Evidence of a sudden increase in the nuclear size of proton-rich silver-96

Abstract

Understanding the evolution of the nuclear charge radius is one of the long-standing challenges for nuclear theory. Recently, density functional theory calculations utilizing Fayans functionals have successfully reproduced the charge radii of a variety of exotic isotopes. However, difficulties in the isotope production have hindered testing these models in the immediate region of the nuclear chart below the heaviest self-conjugate doubly-magic nucleus ¹⁰⁰Sn, where the near-equal number of protons (Z) and neutrons (N) lead to enhanced neutron-proton pairing. Here, we present an optical excursion into this region by crossing the N = 50 magic neutron number in the silver isotopic chain with the measurement of the charge radius of ⁹⁶Ag (N = 49). The results provide a challenge for nuclear theory: calculations are unable to reproduce the pronounced discontinuity in the charge radii as one moves below N = 50. The technical advancements in this work open the N = Z region below ¹⁰⁰Sn for further optical studies, which will lead to more comprehensive input for nuclear theory development.

Fig. 1. Overview of the experimental method.

A 148 MeV ¹⁴N beam from the K-130 cyclotron impinges on a ~ 3 mg cm^{−2 92/nat.}Mo target and produces silver nuclei in the region of N = 50 via fusion–evaporation reactions. The products recoil out of the target, implant into hot graphite, and promptly diffuse out to the catcher cavity before effusing into a transfer tube. The atoms overlap with counter-propagating laser beams and undergo a three-step resonance laser ionization process. The silver ions, along with surface ions and sputtered target-like contaminants, are then guided into the sextupole ion guide (SPIG) by a ~ 1 V per cm field gradient along the tube, and subsequently accelerated to 30 keV, mass separated, and introduced into the radiofrequency quadrupole (RFQ) cooler-buncher. The ions are released as bunches and injected into the JYFLTRAP Penning trap for mass analysis and detection via the PI-ICR method. At the last stage, software processing of the laser frequency-tagged ion impact location data yields the hyperfine spectrum, presented here for ⁹⁹Ag ground-state and isomer (99g and 99m, respectively) and for the ⁹⁶Ag ground-state (96g). The error bars indicate the statistical error.

Fig. 2. Comparison of experimental Ag data to theoretical calculations and other isotopic chains.

a Experimental charge radii of Sn, In, Cd, Ag, Pd, Rh, and Ru isotopes up to N = 74^–. The obtained empirical atomic parameters for the 328 nm transition aided in the recalculation of the charge radii of Ag in cases where literature isotope shifts were available. Similar treatment yielded empirical atomic parameters for the 547.7 nm transition. Where multiple values were available, a weighted mean with the uncertainty given by the standard error of the weighted mean is shown. For asymmetric errors, the larger one is used. b Ground-state change in mean-squared charge radii for ⁹⁶⁻¹⁰⁴Ag (in-source RIS) and ^114−121Ag (collinear laser spectroscopy). The data are compared to theoretical calculations with Fy(Δr, Hartree-Fock-Bogoliubov (HFB)), UNEDF0 and UNEDF2 EDFs. The error bars indicate the statistical error. The systematic error, due to the uncertainty in the atomic parameters, is indicated by the shaded band. c The change in the charge radii for Zn, Mo, and Ag near N = 50 illustrate an increasing trend in the magnitude of the kink as a function of proton number towards ¹⁰⁰Sn. The error bars indicate the statistical error.

Fig. 3. Outlook for the PI-ICR -assisted RIS.

The figure presents the status of optical measurements in the ¹⁰⁰Sn region of the nuclear chart and the projected reach of the PI-ICR-assisted RIS technique at IGISOL. The projections are based on LISE++ simulations and Gemini++ cross-section calculations. They assume a 0.5% efficiency after mass separation and a 10% efficiency through the RFQ and Penning trap as seen in Fig. 1. The absolute laser ionization efficiency for these elements ranges from below 9% in Sn to above 50% in Pd. Only for In the absolute value is not known, however in this estimate we assume it to be of the order of 10%. Depending on the isotope of interest, the primary beam is either ⁴⁰Ca or ⁵⁸Ni, with a projected conservative 50 pnA intensity. With these assumptions, similar statistics as for ⁹⁶Ag can be collected for even the most exotic cases in <12 h of laser spectroscopy. Furthermore, each of the most exotic cases per element have already been extracted from a hot cavity^,,–.