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This work was supported in part by the Helmholtz International Center for FAIR (HIC for FAIR), the Helmholtz Association (grant IK-RU-002), the Russian Ministry of Education and Science (grant No. NSh- 932.2014.2), the Russian Science Foundation (grant No. 17-12-01367), the Polish National Science Center (Contract No. UMO-2011/01/B/ST2/01943), the Polish Ministry of Science and Higher Education (Grant No. 0079/DIA/2014/43,Grant Diamentowy), the Helmholtz- CAS Joint Research Group (grant HCJRG-108), the FPA2009-08848 contract (MICINN, Spain), the Justus- Liebig-Universit¨at Giesen (JLU) and GSI under the JLUGSI strategic Helmholtz partnership agreement. This article is a part of PhD thesis of X.-D. Xu. The authors acknowledge the help of D. Kostyleva in the preparation of the manuscript.

Two-proton decay of the $^{17}\mathrm{Ne}$ low-lying states populated in the $^{1}\mathrm{H}(^{18}\mathrm{Ne},d)^{17}\mathrm{Ne}$ transfer reaction is studied. The two-proton width ${\mathrm{\ensuremath{\Gamma}}}_{2p}$ of the $^{17}\mathrm{Ne}$ first excited $3/{2}^{\ensuremath{-}}$ state at ${E}^{*}=1.288$ MeV is of importance for the two-proton radioactivity theory and nuclear-astrophysics applications. A dedicated search for the two-proton emission of this state was performed leading to the new upper limit obtained for the width ratio ${\mathrm{\ensuremath{\Gamma}}}_{2p}/{\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma}}l1.6(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. An original, ``combined mass'' method is suggested and tested as capable of improving the resolution of the experiment, which is a prime significance for the study of nuclear states with extremely small particle-to-gamma width ratios ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{part}}/{\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma}}$. The condition ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{part}}\ensuremath{\ll}{\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma}}$ is quite common for the states of astrophysical interest, which makes the proposed approach promising in this field.

The $\ensuremath{\beta}$ decay of $^{31}\mathrm{Ar}$, produced by fragmentation of an $^{36}\mathrm{Ar}$ beam at 880 MeV/nucleon, was investigated. Identified ions of $^{31}\mathrm{Ar}$ were stopped in a gaseous time projection chamber with optical readout allowing us to record decay events with emission of protons. In addition to $\ensuremath{\beta}$-delayed emission of one and two protons we clearly observed the $\ensuremath{\beta}$-delayed three-proton branch. The branching ratio for this channel in $^{31}\mathrm{Ar}$ is found to be $0.07\ifmmode\pm\else\textpm\fi{}0.02$%.

The spectrum of $^{9}\mathrm{He}$ was studied by means of the $^{2}\mathrm{H}$($^{8}\mathrm{He}$,$p$)$^{9}\mathrm{He}$ reaction at a laboratory energy of 25 MeV/nucleon and small center-of-mass angles. Energy and angular correlations were obtained for the $^{9}\mathrm{He}$ decay products by complete kinematical reconstruction. The lowest resonant state of $^{9}\mathrm{He}$ is found at 2.0 \ifmmode\pm\else\textpm\fi{} 0.2 MeV with a width of $~2$ MeV and is identified as $1/{2}^{\ensuremath{-}}$. The observed angular correlation pattern is uniquely explained by the interference of the $1/{2}^{\ensuremath{-}}$ resonance with a virtual $1/{2}^{+}$ state (a limit $ag\ensuremath{-}20$ fm is obtained for the scattering length), and with a $5/{2}^{+}$ resonance at energy $\ensuremath{\geqslant}4.2$ MeV.

The nuclear system {sup 5}H was studied using the {sup 3}H(t,p){sup 5}H transfer reaction at a laboratory energy of 57.7 MeV and small center of mass angles. The energy and angular correlations among the {sup 5}H decay fragments were obtained by complete kinematical reconstruction. A broad structure in the {sup 5}H missing mass spectrum above 2.5 MeV with a typical width of several MeV was identified as a mixture of 3/2{sup +} and 5/2{sup +} states. Analysis of interference patterns observed in the measured angular correlations disclosed the 1/2{sup +} ground state of {sup 5}H concealed in the smooth missing mass spectrum. The deduced values for the resonance energy and width are E{sub g.s.}{approx_equal}1.8 MeV and {gamma}{sub g.s.}{approx_equal}1.3 MeV. The estimated cross sections for population of the ground state and the doublet of excited states at {theta}{sub c.m.}=5 deg. are 150{+-}50 {mu}b/sr and 4.6{+-}2 mb/sr, respectively.

The thick target inverse kinematic method was applied to the study of isobaric analog states in the neutron-rich nucleus ${}^{9}\mathrm{Li}.$ For this purpose, an excitation function for ${}^{8}\mathrm{He}+p$ elastic scattering was measured in the center-of-momentum energy range from 1.6 to 5.8 MeV. Three $T=5/2$ states in ${}^{9}\mathrm{Li}$ (isobaric analogs of ${}^{9}\mathrm{He})$ were observed. Restrictions on the spin-parity assignments are provided according to R-matrix calculations, and conclusions regarding the structure of ${}^{9}\mathrm{He}$ are given.