# Weak Binding

### At the Dripline - Physics in the Regime of Weak Binding

The limits of nuclear existence are defined by the nucleon driplines. They outline the combinations of neutrons and protons that can be made into bound systems. The exotic combinations of neutrons and protons encountered far from the region of β stability can significantly affect nuclear structure. Two effects receiving a great deal of theoretical and experimental interest are the changes in shell structure, discussed in the previous section, and the physics of weakly-bound nuclei, where valence neutrons may move outside the core for a sizable fraction of the time leading to spatially extended “core-decoupled” wave functions (e.g. halo nuclei). While changes in the shell structure due to the valence nucleon interactions can be described within a shell-model framework based on well-bound states and harmonic- oscillator wave functions, the effects of weak binding and extended radial distributions go beyond such approaches. At some point, in the proximity of the particle continuum, these familiar models and their assumptions will no longer be valid [Dob07].

Halo nuclei serve as a benchmark to study and understand nuclear structure and correlations at the limit of stability [Tan85, Han87, Esb92], providing a sensitive test to validate and guide theories aimed to provide a predictive description of nuclei. The spatial extent of the valence-neutron wave functions can lead to a number of distinct and often unique observables such as large interaction cross sections [Tan85], narrow momentum distribution of fragments produced in neutron knockout reactions [Baz95], and an enhancement in the low-energy (soft) dipole transition strength [Aum13]. The emergence of low-energy (“soft” E1 and M1) collective excitation modes in weakly-bound nuclei arising from the relative motion of the well-bound core and the more loosely bound valence neutrons [Ike88, Sag95, War97] are of specific interest to studies of many-body quantum systems and understanding the role of nuclei in astrophysical environments.

Experimental data characterizing the excitation properties of halo nuclei is, however, limited and available mainly for E1 modes (i.e. soft-dipole excitations in light nuclei and low-lying E1 modes in medium and heavy nuclei). Excited-state lifetime or Coulomb excitation measurements provide a sensitive method to characterize the properties of halo systems with respect to both electric and magnetic multipole modes. Coulomb excitation is primarily sensitive to E1 and E2 transitions, while excited-state lifetime measurements can be applied to both electric and magnetic transitions. These measurements invariably rely on the detection of γ rays.

Excited-state lifetime measurements performed with GRETINA on the neutron-rich C isotopes ^{17,19}C [Whi15] were crucial to confirm the presence of low-lying spin 1/2^{+} halo states close to the neutron threshold, where the M1 decay mode (a spin-flip between the 0^{+} core and the s_{1/2} valence neutron) was found to be strongly hindered. In addition, a deformed halo structure was recently proposed for ^{31}Ne [Nak09] and ^{37}Mg [Kob14]. It is suggested that configuration mixing across the vanishing N=20 shell gap, resulting in nuclear deformation, increases the number of single-particle levels with low-l components. These deformation effects close to threshold may induce the formation of a p-wave (l=1) halo state, which could be accompanied by sizable M1 and E2 transition strengths.

GRETA at FRIB in the future will enable, for example, sensitive spectroscopic studies of predicted halo nuclei in the Ne-Mg region near the neutron dripline. The large ground-state deformations occurring in neutron-rich Ne and Mg nuclei provide an opportunity to study the interplay between deformation and halo effects [Mis97]. However, the spins and parities of low-lying excited states are unknown in this region, leading to large uncertainties when comparing to theory and interpreting the underlying many-body effects. They can be experimentally constrained or determined by studying the transition strengths connecting the states.

GRETA will be critical for this program of measurements. The excellent energy resolution (which can only be achieved with a γ-ray tracking detector such as GRETA) is necessary to carry out Doppler-shift lifetime measurements and resolve the multiple components that occur for each transition (Figure 2.1.5). The high detection efficiency will enable γγ coincidence measurements, needed to control or remove the effects from feeding transitions, which distort the measured level lifetime and lead to large uncertainties.FRIB will produce dripline nuclei up to Z=40 and perhaps higher, and provide intensities of rare isotopes sufficient to explore the properties of halos and skins, and to discover new modes of excitation associated with weak binding and the particle continuum. Indeed, FRIB will nearly double the number of such nuclei that can be studied with sufficient detail and extend the reach from A=40 to A=90. GRETA’s unique combination of high efficiency and high resolution will be unmatched and essential to utilize FRIB’s capability to study the most exotic nuclei found at or near to the neutron dripline. The sensitivity of GRETA for such studies is illustrated in Figure 2.1.6 for the relativistic Coulomb excitation of ^{40}Mg. Only observed for the first time in 2007 at the NSCL [Bau07], ^{40}Mg is located at the intersection of the N=28 spherical magic number and the neutron dripline [Cra14].

**References:**

[Aum13] T. Aumann and T. Nakamura, Phys. Scr. T**152**, 014012 (2013).

[Bau07] T. Baumann *et al*., Nature **449**, 1022 (2007).

[Baz95] D. Bazin *et al*., Phys. Rev. Lett. **74**, 3569 (1995).

[Cra14] H. L. Crawford *et al*., Phys. Rev. C **89**, 041303(R) (2014).

[Dob07] J. Dobaczewski *et al*., Prog. Part. Nucl. Phys. **59**, 432 (2007).

[Esb92] H. Esbensen and G. F. Bertsch, Nucl. Phys. A**542**, 310 (1992).

[Han87] P. G. Hansen and B. Jonson, Europhys. Lett. **4**, 409 (1987).

[Ike88] K. Ikeda, INS-Report JHP-7 (1988), Nucl. Phys. A**538**, 355c (1992).

[Kob14] N. Kobayashi *et al*., Phys. Rev. Lett. **112**, 242501 (2014).

[Mis97] T. Misu, W. Nazarewicz and S. Aberg, Nucl. Phys. A**614**, 44 (1997).

[Now09] F. Nowacki and A. Poves, Phys. Rev. C **79**, 014310 (2009).

[Nak09] T. Nakamura *et al*., Phys. Rev. Lett. **103**, 262501 (2009).

[Sag95] H. Sagawa *et al*., Z. Phys. A**251**, 385 (1995).

[Tan85] I. Tanihata *et al*., Phys. Rev. Lett. **55**, 2676 (1985).

[War97] D. D. Warner and P. Van Isacker, Phys. Lett. B**395**, 145 (1997).

[Whi15] K. Whitmore *et al*., Phys. Rev. C **91**, 041303(R) (2015).

**Figure 1:*** Simulated spectra of *γ*-ray transitions in *^{35}*Mg obtained with GRETA for (a) Coulomb excitation and (b) lifetime measurements. In (b), three different velocity components are evident for each state The upper right panel shows the level scheme of *^{35}*Mg used in the simulation and a comparison to shell-model calculations.*

**Figure 2:*** A simulation of the spectrum measured using GRETA and the proposed HRS from relativistic Coulomb excitation at 200 MeV/u of the near dripline nucleus *^{40}*Mg produced at FRIB and impinging on a 492 mg/cm*^{2}* *^{207}*Bi target. The peak at 550 keV corresponds to the predicted 2*^{+}* state (E(2*^{+}*) and B(E2) in *^{40}*Mg from [Now09]).*