Constraint on the Ground-state Mass of 21Al and Three-Nucleon Forces

Abstract

Fragmentation cross section of ${}^{28}$Si + ${}^9$Be reaction at 75.8 MeV/u was analyzed for studying the decay mode of single-proton emission in ${}^{21}$Al (the proton-rich nucleus with neutron closed-shell of $N=8$ and $T_z=-5/2$). With the comparison between the measured fragmentation cross section and the theoretical cross section produced by EPAX3.1a for the observed nuclei (i.e. ${}^{20}$Mg, ${}^{21}$Al and ${}^{22}$Si), the expected yield for a particle stable ${}^{21}$Al was estimated. With the exponential decay law, an upper limit of half-life of $13$ ns was determined. Using the single-proton penetration model, the upper limit of single-proton separation energy of $-105$ keV was deduced. This deduced mass limit agrees with the microscopic calculation based on nucleon-nucleon (NN) + three-nucleon (3N) forces in $sd{f}_{7/2}{p}_{3/2}$ valence space, which indicates the importance of 3N forces in ${}^{21}$Al.

3 pages, 2 figures