Data analysis techniques for extracting Gamow–Teller strengths from (p,n) data

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Abstract

Techniques are described to obtain absolute normalizations for Gamow–Teller strength functions from (p,n) spectra. A method using data taken at two different proton energies and a method using polarization transfer data are discussed. Both methods require determining the number of counts due to the Fermi transition which is usually not completely resolved. We discuss methods for normalizing to unresolved Fermi peaks and handling peak shapes encountered in real time-of-flight spectra.

Introduction

Structure overlap matrix elements for the Gamow–Teller (GT) operator between various nuclear states provide particularly interesting nuclear structure information because these matrix elements simply and directly show the relationships between the quantum states of neutrons and of protons in nuclei. Beyond the inherent nuclear structure interest in measuring strengths of GT matrix elements there are applications of GT measurements in neutrino physics and in astrophysics. Neutrino detection by absorption of neutrinos on nuclei occurs through Fermi and GT transitions, and some detection schemes rely exclusively on GT transitions. Some steps in astrophysical nucleosynthesis occur through electron absorption and emission in GT transitions. The density of hot electrons in a stage of supernova explosions is controlled by electron capture into GT states.

Beta decay is without question the most reliable way to measure GT matrix elements. However, its applicability is very limited and, in particular, it is not useful for measuring GT giant resonances or GT transitions involved in some neutrino detectors.

Charge-exchange reactions offer an alternative without the energy limitations of beta decay. However, reaction theory does not have the precision required to convert reaction cross-sections to GT matrix elements with the desired accuracy.

An attempt to bypass the uncertainties of reaction calculations by comparing (p,n) cross-sections to beta decay information is explored in an early paper [1] and explored more fully in a classic paper on the use of (p,n) reactions to measure GT strengths [2]. In Ref. [2] it is shown that the specific GT cross-section does not have a smooth dependence on the nuclear mass number. Therefore, even if specific cross-sections have been measured in neighboring nuclei above and below the mass of an unmeasured nucleus, one cannot reliably interpolate an accurate value for the specific cross-section for an unmeasured nucleus.

On the other hand, the ratio of the specific GT cross-section to the specific Fermi cross-section seems to have no apparent dependence on the nuclear mass but shows a smooth and steep dependence on the proton bombarding energy [2]. By specific cross-section we mean the cross-section divided by the Fermi or GT matrix element squared. As the Fermi transition is seen in all (p,n) spectra from targets with a neutron excess, and the Fermi strength is conserved by the virtue of the Conserved Vector Current (CVC) hypothesis [3], the possibility of obtaining GT strengths by normalizing to the Fermi transition is generally applicable.

This observation provides a recipe for determining GT strengths from a (p,n) spectrum only if the Fermi contribution to the spectrum can be unfolded. Several kinds of complications arise in handling real data. For nuclei with spin greater than zero the IAS transition may contain both F and GT strength. The Fermi peak may lie on a dense background of GT transitions. The underlying GT background may be highly structured precluding an interpolation of a smooth background under the Fermi peak. In addition a quasi-free background may overlap the region of the IAS. We have developed two methods for extracting the Fermi contribution from a complex underlying background.

Section snippets

Description of the method

As we have already mentioned and as is pointed out in Ref. [2] the specific GT and Fermi cross-sections vary significantly between different nuclei even for adjacent mass numbers. Thus, we cannot use globally or locally averaged specific cross-sections for extracting GT strengths from (p,n) cross-sections. In Ref. [2] it is also pointed out that the ratio of the GT specific cross-section to the Fermi specific cross-section at a fixed proton energy is the same for all nuclei but has a strong

Using polarization transfer data

In this technique we make use of the fact that the Fermi operator contains no spin operator. Therefore, if the incident protons are polarized, the neutrons of the Fermi component in the spectrum must have the same polarization as the incident protons. Expressed in terms of the transverse polarization transfer coefficient, DNN=+1.

In a typical experiment with a neutron polarimeter using left–right scattering geometry with, for example, transverse polarization, the proton spin is reversed

Conclusions

We have demonstrated a method of obtaining GT matrix elements from (p,n) spectra that bypasses the theoretical uncertainties of reaction calculations and the experimental uncertainties of measuring absolute cross-sections. We have discussed test cases and shown applications to nuclei considered for neutrino detection where no prior information from beta decay exists.

Acknowledgements

This work was supported by the United States National Science Foundation and the United States Department of Energy. One of us, P.Z., wishes to thank Polish State Committee for Scientific Research for partial support. Many people have contributed to the data taking in the (p,n) project at the Indiana University Cyclotron Facility and it is not practical to list the names here. Among those who contributed were collaborators from Indiana University, Ohio University, Los Alamos National

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