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Register a new userNormal and intruder configurations in $^{34}$Si populated in the $beta^-$ decay of $^{34}$Mg and $^{34}$Al
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The structure of $^{34}$Si was studied through $gamma$ spectroscopy separately in the $beta^-$ decays of $^{34}$Mg and $^{34}$Al at the ISOLDE facility of CERN. Different configurations in $^{34}$Si were populated independently from the two recently identified $beta$-decaying states in $^{34}$Al having spin-parity assignments $J^pi = 4^-$ dominated by the normal configuration $pi (d_{5/2})^{-1} otimes u (f_{7/2})$ and $J^pi = 1^+$ by the intruder configuration $pi (d_{5/2})^{-1} otimes u (d_{3/2})^{-1}(f_{7/2})^{2}$. The paper reports on spectroscopic properties of $^{34}$Si such as an extended level scheme, spin and parity assignments based on log($ft$) values and $gamma$-ray branching ratios, absolute $beta$ feeding intensities and neutron emission probabilities. A total of 11 newly identified levels and 26 transitions were added to the previously known level scheme of $^{34}$Si. Large scale shell-model calculations using the {sc sdpf-u-mix} interaction, able to treat higher order intruder configurations, are compared with the new results and conclusions are drawn concerning the predictive power of {sc sdpf-u-mix}, the $N=20$ shell gap, the level of mixing between normal and intruder configurations for the 0$_1^+$, 0$_2^+$ and 2$_1^+$ states and the absence of triaxial deformation in $^{34}$Si.
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The 0$^+_2$ state in $^{34}$Si has been populated at the {sc Ganil/Lise3} facility through the $beta$-decay of a newly discovered 1$^+$ isomer in $^{34}$Al of 26(1) ms half-life. The simultaneous detection of $e^+e^-$ pairs allowed the determination of the excitation energy E(0$^+_2$)=2719(3) keV and the half-life T$_{1/2}$=19.4(7) ns, from which an electric monopole strength of $rho^2$(E0)=13.0(0.9)$times10^{-3}$ was deduced. The 2$^+_1$ state is observed to decay both to the 0$^+_1$ ground state and to the newly observed 0$^+_2$ state (via a 607(2) keV transition) with a ratio R(2$^+_1$$rightarrow0^+_1/2^+_1$$rightarrow0^+_2$)=1380(717). Gathering all information, a weak mixing with the 0$^+_1$ and a large deformation parameter of $beta$=0.29(4) are found for the 0$^+_2$ state, in good agreement with shell model calculations using a new {sc sdpf-u-mix} interaction allowing textit{np-nh} excitations across the N=20 shell gap.
Bubble nuclei are characterized by a depletion of their central density. Their existence is examined within three different theoretical frameworks: the shell model as well as non-relativistic and relativistic microscopic mean-field approaches. We propose $^{34}$Si and $^{22}$O as possible candidates for proton and neutron bubble nuclei, respectively. In the case of $^{22}$O, we observe a significant model dependence, thereby calling into question the bubble structure of $^{22}$O. In contrast, an overall agreement among the models is obtained for $^{34}$Si. Indeed, all models predict a central proton density depletion of about 40%. This result provides strong evidence in favor of a proton bubble in $^{34}$Si.
Many properties of the atomic nucleus, such as vibrations, rotations and incompressibility, can be interpreted as due to a two component quantum liquid of protons and neutrons. Electron scattering measurements on stable nuclei demonstrate that their central densities are saturated, as for liquid drops. In exotic nuclei near the limits of mass and charge, with large imbalances in their proton and neutron numbers, the possibility of a depleted central density, or a bubble structure, has been discussed in a recurrent manner since the 1970s. Here we report first experimental evidence that points to a depletion of the central density of protons in the short-lived nucleus 34Si. The proton-to-neutron density asymmetry in 34Si offers the possibility to place constraints on the density and isospin dependence of the spin--orbit force-on which nuclear models have disagreed for decades-and on its stabilizing effect towards limits of nuclear existence.
The possibility that an unconventional depletion in the center of the charge density distribution of certain nuclei occurs due to a purely quantum mechanical effect has attracted theoretical and experimental attention in recent years. We report on ab initio self-consistent Greens function calculations of one of such candidates, $^{34}$Si, together with its Z+2 neighbour $^{36}$S. Binding energies, rms radii and density distributions of the two nuclei as well as low-lying spectroscopy of $^{35}$Si, $^{37}$S, $^{33}$Al and $^{35}$P are discussed. The interpretation of one-nucleon removal and addition spectra in terms of the evolution of the underlying shell structure is also provided. The study is repeated using several chiral effective field theory Hamiltonians as a way to test the robustness of the results with respect to input inter-nucleon interactions. The prediction regarding the (non-)existence of the bubble structure in $^{34}$Si varies significantly with the nuclear Hamiltonian used. However, demanding that the experimental charge density distribution and the root mean square radius of $^{36}$S are well reproduced, along with $^{34}$Si and $^{36}$S binding energies, only leaves the NNLO$_{text{sat}}$ Hamiltonian as a serious candidate to perform this prediction. In this context, a bubble structure, whose fingerprint should be visible in an electron scattering experiment of $^{34}$Si, is predicted. Furthermore, a clear correlation is established between the occurrence of the bubble structure and the weakening of the 1/2$^-$-3/2$^-$ splitting in the spectrum of $^{35}$Si as compared to $^{37}$S.
Background: Neutron transfer measurements for the $^{18}$O + $^{28}$Si system have shown that the experimental one-neutron and two-neutron transfer cross sections are well reproduced with spectroscopic amplitudes from two different shell model interactions for the Si isotopes: textit{psdmod} for the two-neutron transfer, and textit{psdmwkpn} for the one-neutron transfer. Purpose: The origin of this ambiguity can be related to a more complex mechanism in the one-neutron transfer that requires the unpairing of neutrons prior to its transfer in the ($^{18}$O,$^{17}$O) reaction. Studying a nucleus where this characteristic is absent ($^{13}$C) should help to elucidate this question. Method: One-neutron transfer cross sections were measured for the $^{13}$C + $^{28}$Si at E$_{lab}$ = 30, and 34 MeV, and compared with coupled reaction channel calculations using spectroscopic amplitudes derived from the textit{psdmod} and textit{psdmwkpn} shell model interactions. Results: The spectroscopic amplitudes from the textit{psdmod} interaction for the relevant states in $^{29}$Si provide a good description of the experimental data and the corresponding values agree with previous estimates obtained from the (d,p) reaction. Conclusions: The experimental data for the one-neutron transfer to $^{28}$Si induced by ($^{13}$C,$^{12}$C) reaction is well reproduced using spectroscopic amplitudes from the textit{psdmod}.
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