### Speaker

Dr
Dmitry Testov
(University of Padova/INFN Padova)

### Description

In the talk it will be reported the results on studies on a mirror nuclei $^{31}$S and $^{31}$P performed at GALILEO $\gamma$-ray spectrometer at LNL Legnaro. Such a systematic inquiry of pairs of mirror nuclei represents a powerful tool to study isospin symmetry breaking effects along the N=Z line. Going beyond the f7/2 shell where the theories still need an adjustment puts a challenge to the experiment. Thus in the medium mass region at high spin states some effects whose role was negligible in the f7/2 shell may give rise to large Mirror Energy Difference values (MED) [1].
Excited states of $^{31}$S and $^{31}$P mirror nuclei were recently studied using $^{12}$C($^{20}$Ne,n}) and $^{12}$C($^{20}$Ne,p}) reactions, see Ref.~ [2]. Investigation of Fig.2 in Ref.~[2] shows the oscillation behaviour of MED values for the negative-parity sequence as a function of spin. Thus, the MED values between $\frac{9}{2}^{-}$ and $\frac{13}{2}^{-}$ (where only one nucleon is excited outside f$_{7/2}$ shell) is $\sim$150~keV. However MED between $\frac{7}{2}^{-}$ and $\frac{11}{2}^{-}$ states are smaller ($\sim$50 keV) and in agreement with calculations which give mixed configurations for these states. The observed MED values between positive parity-states are also on the level of $\sim$50~keV. Since the wave function do not involve excitations to the f7/2 shell the electromagnetic spin-orbit effect is not considered. Description of the MED in sd shell nuclei for negative parity and high spin states involving the electromagnetic spin orbit term is up to now only qualitative (because it involves interactions in two main shells). Additionally, shell-model calculations performed using the USD residual interaction and the Monte Carlo shell model with the SDPF-M interaction reproduce well the excitation energies and the reduced transition probabilities for positive-parity states up to the spin $\frac{13}{2}^{-}$, see Ref.~[3]. However for higher spin-states $\frac{15}{2}^{-}$ and $\frac{17}{2}^{-}$ the same predicts the excitation of one neutron and one proton to the f7/2 shell which is in contradiction to the sdfp interaction which describes the same states without particles in the f7/2 shell. On the experimental side, MED values are available up to spin J=13/2 for both negative and positive parity [2] which is not sufficient to disentangle the theoretical puzzle. Therefore, data on MED values for higher spin states are needed.
Excited levels of $^{31}$P was were previously studied in $^{12}$C($^{20}$Ne, p(n)) [2] and $^{24}$Mg($^{16}$O, 2$\alpha$p(n)) reactions in Ref. [4] up to high spins. In contrast, the more exotic $^{31}$S was observed up to only $\frac{13}{2}^{+}$ and $\frac{13}{2}^{-}$ spin [2]. Therefore, the goal of the reported experiment was to extend the level schemes and study the mirror energy differences in the A=31, T=1/2 mirror nuclei. $^{31}$P and $^{31}$S were produced in the same fusion evaporation reaction $^{24}$Mg($^{12}$C, 1$\alpha$1p) and $^{24}$Mg($^{12}$C, 1$\alpha$1n) respectively. The 45~MeV beam was delivered by the XTU-Tandem accelerator at Laboratori Nazionali di Legnaro (LNL). The detection system was composed of GALILEO $\gamma$-ray spectrometer [5] coupled to 4$\pi$ Si ball Euclides [6] and to Neutron Wall [7]. Using the resolving power of GALILEO spectrometer and its ancillaries we easily disentangled excited levels of $^{31}$P in the collected data [8]. The outcomes of the experiment and MED in A=31 will be discussed.
[1] S.Lenzi, R.Lau, J.Physics, Conf. S. 580 012028 (2015)
[2] D.Jenkins et al., Phys.Rev.C 72 031303(R) (2005)
[3] M.Ionescu-Bujor et al., Phys. Rev. C 73, 024310 (2006).
[4] F.Della Vedova et al., AIP Conf. Proc. 764, 205 (2005).
[5] J.J.Valiente-Dobon et al., INFN LNL Annual report (2014).
[6] D.Testov et al. LNL Annual Report (2015).
[7] J. Ljungvall, M. Palacz, J. Nyberg, Nucl. Instr. and Meth. 524, 741 (2004).
[8] A.Boso et al., LNL Annual Reports (2015).

### Primary author

Dr
Dmitry Testov
(University of Padova/INFN Padova)

### Co-authors

Dr
Alberto Boso
(National Physical Laboratory)
Dr
Francesco Recchia
(Univeristy of Padova/INFN Padova)
Prof.
Silvia Lenzi
(University of Padova)