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.

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.

4D-imaging of drip-line radioactivity by detecting proton emission from 54mNi pictured with ACTAR TPC.

Proton radioactivity was discovered exactly 50 years ago. First, this nuclear decay mode sets the limit of existence on the nuclear landscape on the neutron-deficient side. Second, it comprises fundamental aspects of both quantum tunnelling as well as the coupling of (quasi)bound quantum states with the continuum in mesoscopic systems such as the atomic nucleus. Theoretical approaches can start either from bound-state nuclear shell-model theory or from resonance scattering. Thus, proton-radioactivity guides merging these types of theoretical approaches, which is of broader relevance for any few-body quantum system. Here, we report experimental measurements of proton-emission branches from an isomeric state in 54mNi, which were visualized in four dimensions in a newly developed detector. We show that these decays, which carry an unusually high angular momentum, ℓ = 5 and ℓ = 7, respectively, can be approximated theoretically with a potential model for the proton barrier penetration and a shell-model calculation for the overlap of the initial and final wave functions.

Extending the Southern Shore of the Island of Inversion to

Detailed spectroscopy of the neutron-unbound nucleus ^{28}F has been performed for the first time following proton/neutron removal from ^{29}Ne/^{29}F beams at energies around 230 MeV/nucleon. The invariant-mass spectra were reconstructed for both the ^{27}F^{(*)}+n and ^{26}F^{(*)}+2n coincidences and revealed a series of well-defined resonances. A near-threshold state was observed in both reactions and is identified as the ^{28}F ground state, with S_{n}(^{28}F)=-199(6) keV, while analysis of the 2n decay channel allowed a considerably improved S_{n}(^{27}F)=1620(60) keV to be deduced. Comparison with shell-model predictions and eikonal-model reaction calculations have allowed spin-parity assignments to be proposed for some of the lower-lying levels of ^{28}F. Importantly, in the case of the ground state, the reconstructed ^{27}F+n momentum distribution following neutron removal from ^{29}F indicates that it arises mainly from the 1p_{3/2} neutron intruder configuration. This demonstrates that the island of inversion around N=20 includes ^{28}F, and most probably ^{29}F, and suggests that ^{28}O is not doubly magic.

First Accurate Normalization of the ß-delayed α Decay of

The ^{12}C(α,γ)^{16}O reaction plays a central role in astrophysics, but its cross section at energies relevant for astrophysical applications is only poorly constrained by laboratory data. The reduced α width, γ_{11}, of the bound 1^{-} level in ^{16}O is particularly important to determine the cross section. The magnitude of γ_{11} is determined via sub-Coulomb α-transfer reactions or the ß-delayed α decay of ^{16}N, but the latter approach is presently hampered by the lack of sufficiently precise data on the ß-decay branching ratios. Here we report improved branching ratios for the bound 1^{-} level [b_{ß,11}=(5.02±0.10)×10^{-2}] and for ß-delayed α emission [b_{ßα}=(1.59±0.06)×10^{-5}]. Our value for b_{ßα} is 33% larger than previously held, leading to a substantial increase in γ_{11}. Our revised value for γ_{11} is in good agreement with the value obtained in α-transfer studies and the weighted average of the two gives a robust and precise determination of γ_{11}, which provides significantly improved constraints on the ^{12}C(α,γ) cross section in the energy range relevant to hydrostatic He burning.

Strong Neutron Pairing in core+4n Nuclei.

The emission of neutron pairs from the neutron-rich N=12 isotones ^{18}C and ^{20}O has been studied by high-energy nucleon knockout from ^{19}N and ^{21}O secondary beams, populating unbound states of the two isotones up to 15 MeV above their two-neutron emission thresholds. The analysis of triple fragment-n-n correlations shows that the decay ^{19}N(-1p)^{18}C^{*}→^{16}C+n+n is clearly dominated by direct pair emission. The two-neutron correlation strength, the largest ever observed, suggests the predominance of a ^{14}C core surrounded by four valence neutrons arranged in strongly correlated pairs. On the other hand, a significant competition of a sequential branch is found in the decay ^{21}O(-1n)^{20}O^{*}→^{18}O+n+n, attributed to its formation through the knockout of a deeply bound neutron that breaks the ^{16}O core and reduces the number of pairs.

Measurement of the isoscalar monopole response in the neutron-rich nucleus 68Ni.

The isoscalar monopole response has been measured in the unstable nucleus (68)Ni using inelastic alpha scattering at 50A MeV in inverse kinematics with the active target MAYA at GANIL. The isoscalar giant monopole resonance (ISGMR) centroid was determined to be 21.1 ± 1.9 MeV and indications for a soft monopole mode are provided for the first time at 12.9 ± 1.0 MeV. Analysis of the corresponding angular distributions using distorted-wave-born approximation with random-phase approximation transition densities indicates that the L = 0 multipolarity dominates the cross section for the ISGMR and significantly contributes to the low-energy mode. The L=0 part of this low-energy mode, the soft monopole mode, is dominated by neutron excitations. This demonstrates the relevance of inelastic alpha scattering in inverse kinematics in order to probe both the ISGMR and isoscalar soft modes in neutron-rich nuclei.

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.

Spectroscopy of 26F to probe proton-neutron forces close to the drip line.

A long-lived J(π) = 4(1)(+) isomer, T(1/2) = 2.2(1) ms, has been discovered at 643.4(1) keV in the weakly bound (9)(26)F nucleus. It was populated at Grand Accélérateur National d'Ions Lourds in the fragmentation of a (36)S beam. It decays by an internal transition to the J(π) = 1(1)(+) ground state [82(14)%], by ß decay to (26)Ne, or ß-delayed neutron emission to (25)Ne. From the ß-decay studies of the J(π) =1(1)(+) and J(π) = 4(1)(+) states, new excited states have been discovered in (25,26)Ne. Gathering the measured binding energies of the J(π) = 1(1)(+) -4(1)(+) multiplet in (9)(26)F, we find that the proton-neutron π0d(5/2)ν0d(3/2) effective force used in shell-model calculations should be reduced to properly account for the weak binding of (9)(26)F. Microscopic coupled cluster theory calculations using interactions derived from chiral effective field theory are in very good agreement with the energy of the low-lying 1(1)(+), 2(1)(+), 4(1)(+) states in (26)F. Including three-body forces and coupling to the continuum effects improve the agreement between experiment and theory as compared to the use of two-body forces only.

Search for superscreening effects in a superconductor.

The decay of (19)O(ß(-)) and (19)Ne(ß(+)) implanted in niobium in its superconducting and metallic phases was measured using purified radioactive beams produced by the SPIRAL GANIL facility. Half-lives and branching ratios measured in the two phases are consistent within a 1σ error bar. This measurement casts strong doubts on the predicted strong electron screening in a superconductor, the so-called superscreening. The measured difference in screening potential energy is 110(90) eV for (19)Ne and 400(320) eV for (19)O. Precise determinations of the half-lives were obtained for (19)O, 26.476(9) s, and for (19)Ne, 17.254(5) s.

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.

Migration of nuclear shell gaps studied in the d(24Ne,pγ)25Ne reaction.

The transfer of neutrons onto 24Ne has been measured using a reaccelerated radioactive beam of 24Ne to study the (d,p) reaction in inverse kinematics. The unusual raising of the first 3/2+ level in 25Ne and its significance in terms of the migration of the neutron magic number from N=20 to N=16 is put on a firm footing by confirmation of this state's identity. The raised 3/2+ level is observed simultaneously with the intruder negative parity 7/2- and 3/2- levels, providing evidence for the reduction in the N=20 gap. The coincident gamma-ray decays allowed the assignment of spins as well as the transferred orbital angular momentum. The excitation energy of the 3/2+ state shows that the established USD shell model breaks down well within the sd model space and requires a revised treatment of the proton-neutron monopole interaction.

Prolate-spherical shape coexistence at N=28 in 44S.

The structure of 44S has been studied by using delayed γ and electron spectroscopy. The decay rates of the 02+ isomeric state to the 2(1)+ and 0(1)+ states, measured for the first time, lead to a reduced transition probability B(E2: 2(1)+→0(2)+)=8.4(26) e(2) fm4 and a monopole strength ρ2(E0: 0(2)+→0(1)+)=8.7(7)×10(-3). Comparisons to shell model calculations point towards prolate-spherical shape coexistence, and a two-level mixing model is used to extract a weak mixing between the two configurations.

Breakdown of the Z=8 shell closure in unbound 12O and its mirror symmetry.

An excited state in the proton-rich unbound nucleus 12O was identified at 1.8(4) MeV via missing-mass spectroscopy with the 14O(p,t) reaction at 51 AMeV. The spin-parity of the state was determined to be 0+ or 2+ by comparing the measured differential cross sections with distorted-wave calculations. The lowered location of the excited state in 12O indicates the breakdown of the major shell closure at Z=8 near the proton drip line. This demonstrates the persistence of mirror symmetry in the disappearance of the magic number 8 between 12O and its mirror partner 12Be.

Discovery of a new broad resonance in 19Ne: implications for the destruction of the cosmic gamma-ray emitter 18F.

Six proton-emitting states in 19Ne were studied through the inelastic scattering reaction H(19Ne,p);{19}Ne; (p)18F. Their energies and widths were derived from the protons detected at zero degree, while proton-proton angular correlations between the detector at zero degree and a segmented annular detector were used to determine their spin value. In addition to the known states, a new broad J=1/2 resonance has been evidenced at E_{x} approximately 7.9 MeV, approximately 1.45 MeV above the proton emission threshold. By introducing this resonance, the 18F(p,alpha)15O destruction rate in novae is significantly enhanced. This reduces the chance to observe the cosmic gamma-ray emission of 18F from novae in space telescopes.

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.

Reduction of the spin-orbit splittings at the n = 28 shell closure.

The N = 28 shell closure has been investigated via the 46Ar(d,p)47Ar transfer reaction in inverse kinematics. Energies and spectroscopic factors of the neutron p(3/2), p(1/2), and f(5/2) states in 47Ar were determined and compared to those of the 49Ca isotone. We deduced a reduction of the N = 28 gap by 330(90) keV and spin-orbit weakenings of approximately 10(2) and 45(10)% for the f and p states, respectively. Such large variations for the f and p spin-orbit splittings could be accounted for by the proton-neutron tensor force and by the density dependence of the spin-orbit interaction, respectively. This contrasts with the picture of the spin-orbit interaction as a surface term only.

Enhanced core polarization in (70)Ni and (74)Zn.

The reduced transition probabilities B(E2;0(+) --> 2(+)(1)) of the neutron-rich (74)Zn and (70)Ni nuclei have been measured by Coulomb excitation in a (208)Pb target at intermediate energy. These nuclei have been produced at Grand Accélérateur National d'Ions Lourds via interactions of a 60A MeV (76)Ge beam with a Be target. The B(E2) value for (70)Ni(42) is unexpectedly large, which indicates that neutrons added above N=40 strongly polarize the Z=28 proton core. In the Zn isotopic chain, the steep rise of B(E2) values beyond N=40 continues up to (74)Zn(44). The enhanced proton core polarization in (70)Ni is attributed to the monopole interaction between the neutron in the g(9/2) and protons in the f(7/2) and f(5/2) spin-orbit partner orbitals. This interaction could result in a weakening of magicity in (78)Ni(50).

(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.