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# Study of Proton and Deuteron Pickup Reactions
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ and
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ with 44 $A$ MeV
${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ Radioactive Beam at
ACCULINNA-2 Fragment Separator

E. Yu. Nikolskii  National Research Centre ‘‘Kurchatov Institute’’, Moscow,
Russia  JINR, Flerov Laboratory of Nuclear Reactions, Dubna, Russia  S. A.
Krupko  JINR, Flerov Laboratory of Nuclear Reactions, Dubna, Russia  I. A.
Muzalevskii  JINR, Flerov Laboratory of Nuclear Reactions, Dubna, Russia
Institute of Physics in Opava Silesian University in Opava, Opava, Czech
Republic  A. A. Bezbakh  JINR, Flerov Laboratory of Nuclear Reactions, Dubna,
Russia  Institute of Physics in Opava Silesian University in Opava, Opava,
Czech Republic  R. Wolski  JINR, Flerov Laboratory of Nuclear Reactions,
Dubna, Russia  C. Yuan  Sino-French Institute of Nuclear Engineering and
Technology (IFCEN), Sun Yat-sen University, Zhuhai, China  S. G. Belogurov
JINR, Flerov Laboratory of Nuclear Reactions, Dubna, Russia  National Research
Nuclear University ‘‘MEPhI’’, Moscow, Russia  D. Biare  JINR, Flerov
Laboratory of Nuclear Reactions, Dubna, Russia  V. Chudoba  Institute of
Physics in Opava Silesian University in Opava, Opava, Czech Republic  JINR,
Flerov Laboratory of Nuclear Reactions, Dubna, Russia  A. S. Fomichev  JINR,
Flerov Laboratory of Nuclear Reactions, Dubna, Russia  Dubna State University,
Dubna, Russia  E. M. Gazeeva  JINR, Flerov Laboratory of Nuclear Reactions,
Dubna, Russia  M. S. Golovkov  JINR, Flerov Laboratory of Nuclear Reactions,
Dubna, Russia  A. V. Gorshkov  JINR, Flerov Laboratory of Nuclear Reactions,
Dubna, Russia  L. V. Grigorenko  JINR, Flerov Laboratory of Nuclear Reactions,
Dubna, Russia  National Research Centre ‘‘Kurchatov Institute’’, Moscow,
Russia  National Research Nuclear University ‘‘MEPhI’’, Moscow, Russia  G.
Kaminski  JINR, Flerov Laboratory of Nuclear Reactions, Dubna, Russia  M.
Khirk  JINR, Flerov Laboratory of Nuclear Reactions, Dubna, Russia  Skobeltsyn
Institute of Nuclear Physics, Moscow State University,119991 Moscow, Russia
O. Kiselev  GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt,
Germany  D. A. Kostyleva  GSI Helmholtzzentrum für Schwerionenforschung GmbH,
Darmstadt, Germany  Physikalisches Institut, Justus-Liebig-Universität,
Giessen, Germany  B. Mauyey  JINR, Flerov Laboratory of Nuclear Reactions,
Dubna, Russia  L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
I. Mukha  GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt,
Germany  Yu. L. Parfenova  JINR, Flerov Laboratory of Nuclear Reactions,
Dubna, Russia  A. M. Quynh  JINR, Flerov Laboratory of Nuclear Reactions,
Dubna, Russia  Nuclear Research Institute, Dalat, Vietnam  S. I. Sidorchuk
JINR, Flerov Laboratory of Nuclear Reactions, Dubna, Russia  Voronezh state
university, Voronezh, Russia  P. G. Sharov  JINR, Flerov Laboratory of Nuclear
Reactions, Dubna, Russia  Institute of Physics in Opava Silesian University in
Opava, Opava, Czech Republic  N. B. Shulgina  National Research Centre
‘‘Kurchatov Institute’’, Moscow, Russia  Bogoliubov Laboratory of Theoretical
Physics, JINR, Dubna, Russia  R. S. Slepnev  JINR, Flerov Laboratory of
Nuclear Reactions, Dubna, Russia  S. V. Stepantsov  JINR, Flerov Laboratory of
Nuclear Reactions, Dubna, Russia  A. Swiercz  JINR, Flerov Laboratory of
Nuclear Reactions, Dubna, Russia  G. M. Ter-Akopian  JINR, Flerov Laboratory
of Nuclear Reactions, Dubna, Russia  Dubna State University, Dubna, Russia

###### Abstract

The proton and deuteron pickup reactions
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ and
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ were studied with
radioactive beam produced by the new fragment separator ACCULINNA-2 at FLNR,
JINR. These measurements were initially motivated as the test reactions
intended for the elucidation of results obtained in the study of the extremely
neutron-rich ${}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}$ and
${}^{\makebox[3.5pt][r]{$\scriptstyle
6$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}$ systems created in the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}$ and
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
6$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}$ reactions with the use
of the same setup. In the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction the
${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ ground-state ($3/2^{-}$)
and its first excited state (2.69 MeV, $1/2^{-}$) were identified in the low-
energy region of its excitation spectrum. The differential cross sections for
the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$
population were extracted at the forward center-of-mass angles
($3^{\circ}$–$13^{\circ}$) and compared with the FRESCO calculations.
Spectroscopic factor of $\sim$1.7, derived by a model suggesting the
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}=p+{{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$
clustering was found in accord with the experimental data. The energy spectrum
of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ populated in the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction shows the
strong peak which corresponds to the excitation of the second excited state of
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ (2.25 MeV, $3^{+}$). The
fact that the ground and the first excited states of
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ were not observed in
this reaction is consistent with the shell-model structure of the nuclei
involved.

##  1 Introduction

When conducting multi-parameter experiments dedicated to the study of neutron
drip-line nuclei obtained with very low yield in nuclear reactions, the choice
of reference reaction(s) is an important issue. Such additional measurements
are necessary in order to check: (i) whether the particle detectors work
correctly, (ii) how well the carried out Monte-Carlo (MC) simulations reflect
the real experimental conditions and (iii) how accurately are estimated the
main characteristics of the experiment, such as the spectrum calibration and
resolution assumed over the measured excitation energy of the studied nucleus,
the detection efficiency of reaction products, and so on. All together it can
provide a new reliable information (level scheme, spin–parity data, decay
channels etc.) for the unknown exotic systems.

Recently, the ${}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}$ and
${}^{\makebox[3.5pt][r]{$\scriptstyle
6$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}$ systems were studied in
experiments Bezbakh _et al._ (2020); Muzalevskii _et al._ (2021); Nikolskii
_et al._ (2022) carried out at the fragment separator ACCULINNA-2 in the
Flerov Laboratory of Nuclear Reactions (FLNR, JINR) Fomichev _et al._ (2018).
The achieved intensity of the ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ beam up to
$\approx\\!\\!\\!10^{5}$ pps and the corresponding detection systems allowed
to perform new exclusive measurements aimed, in particular, at the search for
${}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}$ resonances populated in
the proton pick-up reaction ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}$ Bezbakh _et al._ (2020);
Muzalevskii _et al._ (2021). Data collected in the second experiment
Muzalevskii _et al._ (2021) allowed one to derive information on the deuteron-
pickup reaction ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
6$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}$. This reaction was
analyzed in Nikolskii _et al._ (2022) giving new important results concerning
the ${}^{\makebox[3.5pt][r]{$\scriptstyle
6$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}$ excited states.

To check the reliability of the new results obtained for the
${}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}$ and
${}^{\makebox[3.5pt][r]{$\scriptstyle
6$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}$ systems Bezbakh _et al._
(2020); Muzalevskii _et al._ (2021); Nikolskii _et al._ (2022), it was decided
to perform reference measurements using the
${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ secondary beam and
thereby to measure the same proton and deuteron pickup reactions, i. e.
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ and
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$. Originally, these
measurements assumed the two main goals: (i) to check the setup calibration
over the excitation energy range of ${}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}$ and
${}^{\makebox[3.5pt][r]{$\scriptstyle
6$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}$, and (ii) to determine
the real experimental excitation energy resolution which should be compared
with the Monte-Carlo calculations.

At the same time it turns out that the study of the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ and
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reactions is in itself
of considerable interest. In particular, by measuring the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$ reaction
channel, the spectroscopic factor (SF) of the ground state of the
${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ nucleus, representing
the system ${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}={{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}+p$, could
be deduced. Accordingly, this result had stimulated corresponding theoretical
calculations which were compared with experiment. Note that only one
experiment was known before where the ${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ nucleus was studied in
the $d+{{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}$ collisions Kashy _et
al._ (1975). In this work only information about the ground state mass of
${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ was derived. The
performed for the first time spectroscopic study of
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ nucleus, being the
product of the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction allowed us to
obtain information about the ${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ ground state and the
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ level structure that
could be compared with Shell-Model predictions.

##  2 Experimental Setup

The experiment was carried out at the Flerov Laboratory of Nuclear Reactions
(JINR) at the ACCULINNA-2 fragment separator Fomichev _et al._ (2018). The
primary beam of ${}^{\makebox[7.0pt][r]{$\scriptstyle
15$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{N}$ ions with energy 49.7
$A$MeV and intensity $\approx\\!\\!0.5$ p$\mu$A, accelerated by the U-400M
cyclotron, bombarded the 1-mm thick beryllium production target installed at
the initial focal plane of the separator. The secondary
${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ radioactive ion beam
(RIB) was obtained at the final focal plane of the separator where the
cryogenic deutrium gas target was installed. The
${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ beam characteristics
were as follows: intensity $\approx\\!\\!10^{5}$ pps, 80% purity, with energy
in the middle of the $D_{2}$ target 42 $A$MeV and energy spread $\pm 2.5\%$.

The experimental setup shown in Fig. 1 was the same as in Bezbakh _et al._
(2020); Muzalevskii _et al._ (2021). Two BC-404 plastic scintillators placed
at the F3 and F5 focal planes at the time-of-flight (ToF) base 12.3 m allowed
one to identify the RIB projectiles by the $dE$–ToF method Kaminski _et al._
(2020) and determine their energy with precision $\approx\\!\\!0.5\%$ (FWHM).
In Fig. 2 we demonstrate the particle identification of RIB obtained at the F5
focus. It is seen that the ${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ projectiles are well
separated from neighboring ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ and
${}^{\makebox[7.0pt][r]{$\scriptstyle
12$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{B}$ nuclei. The low-
intensity admixture of isotopes ${}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}$,
${}^{\makebox[3.5pt][r]{$\scriptstyle
6$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ and
${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ with $A/Q=3$ at ToF =
160–165 ns can be observed and well separated too. The trajectories of
individual projectiles were measured by a pair of multi-wire proportional
chambers (MWPCs) placed at the distances 28 and 81 cm upstream of the $D_{2}$
target. This allowed one to measure the coordinates of the interaction points
in the target plane with a 1.8-mm accuracy as well as to determine the
inclination angles of each projectile to the ion-optical axis with precision
of $\approx\\!\\!3$ mrad.

The cryogenic target gas cell was supplied with the 6-$\mu$m-thick and 25-mm
diameter stainless-steel entrance and exit windows and filled with deuterium
gas at 27 K. The gas pressure was 1.13 atm. (‘‘thick’’ mode) or 0.56 atm
(‘‘thin’’ mode) resulted in target thickness $3.7\times 10^{20}$ or $1.8\times
10^{20}$ deuterons/cm2, respectively. The gas cell was covered by a pair of
3.5-$\mu$m aluminum-backed Mylar screens kept cooled to the same temperature
to ensure thermal protection.

The main contribution to the ${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$
(${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$) excitation energy
resolution was made by the energy determination of the
${}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$
(${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$) recoils emitted in the
studied reaction. The error in the measured energy was mainly caused by the
uncertainty of the interaction point over ‘‘Z’’ coordinate (along the beam
axis) in the target volume. It was assumed in the data analysis that the
interaction point was in the middle plane of the target. To ensure a
homogeneous thickness of the target, only events generated within the circle
in the target cell with diameter 17 mm were taken into account. This selection
also ensured the rejection of the reactions with the material of the target
frame.

The telescope assembly (side telescopes, see Fig. 1) intended to detect
${}^{\makebox[10.61107pt][r]{$\scriptstyle
3,4$}}_{\makebox[10.61107pt][r]{$\scriptstyle$}}\mathrm{He}$-recoils was
installed at a distance of 179 mm from the target. It consisted of the four
identical $dE$–$E$–$E$ telescopes made of the single-sided silicon detectors
(SSD). The angular range covered by these telescopes for the
${}^{\makebox[10.61107pt][r]{$\scriptstyle
3,4$}}_{\makebox[10.61107pt][r]{$\scriptstyle$}}\mathrm{He}$ recoil nuclei
extended from $\approx\\!\\!6^{\circ}$ to $\approx\\!\\!24^{\circ}$ in the
laboratory system. The 20-$\mu$m thick SSD with a sensitive area $50\times 50$
mm2 was divided into 16 strips, the second and the third telescope layers were
created by the two identical 1-mm thick SSDs (each with $60\times 60$ mm2 area
with segmentation in 16 strips), where the last $E$-detector was used as the
Veto-sensor. To provide particle identification, a sophisticated procedure was
developed for the
${}^{\makebox[0.0pt][r]{$\scriptstyle$}}_{\makebox[0.0pt][r]{$\scriptstyle$}}\mathrm{He}$-recoil
telescopes. Since the energy of the recoils leaving the target was expected to
be too low (starts from $\approx\\!\\!7$ MeV), very thin, 20-$\mu$m $\Delta
E$-detectors were needed for the ${}^{\makebox[10.61107pt][r]{$\scriptstyle
3,4$}}_{\makebox[10.61107pt][r]{$\scriptstyle$}}\mathrm{He}$ identification.
Because of the fabrication inhomogeneity, inherent to the so thin silicon
wafers, the thickness maps were determined by calibration for each of these
thin detectors Muzalevskii _et al._ (2020). Fig. 3a illustrates the particle
identification obtained for all strips in one thin detector, which was
actually implemented for each strip separately, but even in this presentation
it looks quite convincing.

The lithium isotopes emitted as a result of
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}+{{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}$ collisions were detected
by the $64\times 64\leavevmode\nobreak\ \text{mm}^{2}$ central telescope
installed at zero laboratory angle 323 mm downstream the target, see Fig. 1.
The telescope consisted of one 1500-micron Si double-side detector ($32\times
32$ strips with 2 mm pitch) and a set of 16 square CsI(Tl)/PMT modules. The
CsI(Tl) crystals had a cross section of $16.5\times 16.5\leavevmode\nobreak\
\text{mm}^{2}$ and thickness 50 mm each, which allowed to stop all charged
particles in the sensitive volume of the telescope. Each crystal was covered
with a 3.5-$\mu$m-thick aluminized Mylar on its entrance and was coupled with
the Hamamatsu R9880U-20 photomultiplier tube (PMT) by the optical grease. The
particle identification plot obtained in the central telescope is shown in
Fig. 3b.

The key issues of these measurements were (i) the clear
${}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ and
${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ identification provided
at the low particle energy ($\sim$7–20 MeV), (ii) the good energy and angular
resolution of the experimental setup, and (iii) the suficiently high
efficiency of coincidence events occurring between the
${}^{\makebox[10.61107pt][r]{$\scriptstyle
3,4$}}_{\makebox[10.61107pt][r]{$\scriptstyle$}}\mathrm{He}$ recoils and the
${}^{\makebox[10.61107pt][r]{$\scriptstyle
7,8$}}_{\makebox[10.61107pt][r]{$\scriptstyle$}}\mathrm{Li}$ nuclei emitted at
forward direction.

##  3 ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ Reaction

The excitation spectra of ${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ nucleus derived from the
data obtained in the runs with ${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ bombarding the
‘‘thick’’ and ‘‘thin’’ D2 target are presented in Figs. 4a and 4b,
respectively. The spectra are obtained by the missing mass (MM) method
realized by taking the recorded event-by-event data on the
${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ projectiles (the
energy, the trajectory angle, and hit position on the target) and
corresponding ${}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ recoils (the measured
energy and emission angle). The black solid-line histogram in Fig. 4a shows a
well-pronounced peak corresponding to the ground state of
${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ populated in the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$ reaction.
On the right slope of this peak, the presence of the not well-resolved first
excited state of ${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ ($E^{*}=2.69$ MeV Tilley
_et al._ (2004)) is also observed. The solid curve in Fig. 4a demonstrates the
Monte-Carlo calculation for the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$ using the
given above parameters of the experimental setup.

One can clearly see that the MC simulation reproduces quite well the shape of
the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$ peak
demonstrating experimental resolution $\approx\\!\\!2.2$ MeV. Note that in
experiment Muzalevskii _et al._ (2021) the corresponding calculations of the
resolution of ${}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}$ populated in the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}$ reaction at energy near
2 MeV gave the much better value of $\approx\\!\\!1.1$ MeV. The reason for
this $\approx\\!\\!2$ times better resolution in the
${}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}$ experiment is caused by
the larger energy of the ${}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ recoils, as compared to
the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction, and,
therefore, the smaller energy losses in the target. It shows that the target
thickness makes the main contribution to the energy resolution in this energy
range. This is clearly seen on Fig. 4b where the measurement on ‘‘thin’’
target is presented. One can see that the spectrum, obtained on ‘‘thin’’
target, demonstrates a good separation between the ground and the first
excited (2.69 MeV) states of ${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$.

Fig. 5 shows the angular distribution extracted from the experimental data at
the forward center-of-mass angles ($3^{\circ}$–$13^{\circ}$) for the
${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ ground state populated
in the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction.

The differential cross sections were analyzed with the Coupled Reaction
Channels Calculations approach using the code FRESCO Thompson (1988). For the
entrance ($d+{{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}$) and exit
(${{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}+{{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$) channels, the Global
Wood-Saxon optical model potentials found in Ref. Daehnick _et al._ (1980) and
in Ref. Pang _et al._ (2015), respectively, were used. In the calculation,
spectroscopic factor (SF) for the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}=p\,+\,d$ clustering was
set as SF = 1.32, according to the _ab initio_ value obtained by I. Brida et
al. Brida _et al._ (2011).

It should be noted that before our research, the SF for the system
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}=p+{{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}(3/2^{-})$ was unknown.
To evaluate the corresponding SF we carried out the shell-model calculation
KSHELL Shimizu _et al._ (2019) with the modified version of ‘‘YSOX’’
Hamiltonian based on the monopole universal interaction Yuan _et al._ (2012).
Model space was $psd$, including five orbits $0p_{3/2}$, $0p_{1/2}$,
$0d_{5/2}$, $0d_{3/2}$, $1s_{1/2}$ for both, protons and neutrons. Excitation
from $p$\- to $sd$-shell was limited to 0–5 nucleons. This (0–5)$\hbar\omega$
constraint just was chosen just for the consistency comparing with
calculations done for the C, N, O isotopes Yuan _et al._ (2012) where the
Hamiltonian can reproduce well the ground-state energies, drip lines, energy
levels, electric properties, and spin properties of $psd$-shell nuclei. Table
1 presents the SF calculations of ${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}\to{{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}+p$ clustering for the
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}(0^{+})$ ground and
first excited ${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}(2^{+})$ states.

Finally, with this Hamiltonian, SF = 1.74 was obtained for the
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}=p+{{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}(3/2^{-})$ clustering
while the $p+{{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}(1/2^{-})$ cluster
configuration was found to be much less, SF = 0.207. As it is seen from Fig.
5, the solid curve, which corresponds to the FRESCO calculation with the
mentioned SFs for the ${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}$
clustering, demonstrates the consistency of this model with the experimental
data. Thus, the measured differential cross sections of the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$ reaction
at forward center-of-mass angles confirm the modern theoretical approach made
for the ground-state structure of the ${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ nucleus.

##  4 ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ Reaction

In the same run, the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction was studied by
detecting the ${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ recoils. The inclusive
missing mass spectrum of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ obtained in the four
recoil telescopes is shown in Fig. 6. One can see a peak at around
$E^{*}({{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}})=2.5$ MeV sitting on a
large background. The nature of this background is mainly associated with
nuclear reactions generated by the ${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ projectiles on the
entrance and exit windows of the target cell. We made special background
measurements without D2 gas in the target cell. This background is shown by
the filled histogram in Fig. 6. Note that the
${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$-recoil background level
is much higher than that in the case of ${}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$. This situation was
quite expected since the yield of alpha particles is high because of the
intense reaction channels in which the formation of slow alpha particles
occurs with a much larger cross section than for the other light nuclei
(cluster effects, preferred energy dependence, etc.)

In order to reduce the background we applied the condition of coincidences
with the
${}^{\makebox[0.0pt][r]{$\scriptstyle$}}_{\makebox[0.0pt][r]{$\scriptstyle$}}\mathrm{Li}$
isotopes detected in the central telescope. The obtained spectra are shown in
Fig. 7a. As it is seen from Fig. 7 (a), the coincidences with
${}^{\makebox[0.0pt][r]{$\scriptstyle$}}_{\makebox[0.0pt][r]{$\scriptstyle$}}\mathrm{Li}$
nuclei drastically reduced the background, and now the structure at $E^{*}\sim
2.5$ MeV is clearly manifested. In addition, it is important to note that
almost all events near the 2.5-MeV peak are exhausted by the coincidences with
${}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$, which are shown by
black histogram in Fig. 7 (a). It means that the 2.5-MeV structure is
associated with the states of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ decaying by neutron
emission into ${}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$. Since the ground
($2^{+}$) and the first excited (0.980 MeV, $1^{+}$) states of
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ are nucleon stable (see
the energy level list of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ in Table 2), the peak
near 2.5 MeV can be explained by the contribution of the 2.255 MeV ($3^{+}$)
state with possible weak input of the 3.21 MeV ($1^{+}$) state.

Then, the question naturally arises: why the ground and first excited states
of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ are not populated in
this reaction?

We considered this question taking the known theoretical shell-model
calculations made for the ${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}$ and
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ level structures and
then applied the quantum-number selection rules. The followings issues should
be taken into account: according to the Boyarkina study of the $p$-shell
nuclei Boyarkina (1973) the ${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}(0^{+})$ ground state is
a multi-component ensemble of shell-model wave functions. The most abundant
one is $L=0$, $S=0$, $J=0$ component with weight 60%, the next two are of
$L=1$, $S=1$, $J=0$ with smaller weights, 23% and 11%. For the four
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ low-laying states only
their largest components are taken into account here. The two initial levels
of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ are $L=1$, $S=1$ coupled
to $J=2$ and $J=1$, respectively Boyarkina (1973). In the reaction discussed
these levels can not be populated from the major component of
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}$ because
of parity. The non-zero excitation of these states could be due to the
presence of the minor ${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}$
components. The second pair of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ states are the members
of $L=2$, $S=1$ multiplet coupled to $J=3$ and $J=1$, respectively. These
states are excited stronger due to the ${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}$ main
component contribution to the transfer reaction transitions. The component
shell-model wave functions, shown in Table 3, are characterized by
$[f]^{(2T+1)(2S+1)L}$, where $[f]$ is the Young scheme determining the
permutational symmetry of the orbital part of the wave function (w. f.), $T$,
$S$ and $L$ stand for the isospin, spin, and orbital angular momentum,
respectively, and their weights. These w. f. quantum numbers and weights are
shown in the first and second rows, respectively, for the three largest
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}$
components, and in the fourth and fifth columns for the dominant components of
the four ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ states.

The $nlj$ in Table 3 are the quantum numbers of the transfer transitions. The
spectroscopic amplitudes (SA) for the most significant
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}\to{{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}+d$ partitions are
calculated in the frame of Translational Invariant Shell Model (TISM) applied
to $p$-shell nuclei Smirnov and Tchuvil’sky (1977) by means of the
genealogical coefficients tables in Neudachin and Smirnov (1969) or A.T.
Rudchik (1982). For completeness, SA for the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}\to d+d$ clustering equal
to 1.73 is taken from Nemets _et al._ (1988).

The cross section of the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction leading to a
particular ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ state is the square of
the coherent sum of the each component transition amplitudes. It is seen in
Table 3 that the contribution of the main
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}$ w. f.
component to the production of the two initial
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ levels is parity
forbidden. Only the minor ${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}$
components participate in the reaction. Therefore, the resulting cross
sections for these ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ states are reduced in
comparison to the higher-lying states of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$.

The results of spectroscopic amplitude calculations shown in Table 3 imply
that the cross sections for the excitation of the first two
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ states are reduced with
respect to the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}(3^{+})$ state, though
they are not negligible. Having in mind the experimental spectrum shown in
Fig. 7a we conclude that our model predictions overestimate the production the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$ and the
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ first excited state in
the discussed reaction.

We made FRESCO calculations of the differential cross sections for the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction leading to the
population of 2.255 and 3.21 MeV states in
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$, see Fig. 8. In the
calculation, the spectroscopic factors for the configurations
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}=d+{{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}(3^{+})$ and
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}=d+{{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}(1^{+})$ were taken as
0.54 and 0.16, respectively. One can see that in the measured center-of-mass
angular range ($\theta_{\text{CM}}\approx 4^{\circ}\text{--}16^{\circ}$) the
ratio of the cross sections obtained for the 2.25 and 3.21 MeV states is about
4:1.

Finally, after the background subtraction, taking into account empty target
measurement, we fitted the ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ spectrum using the
Monte-Carlo response for the excited state 2.255 MeV ($3^{+}$). The result is
presented in Fig. 7b. It is seen that the spectrum is in a good agreement with
the 2.255 MeV state. However, we cannot rule out the small presence of 3.21
MeV state on the right slope of the 2.255 peak. This contribution around
15–20% is in agreement with FRESCO estimation (see Fig. 8).

##  5 Conclusions

Excitation spectra of ${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ and
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ obtained in the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ and
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reactions were measured
for the first time with the 44 $A$MeV ${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ radioactive beam
produced by the fragment separator ACCULINNA-2 at the U-400M cyclotron (FLNR,
JINR). The angular distribution was obtained for the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$ reaction
channel at the forward center-of-mass angles ($3^{\circ}$–$13^{\circ}$). The
absolute values of the cross sections are well predicted by the modern shell-
model calculation with spectroscopic factor SF $\sim\\!\\!1.7$ for the
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}=p+{{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$
configuration. In the energy spectrum of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ derived from the
deuteron pickup reaction ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$, a strong peak
attributed to the second excited state of
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ (2.25 MeV, $3^{+}$) was
observed. Also, the presence of an unresolved third excited state at 3.21 MeV
($1^{+}$) is possible in the measured ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ spectrum. The absence of
the ground and the first excited states of
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ in the measured spectrum
is explained in complete agreement with the theoretical concepts of the
structures of the ${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ ground state and
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ levels at low excitation
energy.

In general, these and the previous results Bezbakh _et al._ (2020);
Muzalevskii _et al._ (2021); Nikolskii _et al._ (2022) of the first
experiments carried out with secondary beams at the ACCULINNA-2 facility show
a great potential for the studies of light exotic nuclei being close to and
beyond the nuclear drip lines.

###### Acknowledgements.

This work was partly supported by the Russian Science Foundation grant No.
22-12-00054. One of the authors, I. A. M., was supported by the Student Grant
Foundation of the Silesian University in Opava, Grant No. SGF/2/2020, which
was realized within the EU OPSRE project entitled ‘‘Improving the quality of
the internal grant scheme of the Silesian University in Opava’’, No.
CZ.02.2.69/0.0/0.0/19 073/00116951. We acknowledge the interest and support of
this activity from Prof. Yu.Ts. Oganessian and Prof. S.N. Dmitriev.

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0mm flushleft  Clustering Transition $p_{1/2}$ $p_{3/2}$
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\mathrm{g.\,s.}}={{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}(3/2^{-})+p$ 1.74
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\mathrm{g.\,s.}}={{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}(1/2^{-})+p$ 0.207
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}(2^{+})={{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}(3/2^{-})+p$ 0.156 1.32
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}(2^{+})={{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}(1/2^{-})+p$ 0.184
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}(2^{+})={{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}(5/2^{-})+p$ 0.0285
0.0639

Table 1:  SFs for the ${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}\to{{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}+p$ clustering obtained
by the Shell Model Shimizu _et al._ (2019); Yuan _et al._ (2012).

0mm flushleft  $E^{*}$, MeV $J^{\pi}$ $T_{1/2}/\Gamma$ Decay mode 0.0 $2^{+}$
839.9 ms $\beta^{-}$-decay 0.9808 $1^{+}_{1}$ 8.2 fs $\gamma$-emission 2.255
$3^{+}$ 32.3 keV $n$-emission 3.210 $1^{+}_{2}$ 1000 keV $n$-emission 5.4
$1^{+}_{3}$ 650 keV $n$-emission

Table 2:  The list of low-energy ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ states based on Tilley
_et al._ (2004)

0mm flushleft  $E^{*}$ $J^{\pi}$ ${[f]}^{(2T+1)(2S+1)}L$ $[42]^{31}S$
$[411]^{33}P$ $[33]^{33}P$ ${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ 0 $0^{+}$ Weight 60%
23% 11% $nlj$ transition (Spectroscopic Amplitude)
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ 0 $2^{+}$ $[31]^{33}P$
90.4% 0.0 $1D_{2}(0.293)$ $1D_{2}(0.102)$
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ 0.980 $1^{+}$
$[31]^{33}P$ 78.5% 0.0 $2S_{1}(0.088)$ $2S_{1}(-0.245)$ $1D_{1}(0.158)$
$1D_{1}(0.055)$ ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ 2.255 $3^{+}$
$[31]^{33}D$ 82.1% $1D_{3}(-0.732)$ ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ 3.21 $1^{+}$
$[31]^{33}D$ 85.7% $1D_{1}(-0.40)$ ${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ — $1^{+}$ $[00]^{13}S$
100% $1S_{1}(1.73)$

Table 3:  Spectroscopic Amplitudes of the intense
${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}\to{{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}+d$ clustering; the
$E^{*}$ given in MeV

  1. 1.

Experimental setup to study the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ and
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reactions with
${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ secondary beam at the
ACCULINNA-2 fragment separator. The time-of-flight scintillation sensors
(ToF-F3, ToF-F5), position-sensitive beam detectors (MWPC-1,MWPC-2) are
installed upstream the $D_{2}$ cryogenic gas target. Charged particle detector
telescopes for the ${}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$,
${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ recoils and
${}^{\makebox[10.61107pt][r]{$\scriptstyle
7,8$}}_{\makebox[10.61107pt][r]{$\scriptstyle$}}\mathrm{Li}$ decay products
are placed downstream the $D_{2}$ target.

  2. 2.

Particle identification plot measured at the ACCULINNA-2 F5 focal plane when
the setup was tuned to the ${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ secondary beam. The
vertical axis corresponds to the energy loss in the ToF F5 scintillator while
the time of flight is plotted on the horizontal axis.

  3. 3.

(a) $\Delta E$–$E$ particle identification plot obtained from the 16 strips of
one of the recoil telescopes after the thickness correction. The solid lines
show the locations of
${}^{\makebox[0.0pt][r]{$\scriptstyle$}}_{\makebox[0.0pt][r]{$\scriptstyle$}}\mathrm{He}$-isotopes.
It is seen that the ${}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ and
${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ recoil nuclei are
clearly separated; (b) The same plot obtained in central telescope; The solid
lines show the locations of
${}^{\makebox[0.0pt][r]{$\scriptstyle$}}_{\makebox[0.0pt][r]{$\scriptstyle$}}\mathrm{Li}$-isotopes.

  4. 4.

The excitation energy spectra of ${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ measured in the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction with the
‘‘thick’’ (a) and ‘‘thin’’ (b) $D_{2}$ gas targets. The solid curve in panel
(a) represents the MC calculation of the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$ taking
the parameters of the experimental setup. The gray filled histograms represent
the background level measured with the empty target and normalized on the
${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ beam integral. The
arrows mark ${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ first excited state with
$J^{\pi}=1/2^{-}$ and $E^{*}=2.69$ MeV.

  5. 5.

The differential cross-sections for the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction. Points show
the angular distribution for the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$ reaction
obtained in the experiment. (The error bars are statistical only.) The solid
curve shows the result of corresponding FRESCO one-step calculations, see text
for the details.

  6. 6.

The inclusive MM spectrum of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ from the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction. The gray
filled histogram corresponds to the background measurement with the empty
target normalized on the beam integral.

  7. 7.

(a) The excitation spectra of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ obtained in the case of
the ${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ recoil in coincidence
with ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ (filled histogram) and
${}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ (black histogram). The
arrows mark the excitation energy for the ground ($2^{+}$), first
($1^{+}_{1}$), second ($3^{+}$), third ($1^{+}_{2}$)
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ excited states, and the
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ neutron separation
energy ($S_{n}$). (b) The excitation spectrum of
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ obtained from the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction data after the
empty-target subtraction with the condition of coincidences
${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$–${}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ (black histogram) and
${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$–${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ (filled histogram). The
solid curve corresponds to the Monte-Carlo calculation for the contribution of
the 2.255 MeV ($3^{+}$) ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ state.

  8. 8.

The FRESCO calculation of the differential cross sections for the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction populating the
$3^{+}$ state with $E^{*}=2.255$ MeV (solid line) and the $1^{+}_{2}$ state
with $E^{*}=3.21$ MeV (dashed line) of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ (only pure main
components of ${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}$ and
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ wave functions were
taken into account).

5mm  normal

Fig. 1:  Experimental setup to study the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ and
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reactions with
${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ secondary beam at the
ACCULINNA-2 fragment separator. The time-of-flight scintillation sensors
(ToF-F3, ToF-F5), position-sensitive beam detectors (MWPC-1,MWPC-2) are
installed upstream the $D_{2}$ cryogenic gas target. Charged particle detector
telescopes for the ${}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$,
${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ recoils and
${}^{\makebox[10.61107pt][r]{$\scriptstyle
7,8$}}_{\makebox[10.61107pt][r]{$\scriptstyle$}}\mathrm{Li}$ decay products
are placed downstream the $D_{2}$ target.

5mm  normal

Fig. 2:  Particle identification plot measured at the ACCULINNA-2 F5 focal
plane when the setup was tuned to the ${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ secondary beam. The
vertical axis corresponds to the energy loss in the ToF F5 scintillator while
the time of flight is plotted on the horizontal axis.

5mm  normal

Fig. 3:  (a) $\Delta E$–$E$ particle identification plot obtained from the 16
strips of one of the recoil telescopes after the thickness correction. The
solid lines show the locations of
${}^{\makebox[0.0pt][r]{$\scriptstyle$}}_{\makebox[0.0pt][r]{$\scriptstyle$}}\mathrm{He}$-isotopes.
It is seen that the ${}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ and
${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ recoil nuclei are
clearly separated; (b) The same plot obtained in central telescope; The solid
lines show the locations of
${}^{\makebox[0.0pt][r]{$\scriptstyle$}}_{\makebox[0.0pt][r]{$\scriptstyle$}}\mathrm{Li}$-isotopes.

5mm  normal

Fig. 4:  The excitation energy spectra of
${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ measured in the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction with the
‘‘thick’’ (a) and ‘‘thin’’ (b) $D_{2}$ gas targets. The solid curve in panel
(a) represents the MC calculation of the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$ taking
the parameters of the experimental setup. The gray filled histograms represent
the background level measured with the empty target and normalized on the
${}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}$ beam integral. The
arrows mark ${}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ first excited state with
$J^{\pi}=1/2^{-}$ and $E^{*}=2.69$ MeV.

5mm  normal

Fig. 5:  The differential cross-sections for the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction. Points show
the angular distribution for the ${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
3$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
9$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}_{\text{g.s.}}$ reaction
obtained in the experiment. (The error bars are statistical only.) The solid
curve shows the result of corresponding FRESCO one-step calculations, see text
for the details.

5mm  normal

Fig. 6:  The inclusive MM spectrum of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ from the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction. The gray
filled histogram corresponds to the background measurement with the empty
target normalized on the beam integral.

5mm  normal

Fig. 7:  (a) The excitation spectra of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ obtained in the case of
the ${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$ recoil in coincidence
with ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ (filled histogram) and
${}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ (black histogram). The
arrows mark the excitation energy for the ground ($2^{+}$), first
($1^{+}_{1}$), second ($3^{+}$), third ($1^{+}_{2}$)
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ excited states, and the
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ neutron separation
energy ($S_{n}$). (b) The excitation spectrum of
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ obtained from the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction data after the
empty-target subtraction with the condition of coincidences
${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$–${}^{\makebox[3.5pt][r]{$\scriptstyle
7$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ (black histogram) and
${}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}$–${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ (filled histogram). The
solid curve corresponds to the Monte-Carlo calculation for the contribution of
the 2.255 MeV ($3^{+}$) ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ state.

5mm normal

Fig. 8:  The FRESCO calculation of the differential cross sections for the
${{}^{\makebox[3.5pt][r]{$\scriptstyle
2$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{H}}({{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}},{{}^{\makebox[3.5pt][r]{$\scriptstyle
4$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{He}}){{}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}}$ reaction populating the
$3^{+}$ state with $E^{*}=2.255$ MeV (solid line) and the $1^{+}_{2}$ state
with $E^{*}=3.21$ MeV (dashed line) of ${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ (only pure main
components of ${{}^{\makebox[7.0pt][r]{$\scriptstyle
10$}}_{\makebox[7.0pt][r]{$\scriptstyle$}}\mathrm{Be}}_{\text{g.s.}}$ and
${}^{\makebox[3.5pt][r]{$\scriptstyle
8$}}_{\makebox[3.5pt][r]{$\scriptstyle$}}\mathrm{Li}$ wave functions were
taken into account).