Science - 16.08.2019

becomes much smaller (by a factor up to ~8)
than that for room temperature conditions and
remains nearly as low down toEde 0 :001 eV
ðEd=kBe12KÞ.
Substantial rotational dependence for pre-
dissociating Rydberg resonances has been pre-
dicted ( 14 , 15 )foraDRðEdÞin this energy range.
We studied this concept through the storage-
time dependence of the DR rate coefficient,
aDRðEd;tÞ. The rotational populations from
the radiative cooling model reveal how the
Jdistribution is dominated by increasingly lower
levels as the storage time advances (Fig. 3A).
TheaDRðEd;tÞdata were analyzed in time slices
adapted to some of the lowerJlevels (time slices
ItoIVforJ= 3 to 0; see Fig. 3B). Although in
slice I the DR rate at low collision energies is
similar to the room temperature results, this
level decreases as the ions cool rotationally.
Moreover, later slices with dominatingJ=2
or 1 indicate energy-shifted resonances below
the strong peak of time slice IV.
All time-varying DR rates represent linear
combinations of the time-invariant DR rates
aJDRðEdÞfor individualJlevels, weighted by
the average relative level populations in the
various time slices. Using the data for eight
separate intervals between 0.1 and 45 s and
the respective average level populations from
the radiative model, we deduced ( 19 ) state-
resolved rate coefficientsaJDRðEdÞup toJ=2
and the average DR rate from theJ≥3 levels
contributing at early storage times (mainlyJ=3
and 4). These data (Fig. 4A) show the domi-
nance of a single near-Lorentzian peak forJ=0.
Similar peaks with maxima downshifted inEd
are seen forJ≥1, where an increase of the width
points to unresolved peak structure. Moreover,
starting fromJ= 2 the rate atEd<0.01eV
grows. Recent theory, such as figure 13a of ( 14 ),
predicts a similarJ-dependent peak structure at
~0.01 to 0.07 eV but predicts rates up to 10 times
those of the experiment at lower energy, es-
pecially forJ=0.
These energy- and state-resolved DR rates
enable us to derive plasma rate coefficients for
individualJlevels or fully thermal ensembles.
We deconvolved ( 19 , 20 ) the merged-beams DR
rate coefficientsaJDRðEdÞto yield DR cross sec-
tions in narrow energy bins. Subsequently, we
reconvolved theseJ-specific cross sections to
obtain plasma rate coefficientsaJDR;plðTplÞ(see
Fig. 4B) for Maxwellian electron energy dis-
tributions of kinetic temperatureTpl.These
results can be state-population weighted to
obtain a rate coefficient for specified rotational
temperaturesTrotor even for fully thermalized
conditions [seeaDR;thermðTrot¼TplÞin Fig. 4B].
Our results forJ= 0 andJ= 1 at <80 K are
lower than the values ( 19 ) presently applied in
early-Universe models ( 21 , 22 ) and those listed
in astrochemistry databases ( 23 – 25 ) by factors
of 15 to 80. Compared with these previous data,
even the enhancedJ= 2 andJ≥3 average rates
are lower.
A recent study ( 22 ) (Fig. 2) shows that, at
redshiftsz< 15, the only reactions essential

Novotnýet al.,Science 365 , 676–679 (2019) 16 August 2019 2of4

Detection

HeH+ e-

Recombination Dissociation

HeH* H

He

B

A HeH+ @ 250 keV

e-@ 27-100 eV

Electrostatic

deflectors

Electron cooler

Multilayer

cryostat

Particle

detector

0.2

0/1

0.4

0.6

0.8

1

Rotational stateJ

(^00123456)
0.2
0.4
0.6
0.8
Relative state population
Room-temperature
experiments
300 K
CSR
radiation field
C
CSR
1 m
Fig. 1. Dissociative recombination in the cryogenic storage ring, CSR.(A) Scheme of the CSR
ring structure with the injected and stored HeH+ion beam (red), merged electron beam (blue),
reaction products (green), and particle detector. (B) Reaction scheme and position-sensitive
detection of coincident fragments. (C) Equilibrium rotational state populations of HeH+for previous
studies (300 K) and the estimated radiation field in the CSR.
Detuning energy (eV)
-1)
s
3
Rate coefficient (cm 10 −^9
10 −^8
10 −^7
0.001 0.01 0.1 1
B
A
C
CSR
10-50 s CRYRING
Ed = 0
0.044 eV
0102030
He - H detected distance
Probability (arb.)
P(
D)
D (mm)
Angular
dependence
0102030
Probability (arb.)
P(
D)
He - H detected distanceD (mm)
TARN II
300K
Fig. 2. DR for rotationally cold HeH+.(A) Blue circles indicate the merged-beams rate
coefficientaDRas a function of the detuning energyEdafter relaxation to >50%J=0 (this
experiment, 10 s <t< 50 s, mean ± SD); absolute scaling uncertainty ±20% (SEM). Red symbols
represent room temperature data from ( 11 ) (squares, absolute scaling uncertainty ±10% SEM)
and from ( 12 ) [triangles, scaled to ( 11 ) at 0.03 eV]. (B) Fragment distance distribution projected
into the detector plane forEd=0(blue)withfit( 19 ) for isotropic angular distribution (red).
(C) Projected fragment distance distribution forEd=0.044eV(blue)withfit( 19 )forajY 10 j^2
angular distribution of the fragments (red). The angular dependences in (B) and (C) are indicated
schematically. arb., arbitrary units.
RESEARCH | REPORT