Level structure of ${}^{30}$S and its importance in the ${}^{26}$Si($\alpha$,$p$)${}^{29}$P and ${}^{29}$P($p$,$\gamma$)${}^{30}$S reaction rates

The level structure of ${}^{30}$S was studied via the ${}^{28}$Si(${}^3$He,n) and ${}^{32}$S(p,t) reactions at the Nuclear Science Laboratory of the University of Notre Dame and the Research Center for Nuclear Physics of the University of Osaka, Japan. Important experimental information on the energy levels, decay branching ratios, and tentative spin assignments is extracted to calculate the reaction rates for ${}^{29}$P(p,$\gamma$)${}^{30}$S and ${}^{26}$Si($\alpha$,p)${}^{29}$P, which play a critical role in the reaction flow in explosive hydrogen burning.

Figure 1

A combined ${}^{32}$S(p,t)${}^{30}$S spectrum in the range from the ground state up to 12.3-MeV excitation energy is shown for spectrometer angles of $-0.3^{\circ }$ and $8.0^{\circ }$.

Figure 2

Schematic of the experimental setup for ${}^{28}$Si(${}^3$He,n)${}^{30}$S measurement. The neutron detectors were placed 3.6 m away from the center of the reaction chamber, covering an angular range from 11${}^{\circ }$ to 39${}^{\circ }$. The silicon detectors (LESA) were placed inside the reaction chamber, covering an angular range from 90${}^{\circ }$ to 150${}^{\circ }$.

Figure 3

Neutron ToF spectrum for neutron detector N2 at 14${}^{\circ }$. Identification of the different levels in ${}^{30}$S up to $E_x=10$ MeV is shown. Excitation energies in ${}^{30}$S are given in MeV.

Figure 4

LESA-gated neutron ToF spectrum for neutron detector N2 positioned at 14${}^{\circ }$. The ${}^{30}$S levels labeled by their excitation energies correspond to those charged particle decays that were measured in the silicon detectors. Arrows indicate the positions of possible background peaks associated with ${}^{14}$O from ${}^{12}$C target contamination. All excitation energies are given in MeV.

Figure 5

LESA-gated neutron ToF spectrum for neutron detector N5 positioned at 24${}^{\circ }$. Several unbound levels in ${}^{30}$S are identified with decays recorded by the silicon detectors. Arrows indicate the positions of background peaks of ${}^{14}$O from possible ${}^{12}$C target contamination. All excitation energies are given in MeV.

Figure 6

Event-by-event reconstructed spectra for different energy levels in ${}^{30}$S between the proton-decay threshold and the $\alpha$-decay threshold measured in the present ${}^{28}$Si(${}^3$He,n-p) experiment. The different colors separated by vertical lines correspond to the different kinematics used to reconstruct different portions of the spectra. Note that several panels contain peaks corresponding to two different energies as indicated by subscripts, e.g., $p_1$ belongs to $E_{x,1}$. This is because these peaks are not well resolved in the neutron detectors (ToF spectra) but they are well separated in the LESA, where all the decays are identified and followed. Such is the case for the levels at $E_x=5.20$ MeV and $E_x=5.40$ MeV, $E_x=6.00$ MeV and $E_x=6.24$ MeV, $E_x=7.18$ MeV and $E_x=7.33$ MeV, and $E_x=8.06$ MeV and $E_x=7.91$ MeV. In several spectra, contamination from neighboring peaks is observed (unlabeled peaks). The low-energy peak present in the spectra corresponding to $E_x=8.68$ MeV and $E_x=9.22$ MeV, marked by the dashed arrow, arises owing to the presence of carbon contamination in the target. Branching ratios are listed in Table .

Figure 7

Event-by-event reconstructed spectra for different energy levels in ${}^{30}$S above the $\alpha$-decay threshold measured in the present ${}^{28}$Si(${}^3$He,n-p) experiment. The different colors separated by vertical lines correspond to the different kinematics used to reconstruct different portions of the spectra. The low-energy peak present in the spectra, marked by the dashed arrow, arises because of the presence of carbon contamination in the target. In some cases, contamination from neighboring energy levels is observed (unlabeled peaks). Branching ratios are listed in Table .

Figure 8

Contribution of the most relevant resonances to the ${}^{29}$P(p,$\gamma$)${}^{30}$S reaction rate. All other resonances listed in Table fall within the shaded area and make a limited contribution to the reaction rate.

Figure 9

Resonance contribution to the ${}^{29}$P(p,$\gamma$)${}^{30}$S reaction rate calculated in this work and comparison with previous works. Reaction rates are plotted as ratios to the rate calculated by Iliadis et al. [16].

Figure 10

Resonance contribution to the ${}^{26}$Si($\alpha$,p)${}^{29}$P reaction rate calculated using the parameters listed in Table  and comparison with the rates calculated using the statistical codes smoker [49], non-smoker [50], talys [51] and cigar [52].