Calcium isotopes: A prototypical example of structural evolution

Figure 1: Schematic of the Ca isotopic chain in the chart of nuclides, indicating the combined reach of FRIB + GRETA in terms of spectroscopic sensitivity.

The proton-closed-shell Ca isotopes with Z=20 present a unique laboratory to study the evolution of structure as a function of proton-to-neutron ratio. Within this single isotopic chain are some of the clearest examples to date of changing single-particle energies as a result of the spin-isospin component of the nucleon-nucleon interaction, namely the appearance of new sub-shell gaps at N=32 and 34. Recent microscopic calculations [Hag12, Hol12, Hol14] have also highlighted the Ca isotopes as a region in which to test the role of three-nucleon (3N) forces in providing a more complete microscopic description of the atomic nucleus.

Calculations including 3N forces, the only microscopic calculations to properly reproduce the N=28 shell closure in the Ca isotopes, have been validated by recent mass measurements extending to 54Ca [Wie13], but make more subtle predictions regarding the structure of the Ca isotopes in terms of single-particle occupancies.

A recent experiment performed with GRETINA at NSCL has made a first measurement to stringently test these predictions, using γ-ray decays following neutron knockout to study the occupancy of the neutron single-particle states. The demands of the complex level schemes and closely spaced γ-ray transitions required the resolution of GRETINA, but with the limitations of NSCL’s beam intensity and GRETINA’s γ-ray detection efficiency, the measurement was limited in reach to 50Ca. GRETA at FRIB will allow detailed spectroscopy at least as far as 57Ca. The resolving power in both γ singles and γγ coincidence data (Figure 2) with fast beams will allow confirmation of excitation level schemes, and quantification of neutron single-particle occupancies, well into the region where alterations to structure as a result of 3N forces are expected to become significant [Hol14] and where such data can provide a stringent test of nuclear forces, and constrain predictions for the location of the neutron dripline. The structure of the neutron-rich Ca isotopes in this region also determines the location of the neutron dripline, one of the most fundamental benchmarks for energy density functional theories. The key nuclei 60,61Ca have not yet been observed. The position of the neutron dripline in Ca is thought to depend sensitively on both the location of the neutron 1g9/2 orbital, which nominally starts to be filled at N=40 in 60Ca, and a variety of correlations and many-body effects [Men02, Len10]. Calculations with realistic two- and three-body forces [Hag12, Hol12] predict the neutron dripline to be located around 60Ca, while many mean-field and density-functional calculations have the Ca isotopes (at least those with even A) bound out to A=68–76 [Erl12], often with a fine interplay of single-particle and many-body considerations deciding the fate of the most neutron-rich calcium isotopes that can exist [For13]. Undoubtedly, information on the structure of neutron-rich nuclei around 60Ca [Gad14] is critical to benchmark modern calculations, which differ in their prediction of the location of the Ca dripline by more than 10 nucleons. Just as the chain of oxygen isotopes, this situation will repeat for other neutron-rich regions of the nuclear chart, accessible at the right level of detail with the luminosity and sensitivity afforded by fast beams, thick reaction targets, and in-beam spectroscopy with GRETA at FRIB. The pioneering spectroscopy of the key nucleus 60Ca will be possible with GRETA at FRIB with a one-proton knockout reaction from 61Sc projectiles. Figure 2.1.2 shows the simulation of the γ-ray spectrum of 60Ca, first 2+ energy taken from the predictions by [Len10], with GRETA for γ-ray detection.

FRIB will provide unparalleled access along the Ca isotopic chain and with GRETA we will be in a position to take full advantage of this access. Answers to the questions of changing single-particle energies out to 60Ca will lie within experimental reach, as will a more direct quantification of the significance of 3N forces to describe nuclei. GRETA will be critical to provide the detection efficiency and energy resolution to study these systems using the techniques of fast-beam physics.


[Erl12] J. Erler et al., Nature (London) 486, 509 (2012).

[For13] C. Forssen, G. Hagen, M. Hjorth-Jensen, W. Nazarewicz, and J. Rotureau, Phys. Scr. T 152, 014022 (2013).

[Gad14] A. Gade et al., Phys. Rev. Lett. 112, 112503 (2014).

[Hag12] G. Hagen et al., Phys. Rev. Lett. 109, 032502 (2012).

[Hol12] J. D. Holt, T. Otsuka, A. Schwenk, and T. Suzuki, J. Phys. G 39, 085111 (2012).

[Hol14] J. D. Holt, J. Menendez, J. Simonis, and A. Schwenk, Phys. Rev. C 90, 024312 (2014).

[Len10] S. M. Lenzi et al., Phys. Rev. C 82, 054301 (2010).

[Men02] J. Meng et al., Phys. Rev. C 65, 041302(R) (2002).

[Wie13] F. Wienholtz et al., Nature 498, 246 (2013).

Figure 2: (a) Experimental GRETINA spectrum for neutron knockout from 50Ca into 49Ca (blue line), fit with GEANT4 simulation (red line) and a smooth background (grey line). (b) Simulated GRETA spectrum for neutron knockout from 57Ca into 56Ca at FRIB, based on a theoretical level scheme [Hol14]. Inset shows a simulated gamma-gamma coincidence spectrum for the 2+ to 0+ transition at 1.8 MeV. The efficiency for gamma-gamma coincidences will allow determination of level schemes for such detailed studies.

Figure 3: Simulation for 9Be(61Sc, 60Ca + γ) with GRETA at the proposed high rigidity spectrometer (HRS) at FRIB, enabling first spectroscopy of 60Ca.