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The $\beta$-gated $\gamma$-ray spectrum obtained at $A=134$ in~the first 400~ms relative to the~proton pulse from~which long-lived background has been subtracted. Transitions assigned to the daughter nuclei of \textsuperscript{134}In are labeled with filled symbols, while those attributed to activities of daughter or contaminant nuclei are marked with open symbols. Transitions that can be assigned to the \textsuperscript{134}In $\beta$ decay but not to a specific decay branch are indicated by energy only. Lines marked with an~ampersand indicate possible weak transitions whose identification is~uncertain. Energies of~possible peaks, which might correspond to~artifacts due~to~the background subtraction procedure, are given in~parentheses. The presence of a~negative peak at 962 keV is~the consequence of subtracting the contribution from the daughter nucleus \textsuperscript{133}Sn~\cite{10.1007/BF01879878}. Triangular-shaped peaks arising from inelastic neutron scattering in the HPGe detectors~\cite{10.1016/j.nima.2004.11.021, 10.1140/epja/i2007-10553-8, 10.1140/epja/i2013-13028-5, 10.1016/0969-8043(93)90177-C, 10.1016/j.apradiso.2020.109422} are indicated with asterisks. The peak at 197~keV is~also considered as induced by neutrons~\cite{10.1140/epja/i2013-13028-5}. The abbreviations \emph{SE} and \emph{DE} indicate single-escape and double-escape peaks, respectively. Broad peaks marked with a~hash symbol remained unidentified.

(Color online) Time distributions relative to the proton pulse of the 1561-keV transition (blue circles) and the background area (red diamonds) observed in~coincidence with $\beta$~particles at $A=134$ when RILIS was applied to ionize indium. A~function composed of an exponential decay and a~constant background was fitted (solid line) in~the 510-1200~ms time range. The curve corresponding to the background component is~also presented (dashed line). A~Bayesian approach was applied in the statistical analysis of the data~\cite{10.1103/PhysRevC.98.064326}.

Background-subtracted $\gamma$-ray spectra in coincidence with the (a)\,1666-, (b)\,3512- and (c) 3763-keV transitions that depopulate new levels in~\textsuperscript{134}Sn following the $\beta \gamma$~decay of~\textsuperscript{134}In. Vertical dotted lines indicate energies of previously known transitions in~\textsuperscript{134}Sn. (d) The background-subtracted $\gamma$-ray spectrum in~coincidence with the 4041-keV transition in~\textsuperscript{132}Sn observed in the $\beta 2n$ decay of \textsuperscript{134}In.

Decay scheme of \textsuperscript{134}In established in the present work. Excited states in~the daughter nuclei are labeled with energies (in~keV) given relative to the ground state of each tin isotope. The spin-parity assignments for previously known states in~tin isotopes are taken from Refs.~\cite{10.1007/s002180050269, 10.1103/PhysRevLett.77.1020, 10.1103/PhysRevLett.118.202502, 10.1103/PhysRevLett.73.2413}. The~ground-state spin and parity of~\textsuperscript{134}In was~proposed based on~our experimental findings. Shell-model predictions and~systematics discussed in~Sec.~\ref{sec:Discussion_134In-decay} favor the~$7^-$~assignment. The~left vertical scale (in~MeV) shows the excitation energy and (multi-) neutron separation energies with respect to the \textsuperscript{134}Sn ground-state. The~shaded regions represent energy windows for~population of~(multi-) neutron-unbound states. The $Q_{\beta}$, $S_n$, $S_{2n}$ and $S_{3n}$ values are taken from Ref.~\cite{10.1088/1674-1137/abddaf}.

: (Color online) The $\beta$-gated $\gamma$-ray spectrum obtained at $A=135$ when RILIS was applied to ionize indium (upper blue curve) and when one of the RILIS lasers was blocked (lower red curve). Some of the most prominent transitions are labeled with their energies (in~keV). Peaks present in~both spectra originate from the contaminants, while those appearing only in~the RILIS-on mode can be attributed to the $\beta$~decay of \textsuperscript{135}In (square) or its daughter nucleus (marked with ``$d$").

: (Color online) Time distribution relative to the proton pulse of the 347-keV transition (blue circles) and the background area (red diamonds) observed in~coincidence with $\beta$~particles at $A=135$ in~the laser-on mode. A~function composed of an exponential decay and a~constant background was fitted (solid line) in~the 230-1200~ms time range. The curve corresponding to the background component is~also presented (dashed line). A~Bayesian approach was applied in the statistical analysis of the data~\cite{10.1103/PhysRevC.98.064326}.

(Color online) The $\beta$-gated $\gamma$-ray spectra obtained at~$A=135$ in~the laser-on mode in~which different conditions on~time with respect to the proton pulse were applied. [Top panels of (a) and (b):] The orange (gray) curve shows the spectrum gated at~times later than 600~ms relative to the proton pulse, while the black curve shows the spectrum without any condition imposed on the time of the event with respect to the proton pulse. The inset in (a) shows a~portion of the spectrum with an increased energy threshold for~$\beta$ particles. [Bottom panels of (a) and (b):] The $\beta$-gated $\gamma$-ray spectrum recorded in~the first 400~ms relative to the~proton pulse from~which long-lived background was subtracted. Transitions assigned to the $\beta 1n$- and $\beta 2n$-decay branches of \textsuperscript{135}In are marked with squares and diamonds, respectively. Peaks that can be attributed to $\gamma$~rays following \textsuperscript{135}In $\beta$~decay are indicated by energy only, while those assigned to activities of the daughter or contaminant nuclei are marked with ``\textit{d}" and ``c", respectively.

Decay scheme of~\textsuperscript{135}In established in~this work. Excited states in~daughter nuclei are~labeled with energies (in~keV) given relative to~the ground state of~each tin isotope. Levels tentatively proposed in~\textsuperscript{135}Sn and~\textsuperscript{134}Sn are~indicated with dashed lines. The spin-parity assignments for previously known states in~\textsuperscript{134}Sn and \textsuperscript{133}Sn are~taken from Ref.~\cite{10.1007/s002180050269, 10.1103/PhysRevLett.77.1020}. The~ground-state spin and parity of~\textsuperscript{135}Sn and~\textsuperscript{135}In are~based on systematics~\cite{10.1088/1674-1137/abddae}. The~left vertical scale (in~MeV) shows the~excitation energy and (multi-) neutron separation energies with respect to~the \textsuperscript{135}Sn ground~state. The~shaded regions represent energy windows for~population of~neutron-unbound states. The~$Q_{\beta}$, $S_n$, $S_{2n}$ and~$S_{3n}$ values are taken from~Refs.~\cite{10.1088/1674-1137/abddaf}.

(Left panel) Background-subtracted, $\beta$-gated $\gamma$-ray spectra in~coincidence with the 347- and 726-keV transitions that depopulate previously known levels in~\textsuperscript{134}Sn following the $\beta 1n$~decay of \textsuperscript{135}In. Peaks that can be attributed to new transitions in~\textsuperscript{134}Sn are labeled with their energies in~keV. Tentative assignments are given within brackets. Asterisks indicate artifacts due to the background subtraction procedure. The insets display expanded regions whose ranges are indicated with dashed lines. (Right panel) Background-subtracted, $\beta$-gated $\gamma$-ray spectra in~coincidence with newly identified transitions in~\textsuperscript{134}Sn observed in the $\beta$~decay of \textsuperscript{135}In.

Time spectra used to measure the lifetimes of the (a)~$6^+$ 1247-keV, (b)~$4^+$ 1073-keV and (c)~$2^+$ 726-keV states in~\textsuperscript{134}Sn. In~panels (a) and (b), the half-life is~derived from fit of the slopes, while in~panel (c), it is extracted from the centroid-shift measured between the delayed and antidelayed time spectra ($\Delta C$), which is~caused by the lifetime of the level and the shift in~the Prompt Response Distribution curves ($\Delta PRD$)~\cite{10.1088/1361-6471/aa8217, 10.1103/PhysRevC.102.014328, 10.1088/1361-6471/aa6015}. See the text for details.

(a)~Schematic $\beta$-decay scheme of \textsuperscript{134}In showing Gamow-Teller (GT) and first-forbidden (\emph{ff}) transitions that populate neutron-unbound (gray striped areas) and bound states in~the daughter nuclei. The expected excitation energies of unobserved states having core-excited configurations are indicated by black striped areas. Neutron-unbound states for which decay via~$\gamma$-ray emission was observed are indicated. (b) Schematic representation of~proton ($\pi$) and neutron ($\nu$) orbitals relevant for the~$\beta$~decay of \textsuperscript{134}In~\cite{10.1088/0034-4885/70/9/R02}. The~ground-state configuration of~the parent nucleus is~schematically represented by~circles indicating the location of~valence neutrons (full circles) and proton hole (open circle) relative to~the \textsuperscript{132}Sn core.

Experimental (\textit{Expt.}) level scheme of~\textsuperscript{134}Sn along with the results of~the shell-model calculations (SM) (a)~including neutron-core excitations, \textsf{Jin2011} from Ref.~\cite{10.1103/PhysRevC.84.044324}, as well as employing \textsuperscript{132}Sn as a~closed core: (b) \textsf{Kart2007}~from Ref.~\cite{10.1103/PhysRevC.76.024313}, (c)~\textsf{Yuan2016}~from Ref.~\cite{10.1016/j.physletb.2016.09.030} and (d)~\textsf{Cov2011} from Ref.~\cite{10.1088/1742-6596/267/1/012019}. The newly identified states are indicated in~red. The level shown by~the dashed line is~proposed tentatively. The~$(8^+)$ state at~2509~keV~\cite{10.1007/PL00013594} was not~observed in~this work. The~experimental spin-parity assignments for~previously known~states in~\textsuperscript{134}Sn were taken from~Refs.~\cite{10.1007/s002180050269, 10.1007/PL00013594}. The $S_n$ value for~\textsuperscript{134}Sn was~taken from Ref.~\cite{10.1088/1674-1137/abddaf}.

(Color online) Comparison of~predicted~(SM) and experimental~(\textit{Expt.}) reduced transition probabilities $B(E2)$ (in~W.\,u.) for~$E2$ transitions in~\textsuperscript{134}Sn. Presented data are taken from Refs.~\cite{10.1103/PhysRevC.65.051306, 10.1140/epja/i2003-10198-7, 10.1016/j.physletb.2016.09.030, 10.1088/1402-4896/aa7353, 10.1103/PhysRevC.76.024313, 10.1007/s002180050269, 10.1016/j.nuclphysa.2004.09.143, 10.1103/PhysRevC.86.054319}. Uncertainties of~the previously reported experimental results and the~one obtained in~this work are~shown by~the gray and~orange areas, respectively.

Excited states in~\textsuperscript{135}Sn tentatively proposed in~this work (\textit{Expt.}). Calculated excitation energies (SM) for the~$7/2^-$, $9/2^-$ and $11/2^-$ states in~\textsuperscript{135}Sn reported in~Refs.: (a)~\textsf{Sar2004}~\cite{10.1140/epja/i2003-10198-7}, (b)~\textsf{Kart2007}~\cite{10.1103/PhysRevC.76.024313}, (c)~\textsf{Yuan2016}~\cite{10.1016/j.physletb.2016.09.030} and~(d)~\textsf{Cor2002}~\cite{10.1103/PhysRevC.65.051306} are~also presented. Excitation energies relative to~the \textsuperscript{135}Sn ground state are~given in~keV. The~ground-state spin-parity assignment for~\textsuperscript{135}Sn, based on~systematic trends in~neighboring nuclei, was~taken from Ref.~\cite{10.1088/1674-1137/abddae}.