# Ion-molecule reactions below 1 K: Observation of a strong enhancement of the
reaction rate of the ion-dipole reaction
$\mathrm{He}^{+}+\mathrm{CH}_{3}\mathrm{F}$

Valentina Zhelyazkova  Fernanda B. V. Martins  Josef A. Agner  Hansjürg
Schmutz  Frédéric Merkt<EMAIL_ADDRESS>Laboratory of Physical
Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland

###### Abstract

The reaction between He+ and CH3F forming predominantly CH${}_{2}^{+}$ and
CHF+ has been studied at collision energies $E_{\rm coll}$ between 0 and
$k_{\rm B}\cdot 10$ K in a merged-beam apparatus. To avoid heating of the ions
by stray electric fields, the reaction was observed within the orbit of a
highly excited Rydberg electron. Supersonic beams of CH3F and He($n$) Rydberg
atoms with principal quantum number $n=30$ and 35 were merged and their
relative velocity tuned using a Rydberg-Stark decelerator and deflector,
allowing an energy resolution of 150 mK. A strong enhancement of the reaction
rate was observed below $E_{\rm coll}/k_{\rm B}=1$ K. The experimental results
are interpreted with an adiabatic capture model that accounts for the state-
dependent orientation of the polar CH3F molecules by the Stark effect as they
approach the He+ ion. The enhancement of the reaction rate at low collision
energies is primarily attributed to para-CH3F molecules in the $J=1,\,KM=1$
high-field-seeking states, which represent about 8% of the population at the 6
K rotational temperature of the supersonic beam.

Considerable progress has recently been made in experimental studies of
molecular collisions and reactions at low temperatures and collision energies
(see, e.g., Refs. Gilijamse  _et al._ (2006); Bell and Softley (2009); Ni  _et
al._ (2010); Parazzoli  _et al._ (2011); Willitsch (2012); Henson  _et al._
(2012); Chefdeville  _et al._ (2013); Stuhl  _et al._ (2015); Jankunas  _et
al._ (2014); Heazelwood and Softley (2015); Perreault  _et al._ (2017); de
Jongh  _et al._ (2020) and references therein). Investigations below 1 K have
become possible for processes involving neutral molecules Ni  _et al._ (2010);
Henson  _et al._ (2012); Jankunas  _et al._ (2014); Perreault  _et al._
(2017); Zou  _et al._ (2019); Bibelnik  _et al._ (2019); Gawlas and Hogan
(2020). Less progress has been made for ion-molecule reactions, primarily
because ions are easily heated by stray fields, which makes the low
temperature range very difficult to reach. Methods relying on supersonic beams
from Laval nozzles Marquette  _et al._ (1985) and guided ion beams and traps
Gerlich (2008); Paetow  _et al._ (2010); Tran  _et al._ (2018); Markus  _et
al._ (2020) have proven successful to study ion-molecule reactions down to
about 10 K. Approaches to reach the range below 1 K relying on ion traps and
Coulomb crystals are being developed and promising results were reported Bell
and Softley (2009); Willitsch (2012); Dörfler  _et al._ (2019). In the absence
of experimental data on ion-molecule reactions below 10 K, theory has
challenged experiments for several decades Clary (1990), and it is only today
that experiment can respond.

In this letter we present, with the example of the reaction between He+ and
CH3F, experimental results at very low collision energies on barrier-free
exothermic reactions between ions and polar molecules, which are the class
where the strongest low-temperature effects are expected Ausloos (1978);
Bowers (1979); Ng and Baer (1992); Clary (1985); Troe (1987). We report the
observation of a large enhancement of the reaction rate at collision energies
$E_{\rm coll}$ below $E_{\rm coll}/k_{\rm B}$ below 1 K related to the gradual
orientation, upon approach of the ion, of the polar molecule by the Coulomb
field of the ion. Numerous models and approximations have been used to predict
reaction rate constants of ion-dipole reactions below 10 K over the past 50
years Ausloos (1978); Bowers (1979); Ng and Baer (1992); Clary (1985); Clary
_et al._ (1985); Clary (1990); Stoecklin and Clary (1992); Troe (1987, 1996);
Auzinsh  _et al._ (2013a, b); Dashevskaya  _et al._ (2005, 2016). These models
typically predict enhancements of the reaction rates at the lowest
temperatures and collision energies, however, with large differences
concerning the extent of the enhancement and the range over which it takes
place. Our new results provides a basis for the assessment of these models.

Experimentally we have extended a method originally developed to study the
reaction H${}_{2}^{+}$ \+ H${}_{2}\rightarrow$ H${}_{3}^{+}$ \+ H at collision
energies below 1 K Allmendinger  _et al._ (2016a, b) to the reactions of He+
with polyatomic molecules. In brief, the ion reactant (He+) is substituted by
the corresponding Rydberg system (He$(n)$) in a state of high principal
quantum number $n$. The Rydberg electron acts as a distant spectator, does not
affect the reaction Pratt  _et al._ (1994); Wrede  _et al._ (2005); Matsuzawa
(2010), and serves the purpose of shielding the ions from stray fields. The
method combines the advantages of merged-beams approaches to study neutral-
neutral reactions at low collision energies Henson  _et al._ (2012); Jankunas
_et al._ (2014); Perreault  _et al._ (2017) with those offered by Rydberg
atoms and molecules, e.g., the ease of manipulation of their translational
motion with inhomogeneous electric fields Procter  _et al._ (2003); Vliegen
_et al._ (2004); Merkt (2019).

Figure 1:  a) Schematic view of the merged-beam setup used to study the
$\mathrm{He}^{+}+\mathrm{CH}_{3}\mathrm{F}$ reaction at low collisional
energies, with the 50-electrode Rydberg-Stark deflector and the ToFMS. b)
Examples of ToF mass spectra of the product ions recorded with (top panel) and
without (bottom panel) LRyd. The blue and red areas indicate the regions used
to monitor the relative reaction yields (see text).

The CH3F and He beams are produced in supersonic expansions of pure CH3F and
He gas, respectively, through the orifices of two home-made pulsed valves
(pulse duration $\leq 20$ $\mu$s, repetition rate 25 Hz). The two beams
initially propagate along axes separated by a 5∘ angle. The helium atoms are
excited to a Rydberg-Stark state and subsequently merged with the ground-state
CH3F beam using a surface-electrode Rydberg-Stark deflector Allmendinger  _et
al._ (2014, 2016a); Zhelyazkova  _et al._ (2019). After the CH3F and Rydberg-
He beams are merged, they enter a time-of-flight mass spectrometer (ToFMS)
(Fig. 1a), where the reaction product ions are extracted and detected with a
microchannel plate (MCP) detector. The center of the ToFMS along the merged-
beam propagation axis is defined as $y=0$.

The CH3F valve, positioned at $y\simeq-62$ cm, is temperature-stabilized to
$330\pm 0.4$ K, corresponding to a mean forward velocity of the beam of $\sim
870$ m/s. We use two identical fast-ionization gauges separated by 20 cm to
measure the velocity distribution of the CH3F beam. The CH3F beam is skimmed
twice to select its central, coldest part before it is merged with the
deflected Rydberg helium sample (referred to as He($n$) henceforth). The
relative populations of the rotational levels of the ortho- and para-CH3F
molecules in the beam both correspond to a temperature $T_{\rm rot}$ of
$\approx 6$ K, with only seven $J_{K}$ states significantly populated at 6 K,
i.e., $0_{0}$ (9.5%), $1_{0}$ (19.0%), $2_{0}$ (13.9%), $3_{0}$ (5.8%),
$1_{1}$ (23.5%), $2_{1}$ (17.3%) and $3_{1}$ (7.1%). Ortho-para conversion
does not take place in the supersonic expansion and the beam consists of 50%
of the para ($K=1$ states) and 50% of the ortho ($K=0$ states) nuclear-spin
isomer Hanson  _et al._ (2016).

The helium valve is positioned at $y\simeq-100$ cm, and slightly displaced
below the CH3F beam-propagation axis. A pulsed electric discharge at the valve
orifice populates the metastable (1s)1(2s)1 3S1 state of helium (referred to
as He* below) Halfmann  _et al._ (2000); Zhelyazkova  _et al._ (2019). The
copper body of the valve is cooled with a two-stage pulse-tube cryo-cooler and
temperature-stabilized to $100\pm 0.1$ K. The mean velocity of the He* beam in
the forward direction is $\sim 1040$ m/s. The He* beam passes through two
skimmers before it intersects a pulsed-laser beam of wavelength $\sim 260$ nm
(LRyd in Fig. 1a) in the presence of an electric field Zhelyazkova  _et al._
(2019). The He* atoms are excited by the laser to a low-field-seeking $n$
Rydberg state labeled by $k$ ($k=-(n-|m_{\ell}|-1):2:(n-|m_{\ell}|-1)$, where
$m_{\ell}$ is the magnetic quantum number Gallagher (1994)). The laser
radiation is linearly polarized parallel to the electric field and thus
$m_{\ell}=0$. For the experiments presented here, $(n,k)=(30,25)$ or
$(35,26)$. After excitation, the He($n$) atoms fly over the deflector, which
consists of an array of 50 electrodes (dimensions 1 mm $\times$ 30 mm in the
$y$ and $x$ dimensions, respectively), attached to a curved substrate.

The design and operation principle of the deflector are described in Refs.
Allmendinger  _et al._ (2014); Zhelyazkova  _et al._ (2019). The defelctor can
also be used to accelerate or decelerate the He(n) beam by applying chirped
oscillatory potentials of amplitude $V_{\rm amp}$ to the electrodes Hogan  _et
al._ (2012).

After the He($n$) atoms are merged with the CH3F beam, they enter the ToFMS.
To define the 7-$\mu$s-long time interval during which the reaction is
monitored and to optimize the energy resolution of the experiment Allmendinger
_et al._ (2016a), we apply a sequence of two 3-$\mu$s-long electric-field
pulses separated by a field-free interval of 7 $\mu$s. The first pulse sweeps
all ions produced prior to the selected reaction-time interval out of the
reaction zone. The second pulse then extracts all ions generated during the
selected 7-$\mu$s-long reaction time toward the MCP detector. Examples of ToF
traces of the ion products of the $\mathrm{He}(n)+\mathrm{CH}_{3}\mathrm{F}$
and $\mathrm{He}^{*}+\mathrm{CH}_{3}\mathrm{F}$ reactions are displayed in
Fig. 1b. In the lower trace, obtained without LRyd, a prominent peak
corresponding to H2O+ is observed, in addition to several smaller peaks
assigned to OH+, N${}_{2}^{+}$, CH${}_{p\in\\{1,2,3\\}}^{+}$ and
CH${}_{q\in\\{0,1,2\\}}{\rm F}^{+}$ ions. These ions originate from Penning
ionization processes between the He* atoms and either background water,
nitrogen, or CH3F molecules in the vacuum chamber. When LRyd is turned on,
several additional peaks become visible (upper trace). The first broad peak,
at arrival times $<1.6$ $\mu$s, originates from field-ionized He($n$) atoms.
The other peaks correspond to the CH+, CH${}_{2}^{+}$, CH${}_{3}^{+}$, CF+ and
CHF+ products of the He($n$)+CH3F reaction and indicate a rich short-range
chemistry.

The dominant product ions are CH${}_{2}^{+}$, CF+ and CHF+. We determine the
relative reaction yield from the integrated signals within the blue
(I${}_{\mathrm{CH}_{2}^{+}}$) and red
(I${}_{\mathrm{CF}^{+}+\mathrm{CHF}^{+}}$) integration windows indicated in
the top panel of Fig. 1b and monitor them as a function of $E_{\mathrm{coll}}\
(=\mu v_{\mathrm{rel}}^{2}/2)$, given by the selected relative velocity
$v_{\mathrm{rel}}$ of the two beams ($\mu$ is the reduced mass of the He+ \+
CH3F collision partners).

As in previous merged-beam studies of neutral-neutral reactions at low
collision energies Henson  _et al._ (2012); Jankunas and Osterwalder (2015),
we exploit the velocity dispersion resulting from the short opening time of
the CH3F valve ($\leq 20\,\mu$s) and the long distance between the valve
orifice and the reaction region to select a very narrow velocity range
($\approx\pm 5$ m/s) of the CH3F beam around the chosen velocity of 990 m/s.
By applying the appropriate potential waveforms to the deflector, we scan the
He($n$)-beam velocity $v_{\mathrm{He(\textit{n})}}$ in the 750-1200 m/s range,
corresponding to relative velocities
$v_{\mathrm{rel}}=v_{\mathrm{CH_{3}F}}-v_{\mathrm{He(\textit{n})}}$ between
$240$ m/s and $-210$ m/s and collisions energies $E_{\mathrm{coll}}$ between 0
and $(12\ {\rm K})\cdot k_{\mathrm{B}}$.

Figure 2:  a) and b): Measured normalized signals corresponding to the
CH${}_{2}^{+}$ ($I_{\mathrm{CH}_{2}^{+}}$, blue circles) and CF+ \+ CHF+
($I_{\mathrm{CF}^{+}+\mathrm{CHF}^{+}}$, red circles) product ions of the
reaction He++CH3F as a function of the selected final longitudinal velocity
$v_{\mathrm{He}(n)}$ of the beam of He atoms excited to $(n,k)=(30,25)$ (a)
and $(35,26)$ (b) Rydberg-Stark states. The dashed vertical lines indicate the
selected CH3F-beam longitudinal velocity. c) and d): Comparison of the
integrated total product-ion signals ($I_{\mathrm{tot}}$ =
$I_{\mathrm{CH}_{2}^{+}}$ \+ $I_{\mathrm{CF}^{+}+\mathrm{CHF}^{+}}$) for
$v_{\mathrm{He}(n)}>v_{\mathrm{CH_{3}F}}$ (black dots) and
$v_{\mathrm{He}(n)}<v_{\mathrm{CH_{3}F}}$ (open circles) as a function of
$E_{\mathrm{coll}}/k_{\mathrm{B}}$ with the calculated reaction rate constants
averaged over the CH3F rotational states for $T_{\mathrm{rot}}=6$ K, with
(black line) and without (yellow circles) the effect of the average over the
distribution of collision energies.

Decelerating or accelerating the He($n$) atoms away from their initial
velocity of 1040 m/s leads to losses. To account for this effect and Rydberg-
atom-lifetime effects, the values of $I_{\mathrm{CH}_{2}^{+}}$ and
$I_{\mathrm{CF}^{+}+\mathrm{CHF}^{+}}$ measured at each value of
$v_{\mathrm{He(\textit{n})}}$ are normalized to the total amount of He($n$)
that reaches the center of the ToFMS. This normalization factor is determined
in separate pulsed-field-ionization measurements carried out by applying a
pulsed potential of 5 kV to the bottom electrode of the ToFMS and detecting
the resulting He+ ions on the MCP. By scanning the time at which the field-
ionization pulse is applied, we also determine the time
$t_{c,v_{\mathrm{He(\textit{n})}}}$ at which the center of the Rydberg-atom
packet reaches $y=0$ with respect to the time of laser excitation. The
CH3F-valve opening time is then chosen such that the molecules traveling at
990 m/s also arrive at position $y=0$ at time
$t_{c,v_{\mathrm{He(\textit{n})}}}$, which corresponds to the middle of the
7-$\mu$s-long time interval during which the reaction is monitored.

Displayed in the top panels of Fig. 2 are the normalized ion signals
$I_{\mathrm{CH}_{2}^{+}}$ and $I_{\mathrm{CF}^{+}+\mathrm{CHF}^{+}}$ as a
function of $v_{\mathrm{He}(n)}$ obtained from reactions with He($n$) atoms
excited to $(n,k)=(30,25)$ (a) and $(35,26)$ (b) Rydberg-Stark states. The
data points and associated vertical error bars correspond to averages and
standard deviations, respectively, each determined from 8000 experimental
cycles. To be able to directly compare the data recorded at the two different
values of $n$, $V_{\rm amp}$ was chosen such that the depths of the moving
traps were the same for both sets of Rydberg states. The loading of the
Rydberg-atom beam into the moving traps was carefully optimized to avoid
heating, resulting in a translational temperature of
$T_{\mathrm{He}(n)}\approx 140(60)$ mK at both $n$ values, as estimated from
particle-trajectory simulations.

The measured values of both $I_{\mathrm{CH}_{2}^{+}}$ and
$I_{\mathrm{CF}^{+}+\mathrm{CHF}^{+}}$ depicted in Fig. 2a,b increase and
reach a maximum at $v_{\mathrm{He(\textit{n})}}=v_{\mathrm{CH_{3}F}}=990$ m/s
($v_{\mathrm{rel}}=0$), which corresponds to approximately twice the signal
strengths measured at $v_{\mathrm{He(\textit{n})}}=750$ m/s and 1200 m/s. The
collision-energy dependence of the total product-ion yield
$I_{\mathrm{tot}}=I_{\mathrm{CH}_{2}^{+}}+I_{\mathrm{CF}^{+}+\mathrm{CHF}^{+}}$
for $v_{\mathrm{rel}}<0$ (black dots) and $v_{\mathrm{rel}}>0$ (open circles)
is presented in Fig. 2c,d. It reveals a slow increase as
$E_{\mathrm{coll}}/k_{\mathrm{B}}$ decreases from 10 to 1 K, and a sharp
increase below 1 K. The data sets obtained at $n=30$ and 35 confirm the
expectation that the Rydberg electron merely acts as a spectator in fast
capture-type reactions, as already demonstrated in our previous studies of the
H2 \+ H${}_{2}^{+}$ reaction Allmendinger  _et al._ (2016a, b).

The gray horizontal bars in Fig. 2c,d represent the ranges of collision
energies $\Delta E_{\rm coll}$ probed experimentally at the selected values of
$E_{\rm coll}$, and correspond to the energy resolution of our measurements,
given by

$\displaystyle\frac{\Delta E_{\mathrm{coll}}}{k_{\mathrm{B}}}$
$\displaystyle=$ $\displaystyle\Delta T_{\mathrm{res}}+2\sqrt{\Delta
T_{\mathrm{res}}}\sqrt{\frac{E_{\mathrm{coll}}}{k_{\mathrm{B}}}}.$ (1)

In Eq. (1), $\Delta T_{\mathrm{res}}=150$ mK corresponds to the estimated
distribution of relative velocities when $E_{\mathrm{coll}}$ is zero. It is
obtained by adding in quadrature the translational temperatures of the two
beams ($T_{{\rm He}(n)}\approx 140$ mK, and $T_{{\rm CH}_{3}{\rm F}}\approx
50$ mK) in the reaction zone, as determined from numerical particle-trajectory
simulations in the case of the He($n$) beam and from measurements with the
fast-ionization gauges in the case of CH3F.

Figure 3:  a) and b): Calculated energies in CH3F for states with $K=0$ (a)
and $|K|=1$ (b) in the presence of an electric field. (c) and (d): Adiabatic
interaction potentials for the $\mathrm{He}^{+}+\mathrm{CH_{3}F}(J,K,M)$
reaction, $V(R)$, for CH3F in the states highlighted in black, red and green
in a) and b), for $\ell=0$ (dash-dotted lines) and $\ell=25$ (solid lines)
(see text for details). (e) and (f): Calculated values of the reaction rate
constants for CH3F in the indicated states. a), c) and e): $K=0$; b), d) and
f): $|K|=1$.

CH3F has a polarizability volume $\alpha^{\prime}$ of $2.54\times 10^{-30}$ m3
Olney  _et al._ (1997), corresponding to a Langevin-capture rate constant
$k_{\rm L}=\sqrt{\pi\alpha^{\prime}e^{2}/(\mu\epsilon_{0})}$ of
$1.97\times{}10^{-15}$ m3/s. It has a permanent electric dipole moment
$\mu_{\rm el}$ of $6.20\times 10^{-30}$ Cm Marshall and Muenter (1980). In one
of the standard capture models for ion-dipole reactions, based on the locked-
dipole approximation (LDA) Bowers (1979), the dipole moment is assumed to be
locked with the energetically favorable orientation along the collision axis,
which results in the long-range interaction potential

$V_{{\rm
LDA},\ell}(R)=-\frac{\alpha^{\prime}e^{2}}{8\pi\epsilon_{0}R^{4}}-\frac{e\mu_{\rm
el}}{4\pi\epsilon_{0}R^{2}}+\frac{\hbar^{2}\ell(\ell+1)}{2\mu R^{2}}.$ (2)

The LDA leads to an expression for the energy-dependent rate constant

$k_{\rm LDA}(E_{\rm coll})=k_{\rm L}+\frac{e\mu_{\rm
el}}{2^{3/2}\epsilon_{0}\sqrt{\mu E_{\rm coll}}}$ (3)

that diverges at $E_{\rm coll}=0$. The corresponding thermal rate constant

$k_{\rm LDA}(T)=k_{\rm L}+\frac{e\mu_{\rm
el}}{\epsilon_{0}}\sqrt{\frac{1}{2\pi\mu k_{\rm B}T}}$ (4)

is $4.03\times 10^{-13}$ m3/s at the effective temperature of 150 mK in our
experiments at $E_{\rm coll}=0$. The LDA model predicts enhancement factors
$k_{\rm LDA}(T=150\ {\rm mK})/k_{\rm LDA}(E_{\rm coll}=k_{\rm B}\cdot 10\ {\rm
K})$ and $k_{\rm LDA}(T=150\ {\rm mK})/k_{\rm LDA}(E_{\rm coll}=k_{\rm B}\cdot
4\ {\rm K})$ of 8.86 and 5.49, respectively, whereas our experiments yield
values of 1.9 and 1.6 for these factors.

To better describe the rate constants of ion-dipole reactions at low collision
energies, we found it necessary to consider the initial distribution of the
polar molecules over the rotational levels $|JKM\rangle$ in the supersonic
beam and how these states are affected by the growing electric-field strength
they experience upon approach of the He+ ion Clary (1985); Troe (1987). To
analyze our experimental results and test more advanced models, we adapt the
statistical adiabatic-channel model for ion–dipole collisions of Troe Troe
(1987) to our experimental situation. We consider that the signal observed at
each value of $E_{\rm coll}$ in Fig. 2c,d is proportional to a reaction rate
$\langle k(\bar{E}_{\rm coll})\rangle$ that corresponds to the average over a
Gaussian distribution $G(E_{\rm coll})$ of collision energies centered at the
selected $E_{\rm coll}$ value, with widths given by Eq. (1):

$\langle k(\bar{E}_{\rm coll})\rangle=\int_{0}^{\infty}G(E_{\rm coll})k(E_{\rm
coll}){\rm d}E_{\rm coll}.$ (5)

The values of $k(E_{\rm coll})$ are determined as sums of state-specific rate
coefficients over all CH3F $j=|JKM\rangle$ states populated at $T_{\rm rot}=6$
K:

$k(E_{\rm coll})=\sum_{j}{\rm e}^{-E_{j}/(k_{\rm B}T_{\rm rot})}k_{j}(E_{\rm
coll}),$ (6)

where $E_{j}$ is the field-free energy of state $j$. Only $K=0$ (ortho) and
$|K|=1$ (para) CH3F rotational levels with $J\leq 4$ are significantly
populated at 6 K, resulting in 25 $j=|J0M\rangle$ and 48 $j=|J\pm 1M\rangle$
states to be considered in the sum. We then calculate the $R$-dependent
adiabatic-channel potentials by adding the Stark shifts $\Delta E^{\rm
Stark}_{j}(F)$ of the rotational levels to the Langevin-type potentials

$V_{j,\ell}(R)=-\frac{\alpha^{\prime}e^{2}}{8\pi\epsilon_{0}R^{4}}+\frac{\hbar^{2}\ell(\ell+1)}{2\mu
R^{2}}+\Delta E^{\rm Stark}_{j}(F(R))$ (7)

up to electric fields $F$ of $4\times 10^{3}$ kV/cm, corresponding to a He+–
CH3F distance $R$ of 1.9 nm. The calculation of Stark shifts is performed by
diagonalizing the Hamiltonian matrix including the Stark effect in a basis of
symmetric-top rotational wavefunctions as explained, e.g., in Ref. van de
Meerakker  _et al._ (2012). The state-specific rate coefficients at a given
$E_{\rm coll}$ value are obtained from the maximal $\ell$ partial wave
satisfying the Langevin-capture condition $E_{\rm coll}\geq V_{j,\ell}(R)$.

The essential steps of the calculations are illustrated in Fig. 3, which shows
the results for $K=0$ and $\pm 1$ in the left and right columns, respectively.
The top panels depict the rotational energies including Stark shifts, the
middle panels show the adiabatic potentials for $\ell=0$ and 25 for three
representative states, and the bottom panels the corresponding state-specific
rate coefficients. Levels with a positive Stark shift (negative value of the
product $KM$) exhibit long-range energy barriers and vanishing rate constants
at the lowest collision energies. In contrast, the rate constants of states
with negative Stark shifts at low fields continuously grow with decreasing
$E_{\rm coll}$ values, the effect being particularly strong for the states
subject to a linear Stark shift at low fields, as exemplified by the
$J=1,KM=1$ Stark states (Fig. 3f). The yellow dots in Fig. 2c,d represent the
calculated state-averaged rate constants $k(E_{\rm coll})$ [Eq. (6)] and the
black line the rate constants $k(\bar{E}_{\rm coll})$ integrated over the
range of collision energies probed at each selected collision energy [Eq.
(5)]. The enhancement of the rate constants below 1 K is dominated by the
contributions from the $J=1,KM=1$ states, which represent only 8% of the total
population at 6K. The calculated and experimental relative rate constants
agree within the experimental error bars over the entire range of collision
energies, which enables us to plot the experimental result on an absolute
scale in Fig. 2c,d, with a maximal value of $5.4\times 10^{-14}$ m3/s at
$E_{\rm coll}=0$, more than 20 times larger than $k_{\rm L}$ but 7.5 times
smaller than $k_{\rm LDA}(T=150$ mK). Inspection of Fig. 2a,b reveals that the
enhancement of the yield of F-containing ions near $E_{\rm coll}=0$ is
stronger than that of CH${}_{n}^{+}$ ions. We attribute this observation to
the orientation of CH3F molecules in the $J=1,KM=1$ state, which exposes the F
side of the molecule to the He+ ion.

The experimental results presented in this letter are the first to reveal a
strong enhancement of the rate of an ion-dipole reaction below 1 K. The
theoretical analysis of the results leads to the determination of energy-
dependent, state-specific rate coefficients, from which thermal rate constants
can be calculated, and enables us to conclude that the sharp enhancement of
the rates below 1 K originates from states exhibiting a negative linear Stark
shift at low fields. Our results demonstrate the failure of the LDA and the
validity of the adiabatic channel model in the range of $E_{\rm coll}/k_{\rm
B}$ values between 0.1 and 10 K. The enhancement observed experimentally would
be much larger if the CH3F sample could be prepared selectively in states with
positive $KM$ values and this aspect represents an attractive prospect for
future work.

###### Acknowledgements.

We thank Dr. Matija Žeško for help with the development of the experimental
apparatus, Joël Jenny for his contributions to preliminary measurements, and
Katharina Höveler, Dr. Paul Jansen, and Dr. Johannes Deiglmayr for fruitful
discussions. This work is supported by the Swiss National Science Foundation
(Grant No. 200020-172620) and the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (Advanced
Grant No. 743121).

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In search for infalling clumps in molecular clouds
A catalogue of CO blue-profiles

Vol.0 (20xx) No.0, 000–000

Zhibo Jiang
Shaobo Zhang
1      Zhiwei Chen
Yang Yang
Shuling Yu
Haoran Feng
Ji Yang
the MWISP group

Purple Mountain Observatory, Chinese Academy of Sciences,
10 Yuanhua Road, 210023
Nanjing, China<EMAIL_ADDRESS>
University of Science and Technology of China, Hefei 230026, China

Center for Astronomy and Space Sciences, Three Gorges University, Yichang 443002, China

We have started a systematic survey of molecular clumps with infall motions to study the very early phase of star formation. Our first step is to utilize the data products by MWISP to make an unbiased survey for blue asymmetric line profiles of CO isotopical molecules. Within a total area of $\sim$ 2400 square degrees nearby the Galactic plane, we have found 3533 candidates showing blue-profiles, in which 3329 are selected from the &[13] pair and 204 are from the [13]& pair. Exploration of the parametric spaces suggests our samples are in the cold phase with relatively high column densities ready for star formation. Analysis of the spatial distribution of our samples suggests that they exist  virtually in all major components of the Galaxy. The vertical distribution suggest that the sources are located mainly in the thick disk of $\sim$ 85 parsec, but still a small part are located far beyond Galactic midplane.   Our follow-up observation indicates that these candidates are a good sample to start a search for infall motions, and to study the condition of very early phase of star formation.

Z. Jiang et al.
In Search for Infalls

§ INTRODUCTION

Gravitational collapse of dense molecular cloud cores is a key step in the formation of stars <cit.>. Presently due to the limitation of the observational facilities,  it is difficult to obtain a motion picture showing a core in the process of gravitational collapse. However, line profiles can provide signatures of inward collapse motion.  As theoretical modelings show <cit.>, after a collapse happens, the center of the core becomes warmer due to the accumulation of gravitational energy while the outside envelope remains relative cool.  In the configuration of an inflowing core surrounded with a static envelope, the radiation transfer along the line of sight can be simplified by a two layer model for both the gas flowing away and toward the observer <cit.>. For the gas flowing toward the observer, the inner layer with higher excitation is nearer to the observer than the outer layer with lower excitation; for the flow-away gas, emission from the inner layer with higher excitation is absorbed by the outer layer with lower excitation lying closer to the observer. A double-peaked line profile with an absorption dip is produced by the above radiation transfer. The blue peak (gas flowing toward the observer) is stronger than the red peak (gas flowing away from the observer). This effect is especially conspicuous for molecular transition lines with a suitable optical depth and critical density. This kind of profiles are commonly referred to as “blue-profiles”. They have been discussed by many researchers, and are regarded as an indicator of gas inflow motion <cit.>, or infall signature. To distinguish a blue-profile from  multi-component emissions in the line of sight that may also show double-peaks, one needs an optically thin line, whose profile is single-peaked without  a self-absorption feature.  The peak position of the optically thin line should be close to the self-absorption dip between the blue and red peaks.

Observational studies of the blue-profiles started in early 1990's <cit.> and are seen accelerated recently. Up to date, the studies can be classified into two categories. One is case study, i.e. detailed observations toward some particular star-forming complexes to study the physical conditions of regions showing infall signature <cit.>. The other is the deliberated search, i.e., systematical searches for infall signatures in deliberately selected samples of different properties, such as low-mass protostellar objects <cit.>, high-mass star-forming regions <cit.>, high-mass protostellar objects <cit.>, high infrared extinction clouds <cit.>, massive star-forming cores <cit.>, and early dense cores <cit.>, extended green object <cit.>, etc.

Above studies have presented us with diverse hints on the initial phase of star formation, e.g., when the gravitational collapse starts and ends, whether high- and low-mass stars start their life in similar ways, and the time scale of mass-infall phase. However, a comprehensive study on the infall phase is necessary to understand fully the process how dense molecular cores turn into stars, and to contribute to solve the long-standing problem of the origin of the stellar initial mass function.  Previous studies mainly utilized known targets that have shown star-forming activities as a start to look into. This kind of researches will inevitably introduce bias if a statistical study is carried out upon them. We therefore do the work in an opposite direction, i.e., by merely looking for infall signatures in the Galaxy without any other assumption,  we study the physical properties and star-forming activities where the signatures happen. The ongoing Milky Way Imaging Scroll Painting Project <cit.>, a large scale survey of CO (J = 1 - 0) lines in the northern Galaxy, provides an excellent opportunity to start up such a kind of work.

Our project is to set up a sample of CO blue-profiles using the MWISP data by blind search, and refine it by further observations using some more infall-sensitive lines (such as HCO$^+$ lines). The aim of this project is to obtain a comprehensive sample of infall candidates with a high confidence level. This paper is to present the very first result of our project, a preliminary catalogue of CO blue-profiles.

The structure of this paper is arranged in this way: in Sec. <ref> we give a brief introduction to data preparation, strategy of blind search for blue-profiles; in Sec. <ref> we present the main catalogue and the associated line profiles; in Sec. <ref> we discuss the distribution and parameter space of sources; and Sec. <ref> summarizes our results.

§ METHOD

§.§ Data

All data used in this work are based on the MWISP data products. A detailed description of the data acquisition, quality control and archiving scheme can be found in <cit.>. The archive data are in unit of “cells”, the main region of which is an area of 30$\times$ 30. According to the survey strategy,
the outskirts of each cell are observed with the 9-beam Superconducting Spectroscopic Array Receiver <cit.> less than the main region. Consequently, the RMS noise levels are higher in the edge part than in the central. Therefore, a combination with the neighboring cells is necessary to achieve a uniform noise level. At this step, we intentionally extend the area of each cell to some extent (generally by 0.5 arcmin on each side) to avoid possible edge effects. We then cut off unnecessary velocity channels ($\abs[V_{LSR}] \ge$ 200 ) to minimize the unnecessary computation, and possible unreal detections due to untrue signals which might be a problem in the manual check step. The data reduced as such are ready for  machine work.

(left) The distribution of main-beam temperatures of L134 on a time scale of seven years (2011-2017). The blue, green and red histograms represent , [13] and  peak intensities, respectively. (right) The distribution of velocity difference between [12] and [13] in the same period. The figure shows the radial velocities of [12] are overall less than that of [13] by $\sim$ 0.15  (about one channel). A secondary peak at $\sim$ 0.1  is found, mainly caused in the the 2011 observation season.  The results of all nine beams are included.

Because our work relies on the comparison among different lines, it is an essential demand that the observation facility should be stable on a large time scale. Fortunately, MWISP has a scheme that immediately before and after the observation to each cell,  observations toward a “standard source”  were  made to monitor the system performance.  As an example, in Fig. <ref> we show the distributions of T$_{MB}$ and V$_{LSR}$ difference of L134, one of the “standard sources”. We choose this source as an illustration because its line-widths are relative small to allow accurate estimation of the central velocity. The gross data  were collected from 2011 November to 2017 December in all three lines.  The 1$\sigma$  variations of T$_{MB}$ are 0.66 K, 0.47 K, and  0.47 K, or 7.4%, 8.4%, and 20% on relative scale for the three lines, respectively. This suggests the system was reasonably stable within the period of seven years. The radial velocities with respect to local standard of rest (LSR) are also checked within the period. As shown in Fig. <ref>,  V$_{LSR}^{12CO}$ is roughly less than  V$_{LSR}^{13CO}$ by $\sim$ 0.15 km $s^{-1}$ (blue shifted). <cit.> showed a slight velocity shift between  and [13] which is consistent with this result. This  difference could be intrinsic or arise in the observations. Considering that the V$_{LSR}$ differences between $^{12}$CO blue peak and $^{13}$CO center in our selected sample are mostly significantly greater than that value, this discrepancy, even if could arise due to the instrument and observation, does not affect our result too much.

§.§ Search Strategy

As stated above, two lines, one being optically thick and the other optically thin, are necessary to discriminate between blue-profiles and multi-components. We use the $^{12}$CO with $^{13}$CO (hereafter Pair-1), and $^{13}$CO with C$^{18}$O (hereafter Pair-2) as two line pairs to do the work, i.e., we arbitrarily assume  $^{13}$CO as an optically thin line and $^{12}$CO as the optically thick to search for blue-profiles, and then do it again with the other line pair. This scheme is reasonable because  the  $^{13}$CO line could be optically thin in some cases while thick elsewhere. We note that in the former case, the optically thin assumption of [13] lines, which might be not true, does not affect the judgement of  blue-profiles, but might miss some candidates if  emissions are not detected.

Similar to the scheme of the MWISP survey,  the search regions for machine work are split into cells. Then the automatical search is done pixel by pixel within each cell.  As stated in Sec. <ref>, the area for each cell has a 0.5 overlap with the surrounding cells, redundant detections are inevitable, which are cleaned out at later steps.

§.§ Automatic Search

Up to date, MWISP has been accomplished the region l = [12, 230], and b = [-5.25, +5.25], with some coverage at l $<$ 12, covering a total area of $\sim$ 2400 square degrees,  and produced $\sim 10^8$ spectra.  It is impossible to deal with such a large amount of data manually. Initial automatic searches  have to be conducted to minimize the manual tasks.
At this step for each pixel, we assume [13] to be optically thin for Pair-1 and  for Pair-2. First of all, we decomposed the optically thin lines into components with a 1-dimensional watershed algorithm. Each component is Gaussian-like with a peak exceeding the nearby baseline or dip by over 5 RMS of the whole spectrum. Then the first and second moments were extracted for each component as center velocity and velocity dispersion. They were aligned with the optically thick counterpart to cut out segments of profiles to be selected. Two methods were then adopted to find profiles with double peaks.

Method one: we select optically thick profiles fulfilling the following criteria.

1. A peak should appear on the blue side of central velocity. Such peak must exceed the nearby dip or baseline by 3 RMS, and away from the center velocity by more than velocity resolution.

2. The peak on the blue side should be higher than the profile on the red side by at least 3 RMS. If a peak appears on the red side, the component is labelled with “double-peak", or a "shoulder" label will be assigned.

Method two: Gaussian fittings with two components were conducted to the optically thick profiles, and then results fulfilling the following criteria are selected.

1. Two components should reside on both sides of the center velocity, and away from it by more than velocity resolution.

2. The blue side Gaussian component must have a higher integrated intensity and peak.

§.§ Manual Check

First look at the spectra of the candidates resulted from the automatic search suggests that many of them are not really blue-profiles, or hardly to say that. Therefore, further manual check is  necessary to refine the candidate list. Picking up the candidates of  likely blue-profiles is a hard work. We wrote some codes with graphic user interface to assist task. Then the pick-up work is only a couple of mouse clicks.

By checking the spectra of the candidates and comparing with the numeric simulations (c.f., Sec. <ref>), the  candidates are rejected according to the following general rules:

-Spectra of either optically thick or thin lines are noisy: In the real data, the situation is much more complicated than the simulation due to the introduction of noises.  Further more, some candidates appear at the edge of a certain cell where the noise level is higher than those of central areas. Though this situation has been considered in the automatic search, there are still cases that the machine  would misjudge whether a peak is real or noise-induced, especially for optically thin lines.

-Two peaks of the optically thick line are far away (e.g. V$_{red}$-V$_{blue}$$>$ 10 ): This is just empirical since we seldom find blue-profiles with very large peak separation in the literature. The line width (Full Width at Half Maximum, FWHM) of the optically thin line is too large, i.e., $>$10 .

-Multi-peaks or flattened top in the optically thin line: It is usually very difficult to judge whether a blue-profile of the optically thick line comes from a single or multiple components if there exist multi-peaks or flattened top in the assumed optically thin line. Though there are cases that the peaks of the optically thin lines do not coincident with those of the optically thick lines, we suppose they still could arise from multi-components with very complicated physical conditions. However, the candidates with one situation are retained: for Pair-1 selected candidates, the [13] line also shows a blue-profile while the  emission is not detected. The two peaks of the $^{13}$CO line are between those of $^{12}$CO line. In this case it is likely that $^{13}$CO line is also optically thick, but the absorption is fainter than that of the $^{12}$CO line. In such a case self-absorption still exists to show a blue-profile, but the peak separation is smaller than that of the $^{12}$CO line.

§.§ Cleaning Candidates

The manual check is a tiresome work since the output of the automatic search returns hundreds of thousands of candidates. In the manual check step we cautiously relax the above criteria in order to avoid loss of some reliable candidates. After the manual checks, we make the Gaussian fittings to the line profiles. Since the fittings need human interactions in deciding parameters such as fitting ranges, line profiles of the candidates are checked again and some candidates are rejected at this step.

After the manual check, candidates with similar positions and velocities are grouped together. The similarity of two candidates is defined as the following two conditions are satisfied:

$$\Delta p = \sqrt{\Delta l^2cos{^2}b+\Delta b^2} \leq \Delta p_{0}; \Delta V_{c} \leq \Delta V_{0}$$

where $\Delta l$, $\Delta b$ and $\Delta V_{c}$ are the differences of the Galactic coordinates and central velocities of two candidates; $\Delta p_0 = 1.0^\prime$ and $\Delta V_0 =0.2\, $ in this work being based on the spatial and spectral resolution of the MWISP products.  For each group the sources are checked by eyes and those showing  blue-profile most significantly are  selected.

Lastly, in a few cases blue-profiles are detected in both Pair-1 and Pair-2, we merge them to the Pair-2 group since the physical parameters (c.f., Fig. <ref>), such as column densities and system velocities, could be more correctly estimated due to the fact that the optically thin lines are single-peaked.

§ THE CATALOGUE

Finally, a total of 3533 sources are registered as possessing  blue-profiled lines, out of which 3329 sources are selected from Pair-1, and 204 sources are selected from Pair-2.  In Table <ref> we present a subset of the candidates for illustration, while the whole catalogue is presented in the appendix[The full table can also be found at https://www.scidb.cn/en/detail?dataSetId=bc1c08c6e7ba426a9a07b8bad69b2ffb]. For each candidate we assign a name code, which is presented in Column 2. Name codes are based on the positions and velocities of the candidates, i.e., the (l, b) codes are reserved to the second decimal places and v to the first decimal places, and decimal points are removed from the final code.  As an example, if (l, b, v) = (123.450000, 1.230000, 123.4500), the code is assigned as “12345+0123+1235”. Column 3 & 4 give the Galactic coordinates of sources.  Column 5 gives the spatial association to the objects  from some well known catalogs, such as  IRAS PSC, NGC, the RAFGL catalog, the Sharpless catalog, and Lynds' dark nebular catalog, etc. We also checked some other catalogs such as H$_\textsc{II}$ candidates <cit.>, and the MSX dark cloud catalog <cit.>.  In Column 6 we indicate whether our candidates show blue-profiles with other tracers in the literature. The associations in Column 5 & 6 are shown in codes to save the table space, and noted as table footnotes. In Column 7 we give the distances of the sources. The distance of a source is obtained using the online distance calculator[http://bessel.vlbi-astrometry.org/node/378] which is based on the trigonometric parallax measurements of Galactic maser sources <cit.> and assumes all molecular clouds are located on spiral arms. Using a Bayesian approach, this tool is believed to be a major improvement of the kinematic distance estimate of Galactic molecular clouds. For a few sources that are near the tangent direction (l $\sim$ 90), the calculator does not give proper distances.

The second half of the table presents the derived parameters of the candidates.  Columns 8 & 9 (V$_c$, V$_b$) are the characteristic velocities of sources.  V$_c$ represents the “central” velocities, which are derived from Gaussian fittings to the optically thin lines. V$_b$ represents positions where blue peaks are found, which are largely obtained from double-component Gaussian fittings. However, in some cases when Gaussian fittings do not converge, we use the peak positions by eyes. Column 10 presents the skewness parameter, $\delta$V = (V$_{thick}$-V$_{thin}$)/$\Delta$V$_{thin}$, as suggested by <cit.>.

Columns 11-13 (T$_1$, T$_2$, T$_{ex}$) are related temperatures of the sources. T$_2$ represents the peak main beam temperature of the optically thin line. T$_1$ represents the expected main beam temperature of the optically thick line. Since the line profile shows self-absorbed feature, the “expected” peak is derived by Gaussian fitting to the whole profile while excluding the portion that shows self-absorption, i.e., we use the waist and foot portions in the fittings. Though the fitting portions have been carefully adjusted,  we caution that in some cases the derived values of T$_1$ are  sensitive to the fitting portions adopted, so that the errors could be very large – they may reach to the values of T$_1$ themselves in some extreme cases depending on the environments of individual sources, e.g. when multi-components coexist with the blue-profiles. However, in most cases, we expect the uncertainties being less than 20%. T$_{ex}$ is the excitation temperature calculated from T$_1$<cit.>:

$$T_{ex} = T_0[ln(1+\frac{1}{\frac{T_1}{T_0}+\frac{1}{exp({T_0/T_{bg})}-1}})]^{-1} $$
where $T_0 = h\nu_0/k$ =  5.53 K  for Pair-1, or   5.29 K for Pair-2, T$_{bg}$ (= 2.73 K) is the background temperature of the Universe. Here we assume the filling factor being close to unity. We use [13] to estimate the excitation temperatures of Pair-2 sources because in many cases  profiles are very complicated so that we cannot obtain reliable “expected” main beam temperatures. In such cases T$_{ex}$ might be underestimated since the [13] lines are not optically thick enough.

The column densities of H$_2$ (Column 14) are estimated from the integrated intensities of the optically thin lines assuming local thermal equilibrium (LTE). Under such assumption, the column densities of [13] or  are calculated by the following formula <cit.>:

$$ N(\co[13]|\CO) = f_1 \times f_0\times\frac{(T_{ex}+0.88)exp(\frac{T_0}{T_{ex}})}{exp(\frac{T_0}{T_{ex}})-1}\times\frac{\int T_{MB}\,dv \quad(K\,km\,s^{-1})}{f(J_\nu(T_{ex})-J_\nu(T_{bg}))} \qquad(cm^{-2})$$

where f$_0$ is approximately 2.48 $\times 10^{14}$ for both [13] and , T$_0$ equals 5.29 for [13] and 5.27 for , f is the beam filling factor which we assume to be 1.0 in this work, and $J_\nu(T) = T_0/(exp(T_0/T)-1)$. The optical depth correction factor $f_1 = \tau/(1-exp(-\tau))$. Where $\tau$ is calculated by:

The total column densities of molecular hydrogen, $N(H_2)$, are obtained assuming the CO abundance ratios, $ N(H_2) \approx 3.9 \times 10^5 N(^{13}CO)$ or $N(H_2) \approx 3.0 \times 10^6 N(C^{18}O)$<cit.>, which are derived from the infrared dark cloud and close to those from star-forming regions<cit.>. Several factors affect estimations of N($_{H2}$): 1) Assumption of LTE which may not be true if the sources are actually in the process of infall; 2) T$_{ex}$s estimations; 3) Abundances of [13] and  relative to those of molecular hydrogen change from region to region <cit.>;  4) Beam filling factors for the sources are not always close to unity. Therefore, it is difficult to estimate the overall uncertainties of N($_{H2}$). In the last column (Column 15) we indicate the line pairs adopted in searching for the blue-profiles.

The spectra (left) and gas distributions (right) of the candidates. On the left panels, the red, green and blue lines represent , [13] and  emissions, respectively. To enhance s/n ratios of the lines, the spectra are smoothed with median filter for each 3 velocity channels. For the same reason, the  spectra are also smoothed with 3$\times$3 spatial pixels,   The  dashed line indicates the system velocity. On the upper-right corners we indicate the Galactic coordinates (l, b), and the line-pairs used in the searching procedure. On the upper-left are the name codes of the candidates. The right panels show the integrated intensity map of the optically thin lines (contours) overlaid on those of the optically thick lines (grey scale). The red pluses indicate the positions where the blue-profiles are detected.

Fig. <ref> shows some examples of the spectra (left) and the relative location (right) where blue-profiles are detected. Again, for the limitation of the main body, the whole set of the figures is given in the appendix.  Fig. <ref> (05363+0004+0235) shows an ideal blue-profile in  emission with virtually symmetric profiles both in [13] and  lines, the blue-profile happens at the saddle point between two local maxima (right panel); Fig. <ref> (02869+0377+0073) shows a candidate selected from Pair-2. The  line of this source shows complicated peaks;
Fig. <ref> (01272+0069+0173) shows a blue-profile selected from Pair-1, but the red side of the  line is probably contaminated by another component. The  line, weak as it is,  also suggests such a possibility. However, we could recognize this candidate since the contamination is not too serious to affect our judgement;  Fig. <ref> (01282-0019+0349) shows a candidate that does not show clear blue-profile, but the  and [13] peaks are shifted redward with respect to the   peak. Such a configuration happens when infall velocity is relative large while the optical depth is moderate (c.f., the lower-right panel of Fig. <ref>). Fig. <ref> (01432+0268+0156) shows an example that both  and [13] lines exhibit blue-profiles, with the peak separation of  greater than that of the [13] line, while  is marginally detectable. The blue-profile happens at virtually the central part of a dense clump.  The examples presented here are typical cases in our candidates.

In Fig. <ref> we also present some extreme cases, which might be of interests to readers. Fig. <ref> (01288-0024+0355) shows a source with  wide profiles, even for the optically thin lines ([13] and C$^{18}$O), up to FWHM $\sim$ 6.6 and 4.0 , respectively. Fig. <ref> (01116-0014+1503) shows a target that has a very large system velocity, $\sim$ 150 . The kinematic distance being estimated $\sim$ 8.0 kpc, it is one of the most distant object in the catalog. Interestingly, this source presents blue-profiles both in  and [13] lines. Fig. <ref> (02849+0399+0064) shows a source that is rarely seen in the Galactic molecular clouds, i.e., the [13] line intensity is stronger than that of the  line. Aside of strong self-absorption of [12], there could be also a possibility of unusual [13] abundance and excitation environment.

In the right panel of each subset, we show the integrated intensity map of individual candidate. An interesting fact that should be noted here is that the infall-signatures do not always coincide with the clump centers (the points with the highest column densities). It would be interesting to ascertain whether this is a real fact or just an observational effect, which might be helpful in our understandings of the initial phase of star formation.

§ DISCUSSION

§.§ Numerical Experiments

In order to see what a blue-profiled line appears in different environments, and to assist us to identify infall candidates from a large number of outputs from the machine work,  we have done a series of numerical experiments. The experiments tried to simulate cores with inflowing gas, but with very simple models, e.g., fixed infall velocities, optical depths and line widths. Temperature and density profile variations are not considered in the experiments. To do this, we generate an emission line of Gaussian profile centered at 0.0 , and $\sigma$ = 2.0 , which has no physical meaning other than a scale in the velocity dimension, and upon which many other parameters are assumed.  The peak value is normalized to unity. A number of absorption lines, which are also of Gaussian profiles but with negative values, are put upon the emission line to mimic the absorption. The centers of the absorption lines are shifted a little to the red by fractions of $\sigma$, i.e., V$_{in}$ = f$_{dV}\sigma$. Here we use V$_{in}$ to designate the central velocity shift of the absorption feature because it is somehow related to the infall velocity in the reality. The negative maxima are assumed to be a few percent of unit (dip = f$_{dip}$) because the optical depths of infalling gas are expected to be optically thinner than the background emission. In the reality, the widths of the absorption lines are expected to be narrower than those of the emission lines, and so that are  set to some fractions of $\sigma$ ($\sigma_{abs}$ = f$_\sigma\sigma$).

One example of the numerical experiments with f$_\sigma$ = 0.5. The parameters are shown at the upper-right corner of each frame. The blue lines represent the self-absorbed optically thick lines showing  blue-profile lines, and the red lines indicate the un-absorbed optically thin lines for comparison. We also present $\delta V$ suggested by <cit.> for different cases.

In Fig. <ref> we show some results of the experiments with f$_\sigma$ = 0.5 and various f$_{dV}$'s and f$_{dip}$'s. The parameters are shown at the upper-right corner of each frame.  Though we also have done the experiments by varying f$_\sigma$, the results do not show very much difference and are not shown in this paper.
From Fig. <ref> we see that the observability of a blue-profile line strongly depends on the strength of the absorption (f$_{dip}$), but less sensitive to the velocity shift (V$_{in}$). For f$_{dip}$ $\sim$ 0.15, approximately corresponding to the optical depth $\tau\sim$ 0.15, a blue-profile is hardly seen even in our noise-free experiments and is thus not likely to be detected in real observations. In the cases of f$_{dip}\sim$ 0.3 ($\tau\sim$ 0.36),  red shoulders are seen clearly. In such cases real detections are  mostly missed because our auto-search algorithm searches only for double peaks.   The blue-profiles become observable when f$_{dip}\sim$ 0.45 ($\tau\sim$ 0.6) with a small velocity shift but are still unclear at large velocity shifts. For nearly all velocity shifts, the signatures are clearly observable at f$_{dip}\sim$0.6 ($\tau\sim$ 0.9).

At the corner of each frame, we also present the dimensionless skewness parameter, $\delta$V,  suggested by <cit.> as an indicator of the significance of blue asymmetry.  As can be seen from Fig. <ref>, $\abs[\delta V]$ generally increase as f$_{dip}$ but decrease as f$_{dV}$. In fact, our experiments suggest the absolute value of $\delta$V decreases also with  f$_\sigma$.

§.§ Parameter Distributions

Up to date, the MWISP project covers an area of $\sim$ 2400 square degrees toward the northern Galactic plane.  Though the sample is still quite far from complete, due to the fact that the blue-profiles are recognized without any other presumption, the blind search strategy enables us to avoid  bias toward known star-forming regions. This kind of work will provide a better approach to explore parametric space of the infalling molecular clumps. In the following we discuss the parametric distributions of our samples.

In Fig. <ref> we present the distributions of central velocities of the optically thin lines. In the main frame we show the pair-separated distributions while the overall distribution is shown in the inset, and the rest figures are treated in the same way. The distribution is generally in Gaussian style peaked around 5 , and shows excess in both wings.  A large amount of sources gather within  $\abs[V_{LSR}] \le$   10  , suggesting that our sources are mainly located  close to the Sun. We notice here, though not shown in the figure, the smallest and largest central velocity are -75.5 and 150.3 , respectively. An interesting feature seen from Fig. <ref> is that Pair-1 selected sources have lower radial velocities (with a median value of $\sim$ 6.8 ) than  Pair-2 selected sources (median $\sim$ 7.9 ).

Fig. <ref> shows the distributions of excitation temperatures T$_{ex}$. The excitation temperatures are generally low, all less than 50 K, with a minimum value $\lesssim$ 4.5 K. A vast majority of sources ($\sim$ 94%) show T$_{ex}$ less than 20 K. The median value is $\sim$ 11.7 K, which is a little bit less than that of all infall sources in the literature <cit.>. The distribution of Pair-2 does not seem to follow a regular function, probably because of the paucity of samples. On the other hand, the profiles of Pair-1 as well as of the overall are quite smooth. The best log-normal fitting to the overall distribution gives a parameter-pair ($\sigma,\mu$) = (2.41, 0.25) with $\chi^2$ = 3.2. This results is very close to that derived from Planck cold clumps <cit.>, indicating that our sources may be of similar properties to those cold clumps. We note however, as stated in Section <ref>, the excitation temperatures derived from this work are subject to rather large uncertainties.

Frequency distributions of (a) central velocities; (b) excitation temperatures;  (c) derived H$_2$ column densities (cm$^{-2}$ on log scale); (d) Line widths (FWHM) of the optically thin lines. In the inset of (b), the  dashed curve is a log-normal fit with ($\sigma, \mu$) = (2.41, 0.25) to overall T$_{ex}$ distribution. In the inset of (d), the dashed curve is the best log-normal fit with ($\sigma, \mu$) = (0.34, 0.076), to the overall distribution of FWHMs. For each parameter, the bins for both Pair-1 and Pair-2 as well as for the overall are set to same.

Fig. <ref> presents the distributions of column densities of molecular hydrogen, N(H$_2$). It can be clearly seen the column densities traced by [13] (Pair-1) and  (Pair-2) are obviously separated. The values for the former group range from $2.6\times10^{20}$ to $1.1\times10^{23}$ cm$^{-2}$ with a median value of $1.3\times10^{21}$ cm$^{-2}$, while  those for the latter range between $1.1\times10^{21}$ and $1.8\times10^{23}$ cm$^{-2}$ with a median value of $6.4\times10^{21}$ cm$^{-2}$. The column densities of our samples are distributed narrower, and have smaller median value than those infall sources in the literature <cit.>. This may be because the latter utilized a large variety of molecular lines which include high density tracers, and used different observing facilities including ones with high angular resolution.

Our result means that a major part of the Pair-2  and a significant part of Pair-1 sources have higher column densities than the possible star formation threshold, i.e. 6.3$\times10^{21}$ cm$^{-2}$ <cit.>. All of our candidates have column densities less than the threshold of massive star formation proposed by <cit.>, i.e., N(H$_2$) $\sim$2.1$\times10^{23}$ cm$^{-2}$. Three factors may reduce the estimated value of N(H$_2$): 1) large beam size of the telescope (hence low filling factor) may dilute the peak values; 2) our candidates are frequently seen outside of the central part of certain  clumps; and 3) T$_{ex}$'s of Pair-2 selected candidates are often underestimated hence the derived H$_2$ column densities. Therefore, whether our sources are massive star-forming candidates should await further deliberate studies.

The distribution of the column densities from  is roughly symmetric with respect to the median value, suggesting a log-normal profile (note the abscissa is in log-scale). On the other hand, that from [13] shows a log-normal style only in the first several bins, up to $\sim 4.0\times10^{21}$ cm$^{-2}$, and deviate from the log-normal distribution at higher column densities. Since Pair-1 objects account for a vast majority of our sample, the overall distribution generally resembles that from [13] (inset of Fig. <ref>).

Fig. <ref> shows the distributions of the FWHMs of optically thin lines.  The distributions of the sources selected from two pairs do not show significant difference, except for a slightly shift of median values (1.21 vs 1.10  for Pair-1 and Pair-2, respectively). A Kolmogorov–Smirnov (K-S) test with a +0.10  shift of Pair-2 sources results in P-value of $\sim$0.47, rejecting the hypothesis that the two profiles are different. A log-normal fit to the overall distribution (inset) results in a $\sigma$ = 0.35 $\pm$ 0.013 and $\mu$ =0.076 $\pm$ 0.014. A K-S test results in P-value of 0.23, thus accepting the log-normal distribution hypothesis.

In Fig. <ref> we show the distribution of the skewness parameters, $\delta$V, defined by <cit.>.  As can be seen in the figure, the values range between -1.6 and 0.0 with a mean value $\sim$ -0.5. Since our samples are selected in favor of blue-profiles, it is not surprising that the values are mostly less than -0.25, a criterion as significant infall signature suggested by <cit.>.

The distributions of the skewness parameters, $\delta$V, of the sources selected from Pair-1 (blue), Pair-2 (red) and overall (inset).

Though  $\delta$V is defined as inversely correlated  to the line widths of the optically thin line, as shown in Fig. <ref>, we have not found any clear trend of such correlation.

A plot of $\delta$V and line width (FWHM) of all candidates. The blue pluses and red crosses represent Pair-1 and Pair-2 selected sources, respectively.

§.§ Spatial Distribution

Fig. <ref> shows the spatial distribution of our candidates, overlaid on the imaginary face-on view of the Milky Way (credit: Xing-Wu Zheng & Mark Reid  BeSSeL/NJU/CFA[https://astronomy.nju.edu.cn/xtzl/EN/index.html]). It can be seen clearly that a vast majority of our candidates are  located  in the first quadrant, especially those selected from Pair-2, and outside of the 3-kpc molecular ring. This is not surprising because of the facility limitation and the confusion in the inner Galactic molecular clouds. It should be noted here that most of the sources are located in the spiral arms. This may be due to the distance estimator <cit.>, which assumes that molecular clouds are presumably located in the spiral arms. Though this could be true  for a majority of the our sources, we advice the  researchers to interpret this result with caution.

Fig. <ref> is the vertical distribution (source offset from the Galactic midplane) of our candidates. The main frame shows the pair-separated distribution while the inset is that of overall.  Gaussian fitting of the overall distribution shows the FWHM thickness is $\sim$ 85 pc, which is reminiscent of the thin molecular disk suggested  by <cit.>. A majority (3034, $\sim$85.8 %) of the sources are located within this range (i.e., $\abs[z]{} \le$ 42.5 pc). The profile of Pair-1 selected candidates is wider than that of the Pair-2 ones (85 pc vs 54 pc in FWHM). Interestingly, we notice the presence of excess of sources at the foot of the Gaussian fit (inset of Fig. <ref>), similar to that of the vertical distribution of molecular clouds by <cit.>, and suggesting that star formation may also take place in the thick disk component. It is also interesting to mention that a number (16) of sources are located far beyond the Galactic midplane (i.e., $\abs[z]{} \ge$ 200 pc). These sources are worthy to investigate to show if there are star-forming activities even far from the Galactic plane.

Spatial distribution of the infall candidates overlaid on the imaginary face-on view of the Milky Way (credit: Xing-Wu Zheng & Mark Reid  BeSSeL/NJU/CFA). The green $\odot$ sign indicates the location of the Sun. The Galactic center is at the origin. Our candidates are designated by blue pluses (Pair-1) and red crosses(Pair-2).

The vertical distribution. The blue and red bars represents the Pair-1 and Pair-2 selected sources, respectively. The pink dashed curve in the inset is a Gaussian fit to the overall distribution with $\sigma$ = 36 pc (FWHM = 85 pc).

In Fig. <ref> we show source distribution in L -  space. Apart from the fact that sources selected from Pair-2 are more concentrated to the first quadrant, the overall distribution is reminiscent of the result by <cit.>. Our sources exist in virtually all large-scale components in the northern Galaxy, such as  the Sagittarius-Scutum arm, the 3-kpc molecular ring, Lindblad Ring & the local arm, the Perseus arm, and even the outer arm. If our sources represent quite a part of the infalling gas motion, the overall distribution indicates that there exist star-forming activities in nearly all large components in the Galaxy at present epoch.

The source distribution in L -  space. As in Fig. <ref>, our sources are designated as the blue pluses (Pair-1) and red crosses (Pair-2).

§.§ Confirmation Rates

As known to researchers,  and its isotopic molecules are not ideal tracers to the infall motions, and HCO$^+$ would be much more efficient. Therefore,  shortly after we initiated this project, follow-up observations were made with HCO$^+$ (J = 1 - 0) and HCN (J = 1 - 0) lines. <cit.> selected 133 candidates from our sample with a restriction that T$_{MB}$() $\geqq$ 1 K. They confirmed 56 sources to have infall signatures in HCO$^+$ and/or HCN lines. The overall confirmation rate is $\sim$ 42%, the respective  rate being 40% and 49% for Pair-1 and Pair-2. Further, <cit.> used IRAM to carry out mapping observations towards 24 out of the 56 confirmed sources and finally confirmed 9 blue asymmetry profiles in HCO$^+$ (J = 1 - 0) line. These 9 sources are regarded as infall sources with high confidence.

On the other hand, Yu et al. (2023, in prep.) selected a sample of 210 sources with  more relaxed conditions to study the infall signatures. They found a total of 40 sources showing blue-profiles in HCO$^+$ emission line. The gross detection rate is $\sim$ 19%, with 18% for Pair-1 and 28% for Pair-2 objects. In general, Pair-2 selected candidates have higher confirmation rate than Pair-1 selected ones. This is not surprising in light of that  traces higher column density than [13] does. If the sub-sample represents our overall sample adequately, we would expect the confirmation rate being no less $\sim$ 20%.

In conclusion, starting from the [12], [13] and  (J = 1 - 0) lines, our approach to search for infall sources is effective.

§ SUMMARY

Based on the MWISP data, we conducted a survey of infalling clumps in the Galaxy, which presumably show blue asymmetric profiles in the optically thick lines and single peaks in the  optically thin lines. Both &[13] and [13]& pairs are utilized to carry out the work. The automatic search and manual check are conducted to select candidates out of $\sim$ 10$^8$ spectra. The main results are summarized as following:

* A total of 3533 sources are finalized as candidates in the infalling phase of star formation, in which 3329 candidates are selected from the &[13] pair and 204 are from the [13]& pair.

* Though being manually checked and filtered, the candidates show a wide range of spectra with complicated profiles. The locations that show blue-profiles do not always coincide with central parts of molecular clumps where the highest column densities are detected, but a significant part are rather located at the edges.

* The analysis of physical parameters of the sources suggests the Pair-2 candidates are colder, and have higher column densities, than Pair-1 ones. The overall distribution of T$_{ex}$ follows a log-normal style and is consistent to that by <cit.>, suggesting the properties of our sources are quite similar to those of Planck cold  clumps.

* The line widths of the optically thin lines for both Pair-1 and Pair-2 sources are in log-normal style. The mean values of the two groups are different by < 0.1 .  A K-S test indicates that the distribution are the same when line widths of Pair-2 sources are added by 0.1 .

* Most of the sources are located within the first quadrant, especially those selected from the [13]& pair. The system velocities of the candidates ranges from $\sim$ -70 to $\sim$ 150 , and are present in virtually all large scale components in the northern Galaxy. The vertical distribution suggests that our sources are located primarily within the thin disk, but still present in the extended thick disk.

* A sketchy estimation suggests that the confirmation rate of our sample could be no less than $\sim$ 20%, indicating our strategy is a good start to study the very early phase of star formation systematically.

We are deeply obliged to the MWISP working group, Yang Su, Xin Zhou, Yan Sun, Jixian Sun, Dengrong Lu and Binggang Ju, and the observation assistants of the project, who have been working hard in instrument maintenance, taking and reducing the data, without which this work cannot be done. This work is supported by the National Key R&D Program of China (Grant No. 2017YFA0402702), and the National Natural Science Foundation of China (NSFC, Grant Nos., 11873093, U2031202,11903083). MWISP is sponsored by National Key R&D Program of China with grant 2017YFA0402701 and by CAS Key Research Program of Frontier Sciences with grant QYZDJ-SSW-SLH047.  We would like to express our thanks to the anonymous reviewer for constructive suggestions that enable improvement of the manuscript.

§ THE FULL CATALOGUE

§ SPECTRA AND GAS DISTRIBUTIONS OF THE SOURCES