Evaluation of theoretical conversion coefficients using BrIcc

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Abstract

A new internal conversion coefficient database, BrIcc has been developed which integrates a number of tabulations on internal conversion electron (ICC) and electron–positron pair conversion coefficients (IPC), as well as Ω(E0) electronic factors. A critical review of general formulae and procedures to evaluate theoretical ICC and IPC values are presented, including the treatment of uncertainties in transition energy and mixing ratio in accordance with the Evaluated Nuclear Structure Data File. The default ICC table, based on the Dirac–Fock calculations using the so called “Frozen Orbital” approximation, takes into account the effect of atomic vacancies created in the conversion process. The table has been calculated for all atomic shells and to cover transition energies of 1–6000 keV and atomic numbers of Z=5–110. The software tools presented here are well suited for basic nuclear structure research and for a range of applications.

Introduction

Internal conversion coefficients provide important information about the atomic nucleus. Through comparison of experimental values with corresponding theoretical ones, multipolarities and mixing ratios of nuclear transitions are determined. As well as nuclear structure research, knowledge of accurate coefficients is needed, for example, in the determination of total transition rates (required for the normalization of decay schemes), Mössbauer spectroscopy (CEMS) [1], nuclear reaction calculations [2], or decay heat calculations of spent nuclear reactor fuel cells [3].

There is a long history of generation and improvements of theoretical internal conversion coefficient tables. The most recent calculations, based on the relativistic self-consistent Dirac–Fock (DF) method [4], [5] represent a major advance in the improvement of the accuracy of the theoretical coefficients, which now challenges experiments at the percent level [6].

To make the new theoretical values accessible for a very broad user community a new internal conversion coefficient database called BrIcc has been developed [7], which is now adopted by the International Nuclear Structure and Decay Data (NSDD) network [8] for all new data evaluations published in Nuclear Data Sheets and Nuclear Physics A. In this paper, we describe the data tables and procedures used to obtain conversion coefficients for pure and mixed multipolarity transitions for a given atomic number, transition energy, atomic shell, multipolarity and mixing ratio. The procedures are fully compliant with the ENSDF coding rules [9], [10]. BrIcc has been primarily implemented as a nuclear structure data evaluation tool and can be downloaded freely at the NNDC website [11]. A web interface, powered by a simplified (silent) version of the program is currently hosted by the Australian National University [12]. Further details can be found in the program manual [11] which will be updated to reflect future changes.

Section snippets

Specifying nuclear transitions in the ENSDF format

The Evaluated Nuclear Structure Data File, is a computer-based file system, which is maintained by the National Nuclear Data Center at Brookhaven National Laboratory. The content of the file is regularly updated by the NSDD network. For each isotopes the ENSDF file usually contains a number of data sets. Each data set refers to a particular reaction or decay mode of a nucleus. The adopted level and gamma-ray properties are given in the adopted data set [10]. Here we only give a brief

Calculation of conversion coefficients

The conversion coefficient, αic is defined as the ratio of the electron emission rate (Tic) to the gamma emission rate (Tγ):αic=Tic/Tγ.Depending on the electron shells involved it is customary to define conversion coefficients for sub-shells (αL1,αL2, etc.) or for major shells (αK, αL, etc.). Similarly, the conversion coefficient involving electron–positron pair emission (Tπ) is defined asαπ=Tπ/Tγ.For transitions between spin zero states of the same parity, 0i+0f+ (or 0i-0f-), the emission of

Data tables

The main features of the data tables used by BrIcc are summarized in Table 2 and will be discussed below. The BrIccFO and BrIccNH electron conversion coefficient data tables (Section 4.1), based on the DF model [4] have been specifically calculated here. Additional tables on electron conversion coefficients (HsIcc and RpIcc; Section 4.2), on electron–positron pair conversion coefficients (ScPcc and HoPcc; Section 4.3) and on Ω(E0) electronic factors (HsOmg, BeOmg and PaOmg; Section 4.4) were

Implementation of BrIcc

The motivation to develop the program BrIcc[11] was to provide a tool for ENSDF evaluators to derive conversion coefficients according to the procedures outlined in Section 2. As an evaluation tool the program uses an ENSDF data file [10] and will prepare new GAMMA records with calculated conversion coefficient(s). A detailed report file is also created, which is designed to assist the evaluator, for example, to remove or change the new GAMMA records, before in the second step they will be

Summary

BrIcc is a generic tool to evaluate theoretical conversion coefficients for pure and mixed multipolarity transitions. The different implementations of the program are suited to a wide range of applications, including nuclear structure research and data evaluations, as well as software applications using conversion coefficients. The treatment of multipolarities, mixing ratios and uncertainties fully complies with the procedures adopted for the ENSDF. The default data table is based on the new DF

Acknowledgments

Many thanks for members of the NSDD network for helping to develop and to test the BrIcc program. We would like to thank Dr. A.L. Nichols (IAEA) for his continuing interest and support of the project. The authors wish to thank Prof. G.D. Dracoulis for his critical reading of the manuscript. The work was supported in part by the U.S. Department of Energy, under Contract No. DE-AC02-98CH10886.

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