Nuclear properties for astrophysical and radioactive-ion-beam applications (II)

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Abstract

We tabulate the ground-state odd-proton and odd-neutron spins and parities, proton and neutron pairing gaps, one- and two-neutron separation energies, quantities related to β-delayed one- and two-neutron emission probabilities, average energy and average number of emitted neutrons, β-decay energy release and half-life with respect to Gamow–Teller decay with a phenomenological treatment of first-forbidden decays, one- and two-proton separation energies, and α-decay energy release and half-life for 9318 nuclei ranging from  16O to  339136 and extending from the proton drip line to the neutron drip line. This paper is a new and improved version of Atomic Data And Nuclear Data Tables [66 131 (1997)]. The starting point of our present work is the new study (FRDM(2012)) of nuclear ground-state masses and deformations based on the finite-range droplet model and folded-Yukawa single-particle potential published in a previous issue of Atomic Data And Nuclear Data Tables [109–110, 1 (2016)]. The β-delayed neutron-emission probabilities and Gamow–Teller β-decay rates are obtained from a quasi-particle random-phase approximation with single-particle levels and wave functions at the calculated nuclear ground-state shapes as input quantities. A development since 1997 is we now use a Hauser–Feshbach approach to account for (n, γ) competition and treat first-forbidden decay in a phenomenological approach.

Introduction

In a previous issue of Atomic Data and Nuclear Data Tables we presented a calculation of nuclear ground-state masses and deformations for 9318 nuclei ranging from 16O to 339136 and extending from the proton drip line to the neutron drip line [1]. The new version of the finite-range droplet model and folded-Yukawa single-particle potential that was the basis for this calculation is referred to as the FRDM(2012); the year indicates the time when the mass table was finalized, not the year of publication, which could not be foreseen when the manuscript material was put together. We use these ground-state masses and deformations as starting points for calculations of additional ground-state properties that are useful for astrophysical, radioactive-ion-beam, and other applications.

An important feature of a mass model is its reliability for nuclei beyond the region used for the determination of the model constants. In particular, can one expect the model to be reliable for nuclei very far from β-stability and in the region of superheavy elements? In the more than 20 years since the FRDM(1992) was finalized it has proven to be reliable beyond expectation for predicting properties of subsequently discovered nuclei, see for example Refs. [[2], [3]].

In our mass paper [1] we addressed again the FRDM(1992) model reliability for new regions of nuclei by comparing predictions of masses that were not included in the data set to which the model constants were determined to the newest experimental data in AME2012 [4]. There are 720 new masses in this evaluation that were not in the evaluation to which the FRDM(1992) was adjusted. The model error for these 720 new nuclei was found to be 0.5817 MeV compared to 0.669 MeV error in the region of 1654 nuclei to which it was adjusted. In this study no increase in deviations far from stability were observed. The FRDM(2012) cannot be tested against that many new nuclei. However, we did a simulation and adjusted it to the same data set as was used for FRDM(1992) and checked the resulting mass table against the same 720 new nuclei. For these nuclei the model error was considerably reduced, only 0.4948 MeV (Figs. 13 and 14 in Ref. [1]).

We also observed that the FRDM(2012) showed almost no staggering in the neutron separation energy contour lines at Sn=1,2,3, and 4 MeV, (Fig. 8 in Ref. [1]). Furthermore, the fluctuations in the error at neutron magic numbers N=82 and N=126 are much smaller in FRDM(2012) than in FRDM(1992) (Fig. 6 in Ref. [1]) Both of these developments should be beneficial in r-process studies. A first study [5] supports this expectation.

Thus, because the FRDM(2012) represents a significant improvement over FRDM(1992) we present new calculations, similar to those in Ref. [6], but with FRDM(2012) as a starting point, of additional nuclear ground-state properties based on the same model and the same values of model constants, for the same set of 9318 nuclei considered in our mass calculation [1]. Specifically, we consider the following quantities:

The details of the calculations are given in Section 2. The β-decay half-lives and β-delayed neutron-emission probabilities are obtained from a quasi-particle random-phase approximation (QRPA) [7] and first-forbidden decays accounted for in a phenomenological treatment [8]. In the QRPA the single-particle energies and wave functions at the calculated ground-state deformation serve as the starting point. The pairing gaps are obtained in a Lipkin–Nogami microscopic pairing model. The odd-particle spins are obtained as the spin of the last occupied level, when this level is occupied by a single nucleon. Separation energies and energy releases are readily obtained from mass differences. However, there are several reasons to include them in the tabulated data. In a study devoted to nuclear structure far from stability, the presentation would be very incomplete if one-neutron and two-neutron separation energies were not immediately available, together with the other tabulated quantities. Also, the tabulated half-lives depend strongly on the energy released in these decays, so it is only natural to tabulate the half-lives together with the associated energy releases. The delayed neutron-emission probabilities Pνn depend in a complex way on nuclear structure, on the energy released in the β decay, and on the neutron-separation energies in the daughters of the decay. Therefore, it is also natural to tabulate these quantities together. Because of nuclear pairing, the two-neutron and two-proton drip lines occur in different locations than those for one-neutron and one-proton separation energies, so it is useful to tabulate both of these quantities. Finally, we have found that in discussions on far-from-stability topics, it is highly useful to have available material approximately as selected here, namely color overview graphs, and Table 1 of calculated quantities. In fact, before we had these readily available we often noticed their need in deliberations on far-from-stability topics.

In Ref. [6] we wrote: “Our nuclear-structure models provide additional quantities that are too extensive to be made available in printed form. These include (1) calculated single-particle levels at each nuclear ground-state deformation, which are useful for microscopic level-density calculations, (2) β-decay rates between a vast number of states in the mother and daughter nuclei, and (3) additional minima in the potential-energy surface, with associated deformations and excitation energies. We are currently exploring how to provide convenient electronic access to these results”. By now we have actually published in printed form in a recent issue of Atomic Data and Nuclear Data Tables [9] point (3) above in a study of shape isomers. The selected results that we present here are described further in Section 3.

We briefly assess in Section 4 the reliability of the FRDM(1992), FRDM(2012) and of some other models that are also commonly used in astrophysical and radioactive-ion-beam calculations. Calculations of r-process abundances [5] have already used calculated β-decay half-lives and delayed neutron-emission probabilities (but without neutron-γ competition) and from our mass calculation FRDM(2012) [1] show considerable improvements compared to earlier work.

Section snippets

Calculational details

The quantities studied in this paper are obtained in four different ways.

  • 1.

    The odd-proton spin and parity Ωpπ, odd-neutron spin and parity Ωnπ, proton pairing gap ΔLNp, and neutron pairing gap ΔLNn are microscopic quantities obtained simultaneously with the calculated ground-state masses and deformations. They were not published in our mass paper because of space limitations.

  • 2.

    The one-neutron separation energy S1n, two-neutron separation energy S2n, ground-state to ground-state β-decay energy

Tabulated results

Deformed single-particle models provide the starting point for the calculations of nuclear ground-state masses and deformations, which were extensively discussed in our previous paper [1]. Since nuclear wave functions are also provided by these models, one may also use these models to determine electromagnetic moments and transition rates, β-strength functions, β-decay half-lives, and β-delayed neutron-emission probabilities.

The results of our calculations of many such nuclear properties

Extrapability

The usefulness of the results presented in Table 1 for various simulations is closely connected to how the model behaves when applied to nuclei outside the region where model parameters were determined. In 1997 we investigated in a previous version of this paper [6] how a number of mass models, including the FRDM performed in this respect. We find it unnecessary to perform an extensive study of mass models here, except for a few comments on our new FRDM(2012).

Acknowledgments

The initial versions of the codes used to calculate β-decay properties were written in collaboration with J. Krumlinde during three years more than 30 years ago, 1980–1983 [27]. We are grateful for discussions of the results presented here with K.-L. Kratz, S. Nishimura, J. Wu, and G. Lorusso. This work was carried out under the auspices of the NNSA of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396.

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