Unexpected high-energy γ emission from decaying exotic nuclei

Unexpected high-energy γ emission from decaying exotic nuclei A. Gottardo a,∗, D. Verney a, I. Deloncle b, S. Péru c, C. Delafosse a, S. Roccia b, I. Matea a, C. Sotty d, C. Andreoiu e, C. Costache d, M.-C. Delattre a, A. Etilé c, S. Franchoo a, C. Gaulard b, J. Guillot a, F. Ibrahim a, M. Lebois a, M. MacCormick a, N. Marginean d, R. Marginean d, M. Martini f, C. Mihai d, I. Mitu d, L. Olivier a, C. Portail a, L. Qi a, B. Roussière a, L. Stan d, D. Testov g,h, J. Wilson a, D.T. Yordanov a

The N = 52 83 Ga β decay was studied at ALTO. The radioactive 83 Ga beam was produced through the ISOL photofission technique and collected on a movable tape for the measurement of γ -ray emission following β decay. While β-delayed neutron emission has been measured to be 56-85% of the decay path, in this experiment an unexpected high-energy 5-9 MeV γ -ray yield of 16(4)% was observed, coming from states several MeVs above the neutron separation threshold. This result is compared with cutting-edge QRPA calculations, which show that when neutrons deeply bound in the core of the nucleus decay into protons via a Gamow-Teller transition, they give rise to a dipolar oscillation of nuclear matter in the nucleus. This leads to large electromagnetic transition probabilities which can compete with neutron emission, thus affecting the β-decay path. This process is enhanced by an excess of neutrons on the nuclear surface and may thus be a common feature for very neutron-rich isotopes, challenging the present understanding of decay properties of exotic nuclei. The description of β decay as a weak interaction process has reached such a level of precision that it has become a powerful tool in the search for evidence of physics beyond the Standard Model [1]. In nuclei, global β decay properties are driven by the strongly interacting nuclear medium [2,3]; concentrations of Gamow-Teller (G T ) β strength at several-MeV energies have been predicted and observed [2,[4][5][6][7]. However, the understanding of the role of neutron overabundance on radioactive emission in very exotic nuclei is still in its infancy. Current scenarios in several nuclear applications and astrophysics [8] can be substantially affected.
In very neutron-rich nuclei the total energy released through β decay, Q β , can go beyond 10 MeV and subsequently even deeply bound neutrons can decay into protons. When the daughter nu-* Corresponding author.
E-mail address: gottardo@ipno.in2p3.fr (A. Gottardo). cleus is produced in a high-energy configuration above the neutron separation threshold S n , it usually de-excites through β-delayed neutron emission. This process is generally favored in nuclei far from stability due to the low S n value ( 5 MeV) [9]. It is nevertheless an open question how the transformation of a deeply bound neutron into a proton affects the nucleus as a whole. When such an abrupt change of the nuclear density of the decaying parent is induced, the rearrangement of nuclear matter could proceed through collective modes of de-excitation in the daughter isotope, involving also the most superficial nucleons. In this context, the interplay between the closed-core neutron holes after G T β decay and excess surface neutrons remains to be investigated. The presence of a neutron skin in neutron-rich systems can favor particular coherent nuclear excitation modes such as the so-called "pygmy" dipole resonance (PDR) [10]. It is an accumulation of electric dipole strength (E1) in the 5-10 MeV excitation-energy region. The PDR is interpreted as the result of an oscillation of the isoscalar (bal-  anced number of protons and neutrons) inner core against the neutron skin [10].
Recent time-dependent Hartree-Fock-Bogoliubov calculations [11] point out several mass regions of the nuclide chart where these surface effects should be more manifest. Among them, a sudden increase in the neutron skin around 78 Ni, beyond the N = 50 shell closure, has been predicted [11]. This leads to an enhancement by a factor ∼ 3 in the E1 strength at energies between 5 and 10 MeV, exactly where the PDR is expected to occur [11].
The increase is particularly important at atomic number Z = 32, in neutron-rich Ge isotopes such as 83,84 Ge 51,52 . This is related to the shell-model space beyond the N = 50 shell closure, where the underlying microscopic structure involves ν2d 5/2 and ν3s 1/2 neutron orbitals. Their wave functions extend further in space than that of the last proton orbital π1 f 5/2 , and so the neutron skin thickness is increased. In addition, the Q β values beyond N = 50 for Ga isotopes decaying to Ge nuclei are above 11 MeV already in 83 Ga 52 [9]. The phase space for the decay of neutrons belonging to the N = 50 and N = 28 shell closures is thus large, making this region pivotal for the study of the combined effects of neutron excess and decay of inner core neutrons. The present investigation of the highest-energy part of the 80,83 Ge β-delayed gamma emission spectrum was further encouraged by two recent studies [12,5]. In Ref. [12] it was pointed out that, as long as the spin-parity combinations of mother-daughter nuclei permit, Fermi β decay may populate PDR states. In neutron-rich nuclei, however, G T β decay is the dominant process. Madurga et al. [5] report on the β decay of 83 Ga, where high-energy states in the daughter 83 Ge are populated following G T selection rules. The energy spectra of β-delayed neutrons from 83,84 Ga decays are clearly constrained by the underlying nuclear structure, as opposed to a structureless level-density dependence [5].
This letter reports on the β-delayed γ emission of the 83 Ga nucleus, from 5-10 MeV levels in the 83 Ge daughter. These levels are neutron unbound and, contrary to expectations, a significant amount of γ radiation was observed in competition with neutron emission. Results will be compared with theoretical calculations.
The measurement was performed using the low-energy radioactive 80,83 Ga ion beams, which were produced at the photofission Isotope Separation On Line (ISOL) facility ALTO, operated at the IPN in Orsay [13]. The beam was then selected following a standard procedure [14] and delivered to the BEDO setup [15], consisting of a tape station dedicated to β-delayed γ -spectroscopy studies, depicted in Fig. 1. The cylindrical plastic scintillator around the implantation point is for β electron detection, with an average efficiency of 56%. Four Ge detectors and a 2 × 2 × 4 inch LaBr 3 scintillator were used for γ spectroscopy. While the Ge detectors were set with an energy range at around 2.5 MeV, the LaBr 3 scintillator had an 11 MeV range, matching roughly the 11.7 MeV Q-value of the 83 Ga β decay [9]. Germanium semiconductor detectors and the LaBr 3 scintillator in the setup BEDO [15] were calibrated in energy and efficiency using standard γ -ray sources up to 1.5 MeV and for the scintillator with known γ rays from 80 Ga radioactivity up to 5.5 MeV as well. The response function and energy linearity of the LaBr 3 detector were investigated up to 11 MeV using the 27 Al(p, γ ) 28 Si reaction at the ARAMIS accelerator operated at the CSNSM in Orsay [16]. The resolution of the scintillator is 30 keV at 1 MeV and 120 keV at 6-7 MeV.
The 80,83 Ga yields were measured to be ∼ 10 4 and ∼ 10 pps, respectively. Ions were implanted on tape in 3 s spurts, followed by 2 s intervals of decay measurements. The collection time corresponds to roughly ten times the half-life of the 5/2 − 83 Ga ground state, 308(1) ms [17]. The Q β value of 80 Ga decay is 10.3 MeV [9], and the γ -rays are observed to extend up to 8 MeV. This is consistent with previous findings [18] and with the 8.1 MeV neutron separation energy (S n ) of 80 Ge [9]. In the case of 83 Ga, the decay has a slightly larger Q β value of 11.7 MeV [9], but the 83 Ge daughter has an S n value of only 3.6 MeV [9]. Consequently, the γ -rays from the decay would be expected to reach up to roughly 4 MeV. Surprisingly, the energy spectrum is observed to extend all the way up to ∼8-9 MeV. The slope of 83 Ga β-delayed γ emission is identical to the one from 80 Ga until 5 MeV, although with a larger intensity. The slope does not present any kind of change at 3.6 MeV, where the neutron separation threshold lies. After 5 MeV, a broad structure appears: the gamma-ray yield from 83 Ga exceeds that from 80 Ga by two orders of magnitude until about 8-9 MeV. Several observables were studied to cross-check this result. The time distribution of γ rays in the 5-9 MeV range is compatible with 83 Ga half life. The 83 Ga β-delayed neutron emission probability has been measured to be large, between 56(7)% and 85(6)% of the total decay strength [5,19].
Levels populated in 82 Ge from 83 Ga βn decay have been studied in detail in Refs. [19,20], and no γ -rays were reported above 3.4 MeV, thus excluding a contribution from 83 Ga βn branch. Moreover, γ rays above 5 MeV from this branch would imply the population of states less than 2 MeV below the Q β value in 83 Ge. Such a process is strongly suppressed by the Fermi function. The analysis of γ -γ coincidences between the LaBr 3 and the Ge detectors is shown in Fig. 3. The 1238 keV line in 83 Ge [20] is coincident with γ -rays below 4 MeV and then in the 5-5.5 MeV range, proving that the high-energy photons emitted following the decay of 83 Ga do indeed feed the previously observed lower energy levels in 83 Ge [21,20]. The statistical significance of the coincidence is >99%. Finally, the absence of the 1348 keV transition in the γ -γ coincidence spectrum excludes a relevant neutron contribution to the 5-9 MeV signals in the scintillator. The photons in the 5-9 MeV range must therefore have their source in the 83 Ge highenergy levels populated in the 83 Ga β decay.
An estimate of the relative neutron and γ -ray branching was obtained from a simulation of the detector response function. This was done with GEANT4 code [22] and the model was validated up to 11 MeV using the aforementioned ARAMIS γ source [16]. The 83 Ge total γ -ray spectrum observed with the LaBr 3 detector was then unfolded using the simulated response function. The resulting γ -ray intensity spectrum provides an estimate of the total β feeding proceeding through γ -ray emission, I βγ , of states between 5 and 9 MeV relative to those of known intensity for low-energy γ transitions. The 1348 keV line in the β-delayed neutron daughter 82 Ge, with an absolute γ intensity of 62.8(3)% [20], was taken as a reference. With the hypothesis of direct β feeding for all transitions observed, the total I βγ value for states in the 5 to 9 MeV interval works out at 16(4)%. This value, when normalized to the 2.0(4) MeV −1 B(G T ) deduced from neutron emission in 83 Ga [5], corresponds to an average integrated B(G T ) going through γ radiation of 0.4(1) MeV −1 . This strength has escaped observation in Ref. [5,21,20]. The present measurement suggests that this γ branching of the neutron-unbound states accounts for a large part of the β strength previously attributed to the low-lying 83 Ge states.
Significant branching ratios from neutron-unbound states up to 2 MeV in less exotic nuclei have been attributed to neutron emission hindrance due to a centrifugal barrier [6]. In the present case the transferred by the emitted neutron can be as low as 1, so the centrifugal barrier effects are less relevant. A hindrance of neutron emission can come from core-neutron removal spectroscopic factors [7], but even a strong 10 6 suppression factor [7] would imply neutron emission lifetimes of the order of only 10 −16 -10 −17 s.
The high branching ratio measured for γ -ray emission from states up to 5 MeV above the S n value in 83 Ge is all the more surprising. Only fast, possibly collective E1 transitions can compete with neutron emission from levels in this energy range. Other paritychanging electromagnetic transition, like M2 or E3, are suppressed by at least three orders of magnitude due to their higher multipolarity.
Fully microscopic Quasi particle Random Phase Approximation (QRPA) calculations [23,24], with no free parameters, were performed to explore the E1 γ strengths of states populated by radioactivity in 80,83 Ge. The sole input of the QRPA framework of this work is the effective nucleon-nucleon Gogny D1M interaction [25], effective over the whole nuclear chart [26]. The coherent QRPA solutions are built from the quasi-particle spectrum obtained in Hartree-Fock-Bogoliubov (HFB) calculations. Protons and the neutrons are described as pairs of time-reversed companions, and then the standard equal filling approximation, discussed in Ref. [27], is used. For the odd-mass 83 Ge the blocking procedure [28], imposing a fixed value for the occupation of given single-particle orbitals, has been used in order to obtain the quasi-particle (qp) spectrum associated with nuclear states. Several blocked configurations of the unpaired nucleon involving relevant single-particle orbitals were analyzed. Subsequently, the QRPA coherent excitations are built on the same basis as in the HFB calculations, preserving the axial symmetry. In these in-nuclear excitations, all the 2qp proton pairs and all 2qp neutron pairs are considered in the coherent summation building the phonon excitation. However, for odd-mass nuclei, only one component of the two time-reversed components of the blocked quasi-particle level, the "down" one, can take part in the 2qp excitations. For the β decays of 80,83 Ga to 80,83 Ge, the charge exchange code of Ref. [3] (pn-QRPA) provided the population of states in the daughter nuclei. The pn-excitation phonon operator results from the summation on proton-neutron 2qp.  mean nuclear radius is ∼5.5 fm. The β decay from the calculated deformed 83 Ga ground state induces a depletion in neutron density at around 3 fm and a corresponding increase in proton density at 5 fm. This peculiar variation of matter initiates a dipolar oscillation, de-exciting by an E1 transition to the low-energy excited states of 83 Ge. The displayed transition densities show that coherent excitations take place at the nuclear surface, leading to an increase of density around 6 fm. Neutrons and protons contribute jointly, nevertheless the neutron transition density is dominant and peaks more at the surface. This is indeed the expected feature of an isoscalar PDR in neutron-rich nuclei. Fig. 4 also presents a schematic view of the typical elementary spherical single-particle processes which coherently sum-up to build the QRPA G T and E1 strengths.
The calculated G T and E1 spectra are presented in Fig ing the existence of a significant γ -decay branch from neutronunbound states. Consequently, microscopic calculations confirm that the states populated by the G T decay have strong E1 transitions to ground (or low-excited) states. On the contrary, the 80 Ge isotope G T and E1 strengths are suppressed in the region of interest, and shifted to higher energies. The calculation thus fully reproduces the lack of β-delayed γ -ray strength in 80 Ge with respect to 83 Ge.
This result helps to open a new, broader perspective on the pivotal study by Madurga et al. [5]. Firstly, a large part of β feeding to low energy states previously attributed to F F transitions actually seems to proceed through E1 transitions from G T -fed highlying levels. This dominance of G T over F F decays is in contrast with previous calculations beyond N = 50 and close to 78 Ni [29], with consequences on the r-process path. Secondly, G T decays of deeply-correlated neutrons in the closed core need the presence of coherent core-excited levels as final states in the daughter nucleus, much lower in energy than the Q β value, to allow for a sufficient phase space. When the spin-parity combination of mother and daughter nucleus permits, the G T decay can populate collective E1 excitations. A significant high-energy γ -ray radiation may then occur in competition with neutron emission. Only the combination of neutron and γ radiation measurements can reveal the microscopic nature of these states, as is the case for 83 Ga. This mechanism must be general for neutron rich nuclei, impacting also heavier nuclei (N = 82, N = 126 shell closures).
In summary, a significant γ -ray emission was detected in the 5-9 MeV range from the decay of N = 51 83 Ga. It originates from the decay of states neutron-unbound by several MeV, populated by the G T β decay of 83 Ga. State-of-the-art microscopic QRPA calculations show that the G T decay of deeply-bound neutrons can trigger coherent dipolar oscillations (PDR) which in turn engender a significant emission of E1 γ radiation. The process is favored by the rapid development of a neutron skin beyond the N = 50 neutron shell closure. In this regard, the observed change in radioactive emission may be a common feature of very exotic nuclei. It remains for future measurements to better quantify the phenomenon, and explore its evolution in even more neutronrich nuclei. The low production yields of such species in present and future radioactive ion-beam facilities makes it difficult to investigate the PDR in very neutron-rich systems via the standard charge-exchange or Coulomb-excitation reactions. The possibility of using β decay to at least partially study the PDR can thus help to gain a better understanding of radiative capture (n, γ ) cross sections in neutron-rich matter. These are pivotal quantities for nucleosynthesis scenarii of heavy elements via the rapid neutron capture process (r-process) [8,5]. The observed high-energy γ rays feeding low-lying states also lead to a reduction of measured firstforbidden β-decay probabilities, challenging present understanding of their role in very exotic nuclei [29]. The global properties of the β-delayed radiation emission are also relevant for reactor physics and related topics [30][31][32].