Exploring the possible two-proton radioactivity of $^{38,39}$Ti

TL;DR

This study uses advanced nuclear models to analyze the potential two-proton radioactivity of isotopes $^{38,39}$Ti, suggesting $^{39}$Ti as a viable candidate with decay properties comparable to beta decay, and highlighting pairing tendencies in $^{39}$Ti.

Contribution

The paper applies the Gamow shell model and Gamow coupled channel method to predict two-proton radioactivity in $^{38,39}$Ti, providing new theoretical insights into their decay modes.

Findings

$^{39}$Ti is a promising candidate for 2$p$ emission.

Predicted 2$p$ decay width of $^{39}$Ti rivals its beta decay.

$^{38}$Ti shows higher 2$p$ decay energy and broader decay width.

Abstract

Two-proton (2$p$) radioactivity represents a rare decay mode that has been experimentally observed only in a selected few nuclei. The exploration of 2$p$ emission is crucial for elucidating the structure, mass, and nucleon-nucleon interactions within exotic proton-rich nuclei. $^{39}$Ti has long been postulated as a potential candidate for 2$p$ emission; however, experimental investigations have yet to confirm its 2$p$ decay. To provide more accurate information for further studies, we utilize the Gamow shell model (GSM) and the Gamow coupled channel (GCC) method to analyze the prospective 2$p$ radioactivity of isotopes $^{38,39}$Ti. Our calculations suggest that $^{39}$Ti is indeed a viable candidate for 2$p$ emission. Notably, the estimated partial 2$p$ decay width for $^{39}$Ti, predicted from the three-body GCC method, suggests that its 2$p$ decay could rival its $\beta$ decay in likelihood, although this is highly dependent on the specific 2$p$ decay energy. Additionally, our analysis indicates a propensity for pairing between the valence protons in $^{39}$Ti. A similar investigative approach reveals that $^{38}$Ti exhibits a higher 2$p$ decay energy and a broader decay width than $^{39}$Ti, positioning it as a more promising candidate for 2$p$ decay.