Intermediate-energy Coulomb excitation of ${}^{52}\mathrm{Fe}$

The nucleus ${}^{52}\mathrm{Fe}$ with $(N=Z=26)$ has been investigated using intermediate-energy Coulomb excitation in inverse kinematics. A reduced transition probability of $B(E2;0_1^{+}\to 2_1^{+})=817\left(102\right)e^2{\mathrm{fm}}^4$ to the first excited $2^{+}$ state at 849.0(5) keV was deduced. The increase in excitation strength $B(E2\uparrow )$ with respect to the even-mass neighbor ${}^{54}\mathrm{Fe}\mathbf{(}B(E2\uparrow )=620\left(50\right)e^2{\mathrm{fm}}^4\mathbf{)}$ agrees with shell-model expectations as the magic number $N=28$ is approached. This measurement completes the systematics of reduced transition strengths to the first excited $2^{+}$ state for the even-even $N=Z$ nuclei up to mass $A=56$.

Figure 1

(Color online) Particle identification of the beam scattered off the Au target. The correlation of the energy loss measured in the ion chamber vs. the time-of-flight resolves the constituents of the “cocktail beam” (1% lower-level cutoff).

Figure 2

Schematic set-up of SeGA in the configuration used for Coulomb excitation of ${}^{52}\mathrm{Fe}$. The two 37° and 90° rings of SeGA are shown. The angles refer to the directions from the target center to the detector center with respect to the beam direction. A parallel-plate avalanche counter 138 cm upstream of the target position was used to monitor the position of the beam on target.

Figure 3

Gamma-ray spectra in coincidence with ${}^{52}\mathrm{Fe}$ particles at the S800 focal plane. The transitions corresponding to de-excitation of the ${}^{197}\mathrm{Au}$ target and ${}^{52}\mathrm{Fe}$ projectiles are indicated. Laboratory-frame spectra $(\beta =0)$ are shown in the top panels. Doppler-reconstructed projectile-frame spectra assuming a projectile velocity of $\beta =0.31$ at the point of $\gamma$-ray emission are shown in the bottom panels with the simulations overlayed. The solid black lines are the total fits to each spectrum, which contain the sum of the simulated response functions (grey lines) and quadratic backgrounds (dashed lines). The $\gamma$-ray energies determined as a result of the fits are 849.0(6) and 849.2(8) keV for the 37° and 90° SeGA rings, for a weighted average of 849.1(5) keV.

Figure 4

Measured cross section versus maximum laboratory scattering angle (top) and minimum impact parameter (bottom) for ${}^{52}\mathrm{Fe}$ nuclei. For each maximum laboratory scattering angle, the corresponding $\gamma$-ray spectra and particle spectra were analyzed to yield cross sections. The cross sections measured for 4° and 5° are low due to the loss of acceptance past 3.5° in the dispersive direction, reflected in the lower limits on the error for those cross sections.

Figure 5

ECIS calculation for ${}^{52}\mathrm{Fe}$ at $56.9\mathrm{MeV}∕\text{nucleon}$. Shown are the excitation cross sections as a function of center-of-mass scattering angle for Coulomb excitation only and Coulomb plus nuclear excitation. Parameters from ${}^{40}\mathrm{Ar}$ scattering on ${}^{208}\mathrm{Pb}$ at $41\mathrm{MeV}∕\text{nucleon}$ were used in the calculation [21]. Below the maximum scattering angle chosen (dashed line), the contribution from nuclear excitations is less than 6%.

Figure 6

Systematic behavior of reduced transition probability $B(E2\uparrow )$ and energy of the first excited $J^{\pi }=2^{+}$ state $E\left(2^{+}\right)$ for the even-even Fe isotopes. Adopted values, indicated by filled circles, are from 26 while the present measurement is indicated by an open square.

Figure 7

Reduced transition probability to the first excited $J^{\pi }=2^{+}$ state $B(E2\uparrow )$ and energy of the first excited $J^{\pi }=2^{+}$ state $E\left(2^{+}\right)$ for the even-even $N=Z$ nuclei with $A⩾36$. The measurement of $B(E2\uparrow )=817\left(102\right)e^2{\mathrm{fm}}^4$ for ${}^{52}\mathrm{Fe}$ is indicated by the open square. Filled circles indicate adopted values, from 26.