# Pairing-quadrupole interplay in the neutron-deficient tin nuclei: first lifetime measurements of low-lying states in $^{106,108}$Sn

## TL;DR

This study measures the lifetimes of low-lying states in neutron-deficient $^{106,108}$Sn isotopes, revealing the dominance of quadrupole forces and a delicate pairing-quadrupole balance affecting $B(E2)$ transition strengths.

## Contribution

First lifetime measurements of low-lying states in $^{106,108}$Sn, providing new insights into pairing-quadrupole interplay in these nuclei.

## Key findings

- Quadrupole force dominates $B(E2; 2_1^+ o 0_{g.s.}^+$) values.
- Precise $B(E2; 4_1^+ o 2_1^+)$ measurements reveal pairing-quadrupole balance.
- Results explain the $B(E2)$ anomaly in $^{108}$Sn.

## Abstract

The lifetimes of the low-lying excited states $2^+$ and $4^+$ have been directly measured in the neutron-deficient $^{106,108}$Sn isotopes. The nuclei were populated via a deep-inelastic reaction and the lifetime measurement was performed employing a differential plunger device. The emitted $\gamma$ rays were detected by the AGATA array, while the reaction products were uniquely identified by the VAMOS++ magnetic spectrometer. Large-Scale Shell-Model calculations with realistic forces indicate that, independently of the pairing content of the interaction, the quadrupole force is dominant in the $B(E2; 2_1^+ \to 0_{g.s.}^+)$ values and it describes well the experimental pattern for $^{104-114}$Sn; the $B(E2; 4_1^+ \to 2_1^+)$ values, measured here for the first time, depend critically on a delicate pairing-quadrupole balance, disclosed by the very precise results in $^{108}$Sn. This result provides insight in the hitherto unexplained $B(E2; 4_1^+ \to 2_1^+)/B(E2; 2_1^+ \to 0_{g.s.}^+) < 1$ anomaly.