Two-proton Decay Research Articles

Investigation of two-proton decay using modified formation probability

In this study, we investigated two-proton radioactivity using the two-potential approach with a cosh-type potential to calculate the half-lives. The depth parameter V0 = 58.405 MeV and diffuseness a = 0.537 fm in the cosh-type nuclear potential show the lowest standard deviation between the calculated and experimental half-lives. We proposed a linear formula for the formation probability using the linear relationship between log10S2p and A1/3d for the angular momentum state l = 0, 2 and 4. The model achieved the lowest standard deviation (σ = 1.09) using this linear formula compared to previous models and empirical formulas. The proposed formula significantly improved the accuracy of half-life predictions by reducing the standard deviation from 1.73 to 1.09. The predicted half-lives exhibit a hindrance factor in the range of -1.62 to 2.42, which is the lowest compared to earlier theoretical predictions. These results indicate that the proposed linear formation probability formula is suitable for reproducing experimental half-lives. The linear formula for formation probability was generalized for different angular momentum states by conducting least squares fit. We extended the half-life and formation probability predictions to 48 nuclei, and the predicted half-lives are in good agreement with the previous five theoretical models and two empirical formula predictions.

Possible 2p Decay Emission in the Region 4 ≤ Z ≤ 54 Using the Modified CYE Model

Two proton radioactivity is the spontaneous emission of two protons simultaneously from the nucleus. We have extended our CYE model to study this 2p radioactivity. The current work aims to study the 2p radioactivity of nuclei between Z ≥ 4 to Z ≤ 54 . Moreover, the impact of a deformation of the nucleus is also examined. To comprehend two-proton decay, numerous theoretical works have been developed. The half lifetimes for 2p decays calculated using this CYE model are in a good accord with CPPMDN model of K.P. Santhosh, GLDM, ELDM, GLM, Sreeja et al. and Liu et al. and SEB, SHF and UFM. From whence, it appears that the CYE model is a reasonable choice for assessing 2p radioactivity.

Microscopic investigation of one- and two-proton decay from the excited states of 10C

We present microscopic cluster model calculations for the 1p and 2p decays of the 02+ and 22+ states of 10C. With the R-matrix method, we have estimated the decay widths. The obtained 1p and 2p decay widths are in good agreement with the recent experimental data and support the validity of the di-proton approximation for the 2p decay of 10C(02+). We also show the suppression of the 1p decay of the 10C(02+) state due to the structure mismatch with the decay channel.

An empirical formula for the half-lives of one- and two-proton radioactivity

We have proposed an empirical formula for one- and two-proton decays, including the angular momentum term. While investigating the first term in the Viola–Seaborg formula, we found a linear relationship between the logarithmic half-life and the expression [Formula: see text] for each angular momentum state. Furthermore, we obtained a linear relationship between the slope and intercept as functions of the angular momentum (l). Using these relations, we proposed a generalized empirical formula for the half-lives of one- and two-proton radioactivity for all angular momentum states. We analyzed the accuracy of the formula predictions by computing the standard deviation between the predicted and experimental decay half-lives. For the decay of one proton, the standard deviation of the proposed formula is 0.389, while that of the generalized formula is 0.400. These values represent the lowest standard deviations compared to previous models and the empirical formula. In the case of two-proton decay, the standard deviation for the current formula is 1.31, and the generalized formula also exhibits a lower standard deviation of 1.32. This lowest standard deviation value indicates that the proposed formula is suitable for reproducing the experimental half-life. We extended the half-life predictions to another 207 nuclei for one-proton decay and 42 nuclei for two-proton decay cases, which are energetically possible. The estimated half-lives for both one- and two-proton decays agree well with other theoretical predictions.

An empirical formula for the two-proton decay half-lives in the ground and excited states

We proposed an empirical formula for the half-life of two proton emissions in the ground and excited states. The proposed empirical formula has a half-life dependence on the Q-value and the atomic number of the parent, similar to the Geiger-Nuttall law and the Viola and Seaborg formula. The half-lives of 6Be, 12O, 16Ne, 19Mg, 45Fe, 48Ni, 54Zn, and 67Kr nuclei are calculated using the present empirical formula. The empirical formula has the lowest standard deviation with experimental data (σ=1.39) compared to previously predicted formulas, indicating that the formula can reproduce the experimental half-lives well. The predictions of the half-lives are made for another 56 nuclei whose two-proton emission is energetically feasible (Q2P>0). These half-life values are compared with five theoretical models and two empirical formulas. The predicted half-lives are in good agreement with other theoretical predictions. The predicted half-lives of two-proton emission in the excited states of 14O⁎, 17,18Ne⁎, 22Mg⁎, 29S⁎, and 94Ag⁎ nuclei are compared with the experimental half-lives and also with different models' and formulas' predictions. The experimentally observed half-lives of the excited states are better reproduced using the proposed formula compared with previous theoretical predictions. Only the proposed formula can reproduce the experimental half-lives of 94Ag⁎ in excited states.

Roles of tensor force and pairing correlation in two-proton radioactivity of halo nuclei* *Supported by the National Natural Science Foundation of China (U1832120, 11675265), the Natural Science Foundation for Outstanding Young Scholars of Hebei Province, China (A2020210012), the Natural Science Foundation of Hebei Province, China (A2021210010), the Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy

The tensor force and pairing correlation effects on the two-proton radioactivity of Mg and Si with a pronounced two-proton halo are explored in the framework of spherical Skyrme-Hartree-Fock-Bogoliubov theory. It is shown that the halo sizes are enhanced with the increase in the strength of the tensor force and pairing correlation. Furthermore, the increasing halo sizes lead to the enhancement of diproton emission. Then, the tensor force is found to have a small influence on the two-proton decay energies, and the two-proton decay energies calculated with strong surface pairing are smaller than those with weak mixed pairing. Because the two-proton decay energies are relatively large, the predicted order of magnitude of half-lives within the effective liquid drop model is not sensitive to the decay energy variation caused by the tensor force and pairing correlation, which has a value of approximately 10 s.

Observation of a Strongly Isospin-Mixed Doublet in ^{26}Si via β-Delayed Two-Proton Decay of ^{26}P.

β decay of proton-rich nuclei plays an important role in exploring isospin mixing. The β decay of ^{26}P at the proton drip line is studied using double-sided silicon strip detectors operating in conjunction with high-purity germanium detectors. The T=2 isobaric analog state (IAS) at 13 055keV and two new high-lying states at 13 380 and 11 912keV in ^{26}Si are unambiguously identified through β-delayed two-proton emission (β2p). Angular correlations of two protons emitted from ^{26}Si excited states populated by ^{26}P β decay are measured, which suggests that the two protons are emitted mainly sequentially. We report the first observation of a strongly isospin-mixed doublet that deexcites mainly via two-proton decay. The isospin mixing matrix element between the ^{26}Si IAS and the nearby 13 380-keV state is determined to be 130(21)keV, and this result represents the strongest mixing, highest excitation energy, and largest level spacing of a doublet ever observed in β-decay experiments.

Nucleon–nucleon correlations in the extreme oxygen isotopes

There has been an upsurge of interest in two-nucleon decays thanks to the studies of nucleon–nucleon correlations. In our previous work (2021 Phys. Rev. Lett. 126 142501), based on a novel time-dependent three-body approach, we demonstrated that the energy and angular correlations of the emitted nucleons can shed light on the structure of nucleonic pairs formed inside the nucleus. In this work, we apply the new framework to study the decay dynamics and properties of some extreme proton-rich and neutron-rich oxygen isotopes, including two-proton (2p) decays of 11,12O and two-neutron (2n) decay of 26O. Here we show that the low-ℓ components of 11,12O wave functions, which are affected by continuum and configuration-interaction effects, strongly impact decay dynamics and asymptotic correlations. In the calculated wave functions of 11,12O, diproton and cigarlike structures merge together during the tunneling process and the resulting energy and angular correlations are very consistent with the experimental data. The asymptotic correlations of the 2n decay of 26O dramatically change as the 2n decay energy approaches the zero-energy threshold. The small reported value of Q 2n suggests that the 2n decay of this nucleus can be understood in terms of the universal phase-space limit.

The Nuclear Shell Model towards the Drip Lines

Applications of configuration-mixing methods for nuclei near the proton and neutron drip lines are discussed. A short review of magic numbers is presented. Prospects for advances in the regions of four new “outposts” are highlighted: 28O, 42Si, 60Ca and 78Ni. Topics include shell gaps, single-particle properties, islands of inversion, collectivity, neutron decay, neutron halos, two-proton decay, effective charge, and quenching in knockout reactions.

New narrow resonances observed in the unbound nucleus F15

The structure of the unbound F15 nucleus is investigated using the inverse kinematics resonant scattering of a radioactive O14 beam impinging on a CH2 target. The analysis of H1(O14,p)O14 and H1(O14,2p)N13 reactions allowed the confirmation of the previously observed narrow 1/2− resonance, near the two-proton decay threshold, and the identification of two new narrow 5/2− and 3/2− resonances. The newly observed levels decay by 1p emission to the ground of O14, and by sequential 2p emission to the ground state of N13 via the 1− resonance of O14. Gamow shell model (GSM) analysis of the experimental data suggests that the wave functions of the 5/2− and 3/2− resonances may be collectivized by the continuum coupling to nearby 2p- and 1p-decay channels. The observed excitation function H1(O14,p)O14 and resonance spectrum in F15 are well reproduced in the unified framework of the GSM.Received 1 December 2021Accepted 7 April 2022DOI:https://doi.org/10.1103/PhysRevC.105.L051301©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNuclear reactionsNuclear structure & decaysResonance reactionsProperties6 ≤ A ≤ 19Nuclear Physics

Proton decay spectroscopy of S28 and Cl30

States in S28 and Cl30 have been studied using one- and two-proton decay spectroscopies. In the first spectrometer setting, states in S28 were populated following one-neutron knockout from a fast S29 beam. Three new states are observed in S28 from one- and two-proton decays. For the two-proton case the nature of the decay was investigated and found to proceed via sequential two-proton emission. For the second setting, states in Cl30 were populated via one-proton knockout from a fast Ar31 beam. The decay energy of the ground and first excited state were measured with the ground-state decay energy found to be in disagreement with a previous measurement. The spin and parity of these two Cl30 states were inferred from shell-model calculations.Received 2 February 2022Accepted 5 April 2022DOI:https://doi.org/10.1103/PhysRevC.105.044321©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNuclear spin & parityProton emissionUnstable nuclei induced nuclear reactionsProperties20 ≤ A ≤ 38Nuclear Physics

On the masses of A = 54 isospin septet and the isobaric multiplet mass equation * *Supported in part by the National Key R&D Program of China (2018YFA0404401, 2016YFA0400504), National Natural Science Foundation of China (11975280, 11905259)

Using the ground-state mass of 52Ni and two-proton decay energy of 54Zn, the ground-state mass excess of 54Zn is deduced to be –6504(85) keV. This value is about 2 MeV lower than the prediction of the quadratic form of the isobaric multiplet mass equation (IMME). A cubic fit to the existing mass data of the , isospin multiplet yields a surprisingly large d coefficient of IMME, i.e., , being deviated from zero, and the resultant ratio significantly deviates from the systematics. This phenomenon is analyzed in this study, and we conclude that the breakdown of the quadratic form of IMME could be likely due to the mis-assignment of the isobaric analog state (IAS) in the nucleus 54Fe or extremely strong isospin mixing.

Two-proton emission systematics

The simultaneous emission of two protons is an exotic and complex three-body process. It is very important for experimental groups investigating the nuclear stability on the proton drip line to have a simple rule predicting the two-proton decay widths with a reasonable accuracy for transitions between ground as well as excited states in terms of relevant physical variables. In spite of its complexity, we show that the two-proton emission process obeys similar rules as for binary emission processes like proton, alpha and heavy cluster decays. It turns out that the logarithm of the decay width, corrected by the centrifugal barrier, linearly depends upon the Coulomb parameter within one order of magnitude. On the other hand, the universal linear dependence with a negative slope between the logarithm of the reduced width and the fragmentation potential, valid for any kind of binary decay process, is also fulfilled for the two-proton emission with a relative good accuracy. As a consequence of pairing correlations the two protons are simultaneously emitted from a singlet paired state. We evidence that indeed one obtains a linear dependence between the logarithm of the reduced width and pairing gap within a factor of two, giving a good predictive power to this law. It turns out that the diproton and alpha-cluster formation probabilities have similar patterns versus the pairing gap, while in the one-proton case one has a quasi-constant behavior.

Two-proton decay from α -cluster states in C10 and N11

Two-proton decay from excited states in $^{10}\mathrm{C}$ and $^{11}\mathrm{N}$ has been characterized from an analysis of the $2p+2\ensuremath{\alpha}$ and $3p+2\ensuremath{\alpha}$ exit channels. Data from four previously published invariant-mass studies associated with inelastic excitation, multinucleon knockout, and neutron pickup reactions have been considered. A rotational band in $^{10}\mathrm{C}$ was identified built on the second ${0}^{+}$ state which has strong $\ensuremath{\alpha}$-cluster molecular structure. The members of this band were tentatively identified up to ${J}^{\ensuremath{\pi}}={4}^{+}$ and all identified states have a prompt $2p$ decay branch. The spins of the ${0}^{+}$ and ${2}^{+}$ members were deduced from comparisons of the momentum correlations in their $2p$ branches to those from known $2p$ emitters. The ${2}^{+}$ and the tentative ${4}^{+}$ members are both above the $\ensuremath{\alpha}$ threshold and exhibit large reduced decay widths for $\ensuremath{\alpha}$ emission. This band exhibits a similar moment of inertia to its analog in the mirror nucleus $^{10}\mathrm{Be}$. Evidence is also presented for a molecular band in $^{11}\mathrm{N}$ built on the second $3/{2}^{\ensuremath{-}}$ state which $2p$ decays. Tentative members of this band have been assigned up to ${J}^{\ensuremath{\pi}}=9/{2}^{\ensuremath{-}}$ and their excitation energies also match their likely analogs in the mirror nucleus $^{11}\mathrm{Be}$.

Using spin alignment of inelastically excited nuclei in fast beams to assign spins: The spectroscopy of O13 as a test case

Excited states in 13O were investigated using inelastic scattering of an E/A=69.5-MeV 13O beam off of a 9Be target. The excited states were identified in the invariant-mass spectra of the decay products. Both single proton and sequential two-proton decays of the excited states were examined. For a number of the excited states, the protons were emitted with strong anisotropy where emissions transverse to the beam axis are favored. The measured proton-decay angular distributions were compared to predictions from distorted-wave born-approximation (DWBA) calculations of the spin alignment which was shown to be largely independent of the excitation mechanism. The deduced $^{13}$O level scheme is compared to ab initio no-core shell model with continuum (NCSMC) predictions. The lowest-energy excited states decay isotropically consistent with predictions of strong proton 1s1/2 structure. Above these states in the level scheme, we observed a number of higher-spin states not predicted within the model. Possibly these are associated with rotational bands built on deformed cluster configurations predicted by antisymmetrized molecular dynamics (AMD) calculations. The spin alignment mechanism is shown to be useful for making spin assignments and may have widespread use.

β -delayed two-proton decay of S27 at the proton-drip line

The β-delayed two-proton (β2p) decay of S27 was studied using a state-of-the-art silicon array and Clover-type HPGe detectors. An energy peak at 6372(15) keV with a branching ratio of 2.4(5)% in the decay-energy spectrum was identified as a two-proton transition via the isobaric-analog state in P27 to the ground state of Al25 in the β decay of S27. Two-proton angular correlations were measured by the silicon array to study the mechanism of two-proton emission. Based on experimental results and Monte Carlo simulations, it was found that the main mechanism for the emission of β2p by S27 is of sequential nature.Received 3 March 2021Accepted 21 May 2021DOI:https://doi.org/10.1103/PhysRevC.103.L061301©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBeta decayLifetimes & widthsNuclear structure & decaysProton emissionProperties20 ≤ A ≤ 38Nuclear Physics

Fermion Pair Dynamics in Open Quantum Systems.

Three-body decay is a rare decay mode observed in a handful of unbound rare isotopes. The angular and energy correlations between emitted nucleons are of particular interest, as they provide invaluable information on the interplay between structure and reaction aspects of the nuclear open quantum system. To study the mechanism of two-nucleon emission, we developed a time-dependent approach that allows us to probe emitted nucleons at long times and large distances. We successfully benchmarked the new method against the Green's function approach and applied it to low-energy two-proton and two-neutron decays. In particular, we studied the interplay between initial-state nucleon-nucleon correlations and final-state interaction. We demonstrated that the time evolution of the two-nucleon wave function is strongly impacted by the diproton/dineutron dynamics and that the correlations between emitted nucleons provide invaluable information on the dinucleon structure in the initial state.

Virtual Double Beta Decays of Nuclei

A theory of nuclear $$2{\beta }$$ decay that includes $$2{{{\beta }}^{ - }}$$ , $$2{{{\beta }}^{ + }}$$ , $${{{\beta }}^{ + }},EC$$ , and $$EC,EC$$ decays is constructed using results obtained in developing the theory of the two-proton decay of nuclei. The existence of two types of these decays is established. The first type corresponds to $$2{\beta }$$ decays that proceed via two sequential real $${\beta }$$ decays of a parent nucleus and the compound nucleus generating from the parent nucleus. The second type is associated with the virtual nature of $$2{\beta }$$ decays, the widths of which are described by formulas similar to the ones obtained earlier in the second order of perturbation theory in the Hamiltonian of weak interaction. The possibility is demonstrated of successfully describing experimental characteristics of the $$2{\beta }$$ decay for a wide range of nuclei.

Continuum and three-nucleon force in Borromean system: The 17Ne case

Starting from chiral two-nucleon (2NF) and chiral three-nucleon (3NF) potentials, we present a detailed study of 17Ne, a Borromean system, with the Gamow shell model which can capture continuum effects. More precisely, we take advantage of the normal-ordering approach to include the 3NF and the Berggren representation to treat bound, resonant and continuum states on equal footing in a complex-momentum plane. In our framework, 3NF is essential to reproduce the Borromean structure of 17Ne, while the continuum is more crucial for the halo property of the nucleus. The two-proton halo structure is demonstrated by calculating the valence proton density and correlation density. The astrophysically interesting 3/2− excited state has its energy above the threshold of the proton emission, and therefore the two-proton decay should be expected from the state.

New Class of Nuclear Decays Involving Virtual States of Intermediate Nuclei

Nuclear reactions and decays belonging to a new class referred to as a virtual class since virtual intermediate states of $$A\geqslant 2$$ atomic nuclei at off-shell energies are involved in the amplitude of the widths with respect to such processes are studied by considering examples of two-proton and double-beta decays of nuclei, as well as spontaneous ternary fission of even–even actinide nuclei. The widths and angular distributions are calculated for two-protom decays of nuclei, and the half-lives of nuclei with respect to double-beta decay are also determined. The radii of the neck in fissioning nuclei and the heat of the binary fission of the intermediate nucleus in the ground state for spontaneous ternary fission of $${}^{248}$$ Cm, $${}^{250}$$ Cf, and $${}^{252}$$ Cf nuclei are estimated.