Resonance analysis of ${}^{147}\mathrm{Sm}\left(n,\alpha \right)$ cross sections: Comparison to optical model calculations and indications of nonstatistical effects

We have measured the ${}^{147}\mathrm{Sm}\left(n,\alpha \right)$ cross section from $3\text{eV}$ to $500\text{keV}$ and performed an $\mathcal{R}$-matrix analysis in the resolved region $\left(E_n<700\text{eV}\right)$ to extract $\alpha$ widths for 104 resonances. We computed strength functions from these resonance parameters and compared them to transmission coefficients calculated using optical model potentials similar to those employed as inputs to statistical model calculations. The statistical model often is used to predict cross sections and astrophysical reaction rates. Comparing resonance parameters rather than cross sections allows more direct tests of potentials used in the model and hence should offer greater insight into possible improvements. In particular, an improved $\alpha +\text{nucleus}$ potential is needed for applications in nuclear astrophysics. In addition to providing a more direct test of the $\alpha +\text{nucleus}$ potential, the $\alpha$-width distributions show indications of nonstatistical effects.

Figure 1

${}^{147}\mathrm{Sm}\left(n,\alpha \right)$ cross section data (points with error bars) and SAMMY fit (solid curves). Bars below the data show the locations of the fitted resonances. The length of each bar is proportional to the square root of the resonance area.

Figure 2

Strength function plots for the $\alpha$ (top) and neutron (bottom) channels. Solid and dashed staircase plots represent results for $3^{-}$ and $4^{-}$ resonances, respectively. The measured strength functions are equal to the slopes of these staircase plots.

Figure 3

Integral distributions of total $\alpha$ (top) and reduced neutron (bottom) widths for $3^{-}$ (left) and $4^{-}$ (right) resonances in ${}^{147}\mathrm{Sm}$. The histograms show the measured number of resonances having widths greater than a given width vs that width. In an attempt to depict the experimental uncertainties, histograms for the $\alpha$ widths are plotted at the measured widths plus and minus their respective uncertainties. The dashed curves show the expected ${\chi }^2$ distributions for the average widths, number of resonances, and degrees of freedom ($\nu =1$ for neutrons) indicated.

Figure 4

Measured $\alpha$ strength functions averaged over $100\text{−}\text{eV}$ intervals for $J^{\pi }=3^{-}$ ($X$’s) and $4^{-}$ (triangles) resonances. Strength functions for $J^{\pi }=3^{-}$ resonances calculated with the standard $\left(P1\right)$ and modified $\left(P2\right)$ NON-SMOKER parameters are shown as solid and long-dashed lines, respectively, whereas corresponding calculations for $J^{\pi }=4^{-}$ resonances are shown as short-dashed and dotted lines, respectively.

Figure 5

Ratios ($J^{\pi }=3^{-}$ to $4^{-}$ resonances) of $\alpha$ strength functions averaged over $100\text{−}\text{eV}$ intervals. Measured ratios are shown as solid circles. Ratios calculated with the standard $\left(P1\right)$ and modified $\left(P2\right)$ NON-SMOKER parameters are shown as solid and long-dashed lines, respectively.

Figure 6

Energy-level diagrams depicting the ${}^{147}\mathrm{Sm}\left(n,\alpha \right){}^{144}\mathrm{Nd}$ reaction $\left(Q=10.127\text{MeV}\right)$. Excitation energies $E_x$ are given in mega electron volt, whereas laboratory neutron energies $E_n$ are given in electron volt. The energy scales of the ${}^{144}\mathrm{Nd}$ and ${}^{148}\mathrm{Sm}$ parts of the figure differ by a factor of 17 million. $J^{\pi }=3^{-}$ levels in ${}^{148}\mathrm{Sm}$ can $\alpha$ decay to the ground as well as excited (with substantially reduced penetrability) states of ${}^{144}\mathrm{Nd}$. $J^{\pi }=4^{-}$ levels in ${}^{148}\mathrm{Sm}$ are parity forbidden from decaying to the ground state of ${}^{144}\mathrm{Nd}$, but can decay to excited states.

Figure 7

Pulse-height spectra from the ${}^{147}\mathrm{Sm}\left(n,\alpha \right)$ reaction for the 18.340-, 83.775-, and $667.0\text{−}\text{eV}$ resonances. The spectra have been normalized to have equal areas.

Figure 8

Reduced neutron (top), $\alpha$ (middle), and $\gamma$ (bottom) widths for ${}^{147}\mathrm{Sm}$ resonances versus neutron energy. The reduced neutron and $\gamma$ widths are from previous work as compiled in Ref. 17, whereas the $\alpha$ widths are from the present work. Measured widths with $J=3$, 4, or unknown spin assignments are shown as circles, Xs, and squares, respectively. $\alpha$ widths for which only upper limits were determined are plotted as triangles.