Science - 16.08.2019

for the abundance of HeH+are radiative asso-
ciation of H+and He for production and DR for
destruction. Hence, the HeH+abundance from
model calculations is inversely proportional to
the applied DR rate coefficient. At these red-
shifts, a radiation temperatureT~40Krequires
theJ≤1 levels to dominate, whereas the gas
temperature isTpl≤10 K ( 26 ). Comparing for
Tpl= 10 K the DR rate used by Bovinoet al.( 22 )
with ourJ=0andJ= 1 rates, population-
averaged forT= 40 K, the estimated peak HeH+
abundance atz~ 15 increases by a factor of at
least 20 above the previously calculated value
( 22 ) (Fig. 4). This strengthens the role of HeH+
as a potential coolant in primordial star for-
mation and also increases the chance to observe
HeH+from the postrecombination era at low
redshifts. Furthermore, higher abundance pre-
dictions for HeH+indicate that the role of HeH+
in smearing out the cosmic microwave back-
ground should be reexamined ( 27 ). For the HeH+
observation in planetary nebula ( 6 ), high kinetic
temperatures ofTpl≈ 104 K are relevant. The
absolute HeH+DR rate of 3.0 × 10−^10 cm^3 s−^1
used to interpret that observation ( 6 ) is com-
patible with our findings ( 19 ).
Considering the importance of resonant pro-
cesses, our energy- and state-selective rate co-
efficientsaJDRðEdÞoffer a particularly clean,
hitherto unavailable view on the mechanism
of low-energy DR. We analyzed the emission
velocities of the He and H fragments at the
prominent resonance at 0.044 eV, using the

position resolution of our coincidence detec-

tor, and compared them to theEd= 0 behavior.

DistributionsP(D) of the fragment distances

Dprojected into the detector plane (Fig. 2, B and

C) reflect the energy and the angular char-

acteristic of the H and He atoms emitted in a

DR reaction ( 19 ). For bothEd, the end points of

P(D)atD~ 27 mm indicate an emission energy

near 1.55 eV and confirm the well-known ( 28 )

fragmentation pathway into the atomic states

11 S(ground state) for He andn= 2 for H. The

shapes ofP(D), however, reveal different angu-

lar characteristics. AtEd= 0 (Fig. 2B), there is no

distinct electron impact direction and the frag-

ments are emitted isotropically. In contrast, at

Ed= 0.044 eV (Fig. 2C), the collision direction is

aligned with the beam axis and the data reveal

a pure low-order multipoleðjY 10 j^2 Þaround this

axis for the fragment directions. Based on the

well-established axial-recoil approximation ( 29 ),

this pure low-order multipole also applies to the

DR cross section with respect to the internuclear

axis, as well as to the electron partial wave that

drives the DR process ( 30 ). We find the DR

resonance ofJ= 0 HeH+ions at 0.044 eV to be

mostly driven by an electronic partial wave with

angular and magnetic quantum numbersl=1,

m=0(pssymmetry), whose importance was

raised theoretically ( 15 ).

Our new accurate rate coefficient measure-

ments consolidate the gas-phase chemical data

on HeH+that govern its abundance in the post-

recombination era of the early Universe. Moreover,

the ability to obtain state-selective laboratory data

for fundamental molecular reactions is particu-

larly timely, considering the imminent launch of

the James Webb Space Telescope ( 31 ). Its search

for the first luminous objects and galaxies after

the Big Bang will benefit greatly from reliable

predictions on early-Universe chemistry. Our

data show that the rotational excitation can make

a substantial difference in low-temperature reac-

tion rates of small molecules.

REFERENCES AND NOTES

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19. Materials and methods are available as supplementary
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20. O. Novotnýet al.,Astrophys. J. 777 , 54 (2013).


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Novotnýet al.,Science 365 , 676–679 (2019) 16 August 2019 3of4

Detuning energy (eV)

0.001 0.01 0.1

-1)

3 s

Rate coefficient (cm

10 9−

10 8−

Ion storage time (s)

0.1 110

Relative state population

0

0.2

0.4

0.6

0.8

1

100

I

0.1 - 0.3 s

II

0.6 - 1.0 s

III

1.8 - 3.3 s

IV

I

II

III

IV

10 - 50 s

J = 0

1

2

3

4

A

B

3000 K CSR radiation field

Fig. 3. DR during the rotational relaxation of
HeH+.(A) Relative rotational level populations
as functions of ion storage timetfrom the
radiative model (starting temperature: 3000 K;
CSR radiation field: 99% at 6 K, 1% at 300 K)
forJas given and with time slices I to IV in
which the dominantJvaries from 3 to 0.
(B) Rate coefficientaDRðEdÞmeasured in the
marked time slices (mean ± SD).

10 −^9

10 −^8

10 −^9

10 −^8

10 −^9

10 −^8

Detuning energy (eV)

0.0001 0.001 0.01 0.1

10 −^9

10 −^8

Plasma temperatureTpl(K)

10 100 1000

10 −^9

10 −^8

10 −^7

kBTpl(eV)

B 10 − 3 10 − 2 10 − 1

J = 0

J = 2

J = 1

J 3 (av)

A

J = 0

J = 1

J = 2

J 3 (av)

Thermal

Early-universe models

& databases

ate coefficient (cm

3 s

-1)

R

-1)

s

3

Plasma rate coef. (cm

Fig. 4. Rotational-state selective DR rates

for HeH+.(A) Merged-beams rate coefficients

aJDRðEdÞforJ≤2 and average forJ≥3 (mainly

3 and 4; mean ± SD). The dashed lines mark

the shift of the maximum asJincreases.

(B) Solid lines indicate single-Jplasma rate

coefficientsaJDR;plðTplÞforJ≤2 and average (av)

forJ≥3 (mainly 3 and 4; mean with

shaded areas denoting ±SD). The dotted line

represents the fully thermal rate coefficient

aDR;thermðTrot¼TplÞ. Dashed-dotted lines

indicate values applied in early-Universe models

( 21 , 22 ) and astrochemistry databases ( 23 – 25 ).

See ( 19 ) for further discussion, numerical

fitting functions, and parameters.

RESEARCH | REPORT