First-forbidden Decays Research Articles

Competition between allowed and first-forbidden β decays and the r-process

β− decay lifetimes are essential ingredients for r-process yield calculations. In N≈126 r-process waiting point nuclei first-forbidden and allowed β decays are expected to compete. Recent experiments performed at CERN/ISOLDE showed that 207,208Hg decay predominantly via first-forbidden decays. In addition, following on a high statistics study of the β+ /EC decay of 208At, it is suggested that the Z>82, N<126 nuclei provide an excellent testing ground for global calculations addressing the competition between first-forbidden and allowed β decays.

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

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.

Beta spectrum of unique first-forbidden decays as a novel test for fundamental symmetries

Within the Standard Model, the weak interaction of quarks and leptons is characterized by certain symmetry properties, such as maximal breaking of parity and favored helicity. These are related to the V−A structure of the weak interaction. These characteristics were discovered by studying correlations in the directions of the outgoing leptons in nuclear beta decays. Presently, correlation measurements in nuclear beta decays are intensively studied to probe for signatures for deviations from these couplings, which are an indication of Beyond Standard Model physics. We show that the structure of the energy spectrum of emitted electrons in unique first-forbidden β-decays is sensitive to the symmetries of the weak interaction, and thus can be used as a novel probe of physics beyond the standard model. Furthermore, the energy spectrum gives constraints both in the case of right and left couplings of the new beyond standard model currents. We show that a measurement with modest energy resolution of ≈20 keV is expected to lead to new constraints on beyond the standard model interactions with tensor couplings.

Erratum: Effect of first-forbidden decays on the shape of neutrino spectra [Phys. Rev. C91, 025503 (2015)

Received 14 February 2016DOI:https://doi.org/10.1103/PhysRevC.93.049903©2016 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBeta decayPhysical SystemsNeutrinosTechniquesNuclear density functional theoryNuclear Physics

Effect of first-forbidden decays on the shape of neutrino spectra

We examine the effect of First Forbidden (FF) decays on $\beta$-decay neutrino spectra by performing microscopic nuclear structure calculations. By analyzing the FF decay branches of even-even nuclei we conclude that FF decays may be responsible for part of the missing neutrinos in the so called "Reactor Neutrino Anomaly". Further calculations and more experimental data are needed for a firm conclusion.

Evolution of single-particle structure and beta-decay near78Ni

The extended self-consistent beta-decay model has been applied for bet-decay rates and delayed neutron emission probabilities of spherical neutron-rich isotopes near the r-process paths. Unlike a popular global FRDM+RPA model, in our fully microscopic approach, the Gamow-Teller and first-forbidden decays are treated on the same footing. The model has been augmented by blocking of the odd particle in order to account for important ground-state spin-parity inversion effect which has been shown to exist in the region of the most neutron-rich doubly-magic nucleus 78 Ni. Finally, a newly developed form of density functional DF3a has been employed which gives a better spin-orbit splitting due to the modified tensor components of the density functional.

βdecay ofZn81and migrations of states observed near theN=50closed shell

The $\ensuremath{\beta}$ decay of the $N=51$ nucleus $^{81}\mathrm{Zn}$ was studied by means of $\ensuremath{\beta}$-$\ensuremath{\gamma}$ spectroscopy and from isotopically pure beams produced at the Holifield Radioactive Ion Beam Facility (HRIBF). We observe several competing $\ensuremath{\beta}$ transitions populating $^{81}\mathrm{Ga}$ that are interpreted as allowed Gamow-Teller decays to positive parity, core excited states, and first-forbidden decays to negative parity states. The measured $\ensuremath{\beta}$-decay pattern suggests an assignment of ${I}^{\ensuremath{\pi}}=5/{2}^{+}$ for the $^{81}\mathrm{Zn}$ ground state. The systematics of core excited states in $N=50$ isotones indicate a strengthening of the $N=40$ subshell gap near $^{78}\mathrm{Ni}$.

Beta-decay of [formula omitted] nuclei near the [formula omitted] closed neutron shell

Systematic mean-field calculations of the β-decay rates for the nuclei with charge numbers Z = 42 – 49 approaching the possible r-process paths in vicinity of the spherical neutron shell at N = 82 are performed within the DF + CQRPA framework employing a self-consistent approach to the nuclear ground states based on the local energy-density functional (DF) theory. The calculated ground state properties are compared with the available experimental data. The beta-strength-functions of the Gamow–Teller and first-forbidden decays and the total β-decay half-lives are calculated within the continuum QRPA approach. If available, data and half-lives obtained on the basis of the Finite Range Droplet Model and the shell model are compared to our results. The effects of our calculated half-lives on the r-process abundances are explored in local r-process calculations.

Beta-decay rates

Major astrophysical applications involve a huge number of exotic nuclei. Their beta-decay properties play a crucial role in stellar explosive events. An important effort has been developed in last decades to measure the masses and β-decay properties of very neutron-rich nuclei at radioactive nuclear beam facilities. However, most of them cannot be synthesized in terrestrial laboratories and only theoretical predictions can fill the gap. We will concentrate mainly on the β-decay rates needed for stellar r-process modeling and for performing the RNB experiments. An overview of the microscopic approaches to the β-decay strength function is given. The continuum QRPA approach based on the self-consistent ground state description in the framework of the density functional theory is outlined. For the first time, a systematic study of the total β-decay half-lives and delayed neutron emission probabilities takes into account the Gamow–Teller and first-forbidden transitions. Due to the shell configuration effects, the first-forbidden decays have a strong impact on the β-decay characteristics of the r-process relevant nuclei at Z ≈ 28 , N > 50 ; Z ⩾ 50 , N > 82 and Z = 60 – 70 , N ≈ 126 . Suppression of the delayed neutron emission probability is found in nuclei with the neutron excess bigger than one major shell. The effect originates from the high-energy first-forbidden transitions to the states outside the ( Q β − B n ) -window in the daughter nuclei. The performance of existing global models for the nuclides near the r-process paths is critically analyzed and confronted with the recent RIB experiments in the regions of 78Ni, 132Sn and “east” of 208Pb.

Weak interaction rates for astrophysical applications

An important effort has been developed in recent decades to measure the masses and β-decay rates of very neutron-rich nuclei at radioactive ion beam (RIB) facilities. However, major astrophysical applications involve a huge number of exotic species. Most of them cannot be synthesized in terrestrial laboratories and only theoretical predictions can fill the gap. We concentrate on the self-consistent predictions of the β-decay rates needed for stellar r-process modeling and for performing the RIB experiments. The continuum QRPA approach based on the self-consistent ground-state description in the framework of the density functional theory is briefly described. The model for the large-scale calculations of total β-decay half-lives accounts for the Gamow-Teller and first-forbidden transitions. Due to the shell configuration effect, the first-forbidden decays have a strong impact on the total half-lives of the r-process relevant nuclei at N=126, Z=60–70. The performance of existing global models for the nuclides near the r-process paths at N=126 is critically analyzed and confronted with the recent RIB experiments in the region “east” of 208Pb.

Unusual features ofβtransition rates in heavy deformed nuclei

A detailed examination of all the available $\mathrm{log}\phantom{\rule{0.3em}{0ex}}ft$ values for $\ensuremath{\beta}$ transitions in heavy $(A>228)\phantom{\rule{0.3em}{0ex}}\text{nuclei}$ reveals a very similar distribution of these values for the allowed and the first-forbidden decays in this region, in sharp contrast with the observed trends over the whole periodic table. Data for over 500 transitions belonging to both the allowed and forbidden categories are presented in the form of histograms. Physical basis for this unusual behavior is sought by examining the interrelationships between the Nilsson model asymptotic quantum numbers of the $\ensuremath{\beta}$ connected states. Explicit selection rules specific to this region, in terms of these quantum numbers, are proposed and their applicability is demonstrated by citing illustrative examples from the allowed decays of odd-$A$ actinides.

The first-forbidden decays near the r-process paths at N=50, 82, 126

In addition to numerous problems in the quest of the astrophysical site for the r-process, nuclear physics uncertainties of the r-process modeling are still high. For the β-decay rates predictions, they stem mostly from non self-consistency of the nuclear models. Also, the sole consideration of the allowed β-decay commonly used in large-scale microscopic schemes needs to be revised. The first systematic study of the GT and first-forbidden β-decays near the closed neutron shells at N=50, 82, 126 was performed in the self-consistent EDF+CQRPA approach. The importance of the first-forbidden decays for Z≥50, N≈82 nuclei and near N=126 closed shell is shown.

Gamow-Teller and first-forbidden decays near ther-process paths atN=50,82,and126

The $\ensuremath{\beta}$-decay rates of neutron-rich nuclei relevant to the r-process nucleosynthesis are mostly beyond experimental reach. Their predictions demand a self-consistent extrapolation of various nuclear properties away from the experimentally known regions. The allowed transitions approximation commonly used in large-scale microscopic calculations also needs to be revised in different mass regions. The density functional+continuum QRPA approximation to self-consistent calculations of the ground state properties, Gamow-Teller and first-forbidden $\ensuremath{\beta}$-decay transitions of nuclei far from stability is developed. Systematic calculations are performed of the allowed and first-forbidden $\ensuremath{\beta}$-decay rates for the r-process relevant nuclides near the closed neutron shells at $N=50,82,126.$ The importance of first-forbidden decays near $Z>~50,N\ensuremath{\approx}82$ and near $N=126$ is shown. The total $\ensuremath{\beta}$-decay half-lives in the region ``east'' of the ${}^{208}\mathrm{Pb}$ are estimated. A comparison with recent experimental data, global calculations, and self-consistent microscopic predictions is presented.

Nonleptonic weak decays of charmed mesons.

A previous analysis of two-body Cabibbo-allowed nonleptonic decays of [ital D][sup 0] mesons and of Cabibbo-allowed and first-forbidden decays of [ital D][sup +] and [ital D][sub [ital s]][sup +] has been adjourned using more recent experimental data and extended to the Cabibbo-forbidden decays of [ital D][sup 0]. Annihilation and [ital W]-exchange contributions as well as final state interaction effects (assumed to be dominated by nearby resonances) have been included and are in fact crucial to obtain a reasonable agreement with the experimental data, which show large flavor SU(3) violations. New fitting parameters are necessary to describe rescattering effects for Cabibbo-forbidden [ital D][sup 0] decays, given the lack of experimental information on isoscalar resonances. We keep their number to a minimum, three, using phenomenologically based considerations. We also discuss [ital CP]-violating asymmetries.

In-medium and core-polarization effects in 50K(0(-))long-> beta -50Ca(0(+)).

A shell-model calculation in the model space of the (0d,1s) and (0f,1p) major shells is made for the first-forbidden ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}}$ transition $^{50}\mathrm{K}$(${0}^{\mathrm{\ensuremath{-}}}$)${\ensuremath{\rightarrow}}^{50}$Ca(${0}^{+}$). Various truncation schemes were evaluated and the one adopted was to allow at most two neutrons in the \ensuremath{\nu}0${\mathit{f}}_{5/2}$ orbit. An evaluation of the ``final-state'' core-polarization effects is made perturbatively for the two rank-zero matrix elements which contribute to \ensuremath{\Delta}J=0 first-forbidden \ensuremath{\beta} decays. The core-polarization effect is also applicable to \ensuremath{\Delta}J=0 spin-dipole excitations in the A\ensuremath{\approxeq}40 region. Comparison of the shell-model (impulse approximation) prediction to experiment indicates the need for an appreciable in-medium contribution to the timelike component of the weak axial current. The enhancement of 52% found in this comparison is in good agreement with the general trend of predictions for one-pion-exchange processes in \ensuremath{\Delta}J=0 first-forbidden decays in A=16 to 96 nuclei.

Shell-model interpretation of the beta - decay of 212Big, 212Bim1, and 212Bim2.

The ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}}$ decay of the $^{212}\mathrm{Bi}$ ground state (${\mathit{T}}_{1/2}$=61 min) and the isomers $^{212}\mathrm{Bi}^{\mathit{m}1}$ (${\mathit{T}}_{1/2}$=27 min), and $^{212}\mathrm{Bi}^{\mathit{m}2}$ (${\mathit{T}}_{1/2}$=8 min) are considered in the spherical shell model. The wave functions and energy spectra of all even and odd states in the Kuo-Herling model space were calculated for both $^{212}\mathrm{Bi}$ and $^{212}\mathrm{Po}$. Possible candidates for the two $^{212}\mathrm{Bi}$ isomers were located from these results and the allowed and first-forbidden ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}}$ decays rates were formed using a recently developed parametrization of first-forbidden decays in the lead region. It was concluded that $^{212}\mathrm{Bi}^{\mathit{m}1}$ is the yrast ${8}^{\mathrm{\ensuremath{-}}}$ state and $^{212}\mathrm{Bi}^{\mathit{m}2}$ the yrast ${18}^{\mathrm{\ensuremath{-}}}$ state of $^{212}\mathrm{Bi}$. The decay rates calculated for these two ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}}$ emitters are in excellent agreement with experiment. The predictions for the decay of the ground state of $^{212}\mathrm{Bi}$ are not in good agreement with experiment, illustrating the difficulty of calculating weak first-forbidden decay modes reliably.

43K( beta -) 43Ca and the structure of 43K and 43Ca.

The /beta/2) decay of 22 h /sup 43/K (J/sup /pi// = (3/2/sup +/) was reexamined with the main motive of determining the first-forbidden /beta/2) branches to the (3/2/sup -/ and (5/2/sup -/ states more accurately. The branch to the (5/2/sup -/ state at 373 keV was established as 0.9(6)% as opposed to a previous limit of <3%. Other /beta/2) and /gamma/ branching ratios and /gamma/-ray energies were determined with considerably improved accuracy. Shell-model calculations in full (2s,1d)/sup 24/(1f,2p)/sup 3/ and (2s,1d)/sup 23/(1f,2p)/sup 4/ configurational spaces were carried out using the WBMB spherical shell-model interaction. Energy spectra, nucleon pickup spectroscopic factors from /sup 44/Ca, two-nucleon transfer strengths from /sup 41/K, and /gamma/-ray transition rates were calculated for both /sup 43/K and /sup 43/Ca as well as allowed and first-forbidden decays for the known branches in /sup 43/K(/beta/2)) /sup 43/Ca. Results are compared to experiment.

Intruder state collectivity at a double subshell closure from the beta decay of 0- 96Yg to the levels of 96Zr.

Levels of $^{96}\mathrm{Zr}$ populated following the ${\ensuremath{\beta}}^{\mathrm{\ensuremath{-}}}$ decay of the ${0}^{\mathrm{\ensuremath{-}}}$ ground state of $^{96}\mathrm{Y}$ have been investigated by \ensuremath{\gamma}-ray and conversion electron singles, \ensuremath{\gamma}-ray multispectral scaling, \ensuremath{\gamma}-\ensuremath{\gamma} and \ensuremath{\gamma}-${\mathrm{e}}^{\mathrm{\ensuremath{-}}}$ coincidence, and \ensuremath{\gamma}-\ensuremath{\gamma} angular correlation measurements. These data have been used to establish the population of eight excited levels of $^{96}\mathrm{Zr}$, to confirm the ${0}^{+}$ assignment of the 2695-keV level, and to determine a half-life of 5.4(1) s for $^{96}\mathrm{Y}$. The deduced beta transition strengths establish the decay to the ground state, with logft of 5.6, as one of the fastest first-forbidden decays known and support the notion of double subshell closure at Z=40 and N=56. The observed strong hindrance of transitions to excited ${0}^{+}$ states is indicative of shape coexistence. The observed level pattern of the band built on the ${0}_{2}^{+}$ state exhibits similarities to nearby vibrational-like nuclei having four valence protons and four valence neutrons. A four-particle, four-hole interpretation of the ${0}_{2}^{+}$ state is supported by the data, and we determine a deformation parameter, ${\ensuremath{\beta}}_{2}$\ensuremath{\sim}0.2, for this intruder bandhead.

Energy dependence of β-(circularly polarized γ) correlations

An apparatus was constructed for measuring γ-(circularly polarized γ) correlations simultaneously as a function of the β-energy and the angle θ between β- and γ-rays. The circular polarization of the γ-radiation is detected by means of Compton forward scattering. In order to get optimum experimental conditions, two different set-ups were chosen for investigating allowed and first-forbidden β-transitions, respectively. For the study of allowed transitions, a conventional set-up was constructed using a cylindrical magnet and one β-counter only. The experimental set-up for the investigation of first-forbidden transitions consists of two β-counters for the two mean angles θ = 140° and θ = 160° and a 100° cylindrical segment magnet. The β-energy dependence is recorded by a multi-channel analyser divided into four quarters. With the set-up for allowed transitions, the ( υ/ c) dependence of the β-(circularly polarized γ) correlations of the allowed β-transitions of 22Na and 60Co was investigated for the energy range of E β > 44 keV. The results are in good agreement with the predicted υ/ c dependence. With the set-up for first-forbidden decays, the energy dependence of the first-forbidden β-transition of 86Rb was measured.

Beta-Gamma Correlation and Time-Reversal Invariance

The distribution function for the first-forbidden beta-gamma correlation for randomly oriented nuclei, including beta transverse polarization terms, is presented and discussed in connection with the question of time-reversal invariance. Coulomb field effects are included and it is found that even for relatively small $Z$ the time-reversal testing asymmetry is reduced appreciably compared to that calculated for $Z=0$ by Curtis and Lewis. In the limit of high ($\frac{\ensuremath{\alpha}Z}{2R}$), that is, for most first-forbidden decays, a definite relation exists between the ordinary directional correlation asymmetry and the beta polarization-dependent asymmetries. In this approximation it is found that terms which test time-reversal invariance appear in the same manner in all asymmetries but are dominated in general by contributions which do not test time-reversal invariance. For the particular case of ${\mathrm{Au}}^{198}$ it is shown that the experimental results are consistent with time-reversal invariance but are also consistent with an appreciable violation of time-reversal invariance. It is concluded that under favorable conditions it is barely possible that an investigation of the asymmetries for some other beta-gamma cascade could provide a test for time-reversal invariance. However, the extent to which this invariance is or is not violated could not be determined by such an investigation.