Shell structure underlying the evolution of quadrupole collectivity in ${}^{38}\mathrm{S}$ and ${}^{40}\mathrm{S}$ probed by transient-field $g$-factor measurements on fast radioactive beams

The shell structure underlying shape changes in neutron-rich nuclei between $N=20$ and $N=28$ has been investigated by a novel application of the transient field technique to measure the first-excited state $g$ factors in ${}^{38}\mathrm{S}$ and ${}^{40}\mathrm{S}$ produced as fast radioactive beams. Details of the new methodology are presented. In both ${}^{38}\mathrm{S}$ and ${}^{40}\mathrm{S}$ there is a fine balance between the proton and neutron contributions to the magnetic moments. Shell-model calculations that describe the level schemes and quadrupole properties of these nuclei also give a satisfactory explanation of the $g$ factors. In ${}^{38}\mathrm{S}$ the $g$ factor is extremely sensitive to the occupation of the neutron $p_{3/2}$ orbit above the $N=28$ shell gap as occupation of this orbit strongly affects the proton configuration. The $g$ factor of deformed ${}^{40}\mathrm{S}$ does not resemble that of a conventional collective nucleus because spin contributions are more important than usual.

Figure 1

Region of the nuclear chart indicating the primary beam isotopes ${}^{40}\mathrm{Ar}$ and ${}^{48}\mathrm{Ca}$ used to produce the ${}^{38}\mathrm{S}$ and ${}^{40}\mathrm{S}$ secondary beams (red). The $N=20,28$ closed shells are shown outlined in black. Stable isotopes are shaded (blue).

Figure 2

Previously measured $E(2^{+})$ and $B(E2)$ values for the sulfur isotopes [4].

Figure 3

Spectrum of 1540 MeV ${}^{38}\mathrm{S}$ beam particles after passing through 355 mg/cm${}^2$ of Au followed by 100 mg/cm${}^2$ of Fe. The upper panel shows simulations that examine the effect of the energy width of the ${}^{38}\mathrm{S}$ beam, which is assumed to have a Gaussian distribution about 1540 MeV with a specified full width at half maximum (FWHM). These simulated spectra all have the same number of events. The experimental spectrum in the lower panel agrees with the simulations that assume the beam energy has a Gaussian distribution with a FWHM of 1.4% (i.e., a standard deviation of 0.5%). The equivalent momentum width is $\Delta p/p=0.7\%$.

Figure 4

Overhead view of the SeGA detectors and side view of the target chamber showing the magnet, target, and phoswich detector. Projectiles were detected in the downstream phoswich detector.

Figure 5

Coordinate systems used in the present experiment and its analysis.

Figure 6

Phoswich particle identification plot recorded during the ${}^{38}\mathrm{S}$ run. Pulse-shape discrimination was obtained by plotting the integrated charge for the slow (tail) signal versus the full charge-integrated signal.

Figure 7

Time-of-flight (between the cyclotron RF and the phoswich detector) versus the phoswich energy recorded during the ${}^{38}\mathrm{S}$ run. The labeled features are (a) light particles registered in the slow scintillator, (b) ${}^{38}\mathrm{S}$ ions in coincidence with γ rays, and (c) downscaled events. See text for further details.

Figure 8

Random-subtracted lab frame (top) and Doppler-corrected (bottom) γ-ray spectra at $\theta ={40}^{°}$ for ${}^{38}\mathrm{S}$ (left) and ${}^{40}\mathrm{S}$ (right). The sulfur and iron peaks are labeled. The broad feature to the right of the 1292-keV line is mainly its Doppler tail, due to decays within the target, although there is a contribution from a contaminant line as well. The line at 1238 keV is the $4\to 2$ transition emitted by ${}^{56}\mathrm{Fe}$ nuclei at rest.

Figure 9

Random-subtracted Doppler-corrected γ-ray spectra from the ${}^{38}\mathrm{S}$ measurement are shown on the left. The 1238-keV line emitted by ${}^{56}\mathrm{Fe}$ nuclei at rest in the lab frame is shifted towards the ${}^{38}\mathrm{S}$ peak by the Doppler correction as the detection angle approaches ${90}^{°}$. The right panels show simulated spectra used to evaluate the impact of the Doppler broadened line shape on the angular correlation and precession measurements. The insets show the energy range from 1150 to 1550 keV. These simulations, which do not include background, indicate the relative contributions of decays in the target (broad peak) and decays in vacuum (sharp peak), which overlap. The experimental peak is broader than that in the simulations because a simplified model is used for the γ-ray detectors.

Figure 10

Angular correlations for ${}^{38}\mathrm{S}$ and ${}^{40}\mathrm{S}$. The left panels show the angular correlation in the frame of the projectile nucleus, whereas the right panels show the same angular correlations in the lab frame. The Lorentz boost causes a shift in the effective detection angle and an angle-dependent change in the solid angle. Data are normalized to the calculated angular correlation. The difference in anisotropy stems from the alignment produced by Coulomb excitation, which depends on the ratio of $E(2^{+})$ to the beam velocity (i.e., the adiabacity parameter, ξ, see Ref. [22] and references therein.)

Figure 11

Schematic view of the experimental arrangement from above showing only the four SeGA detectors perpendicular to the magnetic field axis. The direction of positive precession angles, $\Delta \Theta$, is indicated.

Figure 12

Transient field parametrization (solid line) for high-velocity light ions from Ref. [2]. Data points are measured transient-field strengths reported in the literature. See Refs. [2, 15, 30] for further details and references.

Figure 13

Monte Carlo simulations (${10}^6$ events). (Lower panel) Doppler broadened γ-ray line shape at ${29}^{°}$ in the laboratory frame. An equivalent spectrum in the projectile frame is shown in the uppermost panel of Fig. 9. Much of the energy width in the laboratory frame stems from the spread in the projectile velocity, which must be Doppler-corrected event by event using the energy from the phoswich detector (Sec. 3a). (Middle panel) The transient-field precession per unit $g$ factor as a function of the emitted γ-ray energy. (Upper panel) Angular correlation coefficients as a function of the emitted γ-ray energy. The effect of vacuum deorientation is indicated by the (red) line labeled $a_k{G}_k$.

Figure 14

Theoretical $g$ factors compared with experiment. The dashed line shows the present shell-model calculations. The previous results for ${}^{38}\mathrm{Ar}$ and ${}^{40}\mathrm{Ar}$ are from Refs. [35] and [36], respectively.

Figure 15

Dominant proton partitions in ${}^{38}\mathrm{S}$ comparing calculations in which neutrons occupy the full $\mathit{pd}$ shell (SDPF) with calculations in which they are restricted to the $f_{7/2}$ shell (SDF). The $g$ factors that represent the diagonal contributions of the most important configurations are indicated.

Figure 16

As for Fig. 15, but for ${}^{40}\mathrm{S}$.