We calculate the decay rates lambda_(beta^-_c) and lambda_(beta^-_b) of the continuum- and bound-state beta^- decays for bare 205Hg80+ and 207Tl81+ ions. For the ratio of the decay rates R_(b/c) = lambda_(beta^-_b)/lambda_(beta^-_c) we obtain the values R_(b/c) = 0.161 and R_(b/c) = 0.190 for bare 205Hg80+ and 207Tl81+ ions, respectively. The theoretical value of the ratio R_(b/c) = 0.190 for the decays of 207Tl81+ agrees within 1% of accuracy with the experimental data R^exp_(b/c) = 0.188(18), obtained at GSI. The theoretical ratio R_(b/c) = 0.161 for 205Hg80+ is about 20% smaller than the experimental value R^exp_(b/c) = 0.20(2), measured recently at GSI.
The spectral shape of the electrons from the two first-forbidden unique beta- decays of Ar-39 and Ar-42 were calculated for the first time to the next-to-leading order. Especially the spectral shape of the Ar-39 decay can be used to characterise this background component for dark matter searches based on argon. Alternatively, due to the low thresholds of these experiments, the spectral shape can be investigated over a wide energy range with high statistics and thus allow a sensitive comparison with the theoretical predictions. This might lead to interesting results for the ratio of the weak ve…
Forbidden (slow) beta decays offer new opportunities to test the invariance of the weak interaction under Lorentz transformations. Within a general effective field theory framework we analyze and reinterpret the only two relevant experiments, performed in the 1970s, dedicated to search for a preferred direction in space in first- and second-forbidden beta decays. We show that the results of these experiments put strong and unique limits on Lorentz violation, and in particular on the presence of several interactions in the modern Lorentz-violating Standard Model extension. We discuss prospects …
It is shown that differences, due to charge-dependent effects, in the 17N and 17Ne ground-state wave functions account for the fact that the experimentally measured branch for the beta+ decay of 17Ne to the first excited state of 17F is roughly a factor of two larger than expected on the basis of nuclear matrix elements which reproduce the corresponding beta- branch in the decay of 17N.
The planned rhenium beta-decay experiment MARE might probe the absolute mass scale of neutrinos with the same sensitivity as the tritium beta-decay experiment KATRIN, which will start data taking in 2011 and will proceed for five years. We present the energy distribution of emitted electrons for the first unique forbidden beta-decay of 187Re. It is found that the p-wave emission of electron dominates over the s-wave. By assuming mixing of three neutrinos the Kurie function for the rhenium beta-decay is derived. It is shown that the Kurie plot near the endpoint is within a good accuracy linear …
The nucleus 54Mn has been observed in cosmic rays. In astrophysical environments it is fully stripped of its atomic electrons and its decay is dominated by the beta- branch to the 54Fe ground state. Application of 54Mn based chronometer to study the confinement of the iron group cosmic rays requires knowledge of the corresponding halflife, but its measurement is impossible at the present time. However, the branching ratio for the related beta+ decay of 54Mn was determined recently. We use the shell model with only a minimal truncation and calculate both beta+ and beta- decay rates of 54Mn. Goo…
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. These days, correlation measurements in nuclear beta decays are intensively studied to probe for signatures for deviations from these symmetries, which are an indication of Beyond Standard Model physics. We show that the structur…
The first-forbidden beta-decay of 17Ne into the 'halo' state J=1/2+ of 17F presents one of the largest measured asymmetries for mirror beta-decay feeding bound final states. This asymmetry is studied in the framework of the Shell Model Embedded in the Continuum (SMEC). The spatial extent of single particle orbits is constrained by the proton capture cross-section 16O(p,gamma)17F calculated in SMEC . This allows to estimate the mirror symmetry breaking in 17F/17O and 17Ne/17N nuclei.
A sensitive search of the 4-fold forbidden non-unique beta decay of V-50 has been performed. A total exposure of 185.8 kg x d has been accumulated. A reliable half-life value with the highest precision so far of $(2.29 \pm 0.25) \cdot 10^{17}$ years of the electron capture decay of V-50 into the first excited state of Ti-50 could be obtained. A photon emission line following the 4-fold forbidden beta decay into the first excited state of Cr-50 could not be observed, resulting in a lower limit on the half-life of the beta decay branch of $1.7 \cdot 10^{18}$ years. This is barely in agreement wi…
R-process nucleosynthesis models rely, by necessity, on nuclear structure models for input. Particularly important are beta-decay half-lives of neutron rich nuclei. At present only a single systematic calculation exists that provides values for all relevant nuclei making it difficult to test the sensitivity of nucleosynthesis models to this input. Additionally, even though there are indications that their contribution may be significant, the impact of first-forbidden transitions on decay rates has not been systematically studied within a consistent model. We use a fully self-consistent covaria…
In this work, the large-scale shell-model calculations for $β$-decay properties have been done. The $β$-delayed $γ$-ray spectroscopy has been performed recently at ILL, Grenoble [M. Si \textit{et al.}, Phys. Rev. C {\bf 106}, 014302 (2022)] to study $β$-decay properties corresponding to $^{137}$Te (($7/2^-))$ $\rightarrow$ $^{137}$I ($J_f$) transitions. We have done a systematic shell-model study for nuclear structure properties and compared the obtained results with the experimental data. Finally, the $β$-decay properties such as the $\log ft$ values and average shape factors have been report…
Calculations are presented for four relatively strong first-forbidden $β$ decays in the region A=11-16 in order to study the very large mesonic-exchange-current enhancement of the rank-zero components. The $μ^-$ capture on $^{16}$O is considered on the same footing. The wave functions utilized include up to 4$\hbarω$ excitations. Two-body exchange-current matrix elements are calculated as well as one-body impulse approximation matrix elements. The resultant enhancement factor that multiplies the impulse-approximation axial-charge matrix element is thereby determined by comparison to experiment…
We propose formulas of the nuclear beta-decay rate that are useful in a practical calculation. The decay rate is determined by the product of the lepton and hadron current densities. A widely used formula relies upon the fact that the low-energy lepton wave functions in a nucleus can be well approximated by a constant and linear to the radius for the $s$-wave and $p$-wave wave functions, respectively. We find, however, the deviation from such a simple approximation is evident for heavy nuclei with large $Z$ by numerically solving the Dirac equation. In our proposed formulas, the neutrino wave …
We have extended the formalism for the two-neutrino double beta decay by including the weak-magnetism term, as well as other second-forbidden corrections. The weak magnetism diminishes the calculated half-lives in $\sim 10%$, independently of the nuclear structure. Numerical computations were performed within the pn-QRPA, for $^{76}Ge$, $^{82}Se$, $^{100} Mo$, $^{128}Te$ and $^{130}Te$ nuclei. No one of the second-forbidden corrections modifies significantly the spectrum shapes. The total reduction in the calculated half lives varies from 6% up to 32%, and strongly depend on the nuclear intera…
We examine time reversal invariance in the beta-decays of 8B(2+) and 8Li(2+) to 8Be(2+) in detail, with particular attention to final state interactions of the two alpha particles from the decay of 8Be, and of the electron (positron) with the daughter nucleus. A R-matrix formulation is used, with the initial state described by a shell model. The R-matrix parameters are obtained by fitting the alpha-αscattering phase shifts and allowed beta-decay rates. Because the nuclear final state interaction effects on the time reversal test come from second forbidden beta-decays, they are small and can be…
A systematic study of the total $β$-decay half-lives and $β$-delayed neutron emission probabilities is performed. The $β$-strength function is treated within the self-consistent density-functional + continuum-QRPA framework including the Gamow-Teller and first-forbidden transitions. The experimental total $β$-decay half-lives for the Ni isotopes with $A\leq$76 are described satisfactorily. The half-lives predicted from $A$=70 up to $A$=86 reveal fairly regular $A$-behaviour which results from simultaneous account for the Gamow-Teller and first-forbidden transitions. For $Z\approx$ 28 nuclei, a…
Current status of experimental investigations of rare single beta decays (48Ca, 50V, 96Zr, 113Cd, 113mCd, 115In, 123Te, 180mTa, 222Rn) is reviewed. Nuclei which decay through single beta decay very often constitute backgrounds in studies of rare effects like double beta decay, solar neutrinos or dark matter. Summary of correction factors used in description of forbidden beta decays is also briefly given.
We discuss the contributions of higher order terms in weak Hamiltonian to the standard two-neutrino double beta decay. The formalism for the unique first forbidden transitions has been developed, and it is shown that they can alter the two-electron energy spectrum. Yet, their effect is too small to screen the detection of exotic neutrinoless double beta decays, which are candidates for testing the physics beyond the standard model.
We point out that lepton number violation is possible even if neutrinos are Dirac particles. We illustrate this by constructing a simple model that allows for lepton number violation by four units only. As a consequence, neutrinoless double beta decay is forbidden, but neutrinoless quadruple beta decay is possible: $(A,Z) \to (A,Z+4) + 4 e^-$. We identify three candidate isotopes for this decay, the most promising one being Nd-150 due to its high $Q_{0ν4β}$-value of 2 MeV. Analogous processes, such as neutrinoless quadruple electron capture, are also possible. The expected lifetimes are extrem…
Neutrinoless double-beta decay is a forbidden, lepton-number-violating nuclear transition whose observation would have fundamental implications for neutrino physics, theories beyond the Standard Model and cosmology. In this review, we summarize the theoretical progress to understand this process, the expectations and implications under various particle physics models, as well as the nuclear physics challenges that affect the precise predictions of the decay half-life. We will also provide a synopsis of the current and future large-scale experiments that aim at discovering this process in physi…
Validation of the effective conversion method in the reactor antineutrino flux calculation is examined using the \textit{ab initio} calculation of the electron and antineutrino spectra from the state-of-the-art nuclear database. It turns out that neglecting the shape variation of beta decay branches between the allowed and forbidden transitions would induce significant bias in the total inverse-beta-decay yields and energy spectral distributions. We propose a new realization of the conversion method with both the allowed and forbidden virtual branches, and apply it to both the \textit{simulate…
A search for the 4-fold forbidden beta decay of \iso{Cd}{113} has been performed with CdZnTe semiconductors. With 0.86 kg $\cdot$ days of statistics a half-life for the decay of $T_{1/2} = (8.2 \pm 0.2 (stat.) ^{+0.2}_{-1.0} (sys.)) \cdot 10^{15}$yrs has been obtained. This is in good agreement with published values. A comparison of the spectral shape with the one given on the Table of Isotopes Web-page shows a severe deviation.
A novel theory of radiative electron capture in second forbidden non-unique transition, is applied to reanalyze experimental data obtained previously for the decay of 59Ni. The measured gamma spectrum is shown to be distorted at the high-energy end, presenting the first direct evidence for the virtual beta-gamma transition through the excited state in 59Co. The complete theoretical predictions, including both the direct and the virtual decay channels, as well as the interference between them, reproduce very well the experimental spectrum. The virtual nuclear component amounts to about 4% of th…
We consider the possibility of Lorentz-invariance violation in weak-decay processes. We present a general approach that entails modifying the W-boson propagator by adding a Lorentz-violating tensor to it. We describe the effects of Lorentz violation on nuclear beta decay in this scenario. In particular we show the expression for a first-forbidden transition with a spin change of two. Using data from an old experiment on the rotational invariance of yttrium-90, we derive several bounds on the Lorentz-violating parameters of the order of 10^(-6)-10^(-8).
Evaluated $2β^{-}(2ν)$ half-lives and their systematics were reexamined in the framework of a phenomenological approach. Decay rate dependence on nuclear deformation, decay energy, shape coexistence, and forbidden transitions was observed. The following analysis showed distinct impacts of decay energy on half-lives and deformation parameters on effective nuclear matrix elements. These findings were used to predict $T_{1/2}$ for 36 isotopes of interest. Present work results were compared with published data.
The 2 nu double beta decay half-lives of six nuclei, whose decays were previously reported as theoretically forbidden, are calculated by including the pairing interaction, which mixes different occupations and opens up the possibility of the decay. All allowed channels for the 0 nu double beta decay are also computed. The estimated 2 nu double beta half-lives suggest that measurements in 244Pu may find positive signals, and that planned experiments would succeed in detecting the 2 nu double beta decay in 160Gd. Limits for the zero neutrino mode, in the analyzed deformed emitters, are predicted…
The half-life of the 2 neutrino double-beta-decay of 160Gd, a process which was previously reported as theoretically forbidden, is estimated by including the pairing interaction, which mixes different occupations and opens channels for the decay. Explicit expressions are presented for the pairing mixing, and for the 2 nu and 0 nu double-beta-decay nuclear matrix elements in the present pseudo SU(3) approach. The estimated double-beta-decay half-lives suggest that the planned experiments would succeed in detecting the 2 nu double-beta-decay in 160Gd, and in putting competitive limits for the ze…
A new approach (called COBRA) for investigating double beta decay using CdTe (CdZnTe) semiconductor detectors is proposed. It follows the idea that source and detector are identical. This will allow simultaneous measurements of 5 $β^-β^-$ - and 4 $β^+β^+$ - emitters at once. Half-life limits for neutrinoless double beta decay of Cd-116 and Te-130 can be improved by more than one order of magnitude with respect to current limits and sensitivities on the effective Majorana neutrino mass of less than 1 eV can be obtained. Furthermore, for the first time a realistic chance of observing double elec…
We report a direct measurement of the Q-value of the neutrinoless double-beta-decay candidate 48Ca at the TITAN Penning-trap mass spectrometer, with the result that Q = 4267.98(32) keV. We measured the masses of both the mother and daughter nuclides, and in the latter case found a 1 keV deviation from the literature value. In addition to the Q-value, we also present results of a new calculation of the neutrinoless double-beta-decay nuclear matrix element of 48Ca. Using diagrammatic many-body perturbation theory to second order to account for physics outside the valence space, we constructed an…
Beta decays of the isotones with N=126 are studied by shell model calculations taking into account both the Gamow-Teller (GT) and first-forbidden (FF) transitions. The FF transitions are found to be important to reduce the half-lives, by nearly twice to several times, from those by the GT contributions only. Possible implications of the short half-lives of the waiting point nuclei on the r-process nucleosynthesis during the supernova explosions are discussed. A slight shift of the third peak of the element abundances in the r-process toward higher mass region is found.
Ab initio calculations of beta-decay half-lives for $N=50$ neutron-rich nuclei
Technische Universität Darmstadt（达姆施塔特工业大学）；ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH（极端物质研究所（EMMI），GSI亥姆霍兹重离子研究中心有限公司）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）；Center for Computational Sciences, University of Tsukuba（筑波大学计算科学中心）
The beta decay process of the 11Li halo nucleus into 9Li and d is studied in a three-body model. The 11Li nucleus is described as a 9Li+n+n system in hyperspherical coordinates on a Lagrange mesh. Various 9Li+d potentials are compared involving a forbidden state, a physical bound state, and a resonance near 0.25 MeV in the s-wave. With an added surface absorption, they are compatible with elastic scattering data. The transition probability per time unit is quite sensitive to the location of the resonance. For a fixed resonance location, it does not depend much on the potential choice at varian…
A microscopic approach to the proton-neutron nuclear response is formulated in the finite-temperature relativistic nuclear field theory framework. The approach is based on the meson-nucleon Lagrangian of quantum hadrodynamics and advances the relativistic field theory for spin-isospin response beyond the finite-temperature random phase approximation. The dynamical contribution to the in-medium proton-neutron interaction amplitude is described in a parameter-free way by the coupling between the single nucleons and strongly-correlated particle-hole excitations (phonons) within the newly develope…
In order to efficiently describe nucleon orbits around a heavy core nucleus, we propose locally peaked Gaussians orthogonalized to the occupied bound states in the core. We show the advantage of those functions in both numerical stability and fast convergence by taking examples of touchstone calcium isotopes $^{62,72}$Ca in $^{60,70}{\rm Ca}+n+n$ three-body models. Both weakly bound configurations and continuum coupling effect are taken into account. We evaluate the neutron radii and the occupation probabilities of two-neutron configurations not only for the ground state but also for some part…
We describe and apply a version of the finite amplitude method for obtaining the charge-changing nuclear response in the quasiparticle random phase approximation. The method is suitable for calculating strength functions and beta-decay rates, both allowed and forbidden, in axially-deformed open-shell nuclei. We demonstrate the speed and versatility of the code through a preliminary examination of the effects of tensor terms in Skyrme functionals on beta decay in a set of spherical and deformed open-shell nuclei. Like the isoscalar pairing interaction, the tensor terms systematically increase a…
As shown in Ref.\cite{Rod09}, the Fermi nuclear matrix element $M^{0ν}_F$ of neutrinoless double beta ($0νββ$) decay can be reconstructed if one is able to measure the isospin-forbidden single Fermi transition matrix element from the ground state of the final nucleus to the isobaric analog state (IAS) of the initial nucleus, for instance by means of charge-exchange reactions of the $(n,p)$-type. Here, simple estimates for $^{82}$Se are made which show that indeed the tiny cross section $σ_{np}(0_f^+\to IAS)$ is dominated by the admixture of the double IAS in the ground state of the final nucle…
We use diagrammatic perturbation theory to construct an effective shell-model operator for the neutrinoless double-beta decay of 82Se. The starting point is the same Bonn-C nucleon-nucleon interaction that is used to generate the Hamiltonian for recent shell-model calculations of double-beta decay. After first summing high-energy ladder diagrams that account for short-range correlations and then adding diagrams of low order in the G matrix to account for longer-range correlations, we fold the two-body matrix elements of the resulting effective operator with transition densities from the recent…
Beta-decay and muon-capture experiments in nuclei are reviewed. The conserved vector current hypothesis is confirmed through the observed constancy of the vector coupling constant determined from the superallowed Fermi transitions and from the measurement of the weak-magnetism term in mirror Gamow-Teller transitions. The axial-vector and pseudoscalar coupling constants in the nucleon are determined from neutron decay and muon capture on the proton respectively. In finite nuclei, evidence for these coupling constants being reduced relative to their free-nucleon values is discussed. Meson-exchan…
We report on a comparison between the theoretically predicted and experimentally measured spectra of the first-forbidden non-unique $β$-decay transition $^{137}\textrm{Xe}(7/2^-)\to\,^{137}\textrm{Cs}(7/2^+)$. The experimental data were acquired by the EXO-200 experiment during a deployment of an AmBe neutron source. The ultra-low background environment of EXO-200, together with dedicated source deployment and analysis procedures, allowed for collection of a pure sample of the decays, with an estimated signal-to-background ratio of more than 99-to-1 in the energy range from 1075 to 4175 keV. I…
The pseudo SU(3) approach has been used to describe many low-lying rotational bands, as well as BE(2) and B(M1) intensities in rare earth and actinide nuclei, both with even-even and odd-mass numbers . The double beta half lives of some of these parent nuclei to the ground and excited states of the daughter ones were evaluated for the two and zero neutrino emitting modes using the pseudo SU(3) scheme. The predictions were in good agreement with the available experimental data for 150Nd and 238U. The double electron capture half-lives of 156Dy, 162Er and 168Yb were also studied using the same f…
The proportionality between single charge-exchange reaction cross sections in the forward direction as found, for example from $(p,n)$ and $(^3$He,$t)$ and from $(n,p)$ and $(d,^2$He) reactions, and the Gamow-Teller (GT) strength into the same final nuclear states has been studied and/or assumed often in the past. Using the most physically justified theory we have at our disposal and for the specific example of the ${}^{76}$Ge-${}^{76}$Se system that may undergo double beta-decay, we demonstrate that the proportionality is a relative good assumption for reactions changing a neutron into a prot…
Measurement of the $^{99}$Tc $β$ spectrum with Silicon Drift Detectors
Università di Milano-Bicocca（米兰比可卡大学）；INFN, Sezione di Milano - Bicocca（意大利国家核物理研究所米兰-比可卡分部）；Politecnico di Milano（米兰理工大学）；INFN, Sezione di Milano（意大利国家核物理研究所米兰分部）；Università degli Studi della Campania “Luigi Vanvitelli”（坎帕尼亚路易吉范维泰利大学）；INFN, Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Università di Catania（卡塔尼亚大学）；INFN – Laboratori Nazionali del Sud (LNS)（意大利国家核物理研究所南部分实验室）；LENA – Laboratorio Energia Nucleare Applicata, Università di Pavia（帕维亚大学应用核能实验室）；Fondazione Bruno Kessler (FBK)（布鲁诺·凯斯勒基金会）
