Total neutron cross-sections for rare isotopes using a digital-signal-processing technique: Case study 48Ca

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Abstract

A digital-signal-processing method was developed and used to measure the total neutron cross-sections of 48Ca from 15 to 300 MeV. This technique allows for cross-sections to be obtained with high statistical accuracy even for samples that are an order of magnitude smaller than those used with conventional (non-digital) techniques. The isotopic and energy dependence of rare-isotope total neutron cross-sections are of considerable value for extracting the n/p asymmetry dependence of optical-model potentials.

Introduction

The complex optical-model potential is a compact representation of the physics required to explain both the elastic-scattering observables (differential cross-sections, analyzing powers and spin rotations) and the inelastic-scattering cross-sections. The interplay between the refracting real potential (which is responsible for the bulk of the elastic scattering) and the absorbing imaginary potential (accounting for all the inelastic processes) generates the angular-dependent observables as well as the evolution of cross-sections with incident energy.

By the fitting of large data sets, the parameters of the optical potential can be extracted [1]. By enforcing causality, a dispersive version of the optical model (DOM) can be generated [2]. The energy dependence of the real potential reports on the effective mass; a device capturing the nucleon–nucleon (N–N) correlation effects. (It is the effective mass that captures the non-localities of the interaction, which lead, in part, to the understanding that the N–N interaction is momentum dependent.) On the other hand, it is the energy dependence of the imaginary potential that reports on the spectroscopic strength or (via integration over energy) the single-particle occupation probabilities. The latter differ from the expectations of an extreme single-particle model, again due to the fact that nuclei are correlated many-body systems.

The evolution of the in-medium (N–N) correlations with n/p asymmetry has attracted considerable attention in the recent years [3]. It has been argued that n/p asymmetry effects are strong [3] or weak [4], [5] functions of the binding energy of the nucleon. Results from nucleon-knock-out reactions, with radioactive beams, make the case that the more strongly bound nucleon, the greater the suppression of single-particle strength [3]. The DOM results are more subtle and indicate a weaker trend, which likely depends on the relative importance of the various low-lying collective excitations and the parity of the particles and holes that can be generated near the Fermi surface.

While there are some notable gaps in the isotopically resolved data for proton reaction cross-sections, the database for total neutron cross-sections of separated isotopes is far from complete. For example, the NNDC reaction database does not contain total neutron cross-sections σtot(n), covering a broad energy range, for the N=28 isotones (i.e. 48Ca, 50Ti, 52Cr or 54Fe), the Ni isotopes, the Sn isotopes, the N=50 or N=82 isotones. As has been shown in standard optical-model analyses (as well as DOM work) such data, often presented as isotopic differences to reduce systematic errors [6], [7], [8], provide sensitivity to the isovector components of the potential. One can view the collection of such data as an effort complementary to the collection of nucleon knock-out cross-sections and transfer reaction data [9] using radioactive beams.

The main problem with measuring σtot(n) on separated isotopes is the need for a substantial amount of target material (significant fractions of a mole) that must be of high isotopic purity. The present work presents a technique (based on digital-signal processing) that significantly lowers the amount of target material needed. The case study for this work is 48Ca (one of the interesting cases mentioned above). Our sample was only 0.056 of a mole, with an inverse areal density of 35 b/atom. This areal density is about 10 times less than conventionally used. Furthermore, we show that the technique we developed would be better suited to even smaller samples than we used in this initial study. This allows for a program of measuring rare (stable) isotope σtot(n) throughout the periodic table.

Section snippets

Beam and sample characteristics

Our source of neutrons was the Los Alamos Neutron Science Center (LANSCE) WNR facility [10], [11]. The LANSCE beam structure is shown in Fig. 1. A proton beam of 800 MeV with an average intensity of 2 μA bombarded a tungsten target producing a white (i.e. continuous energy) source of neutrons. The proton pulses (referred to as micropulses) are less than 1 ns in width and were repeated at 1.8 μs intervals for a period for 625 or 725 μs (referred to as a macropulse). The macropulse was repeated at 60 

Analysis

There are two sources of time uncertainty to consider: the precision of the time measurement of any given peak, and the offset of each macropulse relative to the digitizer clock. The former is an issue for each pulse while the latter must be determined only once for each macropulse.

Two procedures were used to improve the precision of the time of each peak. The first method employed a fit of each peak contained in a peaklet (see Fig. 4). The fit used the convolution of a Maxwell–Boltzmann

Results

The total neutron cross-sections for natC and 40Ca are shown in Figs. 8(a) and 9(a). The percent deviations from the published values of Ref. [7] are shown in Figs. 8(b) and 9(b), for the dead-time corrected and the uncorrected data. Fig. 10 shows both calcium cross-sections along with the available literature data, which is scarce and limited to low energies for 48Ca [15], [16].

The relative cross-section difference between the two calcium isotopes is shown in Fig. 11 for the two extreme cases

Discussion

Due to computer limitations, we adopted a compromise of storing a small fraction of the full waveforms and regions around each peak (the peaklets) determined by a simple algorithm. Analysis of just the peaklets misses some pulses, however the sampling of the full waveform could be used to generate the required correction. This compromise generates data with high statistical significance and, with correction, reproduced known cross-sections with an RMS deviation of 2.6% (carbon) and 2.9%

Conclusions

The total neutron cross-section for 48Ca has been measured by using a digital-signal-processing technique over a large energy domain. A compromise strategy was employed that skirts the need for massive front-end computational power working in real time and makes optimal use of the beam-pulse structure at LANSCE. This technique makes feasible a program for the determination of σtot(n), over a broad intermediate-energy region, for rare stable isotopes throughout the chart of the nuclides.

Acknowledgments

We would like to thank the entire management team of the National Superconducting Cyclotron Laboratory (NSCL) for their help in arranging the loan of the 48Ca sample. We further acknowledge the assistance of John Yurkon (of the NSCL) in the preparation of the target. This work was supported by the US Department of Energy, Division of Nuclear Physics under Grant DE-FG02-87ER-40316 (WU), and has benefited from the use of the Los Alamos Neutron Science Center, operated by Los Alamos National

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