kg per day as a function of the minimum axion energy ¢omin for H (dots), C (dot-dashes), Si (dashes), and Pb (solid). Note that the effect increases with Z for low Z then stabilizes for Z > 14 beyond silicon. 147

Volume 168B, number 1,2

PHYSICS LETTERS

27 February 1986 Axion E v e n t s Wrnin= I KeV vs Z

r o t a l Axion E v e n t s vs Wmin for L:, AI, Fe, Pu E,,, I 10~ ~

........

---:

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......

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z

20

,, / ~o~t-/"

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......

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,,I 01

.......

I

05 1 MINIMUMAXIONENERGY(KeY)

. . . . . I.l! 5

10

Fig. 7. Integrated axion events per kg per day as a function of the minimum axion energy t~min for Li (dots), AI (dotdashes), Fe (dashes), and Pu (solid). Note that the scale is different from that of fig. 6. Note also that for Z > 13, the effect changes by only a factor 1.5 over a very wide range of the periodic table.

In table 1 we give t h e events per kilogram per day for e l e c t r o n s in silicon w i t h Wrnin = 1 k e V (see also fig. 8) and c o m p a r e t h e m to the n e u t r i n o i n d u c e d e l e c t r o n e v e n t s calculated b y the a u t h o r s o f ref. [6] w h o neglected a t o m i c e n h a n c e m e n t factors [8]. Note t h a t b o l o m e t r i c d e t e c t o r design capabilities aim at d e t e c t i n g 10 - 3 - 1 0 - 4 events per kg per day while the axioelectric effect will give up to 25 events per kg per day. Our rates are c o m p a r a b l e to the r e a c t o r antin e u t r i n o d e t e c t i o n rates q u o t e d in table 1, w h i c h were

otJ / ..... 0

/

]

/

I ....

!

40 60 ELEIdENT NUCLEARCHARGEZ

80

I .... 20

! ....

Fig. 8. Integrated axion events per kg per day for tOmin = 1 keV versus Z throughout the periodic table up to plutonium. Note that the effect grows linearly with Z up to Z -~ 14 and then stabilizes. Therefore, the event rate does not place a constraint on the choice of detector materiaL

also calculated [6] neglecting a t o m i c e n h a n c e m e n t s [8]. So far we have t a k e n 2 X ~ = 1. If 2 X e > I, o u r e v e n t rates increase r o u g h l y as ( 2 X e ) 4, because the b r e m s s t r a h l u n g c o m p o n e n t o f the solar flux a n d the a x i o n i z a t i o n cross section b o t h increase as (2X'e) 2 .3 *3 If 2X~ is large (>10), then the solar axion luminosity is dominated by bremsstrahlung and exceeds the photon luminosity. In this case the increase in 2X~ is compensated by an increase in the lower bound on F and no fmthcr gain in the axion detection rate results.

Fable 1 Event rates in a bolometric detector. The rates for the solar neutrino and reactor antineutrino induced events have been obtained From ref. [6] which neglected possible atomic enhancements [8]. Note that the solar axion induced event rates from any atom with Z > 13 can be comparable to those computed in ref. [6] for reactor antineutrinos. Event

2 Xe

Events/kg/d

1 X 10 -a 1.5 X 10 -4 40

recoil electrons from solar ppv's on Si coherent scattering of solar 8 Bv's on Si nuclei events on Si near a nuclear reactor core

148

I0,'

solar axion events on Si with energy deposition 91 keV

1 2 >2

15 130 Xe4 X 130

solar axion events on any atom with 13 < Z with enerty deposition 91 keV

1 2 >2

15-25 130-240 Xe4 X ( 1 3 0 - 2 4 0 )

Volume 168B, number 1,2 Solar

PHYSICS LETTERS

Axion

t:'lux: ' ~-"

27 l"ebruary 1986 Axion

2X~=2

I

. . . . .

250 F~

r ~ ] ~

~q-",

Wmin=lKeV

, : , ....

vs

r

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.-~.

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Events

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05

1

5

10

.~

c)

- . . . . . . . . . . . .

[

L

20

AXION E N E R G Y ( K e Y )

Fig. 9. The flux of solar axions on earth for solar temperature of T = 1 keV and for 2Xe = 2. The dashed line comes from the Primakoff effect and the dotted from bremsstrahlung. The solid line is the total axion flux. Indeed Srednicki [10] argues that 2 X e > 2 in the D F S model. The event rates and the solar flux for 2 X ~ = 2 are s h o w n in figs. 9 - 1 1 and tabulated in table 1. N o t e the gain o f a p p r o x i m a t e l y one order o f m a g n i t u d e in the event rates. Event rates for 2 X ~ > 2 are also tabulated. In fig. 12 w e p l o t the integrated n u m b e r o f events per kg per day in silicon w i t h energy d e p o s i t i o n Fotal Axion Events vs Wmln '_ : -

I

'

"-

--

\

\ ~

\

,

L

100

CHAR(;E Z

I9,101 maxio n ~ 1.8 e V ( 4 X 107 G e V / F )

(4)

for 2 X 'e = 1 (solid line) and 2 X ' e = 2 (dashed line). For comparison, w e also plot the published solar neuAxlon

I

1010

Everlts(Si)

Wrnin-lK,eV

*Tr I r.

T ,~',~r .

--'rHT--" .

•

vs Axmrl r ..... .

.

r ~ Z' .

"

Mass '--':'"1

" ~

105

,

'°°

_

~ ./

~

\

/

i

x

r..

r

-

5

10

Fig. 10. Integrated axion events per kg per day for 2X~ = 2 as a function of the minimum axion energy ~Orrdnfor H (dots), C (dot-dashes), Si (dashes), and lab (solid). Note that the effect increases with Z for low Z then stabilizes for Z > 14 beyond silicon.

'.0

. . . . .

t

~-:

,_ ..........

. . . . . . . . 05 M I N I M U M AXION E N E R G Y ( K e V )

lo - 1 °

/

_ %-J . "/--

._

~o-S

0 1

. .

\

x x

E--

F,

i.~

greater than 1 k e V as a function o f the a x i o n mass

%

/F

E 100

i

80

/.

[

101

60

Fig. 11. Integrated axion events per kg per day Wmin = 1 keV for 2X~ = 2 (dashes) and 2X~ = 1 (solid) versusZ throughout the periodic table up to plutonium. Note that the event rates are enhanced by about an order of magnitude. Note that the effect grows linearly with Z up to Z -- 14 and then stabilizes. Therefore, the event rate does not place a constraint on the choice of detector material.

H, C, Si, Pb: 2X~=2

. . . . . . . . . . . . . . .

]

40 EL~MFNP NUCLEAR

3

,i. ........ 10" ~

1 ........ 10 - I

:

.......

IO O

1 ~0 L

J

......... 102

AXION MA~5 (¢V)

Fig. 12. The integrated number of events per kg per day in sil. icon with energy deposRion greater than 1 keV as a function of the axion mass [eq. (4)] for 2X~ = 1 (solid) and 2 X e = 2 (dashed). For comparison, we also plot the published solar neutrino detector design capabilities [4,6] (dot-dashed). 149

Volume 168B, number 1,2

PHYSICS LETTERS

trino detector design capabilities [4,6] (dot-dashed line). Note that if these minimum design capabilities are met, we will be sensitive to axion masses at least as small as 0.1 eV for 2 X 'e = 1 and 0.06 eV for 2 X 'e = 2. It is therefore feasible either to detect solar axions or to set at lower bound on F w h i c h is an order of magnitude better than the bound of 4 X 107 GeV and does not rely on the astrophysics of red giants.

Conclusions. In this paper we studied the first example of how atomic enhancements can lead to detectable signals even from very weakly coupled particles when the energy transfers are comparable to atomic energies. These enhancements make it possible to have large rates for solar axion detection. In ref. [8], we study the effects of atomic enhancements on the detection of neutrinos and other weakly coupled particles. It is a pleasure to thank David Ritson for illuminating conversations. We ould also like to thank B. Cabrera, M. Karliner, L. Krauss, J. Martoff, D.E. Morris, H. Quinn and R. Wagoner for valuable discussions.

References [1] R.D. Peccei and H.R. Quinn, Phys. Rev. Lett. 38 (1977) 1440; Phys. Rev. D16 (1977) 1791; S. Weinberg, Phys. Rev. Lett. 40 (1978) 223; F. Wilczek, Phys. Rev. Lett. 40 (1978) 279; J.E. Kim, Phys. Rev. Lett. 43 (1979) 103; M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Nucl. Phys. B166 (1980)493;

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27 February 1986

M. Dine, W. Fischler and M. Srednicki, Phys. Lett. 104B (1981) 199; J.E. Moody and F. Wilczek, Phys. Rev. D30 (1984) 130. [2] P. Sikivie, Phys. Rev. Lett. 51 (1983) 1415;52 0984) 695. [3] D.Z. Freedman, D.L. Tubbs and D.N. Schramm, Ann. Rev. NucL Sci.27 (1977) 167. [4] A. Drukier and L. Stodolsky, Phys. Rev. D30 (1984) 2295. [5] M. Goodman and E. Witten, Princeton Universitypreprint. [6] B. Cabrera, L. K.raussand F. Wilczek, Phys. Rev. Lett. 55 (1985) 25. [7] L. Krauss, M. Srednicki and F. Wilczek, University of Californiaat Santa Barbara preprint ITP 85-58, Yale preprint UTP-85-18, submitted to Phys. Rev. Left.; A. De Rfijula,S.L. Glashow and L.J. Hall,Harvard University preprint IIUT P-85/A074 (1985). [8] S. Dimopoulos, G. Starkman and B.W. Lynn, Atomic enhancements in the detection of neutrinos, preprint ITP 804 (1985). [9] D.B. Kaplan, NueL Phys. B260 (1985) 215. [10] M. Srednicki, University of California, Santa Barbara pt eprint 85-0247. [11] D.S. Dicus, E.W. Kolb, V.L. Teplitz and R.V. Wagoner, Phys. Rev. D18 (1978) 1829; D22 (1980) 829; M. Fukujita, S. Watamuxa and M. Yoshimura, Phys. Rev. Lett. 48 (1982) 1522. [12] L.M. Krauss, J.E. Moody and F. Wflczek, Harvard University preprint HUTP-84-A043. [13] N. Inamoto, Phys. Rev. Lett. 53 (1984) 1198; D.E. Morris, LBL report 18690 mc (1984). [14] K. Nomoto and S. Tsutute, Astrophys. J. 250 (1981) 19. [15] J. Preskill, M.B. Wiseand F. Wilczek, Phys. Lett. 120B (1983) 127; L. Abbot and P. Sikivie, Phys. Lett. 120B (1983) 133; M. Dine and W. Fischler, Phys. Lett. 120B (1983) 137.