Quenching of Single-Particle Strength in A=15 Nuclei

Absolute cross sections for the addition of $s$- and $d$-wave neutrons to ${}^{14}$C and ${}^{14}$N have been determined simultaneously via the ($d$,$p$) reaction at 10 MeV/u. The difference between the neutron and proton separation energies, $\mathrm{\Delta }S$, is around $-20$ MeV for the ${}^{14}$C$+$$n$ system and $+8$ MeV for ${}^{14}$N$+$$n$. The population of the $1s_{1\mathrm{/}2}$ and $0d_{5\mathrm{/}2}$ orbitals for both systems is reduced by a factor of approximately 0.5 compared to the independent single-particle model, or about 0.6 when compared to the shell model. This finding strongly contrasts with results deduced from intermediate-energy knockout reactions between similar nuclei on targets of ${}^9$Be and ${}^{12}$C. The simultaneous technique used removes many systematic uncertainties.