Two-proton Decay Research Articles

Beyond the proton drip line: Bayesian analysis of proton-emitting nuclei

The limits of the nuclear landscape are determined by nuclear binding energies. Beyond the proton drip lines, where the separation energy becomes negative, there is not enough binding energy to prevent protons from escaping the nucleus. Predicting properties of unstable nuclear states in the vast territory of proton emitters poses an appreciable challenge for nuclear theory as it often involves far extrapolations. In addition, significant discrepancies between nuclear models in the proton-rich territory call for quantified predictions. With the help of Bayesian methodology, we mix a family of nuclear mass models corrected with statistical emulators trained on the experimental mass measurements, in the proton-rich region of the nuclear chart. Separation energies were computed within nuclear density functional theory using several Skyrme and Gogny energy density functionals. We also considered mass predictions based on two models used in astrophysical studies. Quantified predictions were obtained for each model using Bayesian Gaussian processes trained on separation-energy residuals and combined via Bayesian model averaging. We obtained a good agreement between averaged predictions of statistically corrected models and experiment. In particular, we quantified model results for one- and two-proton separation energies and derived probabilities of proton emission. This information enabled us to produce a quantified landscape of proton-rich nuclei. The most promising candidates for two-proton decay studies have been identified. The methodology used in this work has broad applications to model-based extrapolations of various nuclear observables. It also provides a reliable uncertainty quantification of theoretical predictions.

Two-proton Radioactivity: the Interesting Case of \(^{67}\)Kr and Further Studies

We report on the observation of Kr-67 that has been produced in an experiment performed at the RIKEN/BigRIPS facility. The two-proton decay of Kr-67 has been evidenced and this nucleus is thus the fourth observed long lived ground-state two-proton emitter, after Fe-45, Ni-48 and Zn-54. In addition, the decay of several isotopes in the mass region has been investigated. While for previous cases of two-proton radioactivity, the theoretical models could reproduce the measured data, this is not the case anymore for Kr-67. Two interpretations have been proposed to explain this discrepancy: a transition between real two-proton and sequential decay or the influence of deformation. These hypotheses will be tested in future experiments by measuring the angular and energy correlations of the emitted protons.

An empirical formula for the half-lives of exotic two-proton emission

An empirical formula is proposed for the two-proton decay half-lives. This study is an extension of the empirical formula reported recently by us for calculating the logarithmic half-lives of one-proton emitters. A similar four-parameter formula as a function of angular momentum is proposed for the two-proton emitters. The parameters of the formula are fitted using the results of the effective liquid drop model (ELDM). The obtained formula is found to agree fairly well with the known experimental values of the half-lives as well as with other theoretical model predictions. Apart from the experimentally known 2-p emitters, the results using the formula are found to compare well within an order magnitude with the results of the ELDM. Further calculations are carried out in the heavy and superheavy region for the prediction of one and two-proton emitters.

Two-Proton Virtual Decay of the 19Mg Nucleus in the Superfluid Model

The two-stage two-proton virtual nuclear decay theory and superfluid atomic nucleus model are used to investigate the total and partial widths, and the angular distributions of the emitted protons, for the two-proton diagonal virtual decay of the ground state of the $${}^{{19}}{\text{Mg}}$$ nucleus into the ground state of the 17Ne nucleus. It is shown there is a set of parameters of the proton shell potential and superfluid proton–proton interaction for which the calculated total width of the two-proton decay of the $${}^{{19}}{\text{Mg}}$$ nucleus agrees with its experimental value.

Angular Distributions of Protons for the Two-Proton Decay of Superfluid Nuclei and Diproton Correlations

The approach proposed by A.B. Migdal for describing the virtual singlet diproton state is used to show the effect diproton decay channel has on the width and the angular distribution of emitted protons in the two-proton decay of a parent 45Fe nucleus is negligible. A conclusion is reached on the leading role of the two-stage virtual mechanism of the two-proton decay of the abovementioned nucleus, which corresponds to the sequential emission of two uncorrelated protons and is described in terms of the multiparticle shell nuclear model with allowance for superfluid nucleon–nucleon correlations.

Observation of β-delayed 2He emission from the proton-rich nucleus 22Al

The β-delayed two-proton emission from 22Al was investigated experimentally through the implantation-decay method. A β-delayed two-proton decay branch from 22Al were identified based on the coincidence of the charged particles and γ-ray signals. The relative momentum (qpp) and the opening angle (θpp) distributions of the two β-delayed protons are measured and a strong peak at qpp∼20MeV/c, as well as a peak at θpp∼30∘ are observed clearly. The β-delayed 2He emission from 22Al with a probability of 29 (13)% by fitting the experimental data with the results of Monte Carlo simulations.

Spin alignment following inelastic scattering of Ne17 , lifetime of F16 , and its constraint on the continuum coupling strength

The sequential two-proton decay of the second excited state in $^{17}\mathrm{Ne}$, produced by inelastic excitation at intermediate energy, is studied. This state is found to be highly spin aligned, providing another example of a recently discovered alignment mechanism. The fortuitous condition that the second decay step is slightly more energetic than the first, permits the lifetime of the one-proton daughter, the ground state of $^{16}\mathrm{F}$, to be determined from the magnitude of the final-state interactions between the protons. This new method gave a result [$\mathrm{\ensuremath{\Gamma}}=20.6(57)$ keV] consistent with that obtained by directly measuring the width of the state [$\mathrm{\ensuremath{\Gamma}}=21.3(51)$ keV]. This width allows one to determine the continuum coupling constant in this mass region. Real-energy continuum-shell-model studies yield a satisfactory description of both spectra and widths of low-energy resonances in $^{16}\mathrm{F}$ and suggest an unusual large ratio of proton-proton to proton-neutron continuum couplings in the vicinity of the proton drip line.

Search for 2p Decay of the First Excited State of 17 Ne

Structure of nuclei located near and beyond the drip-lines plays important role in the explosive astrophysical processes. The problem of two-proton decay of the 17Ne first excited state is a good example of such situation. The two-proton radiative capture is a possible bypass of the 15O waiting point in the rp-process. The rate of this process drastically depends on the value of the weak 2

A calculation model to half-life estimate of two-proton radioactive decay process

Partial half-life of the radioactive decay by the two-proton emission mode has been estimated for proton-rich nuclei of mass number $ 18 < A < 68$ by a model based on the quantum mechanical tunneling mechanism through a potential barrier. The Coulomb, centrifugal and overlapping contributions to the barrier have been considered within the spherical nucleus approximation. The present calculation method has been shown to be adequate in reproducing the existing experimental half-life data for 19Mg, 45Fe, 48Ni, and 54Zn 2p-emitter nuclides within a factor six. For 67Kr parent nucleus the calculated partial 2p-decay half-life has been found to be ten times greater than the recent, unique measured value at RIKEN Nishina Center. Prediction for new, yet unmeasured cases of two-proton radioactivity are also reported.

Spectroscopy of excited states of unbound nuclei Ar30 and Cl29

Several states of proton-unbound isotopes $^{30}$Ar and $^{29}$Cl were investigated by measuring their in-flight decay products, $^{28}$S+proton+proton and $^{28}$S+proton, respectively. A refined analysis of $^{28}$S-proton angular correlations indicates that the ground state of $^{30}$Ar is located at $2.45^{+0.05}_{-0.10}$ MeV above the two-proton emission threshold. The theoretical investigation of the $^{30}$Ar ground state decay demonstrates that its mechanism has the transition dynamics with a surprisingly strong sensitivity of the correlation patterns of the decay products to the two-proton decay energy of the $^{30}$Ar ground state and the one-proton decay energy as well as the one-proton decay width of the $^{29}$Cl ground state. The comparison of the experimental $^{28}$S-proton angular correlations with those resulting from Monte Carlo simulations of the detector response illustrates that other observed $^{30}$Ar excited states decay by sequential emission of protons via intermediate resonances in $^{29}$Cl. Based on the findings, the decay schemes of the observed states in $^{30}$Ar and $^{29}$Cl were constructed. For calibration purposes and for checking the performance of the experimental setup, decays of the previously-known states of a two-proton emitter $^{19}$Mg were remeasured. Evidences for one new excited state in $^{19}$Mg and two unknown states in $^{18}$Na were found.

Phenomenological features of two-proton virtual decay of the 45Fe nucleus

On the basis of the theory of diagonal two-proton two-step virtual decays of spherical nuclei that was developed earlier and the superfluid model of the nucleus, the total and partial widths for the two-proton decay of the 45Fe parent nucleus in the ground state to the ground state of the 43Cr daughter nucleus were calculated along with the angular distribution of protons emitted in this decay. The calculated features of this mode of 45Fe decay were shown to be highly sensitive to the choice of form for nucleon shell potentials. It is also shown that there exists a potential such with which one can construct a successful simultaneous description of the experimental total width and the angular distribution of emitted protons for the aforementioned two-proton mode of decay of the 45Fe nucleus.

Search for 2p decay of the first excited state of Ne17

Two-proton decay of the $^{17}$Ne low-lying states populated in the $^1$H($^{18}$Ne,$d$)$^{17}$Ne transfer reaction was studied. The two-proton width $\Gamma_{2p}$ of the $^{17}$Ne first excited $3/2^-$ state at $E^*=1.288$ MeV is of importance for the two-proton radioactivity theory and nuclear-astrophysics applications. A dedicated search for the two-proton emission of this state was performed leading to the new upper limit obtained for the width ratio $\Gamma_{2p}/\Gamma_{\gamma} < 1.6(3) \times 10^{-4}$. A novel, "combined mass" method is suggested and tested capable to improve the resolution of the experiment which is a prime significance for the study of nuclear states with extremely small particle-to-gamma width ratios $\Gamma_{\mathrm{part}}/\Gamma_{\gamma}$. The condition $\Gamma_{\mathrm{part}} \ll \Gamma_{\gamma}$ is quite common for the states of astrophysical interest which makes the proposed approach promising in this field.

Spectroscopy at the two-proton drip line: Excited states in 158W

Excited states have been identified in the heaviest known even-ZN=84 isotone 158W, which lies in a region of one-proton emitters and the two-proton drip line. The observation of γ-ray transitions feeding the ground state establishes the excitation energy of the yrast 6+ state confirming the spin-gap nature of the α-decaying 8+ isomer. The 8+ isomer is also expected to be unbound to two-proton emission but no evidence for this decay mode was observed. An upper limit for the two-proton decay branch has been deduced as b2p≤ 0.17% at the 90% confidence level. The possibility of observing two-proton emission from multiparticle isomers in nearby nuclides is considered.

Entanglement of 0p-, 1s0d- and 1p0f-shell nucleon pairs

The entanglement of pure states of the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-shell nucleon pairs has been studied. The von Neumann entropy of the partial density matrix has been employed to quantify the entanglement of the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-shell nucleon pairs. The Slater decomposition theorem has been used to verify if any pure state of a nucleon pair is an entangled state. Results of calculations have evidenced that a dominant part of the isospin [Formula: see text] proton–neutron states of the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-shell nucleon pairs, respectively, are strongly entangled. It is shown that the calculated data are a source of valuable information on the spin quantum numbers of the entangled protons from two-proton decay.

Transition from direct to sequential two-proton decay in s–d shell nuclei

Transitions among different mechanisms of two-proton decay are studied in general. The introduced improved direct-decay model generalizes the semi-analytical models used before and provides flawless phenomenological description of three-body correlations in $2p$ decays. This is demonstrated by examples of the low-lying $^{16}$Ne state decays. Different forms of transition dynamic are shown to be highly probable beyond the proton dripline for the $s$-$d$ shell nuclei. It is demonstrated that transition dynamic of $2p$ emitters can provide means for extraction of a width of the ground-state resonance of a core+$p$ subsystem of the core+$2p$ system. Practical applicability of the method is demonstrated by properties of the $^{14}$F ground state derived from the $^{15}\mbox{Ne}\rightarrow ^{\,13\!\!}\mbox{O}+2p$ decay data and of the $^{29}$Cl ground state derived from the $^{30}\mbox{Ar}\rightarrow ^{\,28\!\!}\mbox{S}+2p$ decay data.

Numerical approach of some three-body problems

On taking the two-proton decay in nuclear physics as a sample case we formulate a numerical method for three-body problems which are mathematically described by systems of coupled 2d Schrödinger equations in polar coordinates r,ϕ. With some minimal adaptations the method becomes applicable on other cases. The specific feature of the procedure consists in a shuttle propagation along r: two quantities are propagated, the log-derivative matrix and the solution itself, with a backwards propagation of the former, followed by a forwards propagation of the latter. The results show remarkable stability. Numerical illustrations from a simple test model are reported and we also explain how the data obtained in this way can be exploited to obtain useful physical information.

Continuum spectroscopy of light nuclei

Resonance spectroscopy of light nuclei is discussed with emphasis on the invariant-mass measurements performed with the HiRA detector. For three-body exit channels, we consider the exact conditions necessary such that the decay can be described as either sequential or prompt. However experimentally, we find some cases where the decay is intermediate between these two limits. Finally, two-proton decay from isobaric analog states is discussed.

Observation and Spectroscopy of New Proton-Unbound Isotopes ³⁰Ar and ²⁹Cl: An Interplay of Prompt Two-Proton and Sequential Decay.

Previously unknown isotopes (30)Ar and (29)Cl have been identified by measurement of the trajectories of their in-flight decay products (28)S+p+p and (28)S+p, respectively. The analysis of angular correlations of the fragments provided information on decay energies and the structure of the parent states. The ground states of (30)Ar and (29)Cl were found at 2.25(-0.10)(+0.15) and 1.8±0.1 MeV above the two- and one-proton thresholds, respectively. The lowest states in (30)Ar and (29)Cl point to a violation of isobaric symmetry in the structure of these unbound nuclei. The two-proton decay has been identified in a transition region between simultaneous two-proton and sequential proton emissions from the (30)Ar ground state, which is characterized by an interplay of three-body and two-body decay mechanisms. The first hint of a fine structure of the two-proton decay of (30)Ar*(2(+)) has been obtained by detecting two decay branches into the ground and first-excited states of the (28)S fragment.

Interplay between sequential and prompt two-proton decay from the first excited state ofNe16

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Theoretical models for exotic nuclei

We review various theoretical models which have been used to study the properties of the ground state and excited states of nuclei close to and beyond the neutron and proton drip lines. The validity and limitations of these models are discussed with applications to recent experimental findings such as di-neutron correlations in Borromian nuclei, the soft dipole excitations, direct two-neutron and two-proton decays, and odd-even staggerings of reaction cross sections. The role of isoscalar spin-triplet pairing interaction is also pointed out in the low-lying energy spectra as well as the spin- and isospin-dependent decay rates for N = Z and N = Z + 2 nuclei with mass A < 60. A characteristic feature of the Coulomb energy displacement of the Borromian nucleus 11Li is discussed in connection to the energies of isobaric analogue states (IAS) of T = 5/2 multiples in the A = 11 systems.