Magnitude factor systematics of Kalbach phenomenology for reactions emitting helium and lithium ions

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Abstract

We investigated the magnitude factor of the Kalbach phenomenology in order to estimate double differential cross-sections (DDXs) of (p, 3He), (p, 4He), (p, 6Li) and (p, 7Li) reactions at intermediate energies that is several hundreds of MeV. Firstly, we obtained DDXs on target nuclei, Be, C and Al by using a 392-MeV proton beam. Secondly, the magnitude factor has been formulated and parameterized by using the present data and Ag data measured elsewhere. Although the slope parameters of the magnitude factor were found to be independent of targets, absolute values are dependent. The magnitude factor shows a consistency between heavy targets, Al and Ag. In contrast, considerable different tendencies are seen for the light targets. As a result, it has been remarked that the present parameterization is of highly useful in yield estimation for experimental planning of light charged particle production reactions. It allows us to conduct such experiments with the higher efficiency.

Introduction

There is an increasing demand on nuclear data of charged particles in an energy range above a few hundreds of MeV. Since light charged particles (LCPs) such as helium and lithium ions have relatively large stopping power dE/dx, they play a key role in the single-event upset of semiconductors, radiation damages of material, and the DNA double-strand breaks. Double differential cross-sections (DDXs) of LCP production reactions induced by intermediate-energy protons are, therefore, needed for deeper insight of these phenomena.

There are some databases, which compile DDX data of LCP productions. The typical one is the database of JENDLE 3.3 [1] covering an energy range below 20 MeV. Nuclear data up to 150 MeV are compiled in the LA150 library [2]. In the energy range above 150 MeV, measured data are scarce. Spectral DDXs were measured for (p,Li) and other reactions on an Ag target by Green et al. [3] at TRIUMF. As far as we know, they are the only data available at around 400 MeV. In regard to theoretical calculations, the EXCITON model [4] and the QMD model [5] have been developed to describe LCP production reactions. Although TALYS [6] and GNASH [7] are most popular calculation codes based on the EXCITON model, both of them are valid in the incident energy regime up to around 150 MeV. Above 100 MeV, the QMD model has been proved effective [8], [9], [10] for nucleon productions. Although QMD was believed to own a substantial predictive ability for LCP productions, it was pointed out [10] in recent years that it underestimates DDXs of LCP productions. It can be concluded that there is no reliable tool providing DDX of LCP productions above 150 MeV, and therefore, there is an urgent need for its measurements.

In this context, our collaboration has started toward measurements in an incident energy range of 200–650 MeV. For a detailed planning of experiments, it is essential to know cross-sections for estimating how long the beam time is needed. To this end, we investigate systematics of the Kalbach phenomenological equation [11] which predicts angular distributions with relative magnitudes of DDXs. The emission energy dependence of the magnitude factor was investigated [12] for 58Ni(p,p) reactions between 100 and 200 MeV, and no more efforts were made so far. The aim of the present work is to parameterize the magnitude factor of the Kalbach phenomenological equation for (p, 3He), (p, 4He), (p, 6Li) and (p, 7Li) reactions as function of emission energy. It is also essential to investigate its target mass dependence. Treating lithium emission reactions is also the first attempt, since the phenomenology was investigated on reactions emitting particles ranging from protons to helium-4 ions.

Section snippets

Experiment and data

The cross-section data listed in Table 1 were used for the present parameterization. Data on a silver target were measured by Green et al. [3] at TRIUMF. The rest of data for p+9Be, 12C and 27Al reactions were measured at RCNP presently.

In the RCNP experiment, protons were accelerated up to 392 MeV and bombarded a target. Helium and lithium ions emitted from reactions were detected by three counter telescopes consisting of two silicon surface barrier detectors of 50 and 2000μm thick. Detectors

Analyses and discussion

An expression including hyperbolic functions was introduced by Kalbach [12] as the formula for describing angular distributions of nuclear reactions. We focus ourselves within the multi-step direct reaction, since it should be the dominant component of our data which cover the ejectile energy range above 10 MeV [12], [13]. The multi-step direct term for an (a,b) reaction is expressed byd2σdΩdEb=Mηsinhηexp(ηcosθ)where θ is the center-of-mass scattering angle. The parameter η for

Conclusion

We investigated and obtained the magnitude factor systematics for the Kalbach equation in order to estimate absolute cross-sections of reactions with beam energies of around 400 MeV. Energy distributions of (p, He) and (p, Li) reactions were measured on Be, C and Al targets at RCNP using a 392-MeV proton beam. Reasonable shape agreements have been accounted for with the original parameter set for angular distributions. It has been observed that the slope parameter ξ of magnitude factor can be

Acknowledgement

This research was partly supported by the Grant-in-Aid for Scientific Research, Ministry of Education, Science, Culture and Sports, Grant No. 17360460.

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