Inverse-kinematics proton scattering from ${}^{42,44}\mathrm{S}, {}^{41,43}\mathrm{P}$, and the collapse of the $N=28$ major shell closure

Excited states of the neutron-rich isotopes ${}^{42,44}\mathrm{S}$ and ${}^{41,43}\mathrm{P}$ have been studied via inverse-kinematics proton scattering from a liquid hydrogen target, using the GRETINA $\gamma$-ray tracking array to extract inelastic-scattering cross sections. Deformation lengths of the $2_1^{+}$ excitations in ${}^{42,44}\mathrm{S}$ have been determined and, when combined with deformation lengths determined with electromagnetic probes, yield the ratio of neutron-to-proton matrix elements $M_n/M_p$ for the $2_1^{+}$ excitations in these nuclei. The present results for ${}^{41,43}\mathrm{P}(p,p^{\prime })$ are used to compare two shell-model interactions, SDPF-U and SDPF-MU. As in a recent study of ${}^{42}\mathrm{Si}$, the present results on ${}^{41,43}\mathrm{P}$ favor the SDPF-MU interaction.

Figure 1

Relative kinetic energy spectra of the beams measured downstream of the target in the S800. The dashed spectra are the geant4 fits described in the text. The insets are plots of the figure of merit from log-likelihood fits of the simulated beam particles vs the thickness of the outward bulge of the Kapton entrance and exit windows of the target.

Figure 2

Projectile-frame spectrum of ${}^{42}\mathrm{S}$ measured via inverse-kinematics proton scattering.

Figure 3

(a) Projectile-frame spectrum of ${}^{44}\mathrm{S}$ measured via inverse-kinematics proton scattering. (b) Proton-scattering spectrum gated on the 1329-keV $\gamma$ ray.

Figure 4

(a) Projectile-frame spectrum of ${}^{41}\mathrm{P}$ measured via inverse-kinematics proton scattering. (b) Proton-scattering spectrum gated on the 1416-keV $\gamma$ ray.

Figure 5

Projectile-frame spectrum of ${}^{43}\mathrm{P}$ measured via inverse-kinematics proton scattering.

Figure 6

The region of the projectile-frame spectrum of ${}^{44}\mathrm{S}$ surrounding the photopeak of the 1329-keV $\gamma$ ray deexciting the $2_1^{+}$ state. The smooth curve is the geant4 fit corresponding to the best-fit value of the target offset from the focus of GRETINA along the beam axis of 11.1 mm. The inset shows the figure of merit from the fit vs the simulated target offset. The dashed line corresponds to the 95% confidence interval of 0.4 mm.

Figure 7

The low-energy region of the projectile-frame spectrum of ${}^{41}\mathrm{P}$ measured via inverse-kinematics proton scattering. The smooth curve is the geant4 fit corresponding to a mean lifetime of the $J^{\pi }=(3/2^{+})$ first-excited state of 264 ps. The inset shows the figure of merit from the fit vs the simulated mean lifetime. The dashed line corresponds to the 95% confidence interval of 18 ps.

Figure 8

The low-energy region of the projectile-frame spectrum of ${}^{43}\mathrm{P}$ measured via inverse-kinematics proton scattering. The smooth curve is the geant4 fit corresponding to a mean lifetime of the $J^{\pi }=3/2^{+}$ first-excited state of 62 ps. The inset shows the figure of merit from the fit vs. the simulated mean lifetime. The dashed line corresponds to the 95% confidence interval of $\pm 12$ ps.

Figure 9

Partial level schemes of ${}^{42,44}\mathrm{S}$ and ${}^{41,43}\mathrm{P}$ showing levels populated in the present work. Arrow widths are proportional to the measured $\gamma$-ray intensities.

Figure 10

Proton-scattering and electromagnetic deformation lengths ${\delta }_2$ for the $0_{\mathrm{gs}}^{+}\to 2_1^{+}$ excitations of even-even neutron-rich sulfur isotopes. Proton-scattering deformation lengths are from Ref. [22] (open circles) and the present work (solid circles), and electromagnetic deformation lengths (open squares) are from Ref. [23].

Figure 11

Ratios of neutron to proton transition matrix elements $M_n/M_p$ expressed relative to $N/Z$ for even-even neutron-rich calcium, argon, sulfur, and silicon isotopes from Refs. [22, 29, 30, 31, 32, 33] (open symbols) and the present work (solid circles).

Figure 12

Ratios of neutron to proton transition matrix elements $M_n/M_p$ expressed relative to $N/Z$ for even-even $N=28$ isotones from Ref. [30] and the present work compared with shell-model predictions, described in the text.

Figure 13

Measured cross sections for populating excited states in ${}^{41}\mathrm{P}$ (top panel) compared with shell-model predictions of the proton-scattering transition strength $B(p,p^{\prime })$ calculated using the SPDF-U [34] (middle panel) and SPDF-MU [35] (bottom panel) effective interactions. In the bottom panels, the solid bars correspond to $b_n/b_p=1$ and the open bars to $b_n/b_p=3$.

Figure 14

Measured cross sections for populating excited states in ${}^{43}\mathrm{P}$ (top panel) compared with shell-model predictions of the proton-scattering transition strength $B(p,p^{\prime })$ calculated using the SPDF-U [34] (middle panel) and SPDF-MU [35] (bottom panel) effective interactions. In the bottom panels, the solid bars correspond to $b_n/b_p=1$ and the open bars to $b_n/b_p=3$.