# N=16 magicity revealed at the proton drip-line through the study of 35Ca

## TL;DR

This study reports the first measurement of the mass and shell gap of $^{35}$Ca, revealing a significant N=16 magicity at the proton drip-line and confirming $^{36}$Ca as doubly-magic through experimental and theoretical analysis.

## Contribution

First experimental determination of the mass and shell gap of $^{35}$Ca, demonstrating N=16 magicity at the proton drip-line and comparing it with other doubly-magic nuclei.

## Key findings

- Large N=16 shell gap of 4.61 MeV in $^{36}$Ca.
- $^{36}$Ca identified as a doubly-magic nucleus.
- Shell model calculations underestimate the N=16 gap by 840 keV.

## Abstract

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 36Ca by 840(110) keV.