Detailed β -decay study of $^{33}$Ar N. Adimi, 1, 2 R. Dom´ınguez-Reyes, 3 M. Alcorta, 3 A. Bey, 1 B. Blank, 1 M.J.G. Borge, 3 F. de Oliveira Santos, 4 C. Dossat, 1 H.O.U. Fynbo, 5 J. Giovinazzo, 1 H.H. Knudsen, 5 M. Madurga, 3 I. Matea, 1 A. Perea, 3 K. S¨ ummerer, 6 O. Tengblad, 3 and J.C. Thomas 4 $^{1}$Centre d’ ´ Etudes Nucl´eaires de Bordeaux Gradignan - Universit´e Bordeaux 1 - UMR 5797 CNRS/IN2P3, Chemin du Solarium, BP 120, 33175 Gradignan, France $^{2}$Facult´e de Physique, USTHB, B.P.32, El Alia, 16111 Bab Ezzouar, Alger, Algeria $^{3}$Instituto de Estructura de la Materia, CSIC, Serrano 113bis, E-28006-Madrid, Spain $^{4}$Grand Acc´el´erateur National d’Ions Lourds, B.P. 55027, F-14076 Caen Cedex 05, France $^{5}$Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 1520, DK-8000 Aarhus C, Denmark $^{6}$Gesellschaft f¨ ur Schwerionenforschung mbH, Planckstrasse 1, D-64291 Darmstadt, Germany The proton-rich nucleus $^{33}$Ar has been studied by detailed proton and γ -ray spectroscopy at the low-energy facility of SPIRAL at GANIL. Proton and γ -ray singles and coincidence measurements allowed to establish a quasi complete decay scheme of this nucleus. By comparing the proton intensity to different daughter states, tentative spin assignments have been made for some of the states of $^{33}$Cl. The Gamow-Teller strength distribution is deduced and compared to shell-model calculations and a quenching factor is determined. States close to the isobaric analogue state are searched for with respect to isospin mixing. arXiv:1001.2641v1 [nucl-ex] 15 Jan 2010 PACS numbers: 21.10.-k Properties of nuclei, 23.50.+z Decay by proton emission, 29.30.Ep Charged-particle spectroscopy An important part of information about the struc- ture of the atomic nucleus is obtained by nuclear β de- cay. Studies close to the valley of nuclear stability en- able to precisely test our understanding of this structure, whereas experiments and theoretical work with nuclei far away from the stability line enables investigations of the evolution of nuclear structure as a function of isospin. However, further away from stability and in particular on the proton-rich side of the valley of stability, nuclei no longer decay by simple β decay, but by β -delayed parti- cle emission [1]. Therefore, spectroscopic studies become more difficult, as γ -ray spectroscopy has to be combined with particle detection, i.e. proton and α -particle detec- tion. Gamma detection is commonly achieved with high- efficiency germanium detectors which allow to resolve dif- ferent γ lines with good precision. Charged particles are detected with silicon detectors which can reach modest energy resolutions of about 10-20 keV. A combination of charged-particle detection and γ -ray measurements may permit to establish even complicated β -decay schemes and compare them to theoretical predictions from micro- scopic models as the nuclear shell model. A long-standing problem is the observation of ”quench- ing” of the Gamow-Teller (GT) strength, when exper- imental results, either from nuclear β decay or from charge-exchange reactions, are compared with theoretical results. Having a slight mass dependence this quenching reaches a value of about 0.6 for the transition strength. The quenching is seen from a comparison of the ex- perimental and the theoretically calculated transition strength B(GT) [2]. Although this quenching is known since many years Another question of debate is the isospin mixing or isospin purity of nuclear states. In the β decay of proton- rich nuclei, the Fermi transition populates the isobaric analogue state (IAS) of the decaying ground state. For β -emitting nuclei with isospin projection T z < 0, this IAS is within the Q EC window and decays either by γ emission or, for sufficiently proton-rich nuclei, by proton emission. However, as this IAS has an isospin quantum number equal to the one of the parent nucleus, proton emission from this state to states in the β -delayed proton ( β p) emission daughter nucleus is forbidden by isospin conservation and thus only permitted by a small isospin impurity of either the IAS or of the final state after pro- ton emission. As the IAS usually lies in a region with a much higher density of nuclear states than the daughter state, often a nuclear ground state, the IAS has gener- ally a higher degree of isospin impurity than its daughter state. If this is the case, the isospin mixing has its origin mainly in a mixing of the IAS with nearby lying states having a one-unit lower isospin quantum number, but and has been observed for basically all nuclei where these kinds of studies has been performed, two possible expla- nations are still discussed in the literature (see [3]): i) problems in the shell-model calculations which do not take into account enough orbitals to describe the tran- sition strength correctly. In particular, intruder orbitals giving rise to higher-energy excitations are usually not included to keep the model calculations feasible. ii) Sub- nuclear excitations, especially of the Δ resonance, may shift transition strength to excitation energies as high as 100 MeV and are therefore rather difficult to observe ex- perimentally. A paper of Arima [3] retracing to some extent the history of this quenching shows that the GT strength quenching is to a large extent due to two-particle two-hole excitations not included in most calculations. I. INTRODUCTION