VOLUME 75, NUMBER 18 PHYS ICAL REVIEW LETTERS 30 OCTOBER 1995

Proposal to Search for a Monochromatic Component of Solar Axions Using s7Fe

Shigetaka Moriyama*Department of Physics, School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo ku, -Tokyo 113, Japan

(Received 27 March 1995)

A new experimental scheme is proposed to search for almost monochromatic solar axions, whoseexistence has not been discussed heretofore. The axions would be produced when thermally excited"Fe in the Sun relaxes to its ground state and could be detected via resonant excitation of the samenuclide in a laboratory. A detailed calculation shows that the rate of the excitation is up to order 1

event/day kg "Fe. The excitation can be detected efficiently using bolometric techniques.

PACS numbers: 14.80.Mz, 25.40.Ny, 95.30.Cq, 96.60.Vg

The most attractive solution of the strong CP problemis to introduce the Peccei-Quinn global symmetry which isspontaneously broken at energy scale f„[1].The originalaxion model assumed that f„ is equal to the electroweakscale. Although it has been experimentally excluded, vari-ant "invisible" axion models are still viable in which f, isassumed to be very large; since coupling constants of theaxion with matter are inversely proportional to f„experi-mental detection becomes very difficult. Such models arereferred to as hadronic [2] and Dine-Fischler-Srednicki-Zhitnitskii (DFSZ) [3] axions. At present, these invisibleaxions are constrained by laboratory searches, and by as-trophysical and cosmological arguments. One frequentlyquoted window for f„which escapes all the phenomeno-logical constraints, is 10' —10' GeV. Besides this, thereis another window around 10 GeV for the hadronic axionswhich have vanishing tree level coupling to the electron.This is usually called the hadronic axion window. Re-cently, a careful study [4] of the hadronic axion windowrevealed that f, in the range 3 X 10 to 3 X 106 GeV can-not be excluded by the existing arguments, because mostof them were based on the axion-photon coupling which isthe least known parameter among those describing the lowenergy dynamics of the hadronic axions.

Although several authors [5—7] proposed experimentalmethods to search for the axions with f, about 10" GeV,all of the methods are clearly based on the axion-photoncoupling, both at the source and at the detector. Themethods utilize only the Pnmakoff effect; photons in theSun are converted into axions, which are commonly calledthe solar axions, and they are reconverted into x raysin a laboratory. Thus there have been no experimentalalternatives to test the hadronic axion window indepen-dent of the axion-photon coupling. The only experimentin this region [8], in which an emission line arising fromthe radiative decay of axions in the halo of our Galaxyis searched for, also proceeded through the axion-photoncoupling.

Because of axion coupling to nucleons, there is anothercomponent of solar axions. If some nuclides in the Sunhave Ml transitions and are excited thermally, axionemission from nuclear deexcitation could also be possible.

~E(T) = W1 + 2exp( —PT) r~ I ~

where N = 2.9 X 10' g' is the number of Fe atoms

per 1 g material in the Sun [9], PT = (14.4keV)/kT,T~ = 1.3 X 10 6 s, and E~ = 14.4 keV. I,/I ~ rep-resents the branching ratio and contains nuclear-structure-dependent terms, which are important to evaluate the Aux.It was calculated by Haxton and Lee [11]as

1 1 gop + gs2vrn 1 + 62 (p, o

—1/2)P + p, s—i1

, (2)

Fe can be a suitable axion emitter for the followingreasons: (i) "Fe has an M 1 transition between the firstexcited state and the ground state; (ii) the first excitationenergy of Fe is 14.4 keV, which is not too highcompared with the temperature in the center of the Sun(—1.3 keV) [9];and (iii) Fe is one of the stable isotopesof iron (natural abundance 2.2%), which is exceptionallyabundant among heavy elements in the Sun [10]. If theaxion exists, strong emission of axions is expected fromthis nuclide.

These monochromatic axions would excite the samenuclide in a laboratory, because the axions are Dopplerbroadened due to thermal motion of the axion emitter inthe Sun, and thus some axions have energy suitable toexcite the nuclide.

I propose to search for the axions by detecting thisexcitation. Since both the emission and absorption occurvia the axion-nucleon coupling, but not via the axion-photon coupling, this method is free from the uncertaintyof the axion-photon coupling. In addition, this methodhas the merits that there is no need to tune the detectorto a mass of the axions, and the mass can be large farbeyond that of the proposed experiment [6] in whichit is restricted by the high pressure of buffer gas. Inthis Letter, the detection rate of the resonant excitationby the monochromatic solar axions is calculated, andexperimental realities are briefly discussed.

To estimate axion flux from the Sun, the calculation canbe performed as in Ref. [11]. The energy loss due to theaxion emission is

3222 0031-9007/95/75(18)/3222(4)$06. 00 1995 The American Physical Society

VOLUME 75, NUMBER 18 PHYSICAL REVIEW LETTERS 30 OcToaER 1995

where B —0 is the E2/M 1 mixing ratio. p, o andp, 3 are the isoscalar and isovector magnetic moments,respectively: IM, O

—1/2 —0.38 and IIL3 —4.71. p =—1.19 and g = 0.80 are the nuclear-structure-dependentterms. go and g3 are defined as [12]

= a%I.ys(go + g3r3)N, (3)

s(6.2 X 106' (3F —D + 25'go = —7.8 x 10 4

( f /GeV )( 3 )

t62X10 5 1 —zg3 = —78 X 10 (D+ F), (5)

( f /GeV ) 1 + z

m~~z f m ~z 1.3 X 10= 1eV, (6)1+z f 1+z f /GeV

where D and F denote the reduced matrix elements for theSU(3) octet axial vector currents and 5 characterizes theflavor singlet coupling. The naive quark model (NQM)predicts 5 = 0.68 [11],but the latest measurement showsthat S = 0.30 ~ 0.06 [13]. z = m /md —0.56 in thefirst order calculation. m is evaluated to be 1 eV withz = 0.56 and f, = 6.2 X 10 GeV. Using Eqs. (2)—(5),Eq. (1) becomes

BE(T) = 4.6 X 10 ergsg ' s

106 GeVx! C exp( —PT), (7)a

(3F —D + 25'!C(D, F, 5, z) —= —1.19!

)

+(D+F) (8)1+ z'where Pr » 1 is assumed in the solar interior. Ourestimation differs slightly from that of Ref. [11],becausea different value of Fe abundance in the Sun is used [9].

Equation (7) provides an estimation of the differentialaxion Aux at the Earth,

R~ =Ao p, I „,7r/2,

op =2o.oyI /I

(11)

(12)

where o.oy 26 + 10 ' cm is the maximum res-onant cross section of y rays [14], and I „, = 4.7 X10 ' keV is the total decay width of the first excitedstate of Fe. The factor 2 in Eq. (12) represents thedifference of the spin multiplicity between photons andaxions.

sharp peak in Fig. 1 corresponds to the axion flux eval-uated with D = 0.77, F = 0.48, 5 = 0.68, z = 0.56, and

f, = 106 GeV . Also shown is the expected axion fluxgenerated through the Primakoff effect [6]. It is a strik-ing fact that substantial axion emission is expected fromthe nuclear deexcitation. The differential flux at Ey isobtained to be

, (106 GeV)A =2.0 && 10' cm s 'keV ! ! C,

)(10)

where dependences on D, F, S, and z are included in C.The effects of the nuclear recoil and of the redshift dueto the gravitation of the Sun are negligible. The formerdecreases the axion energy by only about 1.9 X 10 eVand the latter about 1.5 X 10 ' eV, which are negligiblysmall compared with the width of the peak in Fig. 1.

In a laboratory, these axions would resonantly exciteFe. The rate of the excitation is calculated as follows.

It is a reasonable approximation that d4(E, )/dE, =A over the natural width of 7Fe, 6(10 neV), around14.4 keV, because the width of the peak in Fig. 1 isextremely broadened to about 5 eV. Hence the rate ofthe excitation per Fe nucleus is

d&b(E, ) 1

dE 4m REexp

$2vr rr(T)(E. —E,)'-

2o(T)z- 10 13

10 12

X p(r)4vrr dr,BE(T)(9)

where R~ is the average distance between the Sun and theEarth. Ro denotes the solar radius. T(r) and p(r) arethe temperature and the mass density at the radius r, re-spectively. o(T) = E~(kT/m). '~ represents the Dopplerbroadening. I is the mass of the Fe nucleus. It shouldbe noted that the number of iron atoms per unit mass isassumed to be uniform as in the framework of the stan-dard solar model (SSM) [8], i.e., that N is independent ofr. In addition, the SSM provides the mass density andthe temperature as a function of the radius r, which arenecessary for calculating Eq. (9). The values of the func-tions are taken from Table XVI in Ref. [8]. Thus Eq. (9)can be evaluated if one fixes D, F, S, z, and f, . The

~10

%10

10 '.—s» I s» I i I I I & & s

0 5 10 15 20axion energy (keV)

FIG. 1. Differential Aux of the axion from the Sun. Thesharp peak corresponds to the axion emission from the Fedeexcitation. The broad part of the differential Aux correspondsto the axion generated through the Primakoff effect.

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VOLUME 75 N UMBER 18 PH YSICAAL REVIEW LETTERS 300 OCTOBER 1995

Equations (10)otal detection rate ass o Fe in the lab

R =3.0X

a oratory,

102 da 'k &10 GeV

g4

where C depends on D, F, S

( )Ic,

A foDdF measurements f ucleon and

ver, the estimatiandF=

a tons of 5 and h

, 15]. In part 1ambiguity [13 ar 1

o instanton effe tthe value of thn sma ler than

ects [15] an

sented ahereforre the detectio

e first orr er calcula-

as a function oc ion rate should

etection rate w th f, =. [11]restrtct hent of Ref

bt""'d fig. 3 The u pp

db nsldering the effe

. Since there ect of axion c

re are both the un o the rate, ex

e upper bound

pi efinit

ic haveand

q

n Fi . 3, expenme

ax

e latest experimental res

We now turn to a de excitation o

realitiaxion, t

gyn internal conver

keV anersion electro

bgh ftheyrayis20 p,

5

SMC('93) 4

4)y

w 3.5 )

1.5

0.5

ps%-02 0 0.2 0.4 0.6

FIG. 3.

0.8.8 1

. 3. Bound forarea is excluded b

S

= 0.56.

h thAlsomeasured recentl

X/1st ord er calculation

x(10 GeV/f, )Qy~.~

+~-g~o

1.5-

o~~-

05-, -. 0~o

NQM

E1430- zo0

-0.5—

—10 0.2 0.4 0.6 0.8 1z=m /m

u d

FIG. 2. CContours of theTh k od 1~N M~M) predtcts 5 =

) [ 3] obtain d 5 = 0.30 ~ 0.06.

ion and the ran e og of the elect oi cult to detect the

addition, dee 7 rays or electr

tectors sho ldg~~~~d and hi h

low energy thres

po 1

o ution. Howeveb

with an aby usin a

}1 o b }1 he techni ue

c contains F—

es.r ec niques in these

a vantages corn ar

nsitivit dI y pis gener

a olorneter forevent/kg dag y '

i e

11 In summ

po

y, new scheme tose a ov

h S d}1g o be excited h

expect the nu

excitationy. Therefore

ci ation accom ampanied with

op

small1

ortion of the axno Fein th

sorbed b hfo th

yt esamene nuclide c

ld 1 bsi ered as a w

a orator .

1 d

y. The nuclide

'k '. Al h h dffi detect thet i cult to

echnique withboloon I ame-enriched

wit an absorb

,hthis new sc erne.

o oho axions from the

I am ver m

mt eSunin

y h idbtdpo

nagaki, H. A, nsakawa, and

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VOLUME 75, NUMBER 18 PHYSICAL REVIEW LETTERS 30 OcToBER 1995

A. Kawamura for their helpful comments. Discussionswith Y. Ito, W. Ootani, and K. Nishigaki helped me tounderstand the bolometric technique.

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