Intruder configurations of excited states in the neutron-rich isotopes ${}^{33}\mathrm{P}$ and ${}^{34}\mathrm{P}$

Excited states in the neutron-rich isotopes ${}^{33}\mathrm{P}$ and ${}^{34}\mathrm{P}$ were populated by the ${}^{18}\mathrm{O}+{}^{18}\mathrm{O}$ fusion-evaporation reaction at $E_{\mathrm{lab}}=24$ MeV. The Gammasphere array was used along with the Microball particle detector array to detect $\gamma$ transitions in coincidence with the charged particles emitted from the compound nucleus ${}^{36}\mathrm{S}$. The use of Microball enabled the selection of the proton emission channel. It also helped in determining the exact position and energy of the emitted proton; this was later employed in kinematic Doppler corrections. 16 new transitions and 13 new states were observed in ${}^{33}\mathrm{P}$ and 21 $\gamma$ rays and 20 energy levels were observed in ${}^{34}\mathrm{P}$ for the first time. The nearly $4\pi$ geometry of Gammasphere allowed the measurement of $\gamma$-ray angular distributions leading to spin assignments for many states. The experimental observations for both isotopes were interpreted with the help of shell-model calculations using the (0+1)$\hslash \omega$ PSDPF interaction. The calculations accounted for both the 0p-0h and 1p-1h states reasonably well and indicated that 2p-2h excitations might dominate the higher-spin configurations in both ${}^{33}\mathrm{P}$ and ${}^{34}\mathrm{P}$.

Figure 1

Comparison between portions of two spectra in coincidence with protons and 429-keV $\gamma$ rays in ${}^{34}\mathrm{P}$ illustrating the power of kinematic reconstruction in improving the resolution; (a) and (b) Doppler corrected spectrum before and after kinematic reconstruction, respectively.

Figure 2

The level scheme of ${}^{33}\mathrm{P}$ established from the current analysis. States and transitions in red (gray) have been observed for the first time. The spins in the figure are from the current analysis and also from the literature. The arrow widths are proportional to the relative intensities of the $\gamma$-ray transitions. Those with less than $5\%$ intensity are drawn with the same width.

Figure 3

Coincident spectra showing some $\gamma$ transitions in ${}^{33}\mathrm{P}$. (a) 1848 gate, the newly observed $\gamma$ peaks are labeled in red (gray) whereas the previously observed ones are labeled in black. (b) 3559 keV, (c) 3881 keV, and (d) 4078 keV gates, showing the reverse coincidence. The very strong ${}^{34}\mathrm{P}$ line appears weakly in the broad high energy ${}^{33}\mathrm{P}$ gates because of overlaps from broad lines in ${}^{34}\mathrm{P}$. ${}^{33}\mathrm{P}$ and ${}^{34}\mathrm{P}$ result from $pn$ and $2pn$ evaporation and are not separated by the proton detection.

Figure 4

Coincidence spectra confirming the placement of the 4227-keV transition in ${}^{33}\mathrm{P}$; (Top) the gate is on the 4227-keV $\gamma$ ray itself, (a–c) gates on three transitions in coincidence with the 4227-keV line. Note the change in energy scale between the top spectrum and the three others.

Figure 5

Coincident spectra showing some transitions in (a) the 2539-keV gate in the Doppler-corrected matrix of ${}^{33}\mathrm{P}$. The newly observed $\gamma$ lines are labeled in red, whereas the previously observed ones are labeled in black; (b) 2877-keV, (c) 3271-keV, and (d) 4087-keV gates, showing the reverse coincidence relationships.

Figure 6

(a), (c) ${\chi }^2$ fits to the measured angular distribution for different spin hypotheses are plotted as function of mixing ratio, $\delta$, for $\gamma$ transitions in ${}^{33}\mathrm{P}$ indicated in the panels. (b), (d) Angular distributions of 3559 and 1298-keV transitions for different spin hypotheses.

Figure 7

The proposed, updated, level scheme of ${}^{34}\mathrm{P}$ constructed from the present analysis. The newly observed states and transitions are marked in red (gray). The spins in the figure are from the current analysis and also from the literature. The arrow widths are proportional to the $\gamma$ emission relative intensities. The transitions that were observed in the earlier analysis (see Fig. 1 in Ref. [21]) from the same data set, but not in coincidence with the newly observed transitions, are also verified, but not shown here for simplicity. Transitions with less than $5\%$ intensity are drawn with the same width.

Figure 8

Confirmation of the coincidence relationship of some newly assigned $\gamma$ rays in ${}^{34}\mathrm{P}$, observed in the 429-keV gate projected on the Doppler-corrected axis in Fig. 1. One of the strongest ${}^{33}\mathrm{P}$ lines appears weakly in (b), because of the overlap of 4144-keV line in ${}^{33}\mathrm{P}$ with the 4140-keV one.

Figure 9

(a) 1048-, (b) 1876-, and (c) 429-keV gates showing the new position of the 2942-keV transition in ${}^{34}\mathrm{P}$. (d) 2942-keV gate illustrating the consistency in coincidence relations.

Figure 10

${\chi }^2$ fits to the measured angular distribution for different spin hypotheses are plotted as a function of mixing ratio $\delta$ for selected transitions in ${}^{34}\mathrm{P}$ indicated in the panels. The corresponding angular distributions for different spin hypotheses are plotted alongside.

Figure 11

Experimental negative-parity yrast states and their shell-model counter parts calculated with the PSDPF interaction along with the $fp$ shell occupancy in the odd-mass phosphorus isotopes, ${}^{31}\mathrm{P}, {}^{33}\mathrm{P}$, and ${}^{35}\mathrm{P}$. The red (light gray) and blue (dark gray) colors represent neutron and proton $fp$ shell occupancies, respectively.

Figure 12

Experimental negative-parity yrast states and their shell-model counter parts calculated with the PSDPF interaction along with the $fp$ shell occupancy in the even-mass phosphorus isotopes, ${}^{32}\mathrm{P}$ and ${}^{34}\mathrm{P}$. The red (light gray) and blue (dark gray) colors represent neutron and proton $fp$ shell occupancies, respectively.