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Volume 119B, number 4,5,6
PHYSICS LETTERS
23•30 December 1982
NEW PARTICLES FROM NUCLEAR REACTIONS IN THE SUN
Georg R A F F E L T l and Leo STODOLSKY
Max-Planck-Institut far Physik und Astrophysik,
ICerner.Heisenberg-Institut far Physik, Munich, Fed. Rep. Germany
Received 26 July 1982
New light particles can be produced by nuclear reactions in the sun. Upon escaping and decaying into photons they
would provide a signal in the 3"-rayspectrum of the quiet sun, for which only low upper limits exist observationally. A
favorable reaction, occurring frequently in the main solar reaction chain, is p + d ~ 3He + 3" (5.5 MeV), where the new
particle could be substituted for the photon. Taking the "standard axion" as an example, we find that it is ruled out for
values of the axion parameter X between 0.31 and 3.0, in the middle of this range by many orders of magnitude. We suggest that an effective way to search for new particles of this sort is to look for a step in the solar 3"ray spectrum at 5.5 MeV.
Among the many speculations in recent years concerning possible new particles, one often finds nonstrongly interacting light neutral bosons. In addition
to direct search for such particles in the laboratory,
one can set limits on their possible existence, or perhaps find evidence for it, by cosmological or astrophysical arguments [ 1]. Such particles would be produced
in large numbers from the thermal energy in the interior of stars. Limits on the particle's properties may be
set by the requirement that their escaping flux from
the stellar interior does not carry away so much energy so as to upset the observed stages of stellar evolution.
This kind of argument is effective when the mass
of the particle in question is not much bigger than the
typical thermal energy k T in the star. In this case electrodynamic processes, particularly 3' + e -+ e + a (we
call the new boson "a") are particularly efficient at
producing the new object, and this method has been
used to set good limits [2] * 1.
Another possibility to set limits is to look for the
3" rays resulting from the decay of the new boson as it
i Based on work to be submitted as a thesis for the "Diplom"
degree at the Ludwig-Maximilians-Universit~it,Munich, Fed.
Rep. Germany.
:~1 Limits on the "standard" and the "invisible" axion have
been set in ref. [3] using astrophysical methods.
0 031-9163/82/0000--0000/$02.75 © 1982 North-Holland
leaves the star, especially the sun [2]. Since 3' rays
from the quiet sun are rare, this method will be sensitive to even relatively low fluxes of new particles. Furthermore, restriction to very light masses is not necessary if we consider production in nuclear reactions in
the center of the star, where MeV energies are involved.
In this note, then, we consider what can be learned
by looking for 3' rays coming from neutral bosons produced in nuclear reactions in the sun. We exemplify
our approach by considering the "standard axion"
and find that it is ruled out by many orders of magnitude when its mass is less that about 265 keV, or
lifetime more than 5.3 ms.
The "standard axion" is a light, neutral pseudoscalar particle characterized by a parameter X giving
the mass and lifetime through m a ~ 75(X + X - 1) keV,
r ~ 0.7 keV/ma)5 s, if standard values are assumed
for the number of generations of quarks and leptons,
N = 3, and the mass ratio of the up to the down quark,
Z = 0.56 [4,5]. For a value o f X = 0.43 -+ 0.05 [6] ,2
we would have m a ~ 200 keV, r ~ 20 ms and an axion with 5.5 MeV energy, due to the large relativistic
time dilation Ea/m a ~ 27 would travel about 0.2 R~
(solar radii) before decaying.
Since the boson in many ways resembles a photon,
~:2 Faissner [7] informs us that a now preferred second solution is rn -~-200 keV, r ~ 20 ms, X = 0.43 -+ 0.05.
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it can be emitted in nuclear reactions in the place o f a
photon [8]. For the pseudoscalar axion, the coupling
to nucleons is through the spin o p e r a t o r a , so that it
will be principally coupled to magnetic transitions.
Donnelly et al. [4] find for the relative emission rate
of axions to photons for spin-operator dominated M1transitions
23/30 December 1982
The factor 1/2 reflects the two possibilities for the 3'
polarization, a a [ a ~ 2.33X 10 - 4 is the relative coupling strength, k a and k are the axion and 3' momenta,
and p and/~ "magnetic m o m e n t " factors for the axion and photon. For isovector transitions, as we need
them below, they are p(1) ~ 0 . 1 5 X - 1.85/X,/~(1)
=/aP - / ~ n ~ 4.71 [4] so that I'a/r'. r ~ 1 0 - 4 - 1 0 - 5
with a narrow dip to zero at X ~ 3.46, where the axion coupling becomes completely isoscalar.
The sun is believed to produce energy practically
totally by conversion of hydrogen into helium, viz. the
effective reaction
p-wave-capture) at the relevant energy, 25 keV [ 10].
From a detailed calculation [ 11 ] this M 1 transition is
believed to be predominantly isovector. Thus at X
= 0.43, for example we find from (1) Pa/FyM1 ~ 0.9
X 10 - 4 or I ' a / P ~ total ~ 2.9 X 10 - 5 , which would give
5.0 X 1033 axions per second. If the axions did not
decay or were not reabsorbed in the sun, this would
give 1.8 X 106 axions/cm 2 s at the earth. The variation o f the production rate with X is plotted in fig. 1.
curve (a): The dip at X = 3.46 results from the axion
becoming pure isoscalar; in reality it would presumably be filled in somwhat by contributions from various isoscalar reactions.
Of other important reactions in the PP-chain, 4He
+ 3He -+ 7Be + 7(1.6 MeV) is E1 [12] and therefore
not capable of producing axions. 7*Li ~ 7Li + 7 (0.48
MeV) is measured to be at least 55% M1 [13] and is
believed to be a proton spin-flip transition [12,14[. It
is, however, of low energy and less frequent than (3).
The annihilation of positrons arising from the PP-chain,
e + + e - -+ 7 + a, has the branching ratio [15]
4p + 2 e - ~ 4He + 2~ + 7's + recoil energy .
Ya.,//I'2.r ~ ~ ( a a / a ) [1 - ¼(ma/me) 2 ]
ra/r~ ~ ~ ( a a / a ) (kJk)3(p/la) 2
1
(1)
(2)
The total energy release of (2) in v's, 3"s and recoil energy is about 26.7 MeV of which about 0.6 MeV is carried away by the neutrinos. Reaction (2) may proceed
through various chains and cycles. We concentrate on
the presumably dominant reaction chains PPI and PPII,
which contribute about 99% to the total o f ( 2 ) , 3 , and
neglect PPIII and the CNO tricycle.
In the PP chains a favorable reaction exists, namely
the deuteron-proton-fusion
p + d ~ 3He + 3' (5.5 M e V ) .
(3)
This reaction occurs 1.87 times for every a-particle
produced by (2), when the PP-chain is assumed to terminate in 87% of all cases via PPI, in 13% via PPII [9].
The luminosity of the sun, 2.4 X 1039 MeV/s corresponds from (2) to the production o f 0.92 × 1038 aparticles per second and therefore to 1.7 X 1038 reactions o f type (3) per second.
To estimate in what fraction o f (3) an axion is produced we use the fact that the M1 (s-wave-capture)
cross section is measured to be (1.3 +- 0.3) X 10 - 3 2
cm 2 (as against (2.9 -+ 0.3) X 10 - 3 2 cm 2 for the E l ,
,a BahcaU and Sears [9] : Solar terminations: 86% PPI, 14%
PPII, BahcaU [9] : 87%, 13%.
324
With the relative coupling constant to electrons % / a
4.6 X 1 0 - 1 t / x 2 [4] this process gives only a small
yield in axions as compared to (3). The " C o m p t o n "
process 3' + e -+ e + a with MeV ~/'s, such as from (3),
.
1034
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Fig. 1. Constraint on the axion parameter X from solar "r-rayastronomy. (A) Axion flux from the sun, due to p + d ~ 3He
+ a, when axions do not decay and are not reabsorbed in the
sun. (B) Axion flux from the sun if the effects of fig. 1 are
considered. (C) Experimental upper limit from observation of
the -/-ray-flux from the quiet sun.
Volume 119B, number 4,5,6
PHYSICS LETTERS
16~°
t
"-LY
-
I0 a8
0.1
I
10
XAXION
Fig. 2. Absorption cross sections for axions. The curves are
marked with the name of the target and refer to the following processes: (017) a + 170 ~ 160 + n (neutron-transition).
(C13) a + 13C ~ 12C + n (neutron-transition). (He3) a + 3He
--*d + p (isovector-transition). (e) a + e ~ e + 3' ("Compton"process, "Primakoff"-process negligible). (p) a + p ~ p + 3'
(Primakoff"-process; "Compton"-process roughly same magnitude). Multiply with Z 2 of target nucleus to obtain the
Primakoff cross section for any nucleus.
is governed by the same small coupling constant and
thus also gives a small axion yield. The "Primakoff"
production 3' + (nucleus or electron) -~ (nucleus or electron) + a from the same 3"s is completely negligible.
We now turn to the absorption of the axion leaving
the nuclear active region of the sun. A particle originating in the center of the sun must pass through roughly
0.7 X 1036 electrons/cm 2, 0.5 × 1036 protons/cm 2
and 0.1 X 1036 alpha-particles/cm 2 to reach the surface. Thus an absorption process will be considered unimportant if the number abundance of a species of target relative to hydrogen times its axion absorption
cross section is estimated to be less than about 10-36
cm 2. In fig. 2 we show estimates of cross sections for
various possibly significant processes at E a = 5.5 MeV.
The largest type of absorption cross section is the
analog of photo dissociation, a + nucleus -+ nuclear
fragments. However, among the nuclei present in the
sun only a few have a few dissociation threshold below 5.5 MeV. The three cases shown 170, 13C and
3He, are potentially interesting since they are made in
nuclear reaction chains and could be more frequent
than indicated by their primordial abundance, while
deuterons are believed to be very rare in the high density areas of the sun due to the rapid reaction (3). We
estimate the dissociation cross sections from photo dis-
23/30 December 1982
sociation data , 4 scaled according to the formulas of
ref. [4], assuming pure Ml-transitions for 170 and
13C to give a generous upper limit. For definiteness,
we assume that the isospin structure of the 170 and
13C dissociation is that of a neutron transition. The relative abundance of the three species exhibits a strong
radial dependence in the sun. With estimated maximum values of 1 X 10 - 3 (3He) and 4 X 10 - 5 (13C)
and much smaller average values [ 18], the axion dissociation of 13C and 3He are unimportant. For 170, a detailed calculation using the production process 160
(p, "y) 17F (e+v)170 *s and assuming the 170 has accumulated during 4.5 × 109 yr gives a maximum abundance of about 10 - 4 at the center of the sun and
much less further out. If the axion flux is assumed to
be reduced only by 170 absorption, the escape probability in a particular solar model [2] is plotted in fig.
3 curve (A). Other solar models yield similar results
[21,221.
For the Primakoff process on nuclei we use the
:t:4 For 13C(3", n) 12C, see ref. [16], For 170(3", n) 160, see
ref. [17]
:~s For the reaction rate of 160 (p, 3') 17F see ref. [19].
. . . . . . . .
i
1
-2
lO
16 6
-10
10
0.1
, i LillJ
i
1
, , ,,,
lO
XAXiON
Fig. 3. Probability for axions (Ea = 5.5 MeV) to escape from
the sun, averaged over the radial distribution of the axion-production rate in the sun. We use the detailed model of Sears
[20]. The four curves show the probability for escape if axions are absorbed by: (A) Only a + ZTO~ 160 + n. (B) Only
a + e- -, e- ÷ 3". (C) Only a ~ 23' (decay). Here we assume that
all axions are produced in the center of the sun: escape probability = exp(-R®/l), 1 = mean distance of flight for axions of
5.5 MeV: (D) Effects (A), (B) and decay with an integration
over the sun according to ref. [120].
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Volume 119B, number 4,5,6
PHYSICS LETTERS
cross section formula of ref. [23] which is in essential
agreement with a recent estimate of the same cross section in ref. [24]. The cross section scales with Z 2 of
the target nucleus, but this rise in cross section is more
than balanced by the decrease in abundance for heavy
nuclei [25]. Consequently, the Primakoff effect is not
important.
The dominant absorption process is then the
"Compton" like electron scattering, a + e ~ e + 3',
which has the cross section at E a = 5.5 MeV of o = 1.8
X 10 -36 cm 2 1IX 2 ,4. The reduction of the flux due
to this process is shown in fig. 3 curve (B) as a function
of X.
We now consider decay of the axion. For orientation, fig. 3 curve (C) shows the reduction in the 5.5
MeV axion flux using exp(-Ro/l), l = [(Ea/ma) 2
- I ] 1/2r assuming that all axions come from the solar
center. Using the solar model [20] and considering absorption by 170, electrons and decay, and assuming
that the axion production is radially distributed like
the solar energy generation, we obtain fig. 3 curve (D).
We see that the naive lifetime estimate gives the dominant effect for the loss of the axion fluz. We find that
varying the solar model has small effects on the results.
At the steep part of the curve, X = 0.3, the variation
among three models [ 2 0 - 2 2 ] is less than a factor two
and a t X = 1 about 10%.
Now, multiplying the number of axions produced
per second in the sun with the probability for escape
[fig. 3 curve (D)] we obtain the axion flux leaving the
sun as shown in fig. 1 curve (B).
For the lifetimes considered here, all axions decay
into two 3"s before reaching the earth. Since we have
monoenergetic axions the energy distribution of the
7's is a box-shaped spectrum with 0 ~<Ev ~< 5.5 MeV.
The best upper limits for 3' rays from the quiet sun, as
far as we know, are from balloon observations in 1966
[26]. The upper limits decrease with energy, reaching
0.8 X 1 0 - 3 / c m 2 s MeV between 4 and 6 MeV. Taking
this to be the upper limit for the height of the " b o x "
we thus infer an experimental upper bound of 6.2
X 1024 axions/s leaving the sun [fig. 1 curve (C)]. We
conclude that axions with 0.31 < X < 3.0 are excluded.
Recent laboratory results obtained by looking for
axions from nuclear de-excitations have also set excel,4 This is essentially the cross section of ref. [4]. Their formula (25), however, appears to be misprinted: Their first
factor 2 has to be cancelled.
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23/30 December 1982
lent limits for the nonexistence of the axion [27,14]
which now appears to be ruled out.
Independent of the question of the axion, we can
say that a particle produced at a rate r compared to
the photon in reaction (3) and with an escape probability p (decay and absorption), must obey
r.p < 10 -14 ,
(4)
assuming it decays into ~, rays on the way to the earth.
We would like to stress therefore that 3' rays from
the quiet sun are an interesting method for searching
for new particles. In particular reaction (3) gives
monoenergetic particles (5.5 MeV) and being both
M1 and E1 can couple to particles of various s p i n parity. Due to the frequent occurrence of (3) compared to any other reaction giving particles of comparable energy, the resulting simple " b o x " 3' ray spectrum should dominate for a wide range of the hypothetical particle's parameters.
Thus solar 3, ray searches should look for a step in
the 3' ray spectrum from the quiet sun at 5.5 MeV.
The existing data still appears to be well above the
level expected from backgrounds such as that from
cosmic rays hitting the sun and there is room for further improvement in the observations. Should such a
particle exist, 3' ray observations would provide a
beautiful way to study the interior of the sun.
We thank R.D. Peccei for many helpful discussions
on the subject and M. Yoshimura for discussions of
previous work. Furthermore, we are indebted to C.
Reppin, E. Rieger, H.-C. Thomas and K. yon Sengbusch
for their help on questions of astrophysics and 3' ray
astronomy. We thank. H. Soenke for his help in overcoming the whims of the computer. One of us (G.R.)
acknowledges financial assistance from his parents and
the Studienstiftung des deutschen Volkes during the
course of this investigation.
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