for the NUMEN collaboration

# One-neutron transfer reaction in the 18O + 48Ti collision at 275 MeV

O. Sgouros<EMAIL_ADDRESS>Dipartimento di Fisica e Astronomia
”Ettore Majorana”, Università di Catania, Catania, Italy  INFN - Laboratori
Nazionali del Sud, Catania, Italy  M. Cutuli  Dipartimento di Fisica e
Astronomia ”Ettore Majorana”, Università di Catania, Catania, Italy  INFN -
Laboratori Nazionali del Sud, Catania, Italy  F. Cappuzzello  Dipartimento di
Fisica e Astronomia ”Ettore Majorana”, Università di Catania, Catania, Italy
INFN - Laboratori Nazionali del Sud, Catania, Italy  M. Cavallaro  INFN -
Laboratori Nazionali del Sud, Catania, Italy  D. Carbone  INFN - Laboratori
Nazionali del Sud, Catania, Italy  C. Agodi  INFN - Laboratori Nazionali del
Sud, Catania, Italy  G. De Gregorio  INFN - Sezione di Napoli, Napoli, Italy
Dipartimento di Matematica e Fisica, Università della Campania ”Luigi
Vanvitelli”, Caserta, Italy  A. Gargano  INFN - Sezione di Napoli, Napoli,
Italy  R. Linares  Instituto de Física, Universidade Federal Fluminense,
Niterói, Brazil  G. A. Brischetto  Dipartimento di Fisica e Astronomia ”Ettore
Majorana”, Università di Catania, Catania, Italy  INFN - Laboratori Nazionali
del Sud, Catania, Italy  D. Calvo  INFN - Sezione di Torino, Torino, Italy  E.
R. Chávez Lomelí  Instituto de Física, Universidad Nacional Autónoma de
México, Mexico City, Mexico  I. Ciraldo  Dipartimento di Fisica e Astronomia
”Ettore Majorana”, Università di Catania, Catania, Italy  INFN - Laboratori
Nazionali del Sud, Catania, Italy  F. Delaunay  Dipartimento di Fisica e
Astronomia ”Ettore Majorana”, Università di Catania, Catania, Italy  INFN -
Laboratori Nazionali del Sud, Catania, Italy  LPC Caen UMR6534, Université de
Caen Normandie, ENSICAEN, CNRS/IN2P3, F-14000 Caen, France  H. Djapo  Ancara
University, Institute of Accelerator Technologies, Turkey  C. Eke  Department
of Mathematics and Science Education, Faculty of Education, Akdeniz
University, Antalya, Turkey  P. Finocchiaro  INFN - Laboratori Nazionali del
Sud, Catania, Italy  M. Fisichella  INFN - Laboratori Nazionali del Sud,
Catania, Italy  M. A. Guazzelli  Centro Universitario FEI, São Bernardo do
Campo, Brazil  A. Hacisalihoglu  Department of Physics, Recep Tayyip Erdogan
University, Rize, Turkey  J. Lubian  Instituto de Física, Universidade Federal
Fluminense, Niterói, Brazil  N. H. Medina  Instituto de Física, Universidade
de São Paulo, São Paulo, Brazil  M. Moralles  Instituto de Pesquisas
Energeticas e Nucleares IPEN/CNEN, São Paulo, Brazil  J. R. B. Oliveira
Instituto de Física, Universidade de São Paulo, São Paulo, Brazil  A. Pakou
Department of Physics, University of Ioannina and Hellenic Institute of
Nuclear Physics, Ioannina, Greece  L. Pandola  INFN - Laboratori Nazionali del
Sud, Catania, Italy  V. Soukeras  Dipartimento di Fisica e Astronomia ”Ettore
Majorana”, Università di Catania, Catania, Italy  INFN - Laboratori Nazionali
del Sud, Catania, Italy  G. Souliotis  Department of Chemistry, University of
Athens and Hellenic Institute of Nuclear Physics, Athens, Greece  A. Spatafora
Dipartimento di Fisica e Astronomia ”Ettore Majorana”, Università di Catania,
Catania, Italy  INFN - Laboratori Nazionali del Sud, Catania, Italy  D.
Torresi  INFN - Laboratori Nazionali del Sud, Catania, Italy  A. Yildirim
Department of Physics, Akdeniz Universitesi, Antalya, Turkey  V. A. B. Zagatto
Instituto de Física, Universidade Federal Fluminense, Niterói, Brazil

###### Abstract

The present article reports new data on the 48Ti(18O,17O)49Ti reaction at 275
MeV incident energy as part of the systematic research pursued within the
NUMEN project. Supplementary measurements of the same reaction on 16O and 27Al
targets were also performed in order to estimate the background arising from
the use of a composite target (TiO2 \+ 27Al). These data were analyzed under
the same theoretical framework as those obtained with the titanium target in
order to reinforce the conclusions of our analysis. Differential cross-section
angular distribution measurements for the 17O8+ ejectiles were performed in a
wide angular range by using the MAGNEX large acceptance magnetic spectrometer.
The experimental results were analyzed within the distorted-wave and coupled-
channels Born Approximation frameworks. The optical potentials at the entrance
and exit channels were calculated in a double folding approach adopting the
São Paulo potential, and the spectroscopic amplitudes for the projectile and
target overlaps were obtained from large-scale shell model calculations. The
differential cross-sections are well-described by the theoretical
calculations, where a weak coupling to collective excitations of projectile
and target is inferred. The sensitivity of transfer cross-sections on
different model spaces adopted in nuclear structure calculations, is also
discussed.

###### pacs:

25.70.Hi, 24.10.Eq, 21.10.Jx

##  I Introduction

Over the past few years, studies for the neutrinoless double $\beta$
(0$\nu$$\beta$$\beta$) decay continue with undiminished interest, since it is
considered the best probe of neutrino nature [1, 2, 3, 4, 5, 6, 7]. Moreover,
if the 0$\nu$$\beta$$\beta$ decay is to be observed, the neutrino absolute
mass scale could be extracted from the measured half-life [4, 8]. However, the
latter is hampered by our limited knowledge of the nuclear matrix elements
(NMEs) for this exotic process which, to date, their values are model
dependent and susceptible to large uncertainties leading to vague conclusion
for the neutrino absolute mass scale [9, 10]. High quality experimental data
from single charge exchange [11] or light-ion induced transfer [12, 13, 14]
reactions have been invoked to constrain the NMEs theories, but the
ambiguities in the nuclear structure models are still too large. In this
respect, more experimental constraints using different probes are highly
desirable.

Recently, a seminal experimental campaign was initiated at Istituto Nazionale
di Fisica Nucleare - Laboratori Nazionali del Sud (INFN-LNS) in Catania within
the NUMEN (NUclear Matrix Elements for Neutrinoless double $\beta$ decay) and
NURE (NUclear REactions for neutrinoless double $\beta$ decay) [15] projects.
NUMEN proposes an innovative experimental approach [16, 17] aiming at
accessing information on the NMEs of 0$\nu$$\beta$$\beta$ decay by means of
the heavy-ion induced double charge exchange (DCE) reactions on various
$\beta$$\beta$ decay candidate targets [7]. This may be achieved by collecting
precise information on the NMEs of the DCE reaction [5] which were recently
proved to be correlated with the NMEs of the 0$\nu$$\beta$$\beta$ decay [3,
18]. However, in order to obtain meaningful information of the NMEs of DCE
reactions, a comprehensive description of the complete DCE reaction mechanism
is imperative.

The direct meson exchange DCE reaction is one of the possible pathways of the
complete DCE mechanism. The same final nuclear states can be, in principle,
populated through two successive single charge exchange (SCE) reactions [19],
through multi-nucleon transfer reactions [20] or a combination between them
[21]. A recent theoretical work for the 20Ne+116Cd reaction at 306 MeV [20]
pointed to a small contribution of multi-nucleon transfer to the DCE cross-
section, provided the appropriate experimental constraints [22, 23] on the
reaction models. Moreover, multi-nucleon transfer reactions are driven from
mean-field dynamics and are susceptible to the kinematical matching conditions
of Brink [24]. However, the contribution of all competitive processes to the
measured DCE cross-section should not be considered “a priori” negligible,
instead global studies of the DCE reactions [25, 26, 27] together with all the
available reaction channels are necessary [23, 28, 29].

Over the past decades, single-nucleon transfer reactions induced by light ions
have been established as a prominent tool of nuclear spectroscopy [12, 30, 31,
32, 33]. In early 50’s, Butler demonstrated that the angular distribution
pattern in (d,p) reactions is strongly dependent on the transferred angular
momentum, thus providing information on the spin and parity of the final state
nuclear wave function [34]. Additional information may be obtained from the
analysis of the cross-section angular distributions. Single-nucleon transfer
reactions favor transitions to final states with high degree of overlap with
the states at the entrance channel allowing the determination of the
spectroscopic factors. Further on, with the advent of radioactive beams these
reactions have been employed to study the structure of exotic nuclei far from
the valley of stability [35, 36, 37].

On the other side, heavy-ion induced transfer reactions have been less studied
than their light ion counterparts. The origin of this shortage is likely
twofold: the late dawn of powerful accelerators and high resolution detection
systems for heavy ions suitable for spectroscopic studies and the supposed
higher degree of complexity in heavy-ion dynamics. The latter consists in the
strong dependence on the reaction cross-sections on Q-value and angular
momentum matching conditions [38, 39, 40] and the presence of strong
absorption phenomena which should be effectively taken into account in the
theoretical model of the reaction. An additional complication may come from
the effect of inelastic excitations prior to and/or after the nucleon transfer
process [41, 42, 43, 44]. However, a substantial progress has been made in the
field, demonstrating the usefulness of heavy-ion induced reactions in studies
for nuclear structure and the reaction mechanism [45, 46, 47, 48, 49, 50, 51,
52, 53, 54].

The analysis of heavy-ion induced transfer reactions is usually performed in
full quantum mechanical approach within the distorted-wave Born approximation
(DWBA) formalism [55, 56, 57]. When inelastic excitations prior or after
transfer become important, the coupled-channels Born approximation (CCBA)
model could be employed [58]. In either theoretical framework, the calculation
depends strongly on the optical potentials (OPs) and the overlap functions.
The former is used to build the distorted waves at the entrance and exit
channels which describe the direct elastic scattering between the interacting
nuclei and also effectively account for absorption phenomena towards other
non-elastic processes through an imaginary term. The OPs can be determined in
phenomenological or double-folding frameworks, but in both cases their
validity should be checked against elastic scattering data. On the other hand,
the structure of the involved nuclei is inherent in the overlap functions.
These quantities are approximated as solutions of a mean-field potential with
fixed geometry weighted by the corresponding spectroscopic amplitude derived
from a nuclear structure model. The advent of powerful computers facilitates
the processing of shell model calculations with large model spaces for the
determination of the spectroscopic amplitudes. However, certain limitations do
exist like the case of nuclei well-beyond closed shells, where a reliable
truncation of the full Hilbert space becomes imperative (e.g. [59, 60]). In
this sense, transfer reactions can be used to test the validity of nuclear
shell model and improve our understanding of the mean-field description of
nuclei.

On the above grounds, the description of heavy-ion induced transfer reactions
is nowadays reasonably under control [43, 53, 61, 62, 63, 64, 65, 66, 67, 68].
During the past few years, a systematic study of one- and two- nucleon
transfer reactions has been initiated by our group for the needs of the NUMEN
project [23, 22, 29, 69, 70, 71, 72]. Transfer reactions can provide valuable
information on the wave functions of nuclei involved in the $\beta$$\beta$
decay process and in conjunction with the information obtained from the study
of the DCE reactions can provide experimental constraints on the nuclear
structures models to be employed for the determination of the NMEs of
0$\nu$$\beta$$\beta$ decay.

Figure 1: Schematic representation of the nuclear reaction network measured in
the 18O+ 48Ti collision. Arrows indicate the reaction paths connecting the
initial and final partitions. The cyan curved arrow represents the elastic and
inelastic scattering transitions.

Extending the aforementioned systematic, a global description in the 18O+48Ti
reaction at 275 MeV was performed under the NUMEN project by measuring all the
available reaction channels. A schematic representation of the explored
reaction network is illustrated in Fig.1. The analysis of the one-proton
transfer reaction has been already completed [69], while the analysis of the
elastic channel will be the subject of a forthcoming publication [73]. The
48Ti was used as target since is the daughter nucleus of 48Ca in the
0$\nu$$\beta$$\beta$ decay process [74, 75, 76]. Therefore, all possible
information about its structure is essential for the determination of the
relevant NMEs. The present article is dedicated to the study of single-neutron
transfer reaction channel. The angular distribution of the measured cross-
sections are analyzed within the DWBA formalism for validating the optical
potential at the entrance channel which was deduced in a parallel analysis of
the elastic scattering data [73] as well as to test the validity of adopted
the spectroscopic amplitudes derived from large-scale shell model
calculations. The role of inelastic excitations prior to transfer process was
also investigated by means of CCBA calculations. Further on, supplementary
measurements of the same reaction on 16O and 27Al targets were performed in
order to estimate the background arising from the different target components
(TiO2+27Al) as well as to reinforce the conclusions of our analysis.
Additionally, this work highlights the selectivity of transfer reactions on
the model space used in the nuclear structure calculations and complements the
work by Ciraldo et al. [71], where the sensitivity of transfer reactions on
the adopted nuclear structure model was inferred.

In what follows, the experimental setup and data reduction are reported in
Sections II and III, respectively, whereas in Section IV the description of
our theoretical approach for the calculation of the one-neutron transfer
cross-sections is presented. The results of the analysis are discussed in
Section V and finally, some concluding remarks are given in Section VI.

##  II Experimental setup

The experiment was conducted at the MAGNEX facility of INFN-LNS laboratoty in
Catania, Italy. A fully stripped 18O ion beam, accelerated at 275 MeV by the
K800 Superconducting Cyclotron, impinged on a (510 $\pm$ 26) $\mu$g/cm2 TiO2
target which was evaporated onto a thin aluminum foil (216 $\pm$ 11
$\mu$g/cm2). Supplementary measurements, under the same experimental
conditions, were repeated using a 27Al target (226 $\pm$ 11 $\mu$g/cm2) as
well as a WO3 one (284 $\pm$ 14 $\mu$g/cm2) with an aluminum backing for
estimating the background contribution. The beam charge was integrated by
means of a Faraday cup placed 150 mm downstream the target position. An
electron suppressor ring polarized at -200V was placed at the entrance of the
Faraday cup to mitigate the error in the beam current measurement due to the
escape of secondary produced electrons.

Figure 2: (a) Reconstructed excitation energy spectrum for the
27Al(18O,17O)28Al one-neutron transfer reaction measured at 275 MeV. The
neutron separation threshold, Sn, of 28Al nucleus is denoted with the dashed
red line. (b) Energy distribution for the 27Al(18O,17O)28Al reaction. The
experimental data are compared to the result of a multi-fit analysis, where
each nuclear state is represented by a Gaussian form factor. The cyan dashed
curve represents the g.s. to g.s. transition, the blue dotted-dashed curves
represent the excited states of 17O nucleus, the brown dotted curves
correspond to excited states of 28Al nucleus with the 17O one being in the
g.s. and the long-dashed green curves represent transitions where both the 17O
and 28Al nuclei are excited. The continuum background above the single-neutron
emission threshold of 28Al is indicated with the solid magenta line. The solid
red line corresponds to the sum of the individual Gaussian curves.

The reaction ejectiles were momentum analyzed by the MAGNEX large acceptance
magnetic spectrometer [77] whose optical axis was set at $\theta_{opt}$=
$None$, thus subtending an angular range between $None$ and $None$ in the
laboratory reference frame. The large acceptance in momentum of the
spectrometer (-14%,+10.3% with respect to the optical axis) allowed the
simultaneous transport at the MAGNEX focal plane of the 17O8+ and 19F9+ ions
coming from the one-neutron and one-proton transfer reactions, respectively.
The solid angle, delimited by four slits at the entrance of the spectrometer,
was reduced to 14 msr for preventing the deterioration of the Focal Plane
Detector (FPD) [78, 79] response from the high ion rate. The FPD is a hybrid
detector comprised a proportional drift chamber, served as energy loss
($\Delta$E) detector and as tracker, followed by a wall of 60 silicon
detectors for measuring the ions residual energy (Er). Using the information
provided by the FPD, the particle identification (PID) was performed. Details
pertinent to this work are provided herewith, while a description of the PID
technique has been discussed in details elsewhere [80]. The discrimination of
the various ion species based on their atomic number was performed adopting
the $\Delta$E-Er technique, while for a given ion the different isotopes were
discriminated following a technique based on the correlation between the ions
kinetic energy and the measured position along the dispersive direction
(horizontal in the case of MAGNEX). Examples of the PID technique can be found
in Refs.[69, 80, 81, 82, 83, 84].

##  III Data reduction

Having identified the 17O8+ events, a software ray reconstruction was
performed for each of the available data sets. This procedure allows one to
obtain the momentum vector of the ions at the target position [85] from the
measured coordinates at the reference frame of the FPD.

###  III.1 The 27Al(18O,17O)28Al reaction

Following the same strategy as the one adopted in the case of the one-proton
transfer reaction channel [69], we present the results for the
27Al(18O,17O)28Al reaction considering that the aluminum backing constitutes a
substantial source of background in the measurements with the TiO2 and WO3
targets. The excitation energy, Ex, was determined as:

$E_{x}=Q_{0}-Q,$ (1)

where Q0 is the ground state (g.s.) to g.s. Q-value for the 27Al(18O,17O)28Al
reaction calculated from the mass imbalance at the entrance and exit channels
and Q is the reaction Q-value calculated adopting the missing mass method [77]
based on relativistic two-body kinematics. Given the large acceptance in
momentum of the spectrometer, the excitation energy spectrum for the
27Al(18O,17O)28Al reaction was measured in a wide energy range and is
presented in Fig. 2a. The achieved energy resolution was $\approx$ 400 keV
full width at half maximum (FWHM). After correcting the experimental yields
for the overall efficiency of the spectrometer [86] and by taking into account
the solid angle and the beam flux of the measurement, the absolute energy
differential cross-sections were deduced and are presented in Fig. 2b. The
spectrum is characterized by a sharp increase in the cross-section between 3.5
and 6 MeV, which is attributed to transitions to the negative parity states of
28Al at 3.46, 3.59, 4.03 and 5.17 MeV owing to an appreciable single-particle
strength. This is compatible with what has been previously observed in (d,p)
reaction experiments [87], while it is further corroborated by our theoretical
calculations which are presented in the following section. Considering that
the 17O nucleus has only 3 bound excited states, the shape of the energy
spectrum is mainly determined by the level density of the 28Al. A multi-fit
analysis performed by using as inputs the known states of 17O and 28Al nuclei,
reproduces the overall shape of the energy distribution adequately-well. It
should be underlined that the individual contribution of each transition could
not be extracted from the fit, but the overall contribution of the various
unresolved states. To this extent, the experimental yields corresponding to
five discrete groups of states were deduced from the fits considering a
variable angular step (between $None$ and $None$), depending on the available
yield. The resulted differential cross-section angular distributions are
presented in Fig. 3. The error in the angular distribution data is dominated
from the statistical uncertainty and, to a lesser extent, from the uncertainty
in the determination of the solid angle. An overall error of about 10 % due to
the uncertainty in the target thickness and the integrated value of the beam
charge, common to all the data points, is not included in the error bars. The
shape of the angular distribution data is characterized by a sharp fall-off in
the differential cross-section ascribed to strong absorption phenomena
manifested after the grazing angle ($\theta$${}_{gr}^{c.m}$= $None$).

Figure 3: Comparison between experimental data and theoretical predictions for
the 27Al(18O,17O)28Al one-neutron transfer reaction at 275 MeV. The
experimental data which are indicated by the black points correspond to five
excitation energy regions in Fig. 2b labeled as (a) Peak 1, (b) Peak 2, (c)
Peak 3, (d) Peak 4 and (e) Peak 5. Theoretical angular distribution cross-
sections for the transitions to the involved states of the ejectile and the
residual nuclei were calculated within the DWBA framework and are presented
with the colored curves. In the legend, each curve is labeled by the
corresponding excitation energy of 28Al for transitions to the 17Og.s. and by
an asterisk in case where 17O is excited to the $\frac{1}{2}$${}_{1}^{+}$
(0.871 MeV) state. In panels (c)-(e), for reasons of clarity only the four
stronger transitions are shown, while the contribution for the rest of
transitions is indicated with the cyan dotted-dashed curve under the notation
”sum rest”. In all cases, the sum of all transitions is illustrated by the red
solid line. The overall result of a CCBA calculation considering the same
final states as the DWBA one is illustrated with the dashed black curve.

###  III.2 The 16O(18O,17O)17O reaction

The excitation energy spectrum of the 16O(18O,17O)17O one-neutron transfer
reaction is presented in Fig. 4a. The distinct structures located at Ex
$\approx$ -4.6 and -3.7 MeV were identified as one-neutron transfer events
originated from the reaction of 18O beam with the aluminum backing of the
target. Thus, using the previously analysed data collected in the measurement
with a self-supporting aluminum target, the energy distribution of the
contaminant events, appropriately normalized, was subtracted from the total
spectrum. The normalization factor was chosen such as the ratio of the
integral for the peaks at Ex $\approx$ -4.6 and -3.7 in the two data sets to
be $\approx$ 1\. The resulted normalization factor was found to be the same as
the one deduced in a parallel analysis for the one-proton transfer reaction on
the same target [69] which was measured under the same experimental
conditions. A very small contribution coming from the one-neutron transfer
reaction with the tungsten component of the target was further subtracted
assuming a uniform distribution throughout the whole energy range. This
distribution was normalized to a small remnant of events at Ex$<$-7 MeV, a
region free of any contamination due to the reaction with the aluminum
backing. After subtracting the contaminant events, the excitation energy
spectrum corresponding to the 16O(18O,17O)17O reaction was deduced and it is
presented in Fig. 4a. Subsequently, by correcting the experiment yields for
the efficiency of the spectrometer and by taking into account the solid angle
and the beam flux of the measurement, absolute energy and angle differential
cross-sections were determined and are presented in Figs. 4b and 5,
respectively. The error in the differential cross-sections includes the
contribution from statistical, solid angle and background subtraction
uncertainties. In this case, since the ejectile and recoil nuclei are
identical the energy profile of the reaction contains, in general,
contributions from transitions to excited states of both nuclei. The
contribution of each transition to the measured cross-sections could be
disentangled via theoretical calculations.

Figure 4: (a) Decomposition of the excitation energy spectrum measured at 275
MeV using a WO3 \+ 27Al target. The total spectrum is depicted with the dashed
black line. The red-filled area represents the normalized background spectrum
originated from the reaction of the beam with the aluminum backing, while the
blue-hatched area corresponds to the background spectrum coming from the
tungsten component of the target. For reasons of clarity, the latter was
scaled by a factor of 5. The spectrum represented by the solid green line
corresponds to the energy profile of the 16O(18O,17O)17O after subtracting
from the total spectrum the background events. (b) Energy distribution for the
16O(18O,17O)17O reaction. The experimental data are compared to the result of
a multi-fit analysis where each nuclear state is represented by a Gaussian
form factor. The line styles and colors used for the description of each curve
are the same as those presented in Fig. 2b. The single-neutron separation
threshold, Sn, of 17O nucleus is denoted with the dashed black line. Figure 5:
Comparison between experimental data and theoretical predictions for the
16O(18O,17O)17O one-neutron transfer reaction at 275 MeV. The experimental
data which are indicated by the black points correspond to three excitation
energy regions in Fig. 4b labeled as (a) Peak 1, (b) Peak 2 and (c) Peak 3.
Theoretical angular distribution cross-sections for the transitions to the
involved states of the ejectile and the residual nuclei were calculated within
the DWBA framework and are presented with the colored curves. In the legend,
each curve is labeled by the corresponding excitation energy of the recoil
nucleus for transitions to the g.s. of the ejectile and a symbol in case where
17O ejectile is excited. Curves marked with an asterisk and a circle refer to
transitions to the $\frac{1}{2}$${}_{1}^{+}$ (0.871 MeV) and
$\frac{1}{2}$${}_{1}^{-}$ (3.055 MeV) states of 17O, respectively. The sum of
all transitions is illustrated by the red solid line. The overall result of a
CCBA calculation considering the same final states as the DWBA one is
illustrated with the dashed black curve.

###  III.3 The 48Ti(18O,17O)49Ti reaction

The excitation energy spectrum of the 48Ti(18O,17O)49Ti one-neutron transfer
reaction is presented in Fig. 6a. The spectrum is contaminated by events
generated by the reaction of the beam with the oxygen and aluminum components
of the TiO2+27Al target. The yield due to such background sources was
determined using the previously analysed data presented in Figs. 2a and 4a.
The two background spectra were scaled using the same normalization factors as
those deduced from the analysis of the one-proton transfer reaction data on
the same target [69], since both reactions were measured under the same
experimental runs. Subsequently, the background yields were subtracted and the
excitation energy spectrum corresponding to the 18O + 48Ti reaction was
deduced and is presented in Fig. 6a. Following the same procedure as in the
previous two cases, the absolute energy differential cross-section as a
function the excitation energy was determined and it is shown in Fig. 6b. The
obtained energy resolution for this data set is $\approx$ 450 keV at FWHM.

For the determination of the angular distribution cross-sections a different
approach was followed for this data set. While in the case of the one-neutron
transfer reaction with the aluminum and oxygen targets the counts were
obtained from the area of the Gaussian functions, in this case, since the
level density of the 49Ti nucleus is appreciably higher, the experimental
yields were determined by integrating four regions of interest (ROI). In more
details, up to the excitation energy of $\approx$ 2 MeV where the level
density for 49Ti is rather low, tests adopting either the ROI or the Gaussian
function approach yielded almost identical results. However, beyond such
energy region it was found that the integrated yields are susceptible to the
results of the fit. Therefore, in order to avoid a model-dependent analysis
and thus increasing the systematic errors in the data reduction, it was
decided to select four discrete ROIs as it is shown in Fig. 6b. The same
prescription was also applied in the analysis of the one-neutron transfer
reaction for the system 18O + 76Se [71], where the density of states in the
77Se nucleus is comparable to the one of 49Ti. The resulted angular
distribution data are presented in Fig. 7.

Figure 6: (a) Decomposition of the excitation energy spectrum measured at 275
MeV using a TiO2 \+ 27Al target. The total spectrum is depicted with the
dashed black line. The red-dotted area represents the normalized background
spectrum originated from the reaction of the beam with the aluminum backing,
while the green-filled area corresponds to the background spectrum coming from
the oxygen component of the target. The spectrum represented by the blue-
hatched area corresponds to the energy profile of the 48Ti(18O,17O)49Ti, after
subtracting from the total spectrum the background events. (b) Energy
distribution for the 48Ti(18O,17O)49Ti reaction. The spectrum is divided in
four regions of interest (ROI) which are indicated by the colored areas.
Figure 7: Comparison between experimental data and theoretical predictions for
the 48Ti(18O,17O)49Ti one-neutron transfer reaction at 275 MeV. The
experimental data which are indicated by the black points correspond to four
excitation energy regions in Fig. 6b labeled as (a) ROI 1, (b) ROI 2, (c) ROI
3 and (d) ROI 4. Theoretical angular distribution cross-sections were derived
within the DWBA and CCBA frameworks and are presented with the colored curves.
In the legend, each curve is marked with the name of the effective interaction
which was employed in the nuclear structure calculations.

##  IV Theoretical analysis

Theoretical cross-section angular distribution for the transfer reactions
under study were calculated under the DWBA and the CCBA frameworks using the
FRESCO code [89]. The transfer operator was built employing the post-
representation and incorporating full complex remnant terms. The distorted
waves at the entrance and exit channels were generated using the double-
folding São Paulo potential (SPP) [90, 91, 92] for the description of the real
and imaginary part of the optical potential, but adopting two different
normalization coefficients for each part. The real part of the optical
potential accounts for the refraction of the incident waves, while the
imaginary part for all non-elastic processes [93]. The normalization
coefficient of the real part, NR, was equal to unity as typically adopted for
heavy ion elastic scattering involving tightly bound nuclei above the Coulomb
barrier [94]. The value of the normalization factor of the imaginary part, NI,
may slightly vary depending on the adopted coupling scheme. In the DWBA
calculations where no couplings to collective states of projectile and/or
target are considered the value of NI was 0.78, whereas in the CCBA approach
where couplings to the low-lying states of the projectile and the target were
taken into account, this factor was further reduced to NI= 0.60. This
prescription has been successfully applied in the past for the description of
various elastic scattering and single-nucleon transfer reaction data [29, 43,
62, 69, 70, 71, 72, 95, 96, 97, 98]. For the case of the 18O + 48Ti reaction,
the optical potential at the entrance channel was checked against elastic and
inelastic scattering data which were measured in the same experiment [73].

The bound state wave functions were calculated as single-particle solutions of
the Schroedinger with a Woods-Saxon potential of certain geometry. For the 17O
core the reduced radius and diffuseness of the potential were 1.26 and 0.70
fm, respectively, while the corresponding values for the heavier cores were
1.20 and 0.60 fm, respectively. This is a typical choice of parameters that
has been adopted in many of our previous works for 18O induced transfer
reactions on different target species [29, 69, 71, 99]. For the 16O core which
is a tightly bound doubly-magic nucleus, the adopted values for the reduced
radius and diffuseness of the potential were 1.20 and 0.60 fm, respectively
[43]. In all cases the depth of the Woods-Saxon potential was varied such as
to reproduce the experimental binding energies of the valence neutron.

In the CCBA calculations, couplings to the low-lying states of the projectile
and target were included using the conventional rotational model, while no
couplings to excited states of the nuclei at the exit partition were
considered. In the rotational model, the deformation of the Coulomb potential
is extracted from the intrinsic matrix element, while the strength of the
nuclear deformation is calculated from the corresponding deformation length.
Considering a transition from an initial state with spin 0+, as in the present
case, to a final state with spin J under the action of an operator of
multipolarity k, the intrinsic matrix element, Mn, is evaluated as:

$M_{n}(E_{k},0^{+}\rightarrow J)=\pm\sqrt{(2J+1)B(E_{k};0^{+}\rightarrow J)},$
(2)

where B(Ek) is the reduced transition probability. The relative sign of Mn(Ek)
is taken as that of the intrinsic quadrupole moment following the prescription
of Ref. [89]. The deformation length is related to the intrinsic matrix
element through the following expression:

$\delta_{k}=\frac{4\pi}{3Ze}\frac{M_{n}(E_{k},0^{+}\rightarrow
J)}{R_{pot.}^{k-1}},$ (3)

where Z is the atomic number of the deformed nucleus and Rpot. is the average
radius of the potential to be deformed (i.e. the SPP). A list with the reduced
transition probabilities used in the CCBA calculations is presented in Table
I.

Table 1: List of the reduced transition probabilities B(Ek;0+ $\rightarrow$ J) used in the CCBA calculations. Nucleus |  B(E2;0+ $\rightarrow$ 2+) |  B(E3;0+ $\rightarrow$ 3-)
---|---|---
| (e2b2) | (e2b3)
18O | 0.0043† | 0.0013⋆
48Ti | 0.072△ | 0.0074⋆
16O | - | 0.0015⋆
($\dagger$) from Ref. [100], ($\bigtriangleup$) from Ref. [101], ($\star$)
from Ref. [102]

The spectroscopic amplitudes for the projectile and target overlaps were
derived within the framework of nuclear shell model using the KSHELL code
[103]. For the calculation of one-neutron spectroscopic amplitudes for the
$\braket{{}^{17}O}{{}^{18}O}$ projectile and $\braket{{}^{16}O}{{}^{17}O}$
target overlaps has been performed by using the psdmod [104] effective
interaction, a modified version of PSDWBT [105]. It considers the 4He as inert
core with the valence neutrons and protons in the $1p2s1d$ orbitals. This
interaction gives reliable results for nuclei around 16O as testified by many
of ours previous studies related to both one-proton and one-neutron transfer
reaction channels [29, 43, 54, 69, 70, 71, 72].

As regards the spectroscopic amplitudes for the $\braket{{}^{28}{\rm
Al}\mid^{27}{\rm Al}}$ overlaps, the the psdmod and SDPF-MU [106] interactions
were used, as it was done previously for the one-proton transfer reaction on
the same target [69], to better assess the relevance of excitations across the
$1p-2s1d$ shell-gap with respect to those across the $2s1d-1f2p$ shell-gap for
the systems under investigation. In fact, at variance with psdmod, the SDPF-MU
interaction is constructed in a model space spanned by the proton and neutron
2s1d and 1f2p orbitals on top of the doubly magic 16O core. It is based on the
VMu potential [107] and has been widely adopted to study the effects of
excitations across the 2s1d-1f2p shell-gap on nuclei approaching the island of
inversion at $N=20$ [108, 109, 110] as well as to compute the spectroscopic
factors of nuclei in Ca region [111, 112, 113, 114]. As a result of our
investigation (see discussion in Sec. V), it was found that the psdmod
interaction is rather inadequate to describe the magnitude of experimental
data for states above $\approx$ 3.5 MeV. Then, to compute the spectroscopic
amplitudes for the $\braket{{}^{49}{\rm Ti}}{{}^{48}{\rm Ti}}$ overlaps the
SDPF-MU interaction was employed.

However, due to the large model space of SDPF-MU, calculations for Al and Ti
isotopes have been limited, respectively, up to 4 and 2 particle-hole
excitation across the $2s1d-1f2p$ shell-gap, while all possible configurations
within the $2s1d$ and $1f2p$ shells have been included. In the Appendix, a
list with the calculated spectroscopic amplitudes obtained with the psdmod
interaction is presented in Table II for the projectile and target overlaps,
while Tables III and IV show the spectroscopic amplitudes for the
$\braket{{}^{28}{\rm Al}}{{}^{27}{\rm Al}}$ and $\braket{{}^{49}{\rm
Ti}}{{}^{48}{\rm Ti}}$ overlaps computed with the SDFP-MU interaction.

Figure 8: Present angular distribution data for the 27Al(18O,17O)28Al reaction
corresponding to (a) ”Peak 3” and (b) ”Peak 4” in Fig. 2b are compared to the
results of DWBA calculations which were performed adopting two different sets
of spectroscopic amplitudes. Figure 9: Present angular distribution data for
the 27Al(18O,17O)28Al reaction corresponding to ”Peak 3” in Fig.2b are
compared to the results of CCBA calculations which were performed adopting two
different normalization coefficients for the imaginary part of the optical
potential at the entrance channel.

##  V Results and discussion

Starting with the case of the 16O(18O,17O)17O reaction, as it was already
mentioned the reaction products at the exit channel are identical nuclei. This
fact may give rise to interference effects owing to the two-body nature of the
reaction, that is the ejectiles at forward angles cannot be distinguished
kinematically from the recoil nuclei. Therefore, the theoretical cross-
sections were obtained from the coherent sum of the scattering amplitudes
f($\theta$) and f($None$-$\theta$). The resulted theoretical curves are
compared to the experimental data in Fig.5, showing a fair agreement. The CCBA
calculations indicate a weak coupling to collective states of the projectile
and target, with a moderate coupling influence to be inferred for the cross-
sections corresponding to ”Peak 2”. The errors in the differential cross-
section data, which include the background subtraction uncertainty, range from
(7 to 21)%, (14 to 31)% and (12 to 34)% for the data of ”Peak 1”, ”Peak 2” and
”Peak 3”, respectively. These values are dominated by the uncertainties in the
background subtraction, although a residual error of about 50% of the initial
one remains, when this source of uncertainty is switched-off from the error
propagation. Overall, the data interpretation is rather satisfactory. In more
details, the data in Peaks 1 and 2 are slightly overestimated from theory by a
factor of $\approx$ 1.2, while the experimental cross-sections in the region
of ”Peak 3” are underestimated by a factor of $\approx$ 0.7.

As mentioned above, for the 27Al(18O,17O)28Al reaction, we have computed the
theoretical cross-sections using both the psdmod and SDPF-MU interactions. It
was found that at low excitations energies, namely for the first three peaks
in Fig.2b, the theoretical cross-sections computed with the two effective
interactions are equivalent and describe well the experimental results, as it
can be seen in Fig.8a for instance for ”Peak 3”. This is not surprising. In
fact, correlations within the $2s1d$ shell are dominant at low-energy and the
matrix elements involving the orbitals of this shell are based on the USD
Hamiltonian [115] for both interactions.

On the other hand, the two interactions provide different results for ”Peak 4”
and ”Peak 5”. In these two energy regions, psdmod calculations significantly
underestimate the experimental values, while a good agreement is obtained with
the SDPF-MU interaction. This is illustrated for ”Peak 4” in Fig.8b, where
theoretical angular distributions in DWBA obtained with both interactions are
compared to the experimental data. The reason of this difference can be traced
back to the important effects of sd-fp cross-shell excitations in the energy
region above $\approx$ 3.5 MeV. As a matter of fact, the main contributions to
the cross-sections corresponding to ”Peak 4” and ”Peak 5” arise from negative-
parity states which can be constructed only by including cross-shell
excitations. The better agreement obtained with SDPF-MU indicates that a more
crucial role is played by the $2p-1f$ orbitals. This was also highlighted in
the 27Al(d,p)28Al transfer studies in Refs. [87, 88], which underline in
particular the role of the $(1d^{-1}_{5/2}1f)$ configuration in contributing
to the high-lying negative-parity states.

The result of this analysis highlights the selectivity of heavy-ion induced
transfer reactions on the details of the adopted model space confirming the
results of the work by Ciraldo et al. [71], claiming for a sizeable
sensitivity of such kind of transfer reactions on the adopted nuclear
structure model. The description of 28Al nucleus favors the use of the SDPF-MU
interaction, a fact that should be taken into account in case where strong
single-particle states of this nucleus can serve as intermediate steps for
second order processes.

Having established the validity of the SDPF-MU interaction, a comparison
between the complete set of experimental data and theoretical calculations is
presented in Fig.3. From an inspection on the angular distributions, it is
evident that the DWBA calculations describe very well the shape and the
magnitude of the experimental data, signaling that the populated final states
are characterized by a substantial single-particle strength. This is well
borne out by the results of the CCBA calculations, where the inclusion of
couplings to the 2${}_{1}^{+}$ and 3${}_{1}^{-}$ collective states of
projectile has a small impact on the predicted cross-sections. Couplings to
exited states of 27Al target were not considered in the calculations and thus,
the imaginary part of the optical potential at the entrance partition was
scaled by a factor of 0.70 instead of 0.60 which is the standard prescription
for the SPP [92]. To further elucidate the effect on the choice of NI,
exploratory calculations adopting the standard value of the normalization
coefficient were performed and the results are visualized in Fig.9. Using as
benchmark the data of Peak 3, it was found that the angular distributions
cross-sections in the measured angular range are rather insensitive to the
choice of NI, while a small change in the slope of the theoretical curves is
observed with the increasing angle. Similar conclusions were also drawn from
the analysis of the rest of the available data. Overall, a very good agreement
is observed between theoretical predictions and experimental data. The
calculations slightly overestimate the data by a factor ranging from 1.0 to
1.15, but the case of Peak 3 where a factor of 1.4 is found.

Figure 10: Present angular distribution data for the 48Ti(18O,17O)49Ti
reaction corresponding to (a) ”ROI 2” and (b) ”ROI 3” in Fig. 6b are compared
to the results of DWBA calculations. Theoretical angular distribution cross-
sections for the transitions to the involved states of the ejectile and the
residual nuclei are presented with the colored curves. In the legend, each
curve is labeled by the corresponding excitation energy of the recoil nucleus
for transitions to the g.s. of the ejectile and an asterisk in case where 17O
ejectile is excited to the $\frac{1}{2}$${}_{1}^{+}$ (0.871 MeV) state. The
sum of all transitions is illustrated by the red solid line. For ROI 3, only
the 7 most important contributions are shown.

Let us now discuss the 48Ti(18O,17O)49Ti reaction. The experimental data are
presented in Fig. 7. Since the majority of the extracted yields is a result of
an 27Al background subtraction, the errors in the data points are dominated
from the background subtraction uncertainties. In more details, the errors in
the differential cross-section data, which includes the background subtraction
uncertainty, range from (5 to 10)%, (8 to 30)% and (9 to 20)% for the data of
ROI 2, ROI 3 and ROI 4, respectively. In this case, a residual error of about
(30-40)% of the initial error value remains, if the background subtraction
uncertainty is switched-off from the error propagation. The errors for the
data of ROI 1, which is free of any background, are less than 10%.

In general, for all the reactions under study the overall errors are typically
smaller than the observed variations in the predicted cross-sections from
different state-of-art theoretical models. Thus, we may claim to have enough
sensitivity to allow a valuable discrimination of different nuclear structure
and reaction models.

The experimental data are compared to theoretical prediction in Fig. 7. Due to
the large number of states introduced in the calculations the total
theoretical cross-sections are reported for each energy region, but the
individual contribution for each transition is given explicitly in Fig. 10
only for ROI 2 and ROI 3, where the calculated cross-sections overestimate the
measured ones by a factor of $\approx$ 1.6 (see Table V). To a leaser extent,
the same observation holds also for ROI 1 where the relevant factor is reduced
to $\approx$ 1.2. As regards the ROI 4 the experimental data are in good
agreement with the results of the DWBA and CCBA calculations (a factor of
$\approx$ 0.9 is found).

The discrepancies met in ROI 2 and ROI 3 could be explained to some extent by
considering the truncation scheme adopted in the calculations of Ti isotopes,
which includes at most 2 particle-hole configurations. However, to further
elucidate this point it may be useful to analyze Fig. 10.

As a matter of fact, in ROI 2 the discrepancy can be attributed to the large
cross-section predicted for the transition to the $\frac{3}{2}$${}_{1}^{-}$
state at 1.382 MeV, whose contribution alone already overestimates the
magnitude of the experimental data. However, the calculated spectroscopic
amplitude for this state is consistent with the value suggested from $(d,p)$
experiments [116], which may indicate that the single-particle component of
this state is overestimated. Furthermore, we should bear in mind that the
spectroscopic factors obtained in [116] were determined by normalizing the
DWBA predictions to the experimental data, so are in principle susceptible to
the experimental uncertainties as well as to the details of the reaction model
(e.g. optical potentials).

As regards ROI 3, it is observed that the two main contributions arise from
the transitions to the $\frac{3}{2}$${}_{1}^{-}$ state as in ROI 2 and to the
$\frac{5}{2}$${}_{3}^{-}$ state at 2.261 MeV. From the previous discussion, it
is expected that the contribution from the $\frac{3}{2}$${}_{1}^{-}$ state is
rather overestimated. Moreover, for the 2.261 MeV state a higher spectroscopic
amplitude is predicted by our calculations as compared to the experimental
value (0.36 versus 0.14).

We may conclude that a slightly different distribution of the single-neutron
strength is needed for the $\frac{3}{2}$${}_{1}^{-}$ and
$\frac{5}{2}$${}_{3}^{-}$ states than that provided by the SDFP-MU
interaction. This seems to point to some deficiencies in the matrix elements
of this interaction concerning configurations of $1f2p$ shell. In fact, $2s1d$
and cross-shell matrix elements, whose reliability has been even testified by
calculations for Al isotopes, do not play a relevant role as evidenced by
comparing results with and without cross-shell excitations that are found to
be very similar. Furthermore, by using the KB3 effective interaction [117],
defined only in the $1f2p$ space, smaller spectroscopic amplitudes are
predicted for the $\frac{3}{2}$${}_{1}^{-}$ and $\frac{5}{2}$${}_{3}^{-}$
states and the theoretical angular distributions cross-sections for the ROI 2
and ROI 3 provide a better description of the experimental data, especially
for ROI 3 (see Fig. 7). A tentative calculation using a value of $\approx$
0.40 for the spectroscopic amplitude for the $\frac{3}{2}$${}_{1}^{-}$ state
was performed. It was found that using such a value the angular distribution
data of both ROIs 2 and 3 can be described reasonably by theory. However, this
is an arbitrary choice and therefore, the obtained results are not included in
the present work.

The above discussion indicated that the SDPF-MU interaction would require
adjustments of some matrix elements. However, given the success of this
interaction to explain the structure of 47Sc nucleus including the one-proton
transfer cross-sections on 48Ti [69] and in prospect of a systematic study, we
may conclude that the SDPF-MU interaction with the present truncation scheme
provides a reasonable description of the data on the 48Ti(18O,17O)49Ti
reaction.

##  VI Summary and conclusions

Absolute differential cross-sections measurements for the (18O,17O) one-
neutron transfer reaction on three different targets namely, 27Al, 16O and
48Ti were performed at the energy of 275 MeV. Angular distributions of the
17O8+ reaction ejectiles were determined in a wide angular range by means of
the MANGEX large acceptance magnetic spectrometer at INFN-LNS. The
differential cross-section data were analyzed under the DWBA framework and
overall a good agreement between experimental and theoretical cross-sections
is inferred. Moreover, CCBA calculations were also performed suggesting a weak
coupling to collective states of the projectile and target nuclei.

Further on, the sensitivity of the calculated cross-sections on the
configuration space used in the large-scale shell model calculation was sought
in the data obtained with the 27Al and 48Ti targets. For the 27Al(18O,17O)28Al
reaction, it was found that the inclusion of $fp$ shell in the adopted model
space is mandatory for the description of the negative parity states of 28Al
(see Fig.8). Moreover, for the case of the 48Ti(18O,17O)49Ti reaction it was
found that the discrepancies met between experimental data and theoretical
predictions (see Fig.7) can be ascribed, to some extent, to the adopted
truncation of the shell model basis. The most striking example was the case of
ROI 3, where a clear improvement between data and theory is observed when a
full fp shell model basis is employed instead of a truncated one. However, for
the rest of the data the differences when using a truncated or a full fp shell
model basis are less evident.

Finally, the results of the present work are complementary to those reported
for the one-proton transfer reaction for the same system. Both results will
help to clarify the degree of competition between sequential nucleon transfer
and the direct meson exchange dynamics in single and double charge exchange
reactions, which is a relevant aspect under scrutiny by nuclear reaction
theory. Moreover, both one-neutron and one-proton transfer data sets can be
used as guidelines to constrain the reaction models for the proper description
of two-neutron and two-proton transfer reaction mechanisms, respectively,
which constitute a piece of the puzzle for the description of the complete DCE
mechanism.

## Acknowledgments

The authors would like to thank the staff of the LNS Accelerator for the
support during the experiment. The research leading to these results was
partially funded by the European Research Council (ERC) under the European
Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement No
714625). We also acknowledge the CINECA award under the ISCRA initiative (code
HP10B51E4M) and through the INFN-CINECA agreement for the availability of high
performance computing resources and support. One of us (G.D.G.) acknowledges
the support by the funding program VALERE of Univerità degli Studi della
Campania ”Luigi Vanvitelli”. We also acknowledge partial financial support
from CNPq, FAPERJ, FAPESP (proc. no. 2019/07767-1) and Instituto Nacional de
Ciência e Tecnologia - Física Nuclear e Aplicações (INCT-FNA, proc. no.
464898/2014-5), Brazil.

##  VII Appendix

Table 2: One-neutron spectroscopic amplitudes for the projectile and target overlaps, calculated using the psdmod interaction. The symbols n, l and j correspond to the principal quantum number, the orbital and the total angular momentum of the transferred neutron orbitals, respectively. Initial state |  nlj |  Final state |  Spectroscopic amplitude
---|---|---|---
| 1d5/2 |  17Og.s. (5/2+) | 1.2708
18Og.s. (0+) | 2s1/2 |  17O0.871 (1/2+) | -0.4345
| 1p1/2 |  17O3.055 (1/2-) | 0.8155
| 1d5/2 |  17Og.s. (5/2+) | -1.0734
| 1d3/2 |  17Og.s. (5/2+) | -0.0799
| 2s1/2 |  17Og.s. (5/2+) | -0.5093
| 1d5/2 |  17O0.871 (1/2+) | 0.4994
18O1.982 (2+) | 1d3/2 |  17O0.871 (1/2+) | 0.1737
| 1p3/2 |  17O3.055 (1/2-) | -0.0207
| 1p3/2 |  17O3.843 (5/2-) | -0.0085
| 1p1/2 |  17O3.843 (5/2-) | -0.6787
| 1p3/2 |  17Og.s. (5/2+) | 0.0988
| 1p1/2 |  17Og.s. (5/2+) | -0.1135
| 1d5/2 |  17O3.055 (1/2-) | -0.2430
18O5.098 (3-) | 1d5/2 |  17O3.843 (5/2-) | 0.5860
| 1d3/2 |  17O3.843 (5/2-) | 0.0888
| 2s1/2 |  17O3.843 (5/2-) | 0.1220
| 1d5/2 |  17Og.s. (5/2+) | 0.9445
16Og.s. (0+) | 2s1/2 |  17O0.871 (1/2+) | -0.9633
| 1p1/2 |  17O3.055 (1/2-) | -0.2810
| 1p3/2 |  17Og.s. (5/2+) | -0.1974
| 1p1/2 |  17Og.s. (5/2+) | 0.5993
| 1d5/2 |  17O3.055 (1/2-) | -0.7256
16O6.130 (3-) | 1d5/2 |  17O3.843 (5/2-) | -0.9309
| 1d3/2 |  17O3.843 (5/2-) | 0.0768
| 2s1/2 |  17O3.843 (5/2-) | -0.2755
Table 3: One-neutron spectroscopic amplitudes for the $\braket{{}^{28}Al}{{}^{27}Al}$ overlaps calculated using the SDPF-MU interaction. The symbols n, l and j correspond to the principal quantum number, the orbital and the total angular momentum of the transferred neutron orbitals, respectively. Initial state |  nlj |  Final state |  Spectroscopic amplitude
---|---|---|---
27Alg.s. (5/2+) | 1d5/2 | 28Alg.s. (3+) | 0.3247
1d3/2 | -0.2148
2s1/2 | 0.5487
1d5/2 | 28Al0.031 (2+) | -0.2607
1d3/2 | 0.4280
2s1/2 | -0.3471
1d5/2 |  28Al0.972 (0+) | -0.5548
1d5/2 | 28Al1.014 (3+) | -0.0090
| 1d3/2 | 28Al1.014 (3+) | 0.4055
| 2s1/2 | 0.2719
27Alg.s. (5/2+) | 1d5/2 | 28Al1.373 (1+) | -0.2881
1d3/2 | 0.5582
1d5/2 | 28Al1.620 (1+) | 0.3908
1d3/2 | 0.1032
1d5/2 | 28Al1.623 (2+) | -0.4035
1d3/2 | -0.2405
2s1/2 | -0.0538
1d5/2 | 28Al2.139 (2+) | 0.0900
1d3/2 | 0.0391
2s1/2 | -0.2229
1d5/2 | 28Al2.201 (1+) | -0.0811
1d3/2 | -0.0320
1d5/2 | 28Al2.272 (4+) | -0.4929
1d3/2 | -0.0285
1d5/2 | 28Al2.486 (2+) | 0.1128
1d3/2 | -0.4223
2s1/2 | -0.2596
1d5/2 |  28Al2.582 (5+) | -0.4314
1d5/2 | 28Al2.656 (4+) | -0.1635
1d3/2 | -0.5499
1d5/2 | 28Al3.347 (2+) | 0.0500
1d3/2 | -0.0248
2s1/2 | -0.1883
1f7/2 | 28Al3.465 (4-) | -0.6114
1f5/2 | 0.0224
2p3/2 | 0.3764
1f7/2 | 28Al3.591 (3-) | -0.3513
1f5/2 | -0.0064
2p3/2 | 0.3741
2p1/2 | -0.0579
1d5/2 |  28Al3.760 (0+) | -0.1401
1f7/2 | 28Al3.876 (2-) | -0.3975
1f5/2 | -0.0399
2p3/2 | 0.2946
2p1/2 | -0.0503
1f7/2 | 28Al4.033 (5-) | 0.7382
1f5/2 | -0.0799
1f7/2 | 28Al4.691 (3-) | -0.3297
1f5/2 | -0.0267
2p3/2 | 0.4658
2p1/2 | -0.0709
27Alg.s. (5/2+) | 1f7/2 | 28Al4.765 (2-) | -0.2452
1f5/2 | -0.0323
2p3/2 | 0.4940
2p1/2 | 0.1309
1f7/2 | 28Al4.904 (2-) | 0.1721
1f5/2 | -0.0249
2p3/2 | 0.2951
2p1/2 | 0.0408
1f7/2 | 28Al4.997 (2-) | 0.1396
1f5/2 | -0.0613
2p3/2 | 0.3182
2p1/2 | 0.3931
1f7/2 | 28Al5.135 (3-) | -0.2723
1f5/2 | 0.0164
2p3/2 | -0.4613
2p1/2 | 0.1493
1f7/2 | 28Al5.165 (6-) | 0.6523
Table 4: One-neutron spectroscopic amplitudes for the $\braket{{}^{49}Ti}{{}^{48}Ti}$ overlaps calculated using the SDPF-MU interaction. The symbols n, l and j correspond to the principal quantum number, the orbital and the total angular momentum of the transferred neutron orbitals, respectively. Initial state |  nlj |  Final state |  Spectroscopic amplitude
---|---|---|---
48Tig.s. (0+) | 1f7/2 |  49Tig.s. (7/2-) | 0.4872
2p3/2 |  49Ti1.382 (3/2-) | -0.8217
2p3/2 |  49Ti1.586 (3/2-) | -0.1145
1f5/2 |  49Ti1.623 (5/2-) | 0.0778
2p1/2 |  49Ti1.723 (1/2-) | -0.4762
1f5/2 |  49Ti1.762 (5/2-) | 0.3684
1f5/2 |  49Ti2.261 (5/2-) | 0.3570
1f5/2 |  49Ti2.471 (5/2-) | -0.1689
1f5/2 |  49Ti2.513 (5/2-) | 0.1710
1f7/2 |  49Ti2.980 (7/2-) | 0.1607
1f7/2 |  49Ti3.042 (7/2-) | 0.1348
2p1/2 |  49Ti3.175 (1/2-) | -0.3715
2p3/2 |  49Ti3.261 (3/2-) | -0.2505
2p3/2 |  49Ti3.428 (3/2-) | -0.0151
2p1/2 |  49Ti3.469 (1/2-) | -0.4048
1f5/2 |  49Ti3.511 (5/2-) | 0.0823
1f5/2 |  49Ti3.618 (5/2-) | -0.0737
| 2p3/2 |  49Ti3.788 (3/2-) | -0.0416
| 1f5/2 |  49Ti3.855 (5/2-) | -0.1019
48Ti0.984 (2+) | 1f7/2 | 49Tig.s. (7/2-) | 0.8999
1f5/2 | -0.0423
2p3/2 | -0.0796
1f7/2 | 49Ti1.382 (3/2-) | -0.2767
1f5/2 | -0.0171
2p3/2 | 0.0069
2p1/2 | -0.1856
1f7/2 | 49Ti1.586 (3/2-) | -0.2823
| 1f5/2 | -0.0913
48Ti0.984 (2+) | 2p3/2 | 49Ti1.586 (3/2-) | 0.6818
2p1/2 | -0.1317
1f7/2 | 49Ti1.623 (5/2-) | 0.1199
1f5/2 | -0.1316
2p3/2 | -0.4205
2p1/2 | 0.0823
1f5/2 | 49Ti1.723 (1/2-) | 0.2164
2p3/2 | 0.6434
1f7/2 | 49Ti1.762 (5/2-) | 0.0894
1f5/2 | -0.2747
2p3/2 | -0.4277
2p1/2 | -0.3669
1f7/2 | 49Ti2.261 (5/2-) | -0.0089
1f5/2 | -0.3213
2p3/2 | 0.5434
2p1/2 | 0.0465
1f7/2 | 49Ti2.471 (5/2-) | -0.2189
1f5/2 | 0.1602
2p3/2 | -0.1679
2p1/2 | 0.1079
1f7/2 | 49Ti2.513 (5/2-) | 0.0162
1f5/2 | -0.1138
2p3/2 | -0.2825
2p1/2 | 0.4077
1f7/2 | 49Ti2.980 (7/2-) | -0.0379
1f5/2 | 0.0193
2p3/2 | 0.6600
1f7/2 | 49Ti3.042 (7/2-) | -0.2316
1f5/2 | -0.0843
2p3/2 | 0.4345
1f5/2 | 49Ti3.175 (1/2-) | -0.3173
2p3/2 | -0.0482
1f7/2 | 49Ti3.261 (3/2-) | -0.1361
1f5/2 | -0.1135
2p3/2 | -0.4522
2p1/2 | 0.0815
1f7/2 | 49Ti3.428 (3/2-) | -0.1108
1f5/2 | -0.1655
2p3/2 | -0.1874
2p1/2 | -0.3613
1f5/2 | 49Ti3.469 (1/2-) | 0.4981
2p3/2 | -0.3551
1f7/2 | 49Ti3.511 (5/2-) | 0.0081
1f5/2 | -0.0871
2p3/2 | -0.1451
2p1/2 | -0.0081
| 1f7/2 | 49Ti3.618 (5/2-) | -0.0328
48Ti0.984 (2+) | 1f5/2 | 49Ti3.618 (5/2-) | 0.0080
2p3/2 | 0.0608
2p1/2 | -0.1720
1f7/2 | 49Ti3.788 (3/2-) | -0.0606
1f5/2 | 0.1221
2p3/2 | -0.1719
2p1/2 | -0.1221
1f7/2 | 49Ti3.855 (5/2-) | -0.0671
1f5/2 | -0.0129
2p3/2 | -0.0764
2p1/2 | -0.2506
48Ti3.359 (3-) | 1d5/2 | 49Tig.s. (7/2-) | -0.0539
1d3/2 | 0.1277
2s1/2 | -0.1464
1d5/2 | 49Ti1.382 (3/2-) | 0.0160
1d3/2 | -0.0406
1d5/2 | 49Ti1.586 (3/2-) | -0.0529
1d3/2 | 0.2503
1d5/2 | 49Ti1.623 (5/2-) | 0.0176
1d3/2 | 0.0151
2s1/2 | 0.0063
1d5/2 | 49Ti1.723 (1/2-) | 0.0024
1d5/2 | 49Ti1.762 (5/2-) | 0.0130
1d3/2 | 0.0258
2s1/2 | 0.0232
1d5/2 | 49Ti2.261 (5/2-) | -0.0226
1d3/2 | -0.0596
2s1/2 | -0.0366
1d5/2 | 49Ti2.471 (5/2-) | -0.0022
2s1/2 | -0.0032
Table 4: continued Initial state |  nlj |  Final state |  Spectroscopic amplitude
---|---|---|---
48Ti3.359 (3-) | 1d5/2 | 49Ti2.513 (5/2-) | 0.0125
1d3/2 | -0.0937
2s1/2 | 0.0353
1d5/2 | 49Ti2.980 (7/2-) | 0.0070
1d3/2 | -0.0203
2s1/2 | 0.0353
1d5/2 | 49Ti3.042 (7/2-) | -0.0218
1d3/2 | 0.0458
2s1/2 | -0.0358
1d5/2 | 49Ti3.175 (1/2-) | 0.0341
1d5/2 | 49Ti3.261 (3/2-) | 0.0049
1d3/2 | -0.0253
1d5/2 | 49Ti3.428 (3/2-) | -0.0085
1d3/2 | 0.0908
1d5/2 | 49Ti3.469 (1/2-) | -0.0059
1d5/2 | 49Ti3.511 (5/2-) | 0.0052
1d3/2 | -0.0290
2s1/2 | -0.0032
1d5/2 | 49Ti3.618 (5/2-) | -0.0062
1d3/2 | 0.0192
2s1/2 | -0.0038
1d5/2 | 49Ti3.788 (3/2-) | -0.0120
1d3/2 | 0.0746
1d5/2 | 49Ti3.855 (5/2-) | 0.0076
1d3/2 | 0.0013
2s1/2 | 0.0026
Table V: One-neutron transfer cross-sections integrated in the angular range [5o-14o] in the centre of mass reference frame for each ROI in Fig. 6b. The populated states which contribute to the overall cross-section at each ROI are reported in the second column. The theoretical cross-sections for the individual transitions were calculated under the DWBA and CCBA frameworks using the psdmod and KB3 interactions and are presented in the third, fourth and fifth column. The sum of the predicted cross-sections for all transitions contributing to each ROI, $\sigma_{tot.}$, is given in the sixth, seventh and eighth column and is compared to the experimental value, $\sigma_{exp.}$, presented in the last column. ROI |  Populated states |  $\sigma_{DWBA}^{psdmod}$ (mb) |  $\sigma_{CCBA}^{psdmod}$ (mb) |  $\sigma_{DWBA}^{KB3}$ (mb) |  $\sigma_{tot.}^{DWBA-psdmod}$ (mb) |  $\sigma_{tot.}^{CCBA-psdmod}$ (mb) |  $\sigma_{tot.}^{DWBA-KB3}$ (mb) |  $\sigma_{exp.}$ (mb)
---|---|---|---|---|---|---|---|---
1 |  17Og.s.+49Tig.s. | 0.529 | 0.637 | 0.547 | - | - | - | 0.446 $\pm$ 0.015
2 |  17Og.s.+49Ti1.382 | 1.448 | 1.409 | 1.218 | 1.890 | 1.865 | 1.579 | 1.057 $\pm$ 0.031
17Og.s.+49Ti1.586 | 0.028 | 0.027 | 0.057
17Og.s.+49Ti1.623 | 0.009 | 0.014 | 0.003
17Og.s.+49Ti1.723 | 0.135 | 0.146 | 0.144
17Og.s.+49Ti1.762 | 0.183 | 0.173 | 0.087
17Og.s.+49Ti2.261 | 0.024 | 0.022 | 0.005
17O0.871+49Tig.s. | 0.063 | 0.074 | 0.065
3 |  17Og.s.+49Ti1.723 | 0.015 | 0.016 | 0.016 | 0.801 | 0.865 | 0.499 | 0.563 $\pm$ 0.020
17Og.s.+49Ti1.762 | 0.029 | 0.027 | 0.014
17Og.s.+49Ti2.261 | 0.184 | 0.166 | 0.005
17Og.s.+49Ti2.471 | 0.047 | 0.040 | 0.026
17Og.s.+49Ti2.513 | 0.049 | 0.069 | 0.009
17Og.s.+49Ti2.980 | 0.040 | 0.064 | 0.020
17Og.s.+49Ti3.042 | 0.022 | 0.028 | 0.028
17Og.s.+49Ti3.175 | 0.016 | 0.018 | 0.022
17Og.s.+49Ti3.261 | 0.012 | 0.014 | 0.029
17O0.871+49Ti1.382 | 0.243 | 0.260 | 0.204
17O0.871+49Ti1.586 | 0.006 | 0.007 | 0.011
17O0.871+49Ti1.623 | 0.002 | 0.003 |  $<$0.001
17O0.871+49Ti1.723 | 0.048 | 0.053 | 0.051
17O0.871+49Ti1.762 | 0.048 | 0.050 | 0.023
17O3.055+49Tig.s. | 0.040 | 0.050 | 0.041
4 |  17Og.s.+49Ti2.980 | 0.035 | 0.055 | 0.017 | 0.562 | 0.633 | 0.655 | 0.645 $\pm$ 0.027
17Og.s.+49Ti3.042 | 0.031 | 0.038 | 0.039
17Og.s.+49Ti3.175 | 0.060 | 0.068 | 0.084
17Og.s.+49Ti3.261 | 0.095 | 0.108 | 0.225
17Og.s.+49Ti3.428 | 0.004 | 0.007 | 0.021
17Og.s.+49Ti3.469 | 0.087 | 0.064 | 0.071
17Og.s.+49Ti3.511 | 0.012 | 0.012 |  $<$0.001
17Og.s.+49Ti3.618 | 0.010 | 0.013 | 0.025
17Og.s.+49Ti3.788 | 0.002 | 0.004 |  $<$0.001
17Og.s.+49Ti3.855 | 0.014 | 0.018 | 0.005
17O0.871+49Ti2.261 | 0.038 | 0.036 |  $<$0.001
17O0.871+49Ti2.471 | 0.012 | 0.010 | 0.006
17O0.871+49Ti2.513 | 0.012 | 0.017 | 0.002
17O0.871+49Ti2.980 | 0.012 | 0.017 | 0.006
17O0.871+49Ti3.042 | 0.008 | 0.009 | 0.010
17O0.871+49Ti3.175 | 0.012 | 0.014 | 0.017
17O0.871+49Ti3.261 | 0.007 | 0.009 | 0.017
17O0.871+49Ti3.428 |  $<$0.001 |  $<$0.001 |  $<$0.001
17O0.871+49Ti3.469 | 0.003 | 0.002 | 0.002
17O3.055+49Tig.s. | 0.073 | 0.092 | 0.075
17O3.055+49Ti1.382 | 0.035 | 0.040 | 0.030

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R. K. Zamanov, A. Kostov, M. Moyseev, N. Petrov, Y. M. Nikolov, D. Marchev, K.
A. Stoyanov, M. S. Minev, V. Radeva, B. Borisov, K. Iłkiewicz, M. F. Bode, G.
Nikolov, A. Kurtenkov, G. Y. Latev, S. Boeva, P. L. Luque-Escamilla
11institutetext: Institute of Astronomy and National Astronomical Observatory,
Bulgarian Academy of Sciences, Tsarigradsko Shose 72, BG-1784 Sofia, Bulgaria
22institutetext: Department of Physics and Astronomy, Shumen University
”Episkop Konstantin Preslavski”, 115 Universitetska Str., BG-9700 Shumen,
Bulgaria 33institutetext: Department of Astronomy, Faculty of Physics, Sofia
University ”Saint Kliment Ohridski”, 5 James Bourchier Blvd., BG-1164 Sofia,
Bulgaria 44institutetext: Departamento de Física (EPSJ), Universidad de Jaén,
Campus Las Lagunillas s/n, A3, E-23071 Jaén, Spain 55institutetext: Naval
Academy, 73 Vasil Drumev str., BG-9026 Varna, Bulgaria 66institutetext:
Departamento de Ciencias Integradas, Centro de Estudios Avanzados en Física,
Matemática y Computación, Universidad de Huelva, E-21071, Huelva, Spain
77institutetext: Astrophysics Research Institute, Liverpool John Moores
University, IC2, 149 Brownlow Hill, Liverpool, L3 5RF, UK 88institutetext:
Office of the Vice Chancellor, Botswana International University of Science
and Technology, Palapye, Botswana 99institutetext: Astronomical Observatory,
University of Warsaw, Al. Ujazdowskie 4, 00-478 Warszawa, Poland
1010institutetext: Departamento de Ingeniería Mecánica y Minera (EPSJ),
Universidad de Jaén, Campus Las Lagunillas s/n, A3, E-23071 Jaén, Spain
Submitted on 21 June 2022; Accepted on xx.xx.xxxx

# The hidden symbiotic star SU Lyn - detection of flickering in U band

R. K. Zamanov 11 A. Kostov 11 M. Moyseev 11 N. Petrov 11 Y. M. Nikolov 11 D.
Marchev 22 K. A. Stoyanov 11 M. S. Minev 1133 J. Martí 44 V. Radeva 55 E.
Sánchez-Ayaso 66 M. F. Bode 7788 B. Borisov 22 K. Iłkiewicz 99 G. Nikolov 11
A. Kurtenkov 11 B. Spassov 11 P. L. Luque-Escamilla 1010 G. Y. Latev 11 S.
Boeva 11

###### Abstract

We report photometric observations of the hidden symbiotic star SU Lyn in the
optical bands. In four nights we detect a weak flickering in U band with
amplitude of about 0.05 magnitudes. No intranight variations are found in B,
V, g’ and r’ bands. This is one more indication that the secondary component
is a white dwarf accreting at low accretion rate.

We also searched for intranight variability of a dozen related object \- RR
Boo, RT Boo, AM Cyg, AG Peg, BF Cyg, NQ Gem, StHa190, V627 Cas, XX Oph, FS Cet
and Y Gem \- however no variability above the observational errors is
detected.

###### keywords:

stars: binaries: symbiotic – accretion, accretion discs – white dwarf – stars:
individual: SU Lyn

##  1 Introduction

The symbiotic stars are interacting binaries with long orbital periods in the
range from 100 days to more than 100 years. They consist of an red or yellow
giant transferring mass to a hot compact object (e.g. Mikołajewska 2012). The
mass donor is a giant or supergiant of spectral class G-K-M. If the giant is
an Asymptotic Giant Branch star, the system usually is a strong infrared
source. More than 250 symbiotic systems are known in our Galaxy (Akras et al.
2019, Merc et al. 2019).

The flickering is a non-periodic variability (on minutes-to-hour time scale)
typical for the accreting white dwarfs in cataclysmic variables (e.g. Bruch
1992, 2021). The systematic searches for flickering in symbiotic binaries
(Dobrzycka et al. 1996; Sokoloski et al. 2001) showed that flickering is
rarely detected in the classical symbiotic stars. Till now, only 11 of the
symbiotic stars are observed to vary in the optical bands on a timescale of
$\sim 10$ minutes with amplitude $>0.1$ magnitude – RS Oph, T CrB, MWC 560, Z
And, V2116 Oph, CH Cyg, RT Cru, o Cet, V407 Cyg, V648 Car, EF Aql, and ZZ CMi.
The last three were identified as flickering sources during the last decade:
V648 Car (Angeloni et al. 2012), EF Aql (Zamanov et al. 2017), and ZZ CMi
(Zamanov et al. 2021).

Here we report (i) photometry of SU Lyn and detection of intranight varibility
in U band and (ii) photometry of 11 related objects in which no variability is
detected.

Table 1: Photometric observations of SU Lyn. In the table are given date (in format YYYY-MM-DD), telescope, band, UT start-end, number of the frames and exposure time, typical observational error (merr), type of variability.  |  |  |  |  |  |  |  |  |  |
---|---|---|---|---|---|---|---|---|---|---
date | telescope | band | UT start-end | frames |  | merr |  | variability |  |
|  |  |  |  |  |  |  |  |  |
|  |  |  |  |  |  |  |  |  |
2020-01-18 | 50/70 Roz | U | 23:53 - 02:23 | 173 x 30 sec |  | 0.007 |  | flickering 0.11 mag |  |
2020-04-07 | 2.0m | U | 18:21 - 20:24 | 60 x 120 sec |  | 0.002 |  | flickering 0.05 mag |  |
2020-04-08 | 2.0m | U | 18:04 - 20:38 | 260 x 30 sec |  | 0.004 |  | flickering 0.05 mag |  |
2020-04-17 | 2.0m | U | 18:12 - 20:28 | 170 x 45 sec |  | 0.020 |  | flickering 0.03 mag |  |
|  | V | 18:14 - 20:27 | 648 x 0.02 sec |  | 0.005 |  | no variability |  |
2021-03-13 | 50/70 Roz | U | 23:42 - 01:41 | 98 x 30 sec |  | 0.008 |  | smooth 0.2 mag |  |
|  | B | 23:43 - 01:42 | 97 x 10 sec |  | 0.005 |  | no variability |  |
2022-04-27 | 40cm Shu | g’ | 18:31 - 21:15 | 282 x 10 sec |  | 0.010 |  | no variability |  |
|  | r’ | 18:30 - 21:15 | 295 x 4 sec |  | 0.010 |  | no variability |  |
|  |  |  |  |  |  |  |  |  |

Figure 1: Detection of intranight variability of SU Lyn with the 50/70 cm
Schmidt telescope of NAO Rozhen in U band.

Figure 2: Low amplitude flickering with $\Delta U\approx 0.05$ is visible in
the observations in U band performed with the 2.0m telescope in APril 2020.

Figure 3: Simultaneous observations in two bands. During the night 2020-04-17 no variability is detected in V band, however a low amplitude variability is visible in U band, with amplitude $\Delta U\approx 0.03$ mag. During the night 2022-04-27 no variability above the observational errors is visible in g’ and r’ bands.  Figure 4: Root mean square deviation versus the average U-band magnitude. The green squares refer to the night 2020-01-18, and the plus signs refer to 2021-03-13. The rms of SU Lyn deviates from the behavior of other stars, which indicates that it is variable.  Table 2: Log of observations on which no variability is detected. In the Table are given object, date of observation, telescope, band, UT start - UT end, number of the frames and exposure time, average magnitude, typical observational error (merr), and the result (no variability).  object | date-obs |  |  | telescope | band | UT start-end |  | frames |  | mag | merr | result |
---|---|---|---|---|---|---|---|---|---|---|---|---|---
RR Boo | 2019-06-21 |  |  | 41cm Jaen | B | 21:10 - 22:01 |  | 67 x 20 sec |  | 11.99 | 0.01 | negative |
|  |  |  |  | V |  |  | 66 x 10 sec |  | 10.21 | 0.01 | negative |
RT Boo | 2019-06-22 |  |  | 41cm Jaen | B | 20:59 - 21:35 |  | 34 x 30 sec |  | 14.03 | 0.03 | negative |
|  |  |  |  | V |  |  | 32 x 20 sec |  | 12.09 | 0.01 | negative |
AM Cyg | 2019-08-27 |  |  | 2.0m Roz | V | 23:04 - 23:59 |  | 281 x 10 sec |  | 14.29 | 0.01 | negative |
AG Peg | 2017-09-26 |  |  | 41cm Jaen | B | 18:44 - 19:51 |  | 145 x 10 sec |  | 9.71 | 0.01 | negative |
|  |  |  |  | V |  |  | 137 x 5 sec |  | 8.56 | 0.01 | negative |
BF Cyg | 2017-09-18 |  |  | 41cm Jaen | B | 18:59 - 20:06 |  | 87 x 20 sec |  | 10.11 | 0.01 | negative |
|  |  |  |  | V |  |  | 87 x 20 sec |  | 9.66 | 0.01 | negative |
NQ Gem | 2018-03-22 |  |  | 41cm Jaen | B | 20:04 - 21:01 |  | 79 x 15 sec |  | 10.16 | 0.01 | negative |
|  |  |  |  | V | 20:33 - 21:01 |  | 52 x 5 sec |  | 8.05 | 0.01 | negative |
StHa190 | 2017-10-02 |  |  | 41cm Jaen | B | 19:02 - 20:07 |  | 53 x 30 sec |  | 11.37 | 0.01 | negative |
|  |  |  |  | V |  |  | 53 x 30 sec |  | 10:54 | 0.01 | negative |
V627 Cas | 2017-09-18 |  |  | 50/70 Roz | B | 01:03 - 02:34 |  | 160 x 30 sec |  | 14.75 | 0.03 | negative |
Y Gem | 2018-10-09 |  |  | 60 cm Bel | B | 02:17 - 03:21 |  | 71 x 30 sec |  | 10.90 | 0.01 | negative |
|  |  |  |  | V |  |  | 71 x 5 sec |  | 9.51 | 0.01 | negative |
FS Cet | 2015-08-17 |  |  | 50/70 Roz | B | 00:54 - 01:47 |  | 130 x 20 sec |  | 12.44 | 0.01 | negative |
| 2016-12-19 |  |  | 50/70 Roz | V | 18:05 - 19:01 |  | 240 x 10 sec |  | 12.35 | 0.01 | negative |
XX Oph | 2018-09-14 |  |  | 50/70 Roz | U | 17:36 - 18:15 |  | 39 x 30 sec |  | 10.25 | 0.01 | negative |
|  |  |  | 50/70 Roz | B | 17:38 - 18:12 |  | 35 x 5 sec |  | 9.87 | 0.01 | negative |

##  2 Observations

We have observed SU Lyn with (i) the 50/70 cm Schmidt telescope of the
National Astronomical Observatory (NAO) Rozhen, Bulgaria, (ii) the 2.0 m RCC
telescope of the NAO Rozhen and (iii) the 40 cm telescope of the Shumen
University ”Episkop Konstantin Preslavski”, Bulgaria (Kjurkchieva et al.
2020). All the telescopes are equipped with CCD cameras. The observations are
plotted on Fig. 3, Fig. 3, and Fig. 3. It has to be noted that on the left
panel of Fig. 3 are plotted two other stars – HD 237533 and TYC 3770-1348-1.
HD 237533 has an average U=9.88 and is brighter than SU Lyn. TYC 3770-1348-1
has an average U=10.82 and is fainter than SU Lyn. Both they are shifted to
appear on the same scale as SU Lyn.

Table 1 is journal of observations of SU Lyn, where are given the date when
the observations begin, the telescope, the filter, UT-start and UT-end of the
run, number of the frames and exposure time, typical observational error (in
magnitudes), and the type of variability visible in the run.

We also observed other 11 objects – three variable stars of Mira-type (RR Boo,
RT Boo and AM Cyg), a sample of symbiotic stars (AG Peg, BF Cyg, NQ Gem,
StHa190, V627 Cas) as well as three other objects (Y Gem, FS Cet, XX Oph).
These observations are performed also with:
– (1) the telescope of the University of Jaén (Spain). This is an astronomical
facility located within the University of Jaén premises and mostly devoted to
educational purposes. It hosts an automated 41 cm telescope equipped with a
CCD camera with Johnson-Cousins filters. Differential photometry in the B and
V bands was conducted as described in Martí et al. (2017).
– (2) the 60 cm telescope of the Belogradchik Astronomical Observatory,
Bulgaria (Strigachev & Bachev 2011). The log of observations with non-
detections is contained in Table 2.

##  3 Intranight variability of SU Lyn in U band

Variability on a time scale of 1 hour is detected in all U band observations.
In 4 nights, it is a low amplitude flickering, with amplitude in the range
$0.03<\Delta U\leq 0.11$ mag. In one night we observe a smooth increase of the
brightness (2021-03-13, right panel of Fig. 3) in U band with 0.2 mag for 2
hours, while no variability is visible in the simultaneous observations in B
band.

The intranight variability is detected only in U band. No variability on a
time scale of 1 hour is visible on our runs at longer wavelengths (B, V, g’,
r’). Likely the red giant is the dominating source in these bands.

For the two runs obtained with the Schmidt telescope (presented on Fig. 3) we
measure the standard deviation of SU Lyn and of about 20 other stars in the
field and plot it on Fig. 4. These two runs are appropriate because the field
of view of the Schmidt telescope is wide and sufficient number of stars can be
measured. The standard deviation is calculated as

$\sigma_{rms}=\sqrt{\frac{1}{N_{pts}-1}\sum\limits_{i}(m_{i}-\overline{m})^{2}},$
(1)

where $\overline{m}$ is the average magnitude in the run, $N_{pts}$ is the
number of the data points. $\sigma_{rms}$ calculated in this way includes the
variability of the star (if it exists) and the measurement errors. For non-
variable stars it represents the precision of the photometry. The rms
deviation of SU Lyn is 5-7 times larger than that expected from observational
errors, indicating that SU Lyn is variable on a timescale of $\sim 1$ hour.

SU Lyn is a binary system composed of a white dwarf and a red giant. Lopes de
Oliveira et al. (2018) estimate that the mass of the white dwarf is $\geq 0.7$
M⊙. In the optical wavelengths there are no prominent emission lines typical
for symbiotic stars – H$\alpha$ is visible as an weak emission, with
equivalent width of about $-0.5$ Å. SU Lyn is bright and variable at X-ray
wavelengths, with periods of high X-ray luminosity and strong UV variability
and classified as a hidden symbiotic star (Mukai et al. 2016). Iłkiewicz et
al. (2022) proposed that SU Lyn can be a progenitor of a classical, persistent
symbiotic system.

The presence of flickering in U band is one more evidence that the hot
component is a white dwarf surrounded by accretion disc (see Sect. 4.1 in
Sokoloski & Bildsten 2010). For a comparison, the amplitudes of the flickering
in U band of a few symbiotic stars are: RS Oph 0.3 - 0.4 mag, CH Cyg 0.4 - 0.5
mag, ZZ CMi 0.05 - 0.25 mag. SU Lyn has a lower amplitude, which means that
the accretion disc is not bright and the white dwarf is accreting at a lower
accretion rate.

##  4 Search for intranight variability of related objects

We also searched for intranight variability of a few related objects – RR Boo,
RT Boo, AM Cyg, AG Peg, BF Cyg, NQ Gem, StHa190, V627 Cas, FS Cet, XX Oph and
Y Gem.

Rapid brightness variations of the Miras RR Boo, RT Boo and AM Cyg are
detected in Hipparcos photometry with amplitude $\approx 0.3$ mag (de Laverny
et al. 1998). However we do not detect a similar variability in our runs.

AG Peg made a transition from a slow symbiotic nova (which drove the 1850
outburst) to a classical symbiotic star (Ramsay et al. 2016). The UV emission
of AG Peg shows stochastic variability (flickering) on time-scales of minutes
and hours (Zhekov & Tomov 2018). We do not detect variability in B and V
bands.

BF Cyg is a symbiotic star which displays signatures of a variable mass-
outflow and formation of a highly-collimated bipolar mass ejection (Shchurova
et al. 2019). No variability is detected in B and V bands.

NQ Gem displays optical spectra similar to that of the symbiotic recurrent
nova T CrB (Greene & Wing 1971) and X-ray emission similar to that of CH Cyg
(Luna et al. 2013). Both T CrB and CH Cyg are known flickering sources,
however we do not detect similar variability of NQ Gem in our B and V band
observations.

StHa190 is the first yellow symbiotic star with rapidly variable bipolar mass
outflow (Munari et al. 2001). We do not detect variability on time scale of 1
hour in B and V bands.

V627 Cas is a symbiotic star (Vrašťák 2018). We do not detect variability on
time scale of 1 hour in B band.

For Y Gem, Sahai et al. (2018) find strong and variable UV and X-ray emission
and strong flickering in the UV continuum. Snaid et al. (2018) observed
flickering in u’ and g’ bands. We do not detect variability on time scale of 1
hour in B and V bands.

FS Cet is included in the Catalog of cataclysmic variables selected from the
Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) Data
Release 5 (Hou et al. 2020). Although the flickering is typical for
cataclysmic varaibles, we do not detect variability on time scale of 1 hour in
B and V bands.

XX Oph is known as Merrill’s iron star (Howell et al. 2009). We do not detect
variability on a time scale of 1 hour in U and B bands.

Conclusions:  We report photometric observations of the symbiotic-like star SU
Lyn performed with the 2.0 m and the 50/70 cm Schmidt telescopes of NAO
Rozhen. In four nights we detect a low amplitude flickering in U band
(amplitude in the range 0.05 - 0.10 mag). This indicates that the secondary
component is a white dwarf accreting at low accretion rate.

For a few related objects (RR Boo, RT Boo, AM Cyg, AG Peg, BF Cyg, NQ Gem,
StHa190, V627 Cas, Y Gem, FS Cet, and XX Oph), the search for rapid optical
variability (in the most cases in B and V bands) give a negative result.

Acknowledgements:  This work is part of the project KP-06-H28/2 08.12.2018
”Binary stars with compact object” (Bulgarian National Science Fund). DM and
BB acknowledge project RD-08-100/2022. JM and PLE acknowledge support from
Programa Operativo FEDER 2014-2020 and Consejería de Economía y Conocimiento
of Junta de Andalucía (Ref. 1380270).

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