N=16 Magicity Revealed at the Proton Drip Line through the Study of

The last proton bound calcium isotope ^{35}Ca has been studied for the first time, using the ^{37}Ca(p,t)^{35}Ca two neutron transfer reaction. The radioactive ^{37}Ca 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 ^{35}Ca 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 ^{36}Ca a doubly magic nucleus. The N=16 shell gaps in ^{36}Ca and ^{24}O 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 ^{36}Ca by 840 keV.

Microsecond Isomer at the N=20 Island of Shape Inversion Observed at FRIB.

Excited-state spectroscopy from the first experiment at the Facility for Rare Isotope Beams (FRIB) is reported. A 24(2)-µs isomer was observed with the FRIB Decay Station initiator (FDSi) through a cascade of 224- and 401-keV γ rays in coincidence with ^{32}Na nuclei. This is the only known microsecond isomer (1 µs≤T_{1/2}<1 ms) in the region. This nucleus is at the heart of the N=20 island of shape inversion and is at the crossroads of the spherical shell-model, deformed shell-model, and ab initio theories. It can be represented as the coupling of a proton hole and neutron particle to ^{32}Mg, ^{32}Mg+π^{-1}+ν^{+1}. This odd-odd coupling and isomer formation provides a sensitive measure of the underlying shape degrees of freedom of ^{32}Mg, where the onset of spherical-to-deformed shape inversion begins with a low-lying deformed 2^{+} state at 885 keV and a low-lying shape-coexisting 0_{2}^{+} state at 1058 keV. We suggest two possible explanations for the 625-keV isomer in ^{32}Na: a 6^{-} spherical shape isomer that decays by E2 or a 0^{+} deformed spin isomer that decays by M2. The present results and calculations are most consistent with the latter, indicating that the low-lying states are dominated by deformation.

Structure of

Detailed spectroscopy of the neutron-deficient nucleus ^{36}Ca was obtained up to 9 MeV using the ^{37}Ca(p,d)^{36}Ca and the ^{38}Ca(p,t)^{36}Ca transfer reactions. The radioactive nuclei, produced by the LISE spectrometer at GANIL, interacted with the protons of the liquid hydrogen target CRYPTA, to produce light ejectiles (the deuteron d or triton t) that were detected in the MUST2 detector array, in coincidence with the heavy residues identified by a zero-degree detection system. Our main findings are (i) a similar shift in energy for the 1_{1}^{+} and 2_{1}^{+} states by about -250 keV, as compared with the mirror nucleus ^{36}S; (ii) the discovery of an intruder 0_{2}^{+} state at 2.83(13) MeV, which appears below the first 2^{+} state, in contradiction with the situation in ^{36}S; and (iii) a tentative 0_{3}^{+} state at 4.83(17) MeV, proposed to exhibit a bubble structure with two neutron vacancies in the 2s_{1/2} orbit. The inversion between the 0_{2}^{+} and 2_{1}^{+} states is due to the large mirror energy difference (MED) of -516(130) keV for the former. This feature is reproduced by shell model calculations, using the sd-pf valence space, predicting an almost pure intruder nature for the 0_{2}^{+} state, with two protons (neutrons) being excited across the Z=20 magic closure in ^{36}Ca (^{36}S). This mirror system has the largest MEDs ever observed, if one excludes the few cases induced by the effect of the continuum.

Extended p_{3/2} Neutron Orbital and the N=32 Shell Closure in

The one-neutron knockout from ^{52}Ca in inverse kinematics onto a proton target was performed at ∼230 MeV/nucleon combined with prompt γ spectroscopy. Exclusive quasifree scattering cross sections to bound states in ^{51}Ca and the momentum distributions corresponding to the removal of 1f_{7/2} and 2p_{3/2} neutrons were measured. The cross sections, interpreted within the distorted-wave impulse approximation reaction framework, are consistent with a shell closure at the neutron number N=32, found as strong as at N=28 and N=34 in Ca isotopes from the same observables. The analysis of the momentum distributions leads to a difference of the root-mean-square radii of the neutron 1f_{7/2} and 2p_{3/2} orbitals of 0.61(23) fm, in agreement with the modified-shell-model prediction of 0.7 fm suggesting that the large root-mean-square radius of the 2p_{3/2} orbital in neutron-rich Ca isotopes is responsible for the unexpected linear increase of the charge radius with the neutron number.

Absence of Low-Energy Shape Coexistence in

The ^{80}Ge structure was investigated in a high-statistics ß-decay experiment of ^{80}Ga using the GRIFFIN spectrometer at TRIUMF-ISAC through γ, ß-e, e-γ, and γ-γ spectroscopy. No evidence was found for the recently reported 0_{2}^{+} 639-keV level suggested as evidence for low-energy shape coexistence in ^{80}Ge. Large-scale shell model calculations performed in ^{78,80,82}Ge place the 0_{2}^{+} level in ^{80}Ge at 2 MeV. The new experimental evidence combined with shell model predictions indicate that low-energy shape coexistence is not present in ^{80}Ge.

78Ni revealed as a doubly magic stronghold against nuclear deformation.

Nuclear magic numbers correspond to fully occupied energy shells of protons or neutrons inside atomic nuclei. Doubly magic nuclei, with magic numbers for both protons and neutrons, are spherical and extremely rare across the nuclear landscape. Although the sequence of magic numbers is well established for stable nuclei, experimental evidence has revealed modifications for nuclei with a large asymmetry between proton and neutron numbers. Here we provide a spectroscopic study of the doubly magic nucleus 78Ni, which contains fourteen neutrons more than the heaviest stable nickel isotope. We provide direct evidence of its doubly magic nature, which is also predicted by ab initio calculations based on chiral effective-field theory interactions and the quasi-particle random-phase approximation. Our results also indicate the breakdown of the neutron magic number 50 and proton magic number 28 beyond this stronghold, caused by a competing deformed structure. State-of-the-art phenomenological shell-model calculations reproduce this shape coexistence, predicting a rapid transition from spherical to deformed ground states, with 78Ni as the turning point.

Binding Energy of

The masses of the neutron-rich copper isotopes ^{75-79}Cu are determined using the precision mass spectrometer ISOLTRAP at the CERN-ISOLDE facility. The trend from the new data differs significantly from that of previous results, offering a first accurate view of the mass surface adjacent to the Z=28, N=50 nuclide ^{78}Ni and supporting a doubly magic character. The new masses compare very well with large-scale shell-model calculations that predict shape coexistence in a doubly magic ^{78}Ni and a new island of inversion for Z<28. A coherent picture of this important exotic region begins to emerge where excitations across Z=28 and N=50 form a delicate equilibrium with a spherical mean field.

Shape Coexistence in

Large-scale shell-model calculations predict that the region of deformation which comprises the heaviest chromium and iron isotopes at and beyond N=40 will merge with a new one at N=50 in an astonishing parallel to the N=20 and N=28 case in the neon and magnesium isotopes. We propose a valence space including the full pf shell for the protons and the full sdg shell for the neutrons, which represents a comeback of the the harmonic oscillator shells in the very neutron- rich regime. The onset of deformation is understood in the framework of the algebraic SU(3)-like structures linked to quadrupole dominance. Our calculations preserve the doubly magic nature of the ground state of ^{78}Ni, which, however, exhibits a well-deformed prolate band at low excitation energy, providing a striking example of shape coexistence far from stability. This new IOI adds to the four well-documented ones at N=8, 20, 28, and 40.

Hindered Gamow-Teller decay to the odd-odd N=Z (62)Ga: absence of proton-neutron T=0 condensate in A=62.

Search for a new kind of superfluidity built on collective proton-neutron pairs with aligned spin is performed studying the Gamow-Teller decay of the T=1, J(π)=0+ ground state of (62)Ge into excited states of the odd-odd N=Z nucleus (62)Ga. The experiment is performed at GSI Helmholtzzentrum für Shwerionenforshung with the (62)Ge ions selected by the fragment separator and implanted in a stack of Si-strip detectors, surrounded by the RISING Ge array. A half-life of T1/2=82.9(14) ms is measured for the (62)Ge ground state. Six excited states of (62)Ga, populated below 2.5 MeV through Gamow-Teller transitions, are identified. Individual Gamow-Teller transition strengths agree well with theoretical predictions of the interacting shell model and the quasiparticle random phase approximation. The absence of any sizable low-lying Gamow-Teller strength in the reported beta-decay experiment supports the hypothesis of a negligible role of coherent T=0 proton-neutron correlations in (62)Ga.

Experimental study of the two-body spin-orbit force in nuclei.

Energies and spectroscopic factors of the first 7/2-, 3/2-, 1/2-, and 5/2- states in the (35)Si21 nucleus were determined by means of the (d, p) transfer reaction in inverse kinematics at GANIL using the MUST2 and EXOGAM detectors. By comparing the spectroscopic information on the Si35 and S37 isotones, a reduction of the p3/2-p1/2 spin-orbit splitting by about 25% is proposed, while the f7/2-f5/2 spin-orbit splitting seems to remain constant. These features, derived after having unfolded nuclear correlations using shell model calculations, have been attributed to the properties of the two-body spin-orbit interaction, the amplitude of which is derived for the first time in an atomic nucleus. The present results, remarkably well reproduced by using several realistic nucleon-nucleon forces, provide a unique touchstone for the modeling of the spin-orbit interaction in atomic nuclei.

Quadrupole collectivity in neutron-rich Fe and Cr isotopes.

Intermediate-energy Coulomb excitation measurements are performed on the N ≥ 40 neutron-rich nuclei (66,68)Fe and (64)Cr. The reduced transition matrix elements providing a direct measure of the quadrupole collectivity B(E2;2(1)(+) → 0(1)(+)) are determined for the first time in (68)Fe(42) and (64)Cr(40) and confirm a previous recoil distance method lifetime measurement in (66)Fe(40). The results are compared to state-of-the-art large-scale shell-model calculations within the full fpgd neutron orbital model space using the Lenzi-Nowacki-Poves-Sieja effective interaction and confirm the results of the calculations that show these nuclei are well deformed.

Unveiling the intruder deformed 02(+) state in 34Si.

The 02(+) state in 34Si has been populated at the GANIL-LISE3 facility through the ß decay of a newly discovered 1(+) isomer in 34Al of 26(1) ms half-life. The simultaneous detection of e(+)e(-) pairs allowed the determination of the excitation energy E(02(+))=2719(3) keV and the half-life T(1/2)=19.4(7) ns, from which an electric monopole strength of ρ(2)(E0)=13.0(0.9)×10(-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)(+)→0(1)(+)/2(1)(+)→0(2)(+))=1380(717). Gathering all information, a weak mixing with the 0(1)(+) and a large deformation parameter of ß=0.29(4) are found for the 0(2)(+) state, in good agreement with shell model calculations using a new SDPF-U-MIX interaction allowing np-nh excitations across the N=20 shell gap.

Structure of neutron-rich Ar isotopes beyond N = 28.

Results from the gamma-ray spectroscopy of {47,48}Ar exemplifying new limits of sensitivity for characterizing neutron-rich nuclei at energies around the Coulomb barrier are presented. The present results, along with interacting shell model calculations, highlight the role of cross-shell excitations and indicate the presence of a nonaxial deformation in 48Ar.

Influence of pairing on the nuclear matrix elements of the neutrinoless betabeta decays.

We study in this Letter the neutrinoless double beta decay nuclear matrix elements (NME's) in the framework of the interacting shell model. We analyze them in terms of the total angular momentum of the decaying neutron pair and as a function of the seniority truncations in the nuclear wave functions. This point of view turns out to be very adequate to gauge the accuracy of the NME's predicted by different nuclear models. In addition, it gives back the protagonist role in this process to the pairing interaction, the one which is responsible for the very existence of double beta decay emitters. We show that low seniority approximations, comparable to those implicit in the quasiparticle RPA in a spherical basis, tend to overestimate the NME's in several decays.

Observation of isomeric decays in the r-process waiting-point nucleus 130Cd82.

The gamma decay of excited states in the waiting-point nucleus (130)Cd(82) has been observed for the first time. An 8(+) two-quasiparticle isomer has been populated both in the fragmentation of a (136)Xe beam as well as in projectile fission of 238U, making (130)Cd the most neutron-rich N = 82 isotone for which information about excited states is available. The results, interpreted using state-of-the-art nuclear shell-model calculations, show no evidence of an N = 82 shell quenching at Z = 48. They allow us to follow nuclear isomerism throughout a full major neutron shell from (98)Cd(50) to (130)Cd(82) and reveal, in comparison with (76)Ni(48) one major proton shell below, an apparently abnormal scaling of nuclear two-body interactions.

Collapse of the N=28 shell closure in (42)Si.

The energies of the excited states in very neutron-rich (42)Si and (41,43)P have been measured using in-beam gamma-ray spectroscopy from the fragmentation of secondary beams of (42,44)S at 39A MeV. The low 2(+) energy of (42)Si, 770(19) keV, together with the level schemes of (41,43)P, provides evidence for the disappearance of the Z=14 and N=28 spherical shell closures, which is ascribed mainly to the action of proton-neutron tensor forces. New shell model calculations indicate that (42)Si is best described as a well-deformed oblate rotor.

Shell model description of the decay out of the superdeformed band of 36Ar.

Large scale shell model calculations in the valence space spanned by two major oscillator shells (sd and pf) describe simultaneously the superdeformed excited band of 36Ar and its spherical ground state. We explain the appearance of this superdeformed band at low excitation energy as a consequence of the very large quadrupole correlation energy of the configurations with many particles and many holes (np-nh) relative to the normal filling of the spherical mean field orbits (0p-0h). We study the mechanism of mixing between the different configurations to understand why the superdeformed band survives and how it finally decays into the low-lying spherical states via the indirect mixing of the 0p-0h and 4p-4h configurations.

Isobaric multiplet yrast energies and isospin nonconserving forces.

The isovector and isotensor energy differences between yrast states of isobaric multiplets in the lower half of the pf region are quantitatively reproduced in a shell model context. The isospin nonconserving nuclear interactions are found to be at least as important as the Coulomb potential. Their isovector and isotensor channels are dominated by J=2 and J=0 pairing terms, respectively. The results are sensitive to the radii of the states, whose evolution along the yrast band can be accurately followed.

(68)(28)Ni(40): Magicity versus superfluidity.

The neutron-rich (66,68)Ni have been produced at GANIL via interactions of a 65.9A MeV 70Zn beam with a 58Ni target. Their reduced transition probability B(E2;0(+)(1)-->2+) has been measured for the first time by Coulomb excitation in a (208)Pb target at intermediate energy. The B(E2) value for (68)Ni(40) is unexpectedly small. An analysis in terms of large scale shell model calculations stresses the importance of proton core excitations to reproduce the B(E2) values and indicates the erosion of the N = 40 harmonic-oscillator subshell by neutron-pair scattering.

Coulomb energy differences in t = 1 mirror rotational bands in (50)Fe and (50)Cr.

Gamma rays from the N = Z-2 nucleus (50)Fe have been observed, establishing the rotational ground state band up to the state J(pi) = 11+ at 6.994 MeV excitation energy. The experimental Coulomb energy differences, obtained by comparison with the isobaric analog states in its mirror (50)Cr, confirm the qualitative interpretation of the backbending patterns in terms of successive alignments of proton and neutron pairs. A quantitative agreement with experiment has been achieved by exact shell model calculations, incorporating the differences in radii along the yrast bands, and properly renormalizing the Coulomb matrix elements in the pf model space.