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The half-lives of the decaying 1 + and 4 − states, T 1/2 = 22.1(2) ms and 53.73(13) ms, respectively, were extracted from the time distributions of transitions in 34 Si: E 0(0 + 2 → 0 + 1 ) and E 1(929.1 keV; 3 − → 2 + ), respectively.
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The structure of Si34 was studied through γ spectroscopy separately in the β− decays of Mg34 and Al34 at the ISOLDE facility of CERN. Different configurations in Si34 were populated independently from the two recently identified β-decaying states in Al34 having spin-parity assignments Jπ=4− dominated by the normal configuration π(d5/2)−1⊗ν(f7/2) an...
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An extended investigation of the low-spin structure of the $^{65}$Ni nucleus was performed at the Institut Laue-Langevin, Grenoble, via the neutron capture reaction $^{64}$Ni(n,$\gamma$)$^{65}$Ni, using the FIPPS HPGe array. The level scheme of $^{65}$Ni was significantly expanded, with 2 new levels and 87 newly found transitions. Angular correlati...
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... The ∆ = 1 states can be interpreted in terms of the low-lying 3/2 + and 1/2 + 1h states of 33 Si coupled to the low-lying 7/2 − and 3/2 − 1p states of 35 Si. The state with maximum spin-parity J π of 5 − predicted at 5.12 MeV can be compared to the proposed experimental 5 − state at 4.97 MeV [65]. The theoretical spectra from the mixed SDPF-U-Mix shown in [65] is similar to the FSU unmixed spectrum in Figure 5. ...
... The state with maximum spin-parity J π of 5 − predicted at 5.12 MeV can be compared to the proposed experimental 5 − state at 4.97 MeV [65]. The theoretical spectra from the mixed SDPF-U-Mix shown in [65] is similar to the FSU unmixed spectrum in Figure 5. ...
Applications of configuration-mixing methods for nuclei near the proton and neutron drip lines are discussed. A short review of magic numbers is presented. Prospects for advances in the regions of four new “outposts” are highlighted: 28O, 42Si, 60Ca and 78Ni. Topics include shell gaps, single-particle properties, islands of inversion, collectivity, neutron decay, neutron halos, two-proton decay, effective charge, and quenching in knockout reactions.
... Level systematics of the N = 20 isotones. The levels in 32 Mg are taken from the present work, while those in 34 Si are from Ref. [83]. The others are adopted from the latest ENSDF database as of this writing. ...
... The systematic behavior of excited levels in the N = 20 isotones is shown in Fig. 11. While the locations of negative-parity states down to 34 Si were discussed previously in Ref. [83], the present work established the lowest firmly assigned negative-parity state in 32 Mg at 2858 keV, further extending the systematics. It can be seen that the lowest negative-parity states remain around 4 MeV from 40 Ca to 34 Si, but at 32 Mg it suddenly drops by 1.4 MeV. ...
Background: The nucleus Mg32 (N=20 and Z=12) plays a central role in the so-called “island of inversion,” where in the ground states sd-shell neutrons are promoted to the fp-shell orbitals across the shell gap, resulting in the disappearance of the canonical neutron magic number N=20.
... The systematic behavior of excited levels in the N = 20 isotones is shown in Fig. 11. While the locations of negative-parity states down to 34 Si were discussed previously in Ref. [83], the present work established the lowest firmly-assigned negative-parity state in 32 Mg at 2858 keV, further extending the systematics. It can be seen that the lowest negative-parity states remain around 4 MeV from 40 Ca to 34 Si, but at 32 Mg it suddenly drops by 1.4 MeV. ...
... All of the calculations predict population of the 1 − 1 state in 32 Mg with cross sections of around 10 mb (see Figs. 7(b-e)). The observed cross section populating the 2551 keV state is close to 34 Si are from Ref. [83]. The others are adopted from the latest ENSDF database as of this writing. ...
Background: The nucleus $^{32}$Mg ($N=20$ and $Z=12$) plays a central role in the so-called "island of inversion" where in the ground states $sd$-shell neutrons are promoted to the $fp$-shell orbitals across the shell gap, resulting in the disappearance of the canonical neutron magic number $N=20$. Purpose: The primary goals of this work are to extend the level scheme of $^{32}$Mg, provide spin-parity assignments to excited states, and discuss the microscopic structure of each state through comparisons with theoretical calculations. Method: In-beam $\gamma$-ray spectroscopy of $^{32}$Mg was performed using two direct-reaction probes, one-neutron (two-proton) knockout reactions on $^{33}$Mg ($^{34}$Si). Final-state exclusive cross sections and parallel momentum distributions were extracted from the experimental data and compared with eikonal-based reaction model calculations combined with shell-model overlap functions. Results: Owing to the remarkable selectivity of the one-neutron and two-proton knockout reactions, a significantly updated level scheme for $^{32}$Mg, which exhibits negative-parity intruder and positive-parity normal states, was constructed. The experimental results were confronted with four different nuclear structure models. Conclusions: In some of these models, different aspects of $^{32}$Mg and the transition into the island of inversion are well described. However, unexplained discrepancies remain, and even with the help of these state-of-the-art theoretical approaches, the structure of this key nucleus is not yet fully captured.
... The corresponding B(E 2; 0 + 1 → 2 + p ) value could be larger than that for the 2 + 1 state, depending on the rigidity of the proton shell gap against ph excitations, the fragmentation of the strength, as well as the proton ph content of the ground state. In the case of 34 Si, similar B(E 2) values have been predicted for the 2 + 1 and 2 + p states [13], but a firm identification of 2 + p state is still lacking. In 68 Ni, shell-model calculations of Langanke et al. [14] have predicted that a large fraction (about twice as large as that of the 2 + 1 state) of the B(E 2) strength goes to 2 + p states present above 4 MeV. ...
... → 2 + 2 cross section of 7.8(9) mb over the 1 • -3.3 • angular range. Subtracting this estimated contribution from the mean value of the two fits, 58(7) e 2 fm 4 , leads to 53(7) e 2 fm 4 , which is in excellent agreement with the values of 50 (13) and 50(10) e 2 fm 4 , obtained in Ref. [18] and [1]. The present experimental results are reported in Table II. ...
The reduced transition probabilities $B(E2; 0^+_{g.s.}\rightarrow2_1^+,2^+_2)$ in $^{70}$Zn and the full $B(E2; 0^+_{g.s.}\rightarrow2^+)$ strength up to S$_n$=7.79 MeV in $^{68}$Ni have been determined at the LISE/GANIL facility using the Coulomb-excitation technique at intermediate beam energy on a $^{208}$Pb target. The $\gamma$ rays emitted in-flight were detected with an array of 46 BaF$_2$ crystals. The angles of the deflected nuclei were determined in order to disentangle and extract the Coulomb and nuclear contributions to the excitation of the 2$^+$ states. The measured $B(E2; 0^+_{g.s.}\rightarrow2_1^+)$ of 1432(124) e$^2$fm$^4$ for $^{70}$Zn falls in the lower part of the published values which clustered either around 1600 or above 2000 e$^2$fm$^4$, while the $B(E2; 0^+_{g.s.}\rightarrow2^+_2)$ of 53(7) e$^2$fm$^4$ agrees very well with the two published values. The relatively low $B(E2; 0^+_{g.s.}\rightarrow2_1^+)$ of 301(38) e$^2$fm$^4$ for $^{68}$Ni agrees with previous studies and confirms a local magicity at $Z=28, N=40$. Combining the results of the low-energy spectra of $^{68}$Ni and $^{70}$Zn and their shell-model interpretations, it is interesting to notice that four different shapes (spherical, oblate, prolate and triaxial) are present. Finally, a summed $E2$ strength of only about 150 e$^2$fm$^4$ has been found experimentally at high excitation energy, likely due to proton excitations across the $Z=28$ gap. The experimental distribution of this high-energy $E2$ excitation agrees with SM calculations, but its strength is about two times weaker.
... The lowest firmly-assigned negative-parity state in 32 Mg was established at 2858 keV in the present work and this observation further extends the systematics. The excitation energy of the lowest negative-parity state drops when going from 34 Si to 32 Mg by 1.4 MeV [50], and this observation is tied to the reduction of the effective size of the N = 20 shell gap [38]. It is worth noting that the excitation-energy drop at 32 Mg is considered to be boosted by correlation effects [9], unlike the systematics established for the N = 18 isotones [38]. ...
... It also accurately reproduces the low excitation energy of the 0 + 2 state and the lowlying level structure of the neighboring nuclei, i.e., 30 Mg and 34 Si, and is often employed for spectroscopic studies around this region (see, for example, Refs. [22,37,50]). Combining the shell model results with the reaction model calculations the exclusive cross sections were obtained, as shown in Fig. 3. ...
Situated in the so-called "island of inversion," the nucleus $^{32}$Mg is considered as an archetypal example of the disappearance of magicity at $N=20$. We report on high statistics in-beam spectroscopy of $^{32}$Mg with a unique approach, in that two direct reaction probes with different sensitivities to the underlying nuclear structure are employed at the same time. More specifically, states in $^{32}$Mg were populated by knockout reactions starting from $^{33}$Mg and $^{34}$Si, lying inside and outside the island of inversion, respectively. The momentum distributions of the reaction residues and the cross sections leading to the individual final states were confronted with eikonal-based reaction calculations, yielding a significantly updated level scheme for $^{32}$Mg and spin-parity assignments. By fully exploiting observables obtained in this measurement, a variety of structures coexisting in 32Mg was unraveled. Comparisons with theoretical predictions based on shell-model overlaps allowed for clear discrimination between different structural models, revealing that the complete theoretical description of this key nucleus is yet to be achieved.
... The corresponding B(E 2; 0 + 1 → 2 + p ) value could be larger than that for the 2 + 1 state, depending on the rigidity of the proton shell gap against ph excitations, the fragmentation of the strength, as well as the proton ph content of the ground state. In the case of 34 Si, similar B(E 2) values have been predicted for the 2 + 1 and 2 + p states [13], but a firm identification of 2 + p state is still lacking. In 68 Ni, shell-model calculations of Langanke et al. [14] have predicted that a large fraction (about twice as large as that of the 2 + 1 state) of the B(E 2) strength goes to 2 + p states present above 4 MeV. ...
... → 2 + 2 cross section of 7.8(9) mb over the 1 • -3.3 • angular range. Subtracting this estimated contribution from the mean value of the two fits, 58(7) e 2 fm 4 , leads to 53(7) e 2 fm 4 , which is in excellent agreement with the values of 50 (13) and 50(10) e 2 fm 4 , obtained in Ref. [18] and [1]. The present experimental results are reported in Table II. ...
The reduced transition probabilities B(E2;0g.s.+→21+,22+) in Zn70 and the full B(E2;0g.s.+→2+) strength up to Sn=7.79MeV in Ni68 have been determined at the LISE/GANIL facility using the Coulomb-excitation technique at intermediate beam energy on a Pb208 target. The γ rays emitted in-flight were detected with an array of 46BaF2 crystals. The angles of the deflected nuclei were determined in order to disentangle and extract the Coulomb and nuclear contributions to the excitation of the 2+ states. The measured B(E2;0g.s.+→21+) of 1432(124) e2fm4 for Zn70 falls in the lower part of the published values which clustered either around 1600 or above 2000e2fm4, while the B(E2;0g.s.+→22+) of 53(7) e2fm4 agrees very well with the two published values. The relatively low B(E2;0g.s.+→21+) of 301(38) e2fm4 for Ni68 agrees with previous studies and confirms a local magicity at Z=28, N=40. Combining the results of the low-energy spectra of Ni68 and Zn70 and their shell-model interpretations, it is interesting to notice that four different shapes (spherical, oblate, prolate, and triaxial) are present. Finally, a summed E2 strength of only about 150e2fm4 has been found experimentally at high excitation energy, likely due to proton excitations across the Z=28 gap. The experimental distribution of this high-energy E2 excitation agrees with shell-model calculations, but its strength is about two times weaker.
... It is proposed to exhibit a central proton density depletion, typically referred to as a "bubble" [1][2][3], and is also one of a small number of nuclei that experiences a drastic reduction of its spin-orbit splitting (here the 1p 3/2 −1p 1/2 splitting) [4] in comparison to the neighboring isotones. It has the properties of a spherical, doubly-magic nucleus, e.g. a high 2 + 1 energy at 3325 keV and the tentative spherical 2 + state at an even higher energy of 5348 keV [5,6], a low B(E2; 0 + 1 → 2 + 1 ) value [7], and a drop in the neutron separation energy (S n ) beyond N = 20 by about 5 MeV [8]. Its N = 20 gap was corroborated by the energy of the 4 − , 5 − states [6]. ...
... It has the properties of a spherical, doubly-magic nucleus, e.g. a high 2 + 1 energy at 3325 keV and the tentative spherical 2 + state at an even higher energy of 5348 keV [5,6], a low B(E2; 0 + 1 → 2 + 1 ) value [7], and a drop in the neutron separation energy (S n ) beyond N = 20 by about 5 MeV [8]. Its N = 20 gap was corroborated by the energy of the 4 − , 5 − states [6]. ...
... For example, the nearby 34 Al nucleus has ground and intruder configurations separated by only 46.6 keV [9]. It follows that deformed configurations, shape coexistence [6,10], and possibly triaxial shapes were predicted [11] and searched for [6,12,13] in the properties of the first few excited states of 34 Si. The abrupt transition from the closed-shell ground state of 34 Si to the intruder-dominated ground state of 32 Mg [14][15][16], with only two protons removed from the 0d 5/2 orbit, is attributed to the subtle balance between the magnitude of the proton and neutron shell gaps that prevent nuclear excitations and the pairing and quadrupole correlations that scale with the amount of particle-hole excitations across these gaps. ...
The structure of $^{33}$Si was studied by a one-neutron knockout reaction from a $^{34}$Si beam at 98.5 MeV/u incident on a $^{9}$Be target. The prompt $\gamma$-rays following the de-excitation of $^{33}$Si were detected using the GRETINA $\gamma$-ray tracking array while the reaction residues were identified on an event-by-event basis in the focal plane of the S800 spectrometer at NSCL (National Superconducting Cyclotron Laboratory). The presently derived spectroscopic factor values, $C^2S$, for the 3/2$^+$ and 1/2$^+$ states, corresponding to a neutron removal from the $0d_{3/2}$ and $1s_{1/2}$ orbitals, agree with shell model calculations and point to a strong $N=20$ shell closure. Three states arising from the more bound $0d_{5/2}$ orbital are proposed, one of which is unbound by about 930 keV. The sensitivity of this experiment has also confirmed a weak population of 9/2$^-$ and 11/2$_{1,2}^-$ final states, which originate from a higher-order process. This mechanism may also have populated, to some fraction, the 3/2$^-$ and 7/2$^-$ negative-parity states, which hinders a determination of the $C^2S$ values for knockout from the normally unoccupied $1p_{3/2}$ and $0f_{7/2}$ orbits.
The cross-shell excited states of Si34 have been investigated via β decays of the 4− ground state and the 1+ isomeric state of Al34. Since the valence protons and valence neutrons occupy different major shells in the ground state as well as the intruder 1+ isomeric state of Al34, intruder levels of Si34 are populated via allowed β decays. Spin assignments to such intruder levels of Si34 were established through γ−γ angular correlation analysis for the negative-parity states with dominant configurations (νd3/2)−1⊗(νf7/2)1 as well as the positive-parity states with dominant configurations (νsd)−2⊗(νf7/2p3/2)2. The configurations of such intruder states play crucial roles in our understanding of the N=20 shell gap evolution. A configuration interaction model derived from the FSU Hamiltonian was utilized in order to interpret the intruder states in Si34. Shell model interaction derived from a more fundamental theory with the valence space in medium similarity renormalization group method was also employed to interpret the structure of Si34.
The last proton bound calcium isotope Ca35 has been studied for the first time, using the Ca37(p,t)Ca35 two neutron transfer reaction. The radioactive Ca37 nuclei, produced by the LISE spectrometer at GANIL, interacted with the protons of the liquid hydrogen target CRYPTA, to produce tritons t that were detected in the MUST2 detector array, in coincidence with the heavy residues Ca or Ar. The atomic mass of Ca35 and the energy of its first 3/2+ state are reported. A large N=16 gap of 4.61(11) MeV is deduced from the mass measurement, which together with other measured properties, makes Ca36 a doubly magic nucleus. The N=16 shell gaps in Ca36 and O24 are of similar amplitude, at both edges of the valley of stability. This feature is discussed in terms of nuclear forces involved, within state-of-the-art shell model calculations. Even though the global agreement with data is quite convincing, the calculations underestimate the size of the N=16 gap in Ca36 by 840 keV.
The level structure of Al36 has been studied via β decay of Mg36 at the Facility for Rare Isotope Beams (FRIB) and the National Superconducting Cyclotron Laboratory (NSCL). A long-lived isomer in Al36 was identified which decays by β to an excited state of Si36. The ground state and the isomeric state of Al36 were found to populate different energy levels of Si36. The results from the two data sets in the present work complement each other. Configuration interaction calculations performed with the FSU shell-model Hamiltonians provide reasonable descriptions to the experimental observations and offer insight into future improvements of the theoretical interpretation.
