Using resonant laser ionization, $\beta$-decay studies, and for the first time mass measurements, three $\beta$-decaying states have been unambiguously identified in ${}^{70}\mathrm{Cu}$. A mass excess of $-62976.1(1.6)\mathrm{keV}$ and a half-life of 44.5(2) s for the $(6^{-})$ ground state have been determined. The level energies of the $(3^{-})$ isomer at 101.1(3) keV with $T_{1/2}=33(2)\mathrm{s}$ and the $1^{+}$ isomer at 242.4(3) keV with $T_{1/2}=6.6(2)\mathrm{s}$ are confirmed by high-precision mass measurements. The low-lying levels of ${}^{70}\mathrm{Cu}$ populated in the decay of ${}^{70}\mathrm{Ni}$ and in transfer reactions compare well with large-scale shell-model calculations, and the wave functions appear to be dominated by one proton–one neutron configurations outside the closed $Z=28$ shell and $N=40$ subshell. This does not apply to the $1^{+}$ state at 1980 keV which exhibits a particular feeding and deexcitation pattern not reproduced by the shell-model calculations.

We report on the first low-energy Coulomb excitation measurements with radioactive $I^{\pi }=6^{-}$ beams of odd-odd nuclei ${}^{68,70}\mathrm{Cu}$. The beams were produced at ISOLDE, CERN and were post-accelerated by REX-ISOLDE to $2.83\mathrm{MeV}/\mathrm{\text{nucleon}}$. $\gamma$ rays were detected with the MINIBALL spectrometer. The $6^{-}$ beam was used to study the multiplet of states ($3^{-}$, $4^{-}$, $5^{-}$, $6^{-}$) arising from the $\pi 2p_{3/2}\nu 1g_{9/2}$ configuration. The $4^{-}$ state of the multiplet was populated via Coulomb excitation and the $B(E2;6^{-}\to 4^{-})$ value was determined in both nuclei. The results obtained illustrate the fragile stability of the $Z=28$ shell and $N=40$ subshell closures. A comparison with large-scale shell-model calculations using the ${}^{56}\mathrm{Ni}$ core shows the importance of the proton excitations across the $Z=28$ shell gap to the understanding of the nuclear structure in the neutron-rich nuclei with $N\approx 40$.

Neutron-rich, radioactive Zn isotopes were investigated at the Radioactive Ion Beam facility REX-ISOLDE (CERN) using low-energy Coulomb excitation. The energy of the $2_1^{+}$ state in ${}^{78}\mathrm{Zn}$ could be firmly established and for the first time the $2^{+}\to 0_1^{+}$ transition in ${}^{80}\mathrm{Zn}$ was observed at 1492(1) keV. $B(E2,2_1^{+}\to 0_1^{+})$ values were extracted for ${}^{74,76,78,80}\mathrm{Zn}$ and compared to large scale shell model calculations. With only two protons outside the $Z=28$ proton core, ${}^{80}\mathrm{Zn}$ is the lightest $N=50$ isotone for which spectroscopic information has been obtained to date. Two sets of advanced shell model calculations reproduce the observed $B(E2)$ systematics. The results for $N=50$ isotones indicate a good $N=50$ shell closure and a strong $Z=28$ proton core polarization. The new results serve as benchmarks to establish theoretical models, predicting the nuclear properties of the doubly magic nucleus ${}^{78}\mathrm{Ni}$.

At the radioactive ion beam facility REX-ISOLDE, neutron-rich zinc isotopes were investigated using low-energy Coulomb excitation. These experiments have resulted in $B(E2,2_1^{+}\to 0_1^{+})$ values in ${}^{74-80}\mathrm{Zn}$, $B(E2,4_1^{+}\to 2_1^{+})$ values in ${}^{74,76}\mathrm{Zn}$ and the determination of the energy of the first excited $2_1^{+}$ states in ${}^{78,80}\mathrm{Zn}$. The zinc isotopes were produced by high-energy proton- $(A=74,76,80)$ and neutron- $(A=78)$ induced fission of ${}^{238}\mathrm{U}$, combined with selective laser ionization and mass separation. The isobaric beam was postaccelerated by the REX linear accelerator and Coulomb excitation was induced on a thin secondary target, which was surrounded by the MINIBALL germanium detector array. In this work, it is shown how the selective laser ionization can be used to deal with the considerable isobaric beam contamination and how a reliable normalization of the experiment can be achieved. The results for zinc isotopes and the $N=50$ isotones are compared to collective model predictions and state-of-the-art large-scale shell-model calculations, including a recent empirical residual interaction constructed to describe the present experimental data up to 2004 in this region of the nuclear chart.

The question of isospin-symmetry breaking in nuclei of the $sd$ shell is addressed. We propose a new global parametrization of the isospin-nonconserving shell-model Hamiltonian which accurately describes experimentally known isobaric mass splittings. The isospin-symmetry violating part of the Hamiltonian consists of the Coulomb interaction and effective charge-dependent forces of nuclear origin. Particular attention has been paid to the effect of the short-range correlations. The behavior of $b$ and $c$ coefficients of the isobaric-mass-multiplet equation (IMME) is explored in detail. In particular, a high-precision numerical description of the staggering effect is proposed and contribution of the charge-dependent forces to the nuclear pairing is discussed. The Hamiltonian is applied to the study of the IMME beyond a quadratic form in the $A=32$ quintet, as well as to calculation of nuclear structure corrections to superallowed $0^{+}\to 0^{+}$ Fermi $\beta$ decay and to amplitudes of Fermi transitions to nonanalog states in $sd$-shell nuclei.