Spectroscopy and lifetime measurements near the proton drip line: ${}^{26,27,28}\mathrm{P}$

We report on the observation of excited states in the neutron-deficient phosphorus isotopes ${}^{26,27,28}\mathrm{P}$ via in-beam $\gamma$-ray spectroscopy with both high-efficiency and high-resolution detector arrays. In ${}^{26}\mathrm{P}$, a previously unobserved level has been identified at 244(3) keV, two new measurements of the astrophysically important $3/2^{+}$ resonance in ${}^{27}\mathrm{P}$ have been performed, $\gamma$ decays have been assigned to the proton-unbound levels at 2216 and 2483 keV in ${}^{28}\mathrm{P}$, and the $\gamma$-ray line-shape method has been used to make the first determination of the lifetimes of the two lowest-lying excited states in ${}^{28}\mathrm{P}$. The expected Thomas-Ehrman shifts were calculated and applied to levels in the mirror nuclei. The resulting level energies from this procedure were then compared with the energies of known states in ${}^{26,27,28}\mathrm{P}$.

Figure 1

Particle identification plot for reaction residues produced from ${}^{26}\mathrm{Si}$ projectiles impinged on a ${}^9\mathrm{Be}$ target for the experiment using CAESAR for $\gamma$-ray detection (also provided in Fig. 1 of Ref. [30]). The S800 ionization chamber was used to measure the energy loss and plastic scintillators in the beam line and the back of the S800 focal plane were used to measure the time of flight. ${}^{26}\mathrm{P}$ (red oval) and ${}^{27}\mathrm{P}$ (orange oval) reaction products are cleanly separated and identifiable.

Figure 2

Doppler-corrected $\gamma$-ray spectra for ${}^{26}\mathrm{P}$ measured with SeGA (top) from the experiment described in Ref. [22] and CAESAR (bottom). In the SeGA spectrum data from the two reaction channels specified have been added together. The red curves are GEANT4 simulations of the observed peaks with a double exponential background and a low-energy cutoff to account for detector thresholds.

Figure 3

Doppler-corrected $\gamma$-ray spectra for ${}^{27}\mathrm{P}$ measured with SeGA (top) from the experiment described in Refs. [37, 38] and CAESAR (bottom). The SeGA spectrum includes data from ${}^9\mathrm{Be}({}^{30}\mathrm{S},{}^{27}\mathrm{P}+\gamma )X$ taken under two S800 magnetic field settings and ${}^9\mathrm{Be}({}^{34}\mathrm{Ar},{}^{27}\mathrm{P}+\gamma )X$. The transition observed with both arrays is consistent with the $\gamma$ decay of the $3/2^{+}$ state reported at 1120(8) keV from the previous in-beam $\gamma$-ray spectroscopy experiment [22] and at 1125(2) keV in a recent ${}^{27}\mathrm{S}\beta$-decay measurement [23, 24].

Figure 4

Doppler-corrected $\gamma$-ray spectra for ${}^{28}\mathrm{P}$ from multinucleon removal from ${}^{34}\mathrm{Ar}$, ${}^{33}\mathrm{Cl}$, and ${}^{30}\mathrm{S}$ (top) and one-neutron knockout using two magnetic-rigidity settings of the S800 spectrograph (bottom) measured with SeGA in the experiment described in Refs. [37, 38]. The transitions labeled 106* and 773* originate from levels with appreciable lifetimes (see Fig. 6).

Figure 5

${}^{28}\mathrm{P}$ level scheme including the $\gamma$-ray transitions observed in this work. The energies for transitions and states are taken from Ref. [39]. The 2216- and 2483-keV transitions have been assigned as the ground-state decays of known states. The placement of the other transitions is the same as in previous experiments.

Figure 6

Doppler-corrected $\gamma$-ray spectra showing the effect of level lifetimes on the 780.8-keV transition in ${}^{27}\mathrm{Si}$ (top), the 773-keV transition in ${}^{28}\mathrm{P}$ (middle), and the 105.64-keV transition in ${}^{28}\mathrm{P}$ (bottom) as measured with SeGA in the experiment described in Refs. [37, 38] for data from the S800 spectrograph magnetic-rigidity setting centered on ${}^9\mathrm{Be}({}^{30}\mathrm{S},{}^{29}\mathrm{S}+\gamma$)X. The insets show the combined ${\chi }^2$ distributions of the lifetime fits for the ${37}^{\circ }$ and ${90}^{\circ }$ data for both settings, ${}^9\mathrm{Be}({}^{30}\mathrm{S},{}^{29}\mathrm{S}+\gamma$)X and ${}^9\mathrm{Be}({}^{30}\mathrm{S},{}^{28}\mathrm{S}+\gamma$)X.

Figure 7

Thomas-Ehrman shift as a function of proton separation energy calculated using a Woods-Saxon potential with several values of $r_0$. The ground-state proton separation energies for ${}^{26,27,28}\mathrm{P}$ are labeled.