#  $\beta^{-}$ decay of neutron-rich 45Cl at magic number N=28

Soumik Bhattacharya1111Corresponding author<EMAIL_ADDRESS>Vandana
Tripathi1222Corresponding author<EMAIL_ADDRESS>S. L. Tabor1 A. Volya1 P.
C. Bender2 C. Benetti1 M. P. Carpenter3 J. J. Carroll4 A. Chester5,6 C. J.
Chiara4 K. Childers5,7 B. R. Clark8 B. P. Crider8 J. T. Harke9 S. N.
Liddick5,6,7 R. S. Lubna6 S. Luitel8 B. Longfellow5,10 M. J. Mogannam5 T. H.
Ogunbeku5,6,8 J. Perello1 A. L. Richard5,9 E. Rubino1 S. Saha2 O. A. Shehu8 R.
Unz8 Y. Xiao5,8 Yiyi Zhu2 1Department of Physics, Florida State University,
Tallahassee, Florida 32306, USA  2Department of Physics, University of
Massachusetts Lowell, Lowell, Massachusetts 01854, USA  3Physics division,
Argonne National Laboratory, Argonne, Illinois 60439, USA  4U.S. Army Combat
Capabilities Development Command Army Research Laboratory, Adelphi, Maryland
20783, USA  5National Superconducting Cyclotron Laboratory, Michigan State
University, East Lansing, Michigan 48824, USA  6Facility for Rare Isotope
Beams, Michigan State University, East Lansing, Michigan 48824, USA
7Department of Chemistry, Michigan State University, East Lansing, Michigan
48824, USA  8Department of Physics and Astronomy, Mississippi State
University, Mississippi State, Mississippi 39762, USA  9Lawrence Livermore
National Laboratory, Livermore, California 94550, USA  10Department of Physics
and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA

###### Abstract

Results from the study of $\beta^{-}$-decay of 45Cl, produced in the
fragmentation of a 140-MeV/u 48Ca beam, are presented. The half-life for 45Cl
$\beta$-decay is measured to be 513(36) ms. The $\beta^{-}$ and $\beta^{-}1n$
decay of 45Cl populated excited states in 45,44Ar, respectively. On the basis
of $\gamma$-ray singles and $\gamma$-$\gamma$ coincidence data, decay schemes
for the two daughter nuclei have been established. They are compared with
shell model calculations using the FSU interaction. The low-lying negative
parity states for 45Ar are well described by a single particle (neutron)
occupying orbitals near the Fermi surface, whereas neutron excitations across
the $N=20$ shell gap are needed to explain the positive-parity states which
are expected to be populated in allowed Gamow-Teller $\beta$-decay of 45Cl.
The highest $\beta$-feeding to the 5/2+ state in 45Ar from the ground state of
45Cl points towards a 3/2+ spin-parity assignment of the ground state of the
parent over the other possibility of 1/2+. The high Q${}_{\beta^{-}}$ value of
45Cl decay allows for the population of $1p1h$ states above the neutron
separation energy in 45Ar leading to positive parity states of 44Ar being
populated by removal of one neutron from the $sd$ shell. The spin-parities of
the excited levels in 44Ar are tentatively assigned for the first time by
comparison with the shell model calculations. The 2978 keV level of 44Ar is
identified as the excited 0+ level which could correspond to a different
configuration from the ground state.

††preprint: APS/123-QED

##  I Introduction

In the past few decades a primary focus of nuclear structure studies has been
understanding whether the known magic numbers that appear to hold good near
stability, remain so as the drip lines are approached [1, 2, 3] where the
proton-neutron asymmetry is large. The magic numbers $N=28$ and $Z=28$ are the
lowest ones whose emergence requires a strong spin-orbit interaction and thus
are of particular interest for the experimental and theoretical study of
exotic nuclei far from stability to understand the isospin dependence of the
spin-orbit interaction. There are several examples of experimental evidence,
accompanied by theoretical calculations, which indicate that the $N=28$ shell
gap below 48Ca reduces continuously with decreasing proton number. Just two
protons away from 48Ca, the excitation energy of first 2+ state in 46Ar drops
considerably [4]. Further, around doubly magic 48Ca which is considered
spherical the nuclear shape changes rather rapidly to develop deformation in
42Si [5] while shape coexistence is observed in ${}^{44}S$ [6, 7, 8, 9, 10,
11].

Figure 1:  Schematic representation of 45Cl decay via $\beta 0n$ and $\beta
1n$ channels. The boxes display the ground-state spin-parity assignments of
the corresponding nuclei. The dominant neutron and proton configuration for
the ground state of parent nucleus 45Cl and the excited states expected to be
populated in 45Ar and 44Ar by $\beta$ and $\beta 1n$ are shown. The arrows
show the transformation of neutron from 45Cl to proton and removal of neutron
from 45Ar involving the possible orbitals to produce excited states of 45Ar
and 44Ar, respectively.

The study of the excitation of protons in odd-$Z$ nuclei through measurements
of excited states in the K, Cl and P isotopes have indicated a near-degeneracy
of the proton $d_{3/2}$ and $s_{1/2}$ orbitals approaching $N=28$ [12]. The
increase of collectivity away from $Z=20$ as well as the degeneracy of
$\pi$$d_{3/2}$ and $\pi$$s_{1/2}$ orbitals can be explained by the monopole
part of the tensor force [13], which is attractive between the $\nu$$f_{7/2}$
and $\pi$$d_{3/2}$. With the degeneracy of the two proton orbitals, the ground
states of odd-$A$ Cl isotopes are found to vary between 3/2+ and 1/2+. The
ground state spin-parity of 45Cl is not known experimentally, though both 1/2+
[12] and 3/2+ [14] are predicted as possible spins based on different
calculations. The ground states of odd-$A$ 37-45Ar, ($Z=18$) isotopes on the
other hand are anticipated to be 7/2- in a simple filling of the orbitals due
to a neutron hole in the $f_{7/2}$ orbital. However, the ground state
spin/parity changes between 5/2- and 7/2- throughout the Ar isotopic chain
from $N=20$ to $N=28$. A charge radius measurement using laser spectroscopy
has found the ground state as 7/2- for 39,41Ar, 5/2- for 43Ar [15] and then
again 7/2- for 45Ar [16].

The $N=26$ 44Ar is proposed to be deformed with a prolate ground state
associated with a high $B(E2)$ value for the 2${}_{1}^{+}$ to 0${}_{1}^{+}$
transition from Coulomb excitation study [17, 18]. The B(E2) value for the
same transition in 46Ar [19, 4] on the other hand is found to be lower
supporting the smaller charge radius for the 46Ar [15] compared to 44Ar.
However, the latest measurement of the $B(E2)$ values from the lifetime
measurement of 2${}_{1}^{+}$ state for 46Ar and 44Ar by Mengoni et al. [20],
reports almost double $B(E2)$ values for the 46Ar than 44Ar which is
unexpected if the of $N=28$ shell gap persists for 46Ar. Different
calculations also show discrepancy between the $B(E2)$ values of these two
nuclei which remains to be resolved. Between the deformed 44Ar and near
spherical 46Ar, the structure of the intermediate 45Ar is therefore of special
interest.

$\beta$-decay is an excellent experimental tool to study the excited states of
neutron rich nuclei near $N=28$. The large $Q_{\beta^{-}}$ value ensures that
a large number of excited states, both bound and unbound, are populated. In
this region of the chart of nuclides, the differences in ground-state spins
and parities between the $\beta$-decay parent and daughter limit the
possibility of direct feeding to the ground state. This is due to the protons
filling the 1$s_{1/2}$ or 0$d_{3/2}$ subshells, whereas the neutrons are
filling the 0$f_{7/2}$ subshell. For odd-$A$ Cl isotopes like 45Cl in this
work, a positive-parity ground state is expected, which will decay to the
positive-parity excited states of odd-$A$ daughter Ar via allowed Gamow-Teller
(GT) transitions and not feed the negative parity ground state directly. The
positive-parity states in the even-odd daughter arise from promoting a proton
or a neutron across the $Z=20$ or $N=20$ shell gap and these $1p1h$ states are
expected at relatively high energies. For 45Cl, the expected 3/2+ ground state
will $\beta$-decay to positive-parity (1/2+, 3/2+ or 5/2+) or negative-parity
(1/2-, 3/2- or 5/2-) states by allowed or first forbidden $\beta$-decays,
respectively. With the large $Q_{\beta^{-}}$ value, the $\beta$-decay can also
populate states above the neutron separation energy (Sn) in 45Ar and therefore
opens up the possibility of studying the excited states in the $\beta 1n$
daughter 44Ar. The investigation of excited states in 44,45Ar is the focus of
this study along with the ground state spin and parity determination for the
parent 45Cl.

##  II Experimental Setup

The experiment was carried out at the National Superconducting Cyclotron
Laboratory (NSCL) [21] at Michigan State University to investigate the
$\beta^{-}$ decay of exotic 45Cl. A 140-MeV/u 48Ca primary beam, was
fragmented using a thick Be target at the target position of the fragment
separator, A1900 [22], to produce the nuclei of interest. A wedge-shaped Al
degrader, which increases the energy dispersion for different fragments, was
placed at the intermediate dispersive image of the A1900 separator to provide
a cleaner particle identification of the cocktail beam.

Figure 2:  The two dimensional plot of partial energy deposition in the
upstream PIN detector ($\Delta E$) and the Time of Flight (ToF) measurement
with respect to the focal plane scintillator detector used for particle
identification of the nuclei of interest in the present work.

After passing through the wedge shaped Al degrader, the selected isotopes were
transported to the Beta Counting System (BCS) [23]. The BCS is equipped with a
$\approx$ 1mm thick pixelated (40 strips x 40 strips) Double-Sided Silicon
Strip Detector (DSSD) at the center. An Al degrader upstream reduced the
energy of the fragments to ensure that the implants stopped at the middle of
the DSSD. The DSSD was followed by a Single-Sided Silicon Strip Detector
(SSSD) which served as a veto detector. This veto detector was used to counter
a large flux of light particles which were transmitted through the DSSD
detector for the particular A1900 settings used for this experiment which can
impair implant-$\beta$ correlations. Dual-gain pre-amplifiers were used for
the DSSD to record the time and position of implants (GeV energy depositions),
as well as subsequent decays (keV to MeV energy depositions). The implant rate
was kept below 200/s to maximize the efficiency of correlating the implanted
ion with the decay products.

Two Si PIN detectors, placed upstream of the DSSD, provided the partial energy
loss information of the fragments. Along with the scintillator at the
intermediate dispersive image of the A1900 these PIN detectors provide the
time of flight information used to generate particle identification plots
(PID) of the incoming implants as shown in Fig. 2. The DSSD and SSSD detector
combination was surrounded by 16 Clover detectors to detect the
$\beta$-delayed $\gamma$ rays with an efficiency of about $5\%$ at 1 MeV. The
efficiency of the array was measured with the SRM [24] and 56Co sources placed
outside of the DSSD and then corrected for the dimensions of the DSSD with
GEANT4 simulations. The time-stamped data were collected using the NSCL
digital data acquisition system [25]. The timing and spatial correlations from
each channel corresponding to the different detectors were used to ensure the
correlation between the implanted fragments in the DSSD and the corresponding
$\beta$-decay event.

##  III Experimental Results

Fig. 2 shows the clear separation of the different isotopes produced in the
present experimental investigation. Selected 45Cl implants from the cocktail
beam were correlated with the emitted $\beta$ particles to obtain half-life.
Further, coincidence with delayed $\gamma$ transitions with the correlated
implant-decay events allowed us to study the excited states of 45Ar and 44Ar
produced via $\beta$ and $\beta$-1n decay respectively. The $\beta$-decay of
other neutron rich P and S nuclei seen in Fig. 2 have been reported and
discussed in our previous publication [26].

Figure 3:  The time difference between the 45Cl implants and correlated
$\beta$ decay events gated by the 542-keV ground state transition in 45Ar. The
experimental data is fitted with exponential decay functions to account for
45Cl decay with suitable background. The half-life is found to be $T_{1/2}$=
513(36) ms. This number is larger than the previous measurement of 400(43) ms
[27] though within 2$\sigma$.

###  III.1 $\beta$-decay of 45Cl

The time differences between 45Cl implantations and $\beta$ particles detected
in the same or one of the adjacent eight pixels of the DSSD, in coincidence
with the strongest ground-state $\gamma$ transition (542 keV) in 45Ar, were
histogrammed to generate a decay curve. The half-life of 45Cl was extracted
from this decay curve, as shown in Fig. 3. A fit using a simple exponential
decay function of 45Cl and a background component accounting for other long-
lived activity gives a half-life of 513(36) ms. The previous half life
measurement for 45Cl with a value of 400(43) ms is taken from the work of
Sorlin et. al. [27]. In that work the half-lives were deduced from
constructing a time histogram of the $\beta$-n coincidences detected after the
identification of the corresponding parent nucleus. For 45Cl only 880 events
were detected and the authors discuss a possible mixing with another implant
with shorter half life. The measured half life of 513 (36) ms obtained in this
work is consistent with the shell model calculations using the FSU interaction
which give a value of 500 ms without including the First Forbidden beta
transitions.

Figure 4:  (a)-(d) Coincidences observed between the $\gamma$ transitions in
45Ar used to establish the level scheme.

The $\gamma$-$\gamma$ coincidences between the transitions observed in 45Ar
are shown in Fig. 4(a-d) and the corresponding level scheme in Fig. 5. Figure
4(a) displays the 542-keV gate which is the strongest transition in 45Ar and
one can see all the known transitions: 798, 876, 1193, 1230, 1525, and 2754
keV along with the newly placed 2554 keV. The 2554-keV transition is proposed
to decay from the highest observed level, at 4326 keV to the 1772-keV level
based on the coincidences shown in Fig. 4 (d). The coincidence gate of 1230
keV shows the 542-keV and 1525-keV transitions only, which belong to the same
cascade [Fig. 4(b)]. The absence of any transition other than 542 keV in the
coincidence gate of 1193 keV confirms that no transition is feeding the
1735-keV level [Fig. 4(c)]. In Ref. [28] two tentative $\gamma$ transitions at
3408 and 2215 keV were reported to decay from the proposed 3950- and 2757-keV
levels, respectively. The existence of the 3950-keV (3946 keV in present
study) level was established prior from the neutron transfer study [16]. The
present work confirms the presence of 2215- and 3404-keV transitions in the
coincidence gate of 542 keV [Fig. 4(a)].

The level scheme in Fig. 5 shows the relative $\beta$ branching of the levels
considering the absolute efficiencies of the detected $\gamma$-rays. The
assignment of the spin-parities of the observed levels of 45Ar is guided by
predictions from shell-model calculations (discussed later in detail) as well
as from the allowed $\beta$ transition rates from the parent nucleus (45Cl).
The $\beta$ decay should primarily populate the $1p1h$ positive parity states
and hence the log$ft$ values from the SM calculations are noted only for the
positive parity states. Table 2 gives the level energies and $\gamma$-rays
decaying from them, possible $J^{\pi}$ values, and relative intensities for
both 45Ar and 44Ar excited states.

Figure 5:  Partial level scheme of 45Ar following $\beta^{-}$-decay of 45Cl
with a $T_{1/2}$ = 513(36) ms and $Q_{\beta^{-}}$ = 11.51(14) MeV. The
transitions marked in black were known before whereas red indicates the new
transition (2554-keV) as well as prior tentative transitions that we were able
to confirm. The branching (relative to 5/2+) is also shown for the excited
states. The shell model calculation using the FSU interaction [29] predicted
the 0p0h and 1p1h excited states and are shown along with the experimental
levels.  Figure 6:  (a)-(d) Coincidences observed between the $\gamma$
transitions in 44Ar. The 1158 keV transition coincidence gate shows
contamination from 44Ca which are marked with blue solid boxes.

###  III.2 $\beta 1n$-decay of 45Cl

The large $Q_{\beta^{-}}$ = 11.51 MeV of 45Cl, along with a low (5.169-MeV)
neutron separation energy (Sn) of 45Ar, leads to a significant beta-delayed
neutron branch populating excited states in 44Ar. The spin-parities of the
states populated in the $\beta$-delayed daughter largely depend on the spin-
parity of excited state in 45Ar .

The $\gamma$ rays in coincidence with the 1158-keV ground-state transition (2+
to 0+) in 44Ar are shown in Fig. 6(a). Here it is worth mentioning that a
closeby $\gamma$ transition (1157 keV) exists in 44Ca (2+ to 0+ transition)
leading to some spurious coincidences marked with solid blue boxes in Fig.
6(a). The strongest transition seen is 853 keV, which is the decay from the
second 2+, 2011 keV level to the first excited 2+ (1158-KeV) level. This
second 2+ state at 2011 keV has been confirmed in an earlier deep inelastic
reaction study by Wan et al. [30]. The coincidence spectrum also shows the
weaker 966-, 2376-, 2797- and 3649 keV transitions which were already reported
in Ref. [28]. The presence and absence of 3649 keV transition in 1158 and 853
gate respectively, fixes the placement of this transition from the 4808 keV to
the 1158 keV level. The highest observed excited level 5354 keV from the
present work is seen to be decaying only to 2978 keV level via the 2376 keV
transition.

The level scheme, formed from the present work is shown in Fig. 7 (left
panel). Along with the experimental levels, the corresponding SM predicted
levels (right panel) are also shown. All the transitions, apart from the 853-,
1158- and 2011-keV transitions are observed for the first time in the $\beta
1n$ decay of 45Cl and are marked in blue in the experimental level scheme
shown in Fig.7 (left panel). Two levels at 2746 keV and 3439 keV, shown in the
experimental level scheme by green dashed line, were not populated in the
$\beta$n channel but are shown for comparison with the shell model
calculations and were seen in the previous study by Fornal et. al. [31].

Figure 7:  Partial level scheme of 44Ar following $\beta 1n$-decay of 45Cl
($Q_{\beta^{-}n}$ = 6.34(14) MeV) is shown in the left panel. The relative
intensity of the deexciting transitions are also reported along with the
associated errors. Two levels are shown by green dashed lines which were
reported previously but not seen in the present work. The transitions which
are seen for the first time from $\beta 1n$ work are marked in blue. The spins
of the levels that are suggested for the first time in the present work are
marked with red (see section B of the discussion). Predictions of shell-model
(SM) calculations using the FSU interaction [29] are shown in the right panel.
The possible $\gamma$-transitions and their relative branching ratios were
also calculated and are noted. The excited states, predicted by the SM but not
observed in the experiment, are shown at the right of the SM level scheme in
red.

##  IV Discussion

###  IV.1 45Ar

The ground state spin parity of 45Cl is expected to be 3/2+ due to an odd
proton in $d_{3/2}$ orbital and a full $\nu$$f_{7/2}$ orbital in a simple
picture as illustrated in Fig. 1. However with the $d_{3/2}$ and $s_{1/2}$
orbitals being nearly degenerate, a $1/2^{+}$ assignment cannot be ruled out.
Below, based on the $\gamma$ decay characteristics and the shell-model
calculations, we suggest a $3/2^{+}$ spin-parity. The shell-model calculations
presented in this work were performed using the shell model code CoSMo [32]
using the FSU interaction. The FSU interaction is a data-driven shell-model
interaction aimed to explain cross-shell excitations between the $sd$ and $fp$
shell and also $p$ and $sd$ shells for neutron-rich $sd$-shell nuclei [29].
The predictions of the FSU interaction have found great success in explaining
many experimental observations [33, 34]. For the calculations quoted here,
when the excitations are confined to the major shells (e.g. $sd$ and $fp$)
they are referred to as $0p0h$ excitations, whereas $1p1h$ calculations
involve movement of a single nucleon between the major shells.

####  IV.1.1 Positive-parity states

From the selection rules of allowed Gamow-Teller (GT) decay, states with
positive parity should have the highest branching in the daughter nucleus. In
a more nuanced picture, the $\beta^{-}$ decay will likely involve the
conversion of a $d_{3/2,5/2}$ neutron into a $d_{3/2}$ proton as 45Ar has a
vacancy in the $\pi d_{3/2}$ orbital. The other possibility is for the
$s_{1/2}$ neutron to transform into an $s_{1/2}$ proton as indicated in Fig.
1. These will create neutron hole states in 45Ar corresponding to $1p1h$
states in the shell-model calculations. We propose the states at 1735, 1772,
3296, 3946, and 4326 keV with the highest branching to be populated via
allowed $GT$ transitions and hence have positive parity. In a recent transfer
study using the reaction 1H(${}^{46}\mathrm{Ar},d)^{45}\mathrm{Ar}$ [16] the
same states were proposed as neutron hole states. The observed states at 1735
and 1772 keV in Ref. [16] were found to have large spectroscopic factors for
$\nu d_{3/2}$ and $\nu s_{1/2}$ hole states but, due to limited experimental
energy resolution, they were not able to resolve the two levels. In this work,
with the excellent resolution of the high purity Germanium detectors, we are
able to assign accurate energies to these two. The shell-model calculations
presented, found the 3/2+ state at a higher energy than the 1/2+ state and as
a result, we assign the 1735- and 1772-keV levels as 1/2+ and 3/2+,
respectively. This is further confirmed by the branching ratio of the decays
of the 3296-keV state as discussed ahead.

The 3296-keV state has the strongest population in the current $\beta$-decay
study. It has decay branches to the $7/2^{-}$ ground state, the 542-keV first
excited $3/2^{-}$ state and a strong branch to the 1772-keV state which we
propose to be the $3/2^{+}_{1}$ state. We could not identify any transition to
the 1735-keV state within our observation capability. As the 3296-keV state
decays to the ground state, it likely has a $5/2^{+}$ spin-parity. The
vicinity of this state to the $5/2^{+}$ 3224-keV state predicted in the SM
calculations ratifies this assignment and the calculated log$ft$ value of 4.98
justify its strong population in beta decay. The predicted decay probabilities
of the $5/2^{+}_{1}$ states to the $3/2^{+}_{1}$ and $1/2^{+}_{1}$ states in
SM calculations are listed in Table 1. The decay to the $3/2^{+}$ state via a
M1 transition is stronger and supports the spin assignments to the doublet of
states at $\approx 1.7$ MeV.

Table 1:  SM predictions (using the FSU interaction) for the branching ratio of the $5/2^{+}_{1}$ state in 45Ar. The experimental value of the $\gamma$ ray transition was used in the calculation of the rates. The difference in branching to the $3/2^{+}$ and $1/2^{+}$ states is used to confirm the spin parity assignment to the two experimental state at $\approx$1.7 MeV. $J_{i}$ $\rightarrow$ $J_{f}$ |  $E_{\gamma}$ (keV) | B(M1) ($\mu_{N}^{2}$) | B(E2)(e2fm4)
---|---|---|---
- |  - | rate(1/sec) | rate(1/sec)
5/2+ $\rightarrow$ 1/2+ | 1525 | - | 104
- | - | - | 1.05e+12
5/2+ $\rightarrow$ 3/2+ | 1525 | 0.35 | 27.3
- | - | 2.19e+13 | 2.77e+11
Figure 8:  The occupation number of different orbitals (proton and neutron)
for the positive parity excited states calculated from shell-model using the
FSU interaction [29] for 45Ar are shown. The energies of the experimental
states corresponding to each proposed SM states in the present work are
indicated in parentheses. The blue dashed columns are the maximum occupancy
for an orbital ($2j+1$). The solid black columns are the occupancy of the 7/2-
ground state and the red columns are the occupancies of the excited states of
45Ar.

The occupation numbers for the ground state and the excited positive-parity
states in 45Ar from SM calculations are shown in Fig. 8. The occupation
numbers for the two states at $\approx 1.7$ MeV clearly establish them as
$\nu$$s_{1/2}$ and $\nu$$d_{3/2}$ hole states, respectively. The occupancy of
the 3296-keV state from the shell-model calculation shows contribution from
the $\nu$$d_{5/2}$ hole along with $s_{1/2}$. This level was also observed via
the 1H(46Ar,45Ar)2H reaction by Lu $\ {et.al.}$ [16] though no spin was
assigned to that state. The assignment of $5/2^{+}$ for 3296 keV from the
present work, as discussed above, is consistent with the observation of a
small peak at 3.29 MeV [16] in the deuteron spectra. Another state at 3.95
MeV, described to have $\ell=0$ parentage in Ref. [16], is also observed in
the present work. The shell-model calculation supports the presence of the
second 1/2+ state at 3978 keV with considerable contribution from both neutron
and proton $s_{1/2}$ orbitals. Therefore, the state at 3946 keV is assigned a
1/2+ spin-parity. The shell model further predicts a closeby 3/2+ at 4264 keV
(see Fig. 5), which we have associated with the 4326-keV state. The higher
energy states (at 3978 keV and 4264 keV) show a rise in occupation number for
protons in the $f_{7/2}$ orbital with respect to the ground-state
configuration while the occupation number for $\pi$$d_{3/2}$ remains the same.
It is accompanied by a slight drop in the occupancy for the $\nu$$f_{7/2}$
orbital. These states could have contribution from conversion of an $f_{7/2}$
neutron to a $f_{7/2}$ proton in the beta decay.

####  IV.1.2  Ground state of parent 45Cl

The strong population of the $5/2^{+}$ at 3296 keV in the $\beta$ decay leads
to the determination of the ground state spin and parity of the parent to be
$3/2^{+}$. The ground-state spin-parity of the neutron-rich odd-mass Cl
isotopes are in the spotlight due to the degeneracy of $\pi$$s_{1/2}$ and
$\pi$$d_{3/2}$ orbitals as one moves from the $N=20$ 37Cl to the neutron-rich
45Cl ($N$=28). Gade et al. [12] systematically showed the reduction of the
$E$(1/2+)-$E$(3/2+) gap as a function of neutron-proton asymmetry for all the
odd-mass K, Cl and P isotopes. Though the ground-state spins have been
experimentally verified for 41Cl and 43Cl as $1/2^{+}$ with a very closeby
$3/2^{+}$, the tentatively assigned $1/2^{+}$ ground state of 45Cl based on SM
calculations in Ref. [12] had not been confirmed experimentally. Two closely
spaced energy states (127 keV apart) are predicted as candidates for the
$1/2^{+}$ and $3/2^{+}$ generated from proton holes in $s_{1/2}$ and $d_{3/2}$
respectively. The present work reports the highest $\beta$-feeding to the
$5/2^{+}$ state in 45Ar from the gs of 45Cl. This is possible only from a
$3/2^{+}$ ground state and can be considered as the first experimental support
for the assignment of $3/2^{+}$ spin to the ground state over $1/2^{+}$ for
45Cl indicating a return of normal filling of orbitals in odd-A Cl isotopes.
$\beta$-decay of 45S into 45Cl can shed further light on the ground state
spin/parity.

####  IV.1.3 Negative parity states

The lower states in 45Ar are supposed to have negative parity arising from the
excitations of the odd neutron(s) within the $fp$ shell. Their population in
$\beta$-decay is either due to feeding from the high-lying states or could
also arise from First Forbidden (FF) transitions.

The excited states at 1340 and 1418 keV are found to be consistent with the
previous $\beta$-decay study by Mrazek et al. [28]. The state at 1.34 MeV was
tentatively reported by Lu et al. [16] in a 1H(46Ar, d)45Ar study though the
45Ar(d, p)45Ar reaction Gaudefroy et. al. [35, 36] couldn’t identify this
state. Gaudefroy et. al. on the other hand, reported a 1420(60)-keV excited
state with $3/2^{-}$ spin-parity and described it as a member of the
multiplets of the $\pi$(2+)$\otimes$$\nu$$f_{7/2}$ configuration with one
proton hole in $s_{1/2}$ and another in $d_{3/2}$. Because of the mixed
nature, both these states were weakly populated in either of the transfer-
reaction study [36, 16]. The present shell-model calculation predicts the
second excited state to be $3/2^{-}$ with a closeby $1/2^{-}$ state (see Fig.
5). The 1340-keV level has a direct $\gamma$-decay branch to the 7/2- ground
state favoring a 3/2- spin assignment over 1/2- spin whereas the 1418-keV
state decays to only the 542-keV $3/2^{-}$ state and not to the ground
$7/2^{-}$ state. Therefore, it is proposed that the second excited state at
1340 keV has a 3/2- spin-parity while the 1418-keV level is a 1/2- consistent
with the $\ell=1$ assignment of Ref. [35] as well as present shell model
predictions with a composite configuration of $\pi$($d_{3/2}$ $\otimes$
$s_{1/2}$) $\otimes$ $\nu$$p_{3/2}$.

The negative-parity energy levels in 45Ar (observed here and from prior
studies) and 43Ar are further compared with the shell-model calculations in
Fig. 9 to understand the evolution of the $N=28$ shell gap. Relatively less
information is available for the negative parity states in 43Ar, as is clear
in the figure. Unlike 45Ar, a ground-state doublet of $5/2^{-}$ and $7/2^{-}$
spins is predicted in 43Ar and can be considered as members of the multiplets
arising from the configuration $\pi d_{3/2}^{-2}\nu f_{7/2}^{-3}$. There is
only tentative experimental evidence of this doublet in 43Ar with 5/2-
proposed to be the ground state [37, 38]. Further the $\beta$-decay of 43Cl
with a 3/2+ gs [39] shows a large branch to the ground state of 43Ar through
First Forbidden(FF) decay which also favors the $5/2^{-}$ assignment. Hence,
though the SM calculations using the FSU interaction correctly predict very
closely spaced 7/2-(gs) and 5/2- state (286 keV in Fig. 9) for 43Ar, the 5/2-
is more probable for the ground state. For 45Ar on the other hand, both the SM
calculations and the experimental observations do not support a close 5/2--
7/2- ground-state multiplet, a signature of the proximity to the $N=28$ shell
closure.

Figure 9:  The low-energy negative-parity states are displayed for 45Ar and
43Ar [37, 41] for comparison both from experiment and shell-model calculations
using the FSU interaction [29]. The experimental energy of $7/2^{-}$ state for
43Ar is yet unknown.

###  IV.2 44Ar

The states populated in 44Ar follow the neutron emission from the $1p1h$
positive parity states with spins of $1/2$, $3/2$ or $5/2$ populated in 45Ar.
The first excited state of even-even 44Ar is at 1158 keV with a $J^{\pi}$ of
2+ known from earlier Coulomb-excitation, in-beam $\gamma$-spectroscopy and
deep inelastic studies [18, 17, 30, 31] and is described as a deformed state
while the second excited one is also a 2+ state at 2011 keV. The spins of the
other excited levels observed at 2978, 4808 and 5354 keV are proposed to be 0+
to 4+ in NNDC [40]. We have tried to make more specific spin assignments to
these by comparing with the predictions of shell-model calculation in the
$0p0h$ valence space. The experimental states, though, are likely to have some
contribution from $2p2h$ configurations as the neutron is likely being emitted
from the $sd$ shell. Our calculations currently cannot accommodate this.

Table 2:  $\gamma$-ray energies along with the corresponding initial levels and initial and final spins for 45Ar and 44Ar observed in the present work are presented. For 45Ar the intensities of the $\gamma$ rays are normalized with respect to the strongest 542-keV $\gamma$ ray. For 44Ar the branching from each level is shown with each branch normalized to the strongest one from that level. 45Ar |  |  |
---|---|---|---
$E_{i}~{}$ |  $J_{i}$ $\rightarrow$ $J_{f}$ |  $E_{\gamma}$ | Irel
(keV) |  |  (keV) |
542(1) |  3/2- $\rightarrow$ 7/2- | 542(1) | 100(10)
1340(1) |  3/2- $\rightarrow$ 7/2- | 1340(1) | 11.4(13)
|  3/2- $\rightarrow$ 3/2- | 798(2) | 5.7(7)
1418(2) |  1/2- $\rightarrow$ 3/2- | 876(1) | 11.4(12)
1735(1) |  1/2+ $\rightarrow$ 3/2- | 1193(1) | 13.0(15)
1772(1) |  3/2+ $\rightarrow$ 3/2- | 1230(1) | 37.0(39)
2757(2) |  (1/2-) $\rightarrow$ 3/2- | 2215(2) | 2.1(4)
3296(2) |  5/2+ $\rightarrow$ 3/2+ | 1525(1) | 18.0(20)
|  5/2+ $\rightarrow$ 3/2- | 2754(1) | 29.0(32)
|  5/2+ $\rightarrow$ 7/2- | 3296(2) | 12.1(16)
3946(2) |  1/2+ $\rightarrow$ 3/2- | 3404(2) | 1.3(4)
4326(3) |  3/2+ $\rightarrow$ 3/2+ | 2554(2) | 2.6(5)
|  3/2+ $\rightarrow$ 3/2- | 2986(2) | 2.1(4)
|  3/2+ $\rightarrow$ 3/2- | 3784(3) | 3.7(7)
44Ar |  |  | Rel. Branching
1158(1) |  2+ $\rightarrow$ 0+ | 1158 (1) | 100
2011(1) |  (2+) $\rightarrow$ 2+ | 853(1) | 68(24)
|  (2+) $\rightarrow$ 0+ | 2011(1) | 100
2978(1) |  (0+) $\rightarrow$ (2+) | 966(1) | 100
|  (0+) $\rightarrow$ 2+ | 1818(1) | 83(33)
4808(2) |  (2+) $\rightarrow$ (2+) | 2797(2) | 100
|  (2+) $\rightarrow$ 2+ | 3649(2) | 4.3(12)
|  (2+) $\rightarrow$ 0+ | 4808(2) | 4.7(16)
5354(2) |  (1+) $\rightarrow$ (0+) | 2376(1) | 100

The experimental levels (left panel) and SM predicted states (right Panel) for
44Ar are shown in Fig. 7 along with the relative intensities of the
$\gamma$-transitions from each level. The experimental 2978-keV level decays
to the first and second 2+ states via the 1818- and 966-keV transitions,
respectively, where the 966-keV decay dominates over the 1818-keV branch. This
2978-keV level lies close in energy to 4 predicted states (0+, 4+, 2+ and 3+).
The calculated 4+ (2978 keV) and 2+ (3013 keV) states have higher transition
rates to the 4${}^{+}_{1}$ (2680 keV) and 0+ (gs) states, respectively, which
is not observed in the decay of experimental 2978-keV level. This leaves the
two spins, 3+ (3047 keV) and 0+ (2717 keV), as the most probable candidates
for this level.

Figure 10:  (a) The experimental low-lying 2${}_{1}^{+}$ and 0${}_{2}^{+}$
energies of Ar isotopes as a function of neutron number. The shell-model
(using the FSU interaction) predicted states are also shown as closed (open)
star for 2${}_{1}^{+}$ (0${}_{2}^{+}$) spin. The 0${}_{2}^{+}$ spin for 42Ar
is adopted from one of the possible spins predicted in NNDC [41] for the
2512.5-keV level for comparison purposes. (b) Comparison of 2${}_{1}^{+}$ and
0${}_{2}^{+}$ energies in Ca, Ar and S nuclei near magic numbers $N=28$ and
$Z=20$. From the doubly magic 48Ca (in center), the left (right) isotones
(isotopes) have two protons (neutrons) less than the previous one, keeping the
$N=28$ ($Z=20$) magic number. The experimental values for the nuclei (other
than 44Ar) are taken from Refs. [42, 18, 43, 37, 44, 45, 46, 41].

The level at 4808 keV decays to the ground state and the excited 2+ (1158- and
2011-keV) states. Therefore, among the prior suggested spin-parity
assignments, 4+, 3+ or 0+ [40] are not possible for this state. Between the
remaining 2+ and 1+ spin, the shell model does not predict any 1+ state nearby
(Fig. 7), therefore the spin for this level is suggested to be 2+
corresponding to the level 4842 keV from the calculation. Further, the
calculations (Fig. 7) predict that the 4842-keV level (exp. 4808 keV level)
has the most intense decay branch to the gs and the excited 2+ states, which
matches with the experimental observation. If the spin-parity of 2978-keV
state is assigned as 3+ then the shell-model predicts a strongest decay branch
from 4808-keV to 2978-keV level. The absence of a decay path from 4808-keV to
2978-keV state encourages us to assign the 2978-keV state as the excited
$0^{+}$ over the $3^{+}$ possibility. The systematics of excited 0+ in Ar
isotopes will be discussed next.

The highest observed level from the present $\beta$n decay work is at 5354 keV
with a decay only to the newly assigned 0+ 2978-keV level. This 5354-keV level
was proposed to decay to the 2011-keV (2${}^{+}_{2}$) and 1158-keV
(2${}^{+}_{1}$) states via the 3342- and 4195-keV transitions in the earlier
44Cl beta-decay work [28] but with 3-5 times less intensity than the 2376 keV
transition. The observation of the strong 2376-keV transition to the 2978-keV
(0+) state rules out 0+ and 3+ assignments for the 5354 keV level. The shell
model predicts a 2+ at 5141 keV and a 1+ at 5208, both of which are good
candidates but the 2+ is predicted to decay by a strong transition to the
2${}^{+}_{2}$ state not consistent with the experiment. Therefore, the 5354
keV is assigned as 1+, consistent with all experimental observations. The
population of 1+ and 2+ in the delayed neutron decay suggests the population
of a $3/2^{+}$ unbound state in 45Ar which decays by a $\ell=0$ neutron.

###  IV.3 Even-Even Isotopes near $N=28$

To understand the evolution of shape away from the $N=28$ shell closure, the
excited state energies of 2${}_{1}^{+}$ and 0${}_{2}^{+}$ excited states are
plotted for even-even Ar isotopes as a function of neutron number in Fig.
10(a). With $N=20$, both the 2${}_{1}^{+}$ and 0${}_{2}^{+}$ are high in
energy for 38Ar, reflecting the large shell gap between the $d_{3/2}$ and
$f_{7/2}$ orbitals. As we increase the neutron number approaching half
occupancy of the $f_{7/2}$ orbital, the lowering of the first 2+ state
indicates an increasing collectivity, and reduction of the $N=28$ shell gap.
In the Ar isotopic chain, it is interesting to notice that the most collective
behavior is for the ground state of 44Ar ($N=26$) signified by the lowest
energy of 2${}_{1}^{+}$. After that, the increase of the 2${}_{1}^{+}$ energy
points towards the restoration of the shell gap between the $\nu$$f_{7/2}$ and
$\nu$$p_{3/2}$ orbitals in 46Ar. With an additional neutron pair above $N=28$,
the 2+ state comes down in energy for 48Ar.

A different trend is seen for the 0${}_{2}^{+}$ state, which generally
represents a different shape of the nucleus from the ground state. For 40Ar,
the 0${}_{2}^{+}$ state is described to be part of a super-deformed band in
Ref. [47]. With increasing neutron number, the energy of this state is found
to increase, attaining a maximum value for 44Ar. After that, the experimental
0${}_{2}^{+}$ state shows a decreasing trend again for 46Ar. As can be seen
from Fig. 10(a), the shell-model calculations with the FSU interaction (solid
black stars) closely mirror the 2${}_{1}^{+}$ values for 38-48Ar. For the
0${}_{2}^{+}$ states (open red star) from $0p0h$ configurations, the shell-
model predictions show an increasing trend in energy with decreasing neutron
number, in disagreement with the experiment. It may be inferred that the
0${}_{2}^{+}$ states for 38-42Ar isotopes have a contribution from $2p2h$
configuration which is beyond the scope of present SM calculations. It will be
interesting to search for the 0${}_{2}^{+}$ state in 48Ar, which is predicted
to be very high (4.3 MeV) in the present SM calculation.

For further systematic analysis, experimental 2${}_{1}^{+}$ and 0${}_{2}^{+}$
states are plotted for selected nuclei around $Z=20$, $N=28$ magic shell
closures in Fig. 10(b). The doubly magic 48Ca (in the middle) shows a high
lying 2${}_{1}^{+}$ and excited 0${}_{2}^{+}$ representing a pronounced
$Z=20$, $N=28$ shell gap. With two fewer protons, for 46Ar the 2${}_{1}^{+}$
and 0${}_{2}^{+}$ are lower in energy with a further decrease in the state for
44Ar [Fig 10(a)] indicating the deformation associated with the ground state.
Reducing two more protons, for 44S the $2^{+}_{1}$ drops further and
importantly the spacing between the 0${}_{2}^{+}$ and 2${}_{1}^{+}$ levels
collapses resulting in low lying prolate-spherical shape co-existence in 44S
[6, 10]. In contrast, for the isobar 44Ar, the $2^{+}_{1}$ and 0${}_{2}^{+}$
show a large separation. In Fig. 10(b) the isotopes of Ca away from the $N=28$
shell closure are also shown to the right of 48Ca and one can notice the same
trend of reduction of the gap between the 2${}_{1}^{+}$ and 0${}_{2}^{+}$
states along with lowering of the energy of 0${}_{2}^{+}$. Therefore, the
systematics suggests that if we decrease either the proton or neutron number
away from doubly magic 48Ca, keeping the other magic number constant, the
0${}_{2}^{+}$ which broadly represents a different shape in excited state
moves lower in energy, approaching the possibility of shape coexistence. But
with both proton and neutron number away from the magic number, the nuclei
seem to favor one shape at low excitation energy.

##  V Summary

The $\beta^{-}$ decay of 45Cl is reported here, from an experiment performed
at the NSCL following the fragmentation of a 48Ca primary beam. The half-life
($T_{1/2}$) of 45Cl is measured to be 513(36) ms, which is longer than the
prior measurement from GANIL but consistent with shell model calculations
using the FSU interaction. The level schemes of 45Ar and 44Ar are established
from the observed $\gamma$-$\gamma$ coincidences in the $\beta$ and $\beta 1n$
channels, respectively. Many of the prior tentative placements of transitions
in 45Ar have been verified and a new $\gamma$-transition at 2554 keV has been
added. The experimentally observed levels are compared with SM calculations
for both 44,45Ar with excellent agreement. From the predicted occupancy of
different orbitals and the decay pattern of the $\gamma$ transitions from the
excited levels, the spin-parity of the levels of 45Ar populated via GT
transitions are proposed. The higher lying positive-parity states of 45Ar are
candidates for $1p1h$ excitations consistent with their population in prior
transfer reactions. The maximum feeding to the 5/2+ state in 45Ar, supported
by the small log$ft$ value calculated from SM calculations, allowed us to
assign a spin parity of $3/2^{+}$ to the ground state of the parent 45Cl. The
spin and parity for the levels in 44Ar are proposed by comparing with SM
calculations. An excited 0${}_{2}^{+}$ state is proposed for the first time in
44Ar at 2978 keV. The SM calculations reproduce the experimental evolution of
the 2${}_{1}^{+}$ state for the even-$A$ $Ar$ isotopes (from $N=20$ to 30)
reasonably well and suggest maximum collectivity for the ground state of 44Ar.
However, the trend of the excited 0${}_{2}^{+}$ in even-even Ar isotopes is
not that consistent with the calculations. The accuracy of the present shell
model calculations for predicting the 0${}_{2}^{+}$ states will get validation
with the experimental observation of the yet unknown 0${}_{2}^{+}$ state for
48Ar in future experimental endeavors.

##  VI Acknowledgement

We thank the NSCL operation team and the A1900 team, especially Tom Ginter,
for the production and optimization of the secondary beam. This work was
supported by the U.S. National Science Foundation under Grant Nos. PHY-2012522
(FSU), PHY-1848177 (CAREER); U.S. Department of Energy, Office of Science,
Office of Nuclear Physics under award Nos. DE-SC0020451 (FRIB), DE-
FG02-94ER40848 (UML), DE-AC52-07NA27344 (LLNL), DE-AC02-06CH11357(ANL) and
also by the U.S. Department of Energy (DOE) National Nuclear Security
Administration Grant No. DOE-DE-NA0003906, and the Nuclear Science and
Security Consortium under Award No. DE-NA0003180.

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# Instant One-Shot Word-Learning for Context-Specific
Neural Sequence-to-Sequence Speech Recognition

###### Abstract

Neural sequence-to-sequence systems deliver state-of-the-art performance for
automatic speech recognition (ASR). When using appropriate modeling units,
e.g., byte-pair encoded characters, these systems are in principal open
vocabulary systems. In practice, however, they often fail to recognize words
not seen during training, e.g., named entities, numbers or technical terms. To
alleviate this problem we supplement an end-to-end ASR system with a
word/phrase memory and a mechanism to access this memory to recognize the
words and phrases correctly. After the training of the ASR system, and when it
has already been deployed, a relevant word can be added or subtracted
instantly without the need for further training. In this paper we demonstrate
that through this mechanism our system is able to recognize more than 85% of
newly added words that it previously failed to recognize compared to a strong
baseline.

Index Terms: speech recognition, one-shot learning, new-word learning

##  1 Introduction

Up until recently automatic speech recognition (ASR) systems were implemented
as Bayes classifiers in order to search for the word sequence $\hat{W}$, among
all possible word sequences $W$, with the highest posterior probability given
a sequence of feature vectors $X$ which is the result of pre-processing the
acoustic signal to be recognized:

$\displaystyle\hat{W}$ $\displaystyle=\operatorname*{argmax}_{W}P(W|X)$
$\displaystyle=\operatorname*{argmax}_{W}P(X|W)P(W)$

In the context of ASR $P(X|W)$ is called the acoustic model, $P(W)$ the
language model. The space of allowed word sequences to search among was
usually defined by a list of words, the vocabulary, of which permissible word
sequences could be composed. Words that were not in the vocabulary could not
be recognized. In turn this means that by adding words to the vocabulary and
appropriate probabilities to the language model, previously unknown words
could be easily added to the ASR system manually or even automatically.

In contrast, for neural sequence-to-sequence trained end-to-end ASR systems,
this is not possible anymore. While in principal end-to-end systems are open-
vocabulary systems, when using appropriate modeling units, such as byte-pair
encoded (BPE) characters, in practice, words not seen during training are
often not reliably recognized. This is especially true for named entities. The
reasons for that are that, a) the end-to-end network implicitly learns
language model knowledge when being trained on transcribed speech data, and b)
especially named entities often have a grapheme-to-phoneme relation that
deviates from the general pronunciation rules of the language, as learnt
implicitly by the networks of the end-to-end system.

In order to solve this problem, in this paper we extend an end-to-end ASR
system by a memory for words and phrases. We further introduce a mechanism
that enables the system to recognize the words stored in this memory without
further training. This enables us to add new words and short phrases (only
text, no audio) to the recognition system, long after the training of the ASR
system has finished, and when it has already been deployed, without the need
for further training.

This is achieved by, a) a memory-attention layer which predicts the
availability and location of relevant information in the memory, and b) a
memory-entry-attention layer which extracts the information of a memory entry.

Fig. 1: Left: Baseline model, Middle: MEM model similar to [1], Right: 2MEM
model. Dark blue: The two main components that are added compared to the
baseline.

##  2 Related Work

The problem of new or rare words in speech recognition with sequence-to-
sequence models is an active field of research. The closest to our work is
[1]. In their work, they train a LSTM-based ASR model based on [2] which
outputs graphemes. The model is supplied by dynamically biased context of rare
words. [3] injects additional phonetic information on top of that. [4]
predicted a vector presenting the context of a word with a low confidence
(misrecognized) and searched for the nearest vectors in a big corpus to find a
substitution. In [5] a neural machine translation is augmented by a memory of
word pairs to translate unseen or sparse pairs in the training data, but only
for single words to be translated.

In our work, we build a memory for new words and phrases. The first modeling
of a memory was done with Recurrent Neural Networks (RNNs) and Long-Short Term
Memory (LSTMs), which capture long-term structure within the sequence in a
latent state (local memory). In praxis, many applications require addressable
memory (global memory) for the neural network in a kind of Neural Turing
Machines [6]. For instance, Memory Networks [7] and End-To-End Memory Networks
[8] are used to store answers for question-answering applications. Similarly,
Pointer Networks [9] circumvent the out-of-vocabulary (OOV) problem by copying
words from the input sequence that are not contained in the output vocabulary.
The network does not possess any memory. A well-known example of a Pointer
Network is the summarization with Pointer-Generator Networks [10]. [11] build
a memory-augmented neural network for meta-learning which saves sample-label
pairs and predicts upon the similarity of the input and the samples encoded in
the memory. The most frequent memory samples are injected into the weights as
long-term memory. [12] aim to automatically spell-correct ASR output text
using a pointer network to copy out-of-vocabulary (OOV) words directly. They
incorporate phonetic information as well, however they do not mention any kind
of attending to audio as in our work.

Other related works address the problem of adaptation to a new domain or
enhance the model by rescoring the output with a language model via two pass
decoding. These works does not aim to solve the problem of OOV words directly.
[13] incorporate a multi corpora language model for second pass rescoring,
while [14] and [15] rescore with a second model by attending to the audio or
as in [16], where the second model attends to both the audio and the output
using a deliberation model.

##  3 Method

###  3.1 Baselines

As baseline we use a transformer-based sequence-to-sequence model [17, 18]. It
consists of 24 encoder layers and 8 decoder layers with a model dimension of
1024 and feed-forward dimension of 2048 (see fig. 1, left). The inputs $X$ to
the encoder are mel-filterbank coefficients with 40 features. Before the
encoder layers a two-layer convolutional neural network with 32 channels and
time stride two is used to downsample the input spectrogram [19]. The decoder
has as input the BPE tokens of the already decoded sequence
$Y_{0},\ldots,Y_{t-1}$ and predicts a probability distribution
$P(Y_{t}|Y_{0},\ldots,Y_{t-1};X)$ over the BPE vocabulary. The BPE consists of
4000 tokens.

For comparison we trained a memory-enhanced model (MEM) similar to [1] (see
fig. 1, middle). However we replaced the LSTMs they used with a transformer
model. Furthermore we run the baseline decoder together with the memory
decoder and combine the output at the end (see section 3.3). This has the
advantage that we are able to change the baseline after the training.

Our proposed model111A demo can be found under https://huberchristian.eu (see
fig. 1, right) changes the memory-decoder compared to the MEM model such that
the output is computed in a two-step fashion. First, the availability and
location of relevant information is predicted, and second, the information of
a memory entry is extracted. We call this the two-step memory-enhanced model
(2MEM). Both the MEM model and the 2MEM model predict a probability
distribution $P(Y_{t}|Y_{0},\ldots,Y_{t-1};X;Z)$ over the BPE vocabulary,
where $Z=(Z_{1},\ldots,Z_{L})$ are additional words/phrases we want the model
to recognize.

To demonstrate that our model is able to be used with any baseline model we
also evaluate it using a LSTM-based baseline [19]. This baseline consists of 6
encoder layers and 2 decoder layers with a model dimension of 1536.

###  3.2 Memory Encoder

Our memory can contain (similar to [1]) words or phrases in each memory entry.
We represent each memory entry as BPE and refer to them as
$Z_{1},\ldots,Z_{L}$, where $Z_{l}\in\\{1,\ldots,|V_{BPE}|\\}^{e_{l}}$,
$l\in\\{1,\ldots,L\\}$. The term $e_{l}$ denotes the number of tokens in the
memory entry $Z_{l}$.

The memory encoder starts with an embedding layer which output is denoted by
$Z_{l}^{emb}\in\mathbb{R}^{e_{l}\times d_{model}}$, where $d_{model}$ is the
dimension of the model. Then a transformer encoder is applied. It consists of
eight layers, if not mentioned otherwise. The output of the encoder is denoted
by $Z_{l}^{e}\in\mathbb{R}^{e_{l}\times d_{model}}$.

After that we compute the mean of each encoded memory entry $Z_{l}^{e}$ over
the BPE tokens of the entry. This leaves us with one vector per memory entry,
which can be interpreted as summary vector of the memory entry, denoted by
$Z_{l}^{s}\in\mathbb{R}^{d_{model}}$. We add to these vectors $Z_{l}^{s}$ a
learned dummy vector $Z_{0}^{s}$, which is later used to determine when there
is no relevant information in the memory.

###  3.3 Memory Decoders

Both the decoders in the MEM model and the 2MEM model consist of $M$ blocks.
In our experiments we use $M=4$ if not mentioned otherwise. Each block starts
with a decoder layer similar to the baseline model. Then a memory-attention
layer is applied. It extracts the availability and location of relevant
information of the memory. This is done by calculating similarity scores,
where for the query input $Q$ and the key input $K$ the decoder layer output
and $Z_{l}^{s}$ are used, respectively.

$\displaystyle\hat{Q}$ $\displaystyle=W^{Q}Q,\qquad$ $\displaystyle\text{
shape }T\times d_{model}$ $\displaystyle\hat{K}$ $\displaystyle=W^{K}K,\qquad$
$\displaystyle\text{ shape }(L+1)\times d_{model}$ $\displaystyle scores$
$\displaystyle=\hat{Q}\hat{K}^{T},\qquad$ $\displaystyle\text{ shape
}T\times(L+1)$ $\displaystyle gate$ $\displaystyle=scores[:,0],\qquad$
$\displaystyle\text{ shape }T$

where $T$ is the number of tokens in the target sequence, $W^{Q}$ and $W^{K}$
are weight matrices and $scores[:,0]$ are the similarity scores corresponding
to the learned dummy vector $Z_{0}^{s}$.

The main difference between the MEM model and the 2MEM model is the way in
which the information is extracted of the memory. For the MEM model all the
information of a memory entry has to be encoded in the vector $Z_{l}^{s}$. For
the 2MEM model the vector $Z_{l}^{s}$ has to only contain the information if a
memory entry is currently relevant. If thats the case the memory-entry-
attention layer can extract the information.

In the MEM model the score output of the memory-attention layer is processed
by a softmax layer and the result is multiplied with a linear transformation
of values $V$ generated by $Z_{l}^{s}$.

$\displaystyle\hat{V}$ $\displaystyle=W^{V}V,\qquad$ $\displaystyle\text{
shape }(L+1)\times d_{model}$ $\displaystyle output$
$\displaystyle=sm(scores)\hat{V},\qquad$ $\displaystyle\text{ shape }T\times
d_{model}$

where $W^{V}$ is a weight matrix, $sm$ is the softmax function, which is
computed w.r.t. the last dimension. The memory-attention layer together with
this transformation is equivalent to an attention layer similar to the
encoder-decoder attention. The difference is that the gate output is used in
the further processing.

In the 2MEM model the memory-entry-attention layer is used to extract relevant
information of a specific memory entry. This is done by using an attention
mechanism similar to the encoder-decoder attention, however not the vectors
$Z_{l}^{s}$ are used to generate the values as in the MEM model. For the query
again the decoder layer output is used and for the keys and values, we use
$Z_{l}^{e}$ and $Z_{l}^{emb}$, respectively, where $l$ is the argmax of the
scores of the memory-attention layer for a given query.

Let ${l=\operatorname*{argmax}(scores_{t})}$ be the index of the largest score
for the query $Q_{t}$ at time step $t$. If $l$ is not zero, i.e. the index
does not correspond to the learned dummy vector, the following is computed:

$\displaystyle\hat{Q}$ $\displaystyle=\bar{W}^{Q}Q_{t},\qquad$
$\displaystyle\text{ shape }d_{model}$ $\displaystyle\hat{K}$
$\displaystyle=\bar{W}^{K}Z_{l}^{e},\qquad$ $\displaystyle\text{ shape
}e_{l}\times d_{model}$ $\displaystyle\hat{V}$
$\displaystyle=\bar{W}^{V}Z_{l}^{emb},\qquad$ $\displaystyle\text{ shape
}e_{l}\times d_{model}$ $\displaystyle output$
$\displaystyle=sm(\hat{Q}\hat{K}^{T})\hat{V},\qquad$ $\displaystyle\text{
shape }T\times d_{model}$

where $\bar{W}^{Q}$, $\bar{W}^{K}$ and $\bar{W}^{V}$ are weight matrices. If
the maximum score corresponds to the learned dummy vector (see section 3.2),
no attention is calculated. A residual connection is used around the attention
layer in the MEM model and the memory-entry-attention layer in the 2MEM model.

For both the MEM model and the 2MEM model, the outputs of the baseline decoder
and the memory decoder are combined at the end by a weighted sum. The
weighting is calculated as a linear transformation with one output neuron of
the stacked gate outputs of all memory attention layers followed by a sigmoid
layer.

##  4 Training

During training we freeze the original baseline components and train only the
memory related components.

###  4.1 Memory Content during Training

The content of the memory during training is sampled for each batch dependent
on the target labels of the batch. We randomly select up to three words of a
target label and use these as a memory entry. In total we sample 200 memory
entries for each batch.

###  4.2 Loss Function

The loss function $L$ consists of two cross entropy parts. The first one
classifies the next token $Y_{t}$ of the sequence and the second one
classifies the most important memory entry:

$\displaystyle L$
$\displaystyle=\frac{1}{T}\sum_{t=1}^{T}CE(f_{\theta}(Y_{t-1},\ldots,Y_{0};X;Z),Y_{t})$
$\displaystyle+\frac{\lambda}{MT}\sum_{m=1}^{M}\sum_{t=1}^{T}CE(scores_{t}^{m},label^{mem}_{t}),$

where $f_{\theta}(Y_{t-1},\ldots,Y_{0};X;Z)$ is the output distribution of the
decoder given the already decoded sequence $Y_{t-1},\ldots,Y_{0}$, the
audiofeatures $X$ and the memory/context $Z=(Z_{l})_{l}$. Furthermore,
$scores_{t}^{m}\in\mathbb{R}^{L+1}$ are the score output of the memory
attention layer in the $m$-th memory decoder block and
$label_{t}^{mem}\in\\{0,\ldots,L\\}$ is the memory label. This memory label is
constructed when sampling the memory content (see section 4.1). It contains
the index zero of the learned dummy vector if a token is not chosen for the
memory and otherwise the index of the corresponding memory entry. We use
$\lambda=1$ and label smoothing of $0.1$.

We experienced that the MEM model learns to only focus on the baseline decoder
output. Therefore, we force the model to use the memory when advantageous.
This is done by permuting the output of the baseline decoder and the memory
decoder dependent on $label^{mem}$ with a certain probability before the
weighted sum is applied. This forces the model to use the memory decoder
output if there is relevant information in the memory and the baseline decoder
output otherwise. In particular, the probabilities of the label index and a
random other index of the baseline decoder output are interchanged where
$label^{mem}$ is non-zero and the same is done for the memory decoder output
where $label^{mem}$ is zero. From the permuted probabilities no gradient is
propagated backwards to not confuse the model.

###  4.3 Data

For training and evaluation of our models, we used Mozilla Common Voice v6.1
[20], Europarl [21], How2 [22], Librispeech [23], MuST-C v1 [24], MuST-C v2
[25] and Tedlium v3 [26] datasets. The data split is presented in the
following table 1.

Corpus | Utterances | Speech data [h]
---|---|---
A: Training Data
Mozilla Common Voice | 1225k | 1667
Europarl | 33k | 85
How2 | 217k | 356
Librispeech | 281k | 963
MuST-C v1 | 230k | 407
MuST-C v2 | 251k | 482
Tedlium | 268k | 482
B: Test Data
Tedlium | 1155 | 2.6
New-words testset | 239 | 0.5
Table 1:  Summary of the data-sets used.

Furthermore we created a new-words testset containing 239 utterances each
containing a word, e.g. named entities, we assumed the model could do wrong
because it has not seem these words during training. We use this new-words
testset to evaluate the performance of the models to learn these new words
when they are provided as additional context through the memory.

##  5 Results

###  5.1 Evaluation

For the evaluation we report an accuracy on new-words testset with empty and
full memory as well as the WER on the ted testset also with empty and full
memory. As memory entries we use all the (239) new words of the new-words
testset. The accuracy is thereby calculated such that the output of the model
is counted as correct if the new word is present in the transcript.

The results can be seen in table 2. We obtained that the MEM model learned to
only focus on the baseline decoder. A reinitialization of the parameters in
the weighted sum during training did not help. This changes when permuting the
output probabilities of the decoder (see section 4.2) with probability 0.5.
The accuracy on the new-words testset increases from 44.8% to 79.5%.

Surprisingly, the 2MEM model works well on the new-words testset without
permuted output probabilites (88.7%), however there is also a performance gain
when permuting the output probabilities of the 2MEM model (90.4%).

On the ted testset the performance drops slightly for all models with good
performance on the new-words testset. This happens since the models sometimes
uses a word in the memory when the target word starts similarly.

Metric |  Acc.$\uparrow$ (%) |  |
---|---|---|---
new words testset |  WER$\downarrow$ (%) |  |
ted testset |  |  |  |
Model Full memory | ✗ | ✓ | ✗ | ✓
Transformer baseline | 45.2 | 5.0
MEM model | 44.8 | 44.8 | 4.8 | 4.8
\+ permute 0.5 | 44.4 | 80.8 | 5.0 | 5.3
2MEM model | 42.3 | 88.7 | 4.9 | 5.2
\+ permute 0.5 | 45.2 | 90.4 | 5.0 | 5.2

Table 2:  Summary of the results. Accuracy on the new-words test set and WER
on the ted test set.

In table 3 an example of correcting the sentence ”[we will] hopefully have
covid nineteen behind [us soon]” with the model 2MEM with permutation
probability 0.5 can be seen. The word covid nineteen was not seen in the
training data.

a) Decoding with empty memory  hope fully have co ve t nin et een behind 0.90
0.88 0.89 0.83 0.89 0.93 0.93 0.88 0.88 0.89 0 0 0 0 0 0 0 0 0 0 b) Decoding
with word ”covid” as $Z_{1}$ hope fully have co v id nin et een behind 0.90
0.88 0.87 0.03 0.03 0.03 0.92 0.88 0.88 0.89 0 0 0 1 1 1 0 0 0 0

Table 3:  Example for correcting ”covid nineteen”. Rows: Predicted tokens,
gate (weighting between baseline decoder and memory decoder) and memory
location output (argmax of the scores; all layers have the same argmax in this
example).

###  5.2 Ablation

For the ablation we start with the best performing model, the 2MEM model with
permutation probability $0.5$, and explore different changes. The results can
be seen in table 4.

Metric |  Acc.$\uparrow$ (%) |  |
---|---|---|---
new words testset |  WER$\downarrow$ (%) |  |
ted testset |  |  |  |
Model Full memory | ✗ | ✓ | ✗ | ✓
LSTM baseline | 47.3 | 3.9
2MEM model, permute 0.5 | 45.2 | 90.4 | 5.0 | 5.2
\+ encode values | 44.8 | 90.4 | 4.9 | 5.2
\+ residual connection | 44.8 | 88.3 | 5.1 | 5.3
\+ LSTM baseline | 46.9 | 92.1 | 3.9 | 4.2
one memory |  |  |  |
encoder layer | 43.1 | 84.5 | 5.3 | 6.0
one memory |  |  |  |
decoder layer | 42.7 | 87.9 | 5.2 | 7.1

Table 4:  Summary of the ablation results. Accuracy (in %) on the new-words
test set, WER on the Ted test set.

We tried to use $Z_{l}^{e}$ instead of $Z_{l}^{emb}$ (see sections 3.2 and
3.3) as value input for the memory-entry-attention layer. We refer to this as
encode values and obtained that using these values delivers almost the same
performance. Furthermore, we tried to add residual connections to the scores
of the memory-attention layer. The performance on the new-words testset as
well as on the ted testset decreased. As already mentioned in section 3.1 our
model can be used with any baseline. We substituted our transformer-based
baseline with a LSTM-based one which has a better performance on the ted
testset. We obtain that this performance increase transfers to the new-words
testset. We also trained models with only one memory encoder or one memory
decoder layer. We see that this also works on the new-words testset, however
the performance on the ted testset degrades to 6.0% and 7.1%, respectively,
when the new words are in the memory. It seems that the memory decoder layers
are more critical than the memory encoder layers.

Overall the 2MEM model with LSTM-based baseline performed the best with 92.1%
accuracy on our new-words testset. This model was able to correct more than
85% of the errors via the memory component.

##  6 Conclusion and Future Work

In this paper we demonstrated that it is possible to enhance a sequence-to-
sequence ASR model with a memory component that allows to add new words to the
recognition system, e.g., named entities, during deployment without the need
for further training. In this way more than 85% of the previously
misrecognized words not seen during training, were recognized correctly. Our
2MEM model outperforms the MEM model (which is similar to the model in [1])
significantly.

One drawback of the proposed method is that one only provides text for the
memory. Therefore, if the pronunciation of a new word deviates from the
implicitly learned pronunciation rules, it is unlikely to be found by the
memory-attention layer. We therefore plan to extend our model by populating
the memory with an audio sample of the new word in addition to text.
Furthermore, a subword regularization [27], where a word can be encoded into
multiple BPE candidates, could improve the performance of the system.

##  7 Acknowledgements

The projects on which this paper is based were funded by the Federal Ministry
of Education and Research (BMBF) of Germany under the numbers 01IS18040A and
01EF1803B.

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