Isotopically resolved neutron total cross sections at intermediate energies

The neutron total cross sections ${\sigma }_{\mathrm{tot}}$ of ${}^{16,18}\mathrm{O},{}^{58,64}\mathrm{Ni}$, ${}^{103}\mathrm{Rh}$, and ${}^{112,124}\mathrm{Sn}$ have been measured at the Los Alamos Neutron Science Center from low to intermediate energies $(3\le E_{\mathrm{lab}}\le 450 \mathrm{MeV})$ by leveraging wave-form-digitizer technology. The ${\sigma }_{\mathrm{tot}}$ relative differences between isotopes are presented, revealing additional information about the isovector components needed for an accurate optical-model description away from stability. Digitizer-enabled ${\sigma }_{\mathrm{tot}}$-measurement techniques are discussed and a series of uncertainty-quantified dispersive optical model (DOM) analyses using these new data is presented, validating the use of the DOM for modeling light systems $\left({}^{16,18}\mathrm{O}\right)$ and systems with open neutron shells $({}^{58,64}\mathrm{Ni} \mathrm{and} {}^{112,124}\mathrm{Sn})$. The valence-nucleon spectroscopic factors extracted for each isotope reaffirm the usefulness of high-energy proton reaction cross sections for characterizing depletion from the mean-field expectation.

Figure 1

Experimental ${\sigma }_{\mathrm{tot}}$ data are shown from 2–500 MeV for nuclides from $A=12$ to $A=208$ [8, 9, 10, 11, 12]. Predictions for ${\sigma }_{\mathrm{tot}}$ given by the “strongly absorbing sphere” (SAS) model [Eq. (1)] are shown as thin dashed lines for each nucleus. Regular oscillations about the SAS model are visible as is the trend for the oscillation maxima and minima to shift to higher energies as $A$ is increased.

Figure 2

Experimental configuration at WNR facility. Samples are cycled into and out of the beam using a linear actuator with a period of 150 seconds. Times of flight (TOFs) are determined by the TOF detector and used to calculate neutron energies.

Figure 3

Neutron-beam structure at WNR facility. “Macropulses” of protons (d) are delivered to WNR's tungsten Target 4, where they generate neutrons by spallation. Each macropulse consists of $\approx 350$ proton “micropulses” (c). Neutrons from each micropulse (b) disperse in time as they travel along the flight path so that $\gamma$ rays and high-energy neutrons catch up to low-energy ones from the previous pulse (a).

Figure 4

The effects of timing corrections on the $\gamma$-ray peak of a typical run are shown. The uncorrected spectrum is shown in black, the spectrum after correction with our software CFD is shown in blue, and the spectrum after correction with both our software CFD and $\gamma$ averaging is shown in magenta. For this run, the final $\gamma$-ray peak FWHM after both corrections is 0.866 ns, comparable to the precision we achieved in our Ca study [27], which also employed $\gamma$ averaging.

Figure 5

The time difference between adjacent TOF-detector events for a single run is plotted (black histogram). Below a certain minimum time difference (the “dead time”), no events are recorded. A logistic fit (red line) models the detector's dead-time response and is used to generate a dead-time correction. The underlying linearly decreasing count rate (gray dashed line) is incorporated into the logistic model. From the fit, a mean dead time of 228.1 ns was extracted for the Sn and O run configurations (a similar procedure was used to recover a dead time of 159.7 ns for the Ni and Rh run configurations).

Figure 6

TOF spectra after the analytic dead-time correction and the veto and integrated charge gating for the blank sample (in red) and the ${}^{\text{nat}}\mathrm{C}$ sample (in blue), from the Ni/Rh experiment. The $\gamma$-ray peak is visible as a sharp spike at 90 ns, followed by the highest-energy neutrons at 130 ns.

Figure 7

(a) A comparison of literature data (taken with analog techniques) and our results (signals processed with a digitizer, or “DSP”) for natural C, Ni, Sn, and Pb. The absolute cross sections are shown from 3–500 MeV. (b) Relative differences between the literature data and our data are shown in percent. From 3–100 MeV, our data are fully consistent with the literature but above 100 MeV, a difference arises, peaking at $\approx 5$% at 300 MeV.

Figure 8

The ${\sigma }_{\mathrm{tot}}$ relative difference between deuterium and hydrogen, as calculated by subtraction of our O ${\sigma }_{\mathrm{tot}}$ results from ${\mathrm{D}}_2\mathrm{O}$ and ${\mathrm{H}}_2\mathrm{O}$. Data from our measurement are shown as red squares; the data of Abfalterer et al. [33], which were generated using ${\mathrm{CH}}_2$, ${\mathrm{C}}_8{\mathrm{H}}_{18}$, and ${\mathrm{D}}_2\mathrm{O}$ targets, are shown as black circles.

Figure 9

Neutron ${\sigma }_{\mathrm{tot}}$ for ${}^{16,18}\mathrm{O}$, ${}^{58,64}\mathrm{Ni}$, and ${}^{112,124}\mathrm{Sn}$: Our results and literature data. In the upper three panels, our digitizer-measured isotopic results are shown in red and corresponding analog-measured literature data [8, 34, 36, 37, 38, 39, 40, 41, 42] are shown in blue. The data for ${}^{18}\mathrm{O}$ have been shifted up by 1 barn for visibility. The lower three panels show residuals between our data and the literature data shown in the upper panels.

Figure 10

Neutron ${\sigma }_{\mathrm{tot}}$ for ${}^{103}\mathrm{Rh}$: Our results and literature data. In panel (a), our digitizer-measured results are shown in red and corresponding analog-measured literature data [10] are shown in blue. Panel (b) shows the residuals between our data and the literature data, where they exist.

Figure 11

${}^{16,18}\mathrm{O}$, ${}^{58,64}\mathrm{Ni}$, ${}^{112,124}\mathrm{Sn}$ neutron ${\sigma }_{\mathrm{tot}}$ relative differences from our measurement. In each panel, the colored bands indicate regions of $1\sigma$ uncertainty due to target thickness imprecision (blue) and from both target thickness and statistics (red). The gray dashed lines show the prediction for the ${\sigma }_{\mathrm{tot}}$ relative difference per the strongly absorbing sphere (SAS) model of Eq. (1), which assumes a simple $A^{\frac{1}{3}}$ size scaling for the nuclear radius. The gray dotted lines show the SAS model prediction but with an $A^{\frac{1}{6}}$ size scaling. The black dash-dotted lines shows the ${\sigma }_{\mathrm{tot}}$ relative differences from the median parameter values of the O, Ni, and Sn DOM analyses performed in this work (detailed in the following section).

Figure 12

${}^{16}\mathrm{O}$: Constraining experimental data and DOM fit. See introduction of Appendix pp3 for description.

Figure 13

${}^{18}\mathrm{O}$: Constraining experimental data and DOM fit. See introduction of Appendix pp3 for description.

Figure 14

${}^{40}\mathrm{Ca}$: Constraining experimental data and DOM fit. See introduction of Appendix pp3 for description.

Figure 15

${}^{48}\mathrm{Ca}$: Constraining experimental data and DOM fit. See introduction of Appendix pp3 for description.

Figure 16

${}^{58}\mathrm{Ni}$: Constraining experimental data and DOM fit. See introduction of Appendix pp3 for description.

Figure 17

${}^{64}\mathrm{Ni}$: Constraining experimental data and DOM fit. See introduction of Appendix pp3 for description.

Figure 18

${}^{112}\mathrm{Sn}$: Constraining experimental data and DOM fit. See introduction of Appendix pp3 for description.

Figure 19

${}^{124}\mathrm{Sn}$: Constraining experimental data and DOM fit. See introduction of Appendix pp3 for description.

Figure 20

${}^{208}\mathrm{Pb}$: Constraining experimental data and DOM fit. See introduction of Appendix pp3 for description.