arXiv subjects

Long-Jun Wang

Publications and source records attributed to Long-Jun Wang.

At least 19 recordsLinked to original sources

arXiv2026

Projected shell model description of nuclear level density: Collective, pair-breaking, and multiquasiparticle regimes in even-even nuclei

There is overwhelmingly experimental evidence indicating that excited nuclear states are dominated by quasiparticle (qp) excitations, which form many-body configurations with broken nucleon-pairs from different orbitals. By using these multi-qp states as building blocks for a shell-model basis, we propose a novel shell-model method to calculate the nuclear level density (NLD) in deformed nuclei. The shell-model diagonalization with two-body residual interactions yields a large ensemble of eigenstates of angular momentum and parity. We demonstrate that NLD as a statistical quantity depends sensitively on the structure of deformed single-particle states. As the first example to introduce this method, we take a well-deformed rare-earth nucleus, $^{164}$Dy, for which NLD has been studied extensively by the Oslo method. By a quantitative comparison with discrete levels from spectroscopic measurements, we show that while the pronounced stepwise structure in the low-energy NLD curve can be understood as the collective excitation and nucleon-pair breaking, the exponential growth of levels in the higher-energy NLD can be described by the combination of the broken-pair states, subject to the Pauli principle. According to the nature of NLD with increasing excitation, we divide the entire NLD curve into (1) collective regime, (2) pair-breaking regime, and (3) multi-qp regime. We discuss the formation mechanism and characteristic features of NLD for the three regimes. In addition, the parity dependence and angular-momentum dependence in NLD are investigated with a strong emphasis on the structure effect.

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arXiv2026

Nuclear level density studied in odd-mass nuclei in the framework of the projected shell model

In a recent article [Phys. Rev. C 108, 034309 (2023)], we proposed a projected shell model method for the calculation of nuclear level density (NLD) in deformed even-even nuclei. The current article presents the subsequent study of NLDs in odd-mass nuclei as well as a comparative analysis between our calculated NLDs in adjacent even-even and odd-A systems. Since one nucleon in the odd-mass system remains blocked from participating in the pair formation, resulting in a weakened pairing (assessed by a smaller BCS pairing gap), pronounced differences between the NLDs in an odd-mass (both even-odd and odd-even) nucleus and its immediate even-even neighbour have been found. In general, the structure-dominated variations, which were found to be prominent in the even-even NLD at low energies, are greatly suppressed in the odd-mass systems. Specifically, from excitation energy as low as 2 MeV, the calculated densities of odd-parity and even-parity levels in odd-mass nuclei show an equal division signaling faster attainment of the statistical behavior. Nuclear level-spin distributions of both parities have been seen to adopt a regular Gaussian shape earlier than that found in the even-even system. Moreover, the pleasant property of our shell-model results, that each of our calculated levels is an eigenstate of angular momentum, allows us to extract the values of the energy-dependent dispersion $\sigma$ of Ericson's spin-distribution formula and plot $\rho(E, I, \pi)$, the energy-, spin-, and parity-dependent level density.

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arXiv2026

Nuclear matrix element of $2\nu\beta\beta$ decay of $^{76}$Ge: roles of high-lying states and two-body currents

We present a microscopic analysis of the nuclear matrix element (NME) of the two-neutrino double-$\beta$ ($2\nu\beta\beta$) decay for open-shell heavy deformed nuclei, taking into account the fact that nuclear level density increases rapidly with excitation energy as well as the contribution of two-body current (2BC). Taking $^{76}$Ge $\rightarrow$ $^{76}$Se decay as an example, we found that due to the rapid increase of the level density of the intermediate nucleus $^{76}$As with excitation energy $E_n$, the single-$\beta$ Gamow-Teller (GT) matrix elements become highly fragmented with very small magnitude, and exhibit seemingly random sign patterns at high $E_n$ region. This leads to an effective cancellation at high $E_n$ region in calculating the $2\nu\beta\beta$ NME which then turns out to converge at $E_n \lesssim 5$ MeV, indicating that the contribution of high-lying states of the intermediate nucleus to $2\nu\beta\beta$ NME is negligible. Besides, the 2BC in the transition operator is found to contribute $\sim 10\%$ quenching to the $2\nu\beta\beta$-decay NME of $^{76}$Ge.

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arXiv2026

Systematic study of the half-lives of nuclear bound-state $\beta^-$ decay

Nuclear bound-state $\beta^-$ decay ($\beta_{\text b}$ decay) is a novel weak-interaction process that becomes possible when atoms are highly ionized, such as in stellar environments or heavy-ion storage rings. In this work we present a systematic theoretical calculations for the $\beta_{\text b}$-decay half-lives of interesting candidates for the first time, where both allowed Gamow-Teller transitions and first-forbidden transitions are taken into account by the microscopic projected shell model, and the lepton phase space is calculated by the Takahashi-Yokoi model. We analyzed the structure informations for hundreds of nuclei near the $\beta$-stability line, and select 16 interesting candidates belonging to two categories, i.e., nuclei with negative $Q$ values and positive $Q$ values in neutral atoms respectively. Among these candidates, we recommend $^{243}\mathrm{Am}^{95+}$, $^{194}\mathrm{Os}^{76+}$, $^{227}\mathrm{Ac}^{89+}$, $^{228}\mathrm{Ra}^{88+}$, $^{241}\mathrm{Pu}^{94+}$, $^{247}\mathrm{Cm}^{96+}$ and $^{250}\mathrm{Cm}^{96+}$ as promising ones for future studies of storage-ring experiments because their $\beta_{\text{b}}$-decay half-lives are predicted to be much shorter than the half-lives in neutral atoms. These findings provide essential nuclear inputs for astrophysical models and identify specific candidates where experimental verification would be most valuable.

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arXiv2025

Effective $\beta$-decay rates of $r$-process waiting points in realistic stellar environments

Reliable nuclear weak rates are key inputs for understanding the origin of heavy elements and constraining the environments of the corresponding stellar nucleosynthesis. We present the effective stellar $\beta^-$-decay rates of the $N=50, 82, 126$ $r$-process waiting-point nuclei in realistic stellar environments with high temperature, high density and strong magnetic field. Both allowed and first-forbidden transitions are considered, and transitions from the low-lying states of parent nuclei due to the thermal population are taken into account properly. The stellar $\beta^-$-decay rates of the $N=50, 82$ waiting points are not sensitive to stellar temperature, while those of the $N=126$ waiting points increase rapidly with stellar temperature. With the increase of stellar density, the electron chemical potential increases accordingly, which leads to reduction of the stellar $\beta$-decay rates. Besides, the stellar $\beta$-decay rates are found to increase rapidly with the magnetic field $B$ when $B \gtrsim 10^{14}$ G. Depending on the stellar temperature, density and magnetic field, the rates may vary by several orders of magnitude, which indicates that dynamic $\beta$-decay rates for corresponding stellar conditions may be indispensable inputs for understanding the $r$-process nucleosynthesis.

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arXiv2025

Many-body correlations as the origin of Gamow-Teller quenching in nuclear $\beta$-decay

The longstanding quenching problem of Gamow-Teller (GT) strength in nuclear $\beta$-decay is attributed to missing contributions in the transition operator and/or incomplete nuclear correlations in the many-body wavefunction. Recent studies have predominantly emphasized operator renormalization, including chiral two-body currents, while the effects of many-body correlations--especially in heavy open-shell nuclei--remain underappreciated. We present a large-configuration shell-model calculation that incorporates chiral two-body weak current and treats both mechanisms on equal footing. Taking the neutrinoless double $\beta$-decay candidate $^{76}$Ge as an example, we demonstrate that strong nuclear correlations drive a substantial portion of GT strength to high excitation energies, leading to a pronounced suppression of low-energy strength responsible for the apparent quenching. We identify that the quenching originates mainly from deformation, cross-shell correlations, and mixing among densely-spaced highly excited states. In contrast, the chiral two-body current contributes only a modest $5-15\%$ reduction, depending on the coupling constants employed. Our results thus suggest many-body correlations as the primary origin of GT quenching and provide a unified microscopic explanation for this phenomenon in nuclear $\beta$-decay.

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arXiv2025

Anomaly in first-forbidden transitions of $^{176}$Lu

$^{176}$Lu is the key nucleus for understanding the evolution of planetary bodies in the solar system, and the temperature and nucleosynthesis of the $s$ process, due to its very long terrestrial half-life $T_{1/2} \approx 3.7\times 10^{10}$ years. The very long half-life is caused by two anomalous first-forbidden transitions from the $7^-$ state with extremely large comparative half-life log$ft \approx 19$ which have never been appeared in other cases of the existing nuclear databases. We analyze the underlying mechanism and reason for the anomaly in first-forbidden transitions of $^{176}$Lu for the first time, which is based on the projected shell model. It is found that the possible $K$-forbidden nature is indispensable for describing the two extremely weak first-forbidden transitions, and the transition strengths are very sensitive to the detailed configuration mixing and $K$ mixing in the nuclear wave functions. The half-life of the $7^-$ state is calculated to be $T_{1/2} \approx 1.95 \times 10^{10}$ years.

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arXiv2025

Microscopic nuclear structure study of $^{229}$Th by Projected Shell Model

$^{229}$Th, a crucial candidate for nuclear clocks and many other applications, is a typical heavy nucleus with an extremely low-energy isomeric state $^{229m}$Th. A detailed study of the nuclear structure of $^{229}$Th is performed here by the microscopic model of state-of-the-art projected shell model. Our calculation describes well low-energy levels of $^{229}$Th, and provides a reduced transition probability $B(M1)$ of $0.0240$ W.u. for the isomeric transition which agrees well with the radiative lifetime of $^{229m}$Th measured recently. Our result supports a small multipole mixing for the cross-band transition of the second-excited state of $^{229}$Th, suggesting that further investigations on the inconsistencies in the decay of the second-excited state should be necessary. The physics behind these properties is revealed by the analysis of the nuclear wave functions. Our findings provide a deep insight into $^{229}$Th from the microscopic nuclear structure point of view, and offer the chance for further studies for nuclear clocks and relevant topics by microscopic nuclear structure theory.

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arXiv2025

Stellar weak rates of the $rp$-process waiting points: Effects of strong magnetic fields

Incorporating microscopic nuclear-structure information into the discussion of bulk properties of astronomical objects such as neutron stars has always been a challenging issue in interdisciplinary nuclear astrophysics. Using the $rp$-process nucleosynthesis as an example, we studied the effective stellar $\beta^+$ and electron capture (EC) rates of eight waiting-point (WP) nuclei with realistic stellar conditions and presence of strong magnetic fields. The relevant nuclear transition strengths are provided by the projected shell model. We have found that, on average, due to the magnetic field effect, the $\beta^+$ and EC rates can increase by more than an order of magnitude for all combinations of density and temperature, as well as in each of WPs studied. We relate the onset field strength, at which the weak rates begin to increase, to nuclear structure quantities, $Q$ value or electronic chemical potential $\mu_e$. The enhanced weak rates may change considerably the lifetime of WPs, thereby modifying the current understanding of the $rp$-process.

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arXiv2024

Calculations of bound-state $β^-$-decay half-lives of highly ionized $^{163}$Dy$^{66+}$, $^{187}$Re$^{75+}$ and $^{205}$Tl$^{81+}$

We propose a theoretical method to calculate the bound-state $β$-decay half-lives of highly-ionized atoms, which is based on the combination of the Takahashi-Yokoi model and our recently-developed projected shell model that can take into account both allowed and first-forbidden transitions of nuclear $β$ decay. Three examples that are of much experimental interests, $^{163}$Dy$^{66+}$, $^{187}$Re$^{75+}$ and $^{205}$Tl$^{81+}$ are taken for calculations. The ground and low-lying states of related nuclei are described reasonably. The bound-state $β$-decay half-lives of $^{163}$Dy$^{66+}$ and $^{187}$Re$^{75+}$ are described within a factor of two and four by our calculations without and with the quenching factors in allowed and first-forbidden transitions. The bound-state $β$-decay half-life of the last $s$-process branching point $^{205}$Tl$^{81+}$ is predicted to be 58 and 305 days for cases without and with the quenching factors in calculations. The presented method provides a theoretical way to calculate systematically the bound-state $β$-decay half-lives of nuclei from light to heavy ones including odd-mass and even-mass cases for the first time.

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arXiv2023

Stellar $\beta$-decay rate of $s$-process branching-point $^{204}$Tl: forbidden transitions

We propose a theoretical method to calculate the stellar $\beta$-decay rates of nuclei in stellar environments with high temperature and density, based on the projected shell model, where contributions from both allowed and first-forbidden transitions are taken into account. As the first example, the stellar $\beta$-decay rate of one of the last $s$-process branching-point nuclei, $^{204}$Tl, is calculated and studied, where all related transitions are first-forbidden transitions. For the terrestrial case, the ground-state to ground-state transition is unique first-forbidden transition, which is described reasonably by our calculations. At the typical $s$-process temperature ($T\approx 0.3$ GK), non-unique first-forbidden transitions from thermally populated excited states of the parent nucleus are involved, the effective rate from our calculations is much lower than the one from the widely used data tables by Takahashi and Yokoi. Effect of the quenching factors for nuclear matrix elements in first-forbidden transitions on the stellar $\beta$-decay rates is discussed as well.

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arXiv2023

First-forbidden transition of nuclear $β$ decay by projected shell model

The first-forbidden transition of nuclear $β$ decay is expected to play crucial roles in many aspects in nuclear physics, nuclear astrophysics and particle physics such as the stellar $β$-decay rates and the reactor anti-neutrino spectra. In this work we develop the projected shell model (PSM) for description of first-forbidden transition of nuclear $β$ decay for the first time. Detailed theoretical framework and logics are provided, and 35 dominant first-forbidden transitions that are expected to be important for the reactor anti-neutrino spectra problems are calculated and compared systematically with the data to test the new development of the PSM. The corresponding experimental Log$f_0 t$ values are described reasonably, and the quenching factors of nuclear matrix elements are found to affect the Log$f_0 t$ values as well as the related shape factors, which may be helpful for better understanding of the reactor anti-neutrino spectra problems.

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arXiv2023

Stellar weak-interaction rates for $rp$-process waiting-point nuclei from projected shell model

We propose a projected shell model (PSM) for description of stellar weak-interaction rates between even-even and odd-odd nuclei with extended configuration space where up to six-quasiparticle (qp) configurations are included, and the stellar weak-interaction rates for eight $rp$-process waiting-point (WP) nuclei, $^{64}$Ge, $^{68}$Se, $^{72}$Kr, $^{76}$Sr, $^{80}$Zr, $^{84}$Mo, $^{88}$Ru and $^{92}$Pd, are calculated and analyzed for the first time within the model. Higher-order qp configurations are found to affect the underlying Gamow-Teller strength distributions and the corresponding stellar weak-interaction rates. Under $rp$-process environments with high temperatures and densities, on one hand, thermal population of excited states of parent nuclei tends to decrease the stellar $β^+$ decay rates. On the other hand, the possibility of electron capture (EC) tends to provide increasing contribution to the rates with temperature and density. The effective half-lives of WP nuclei under the $rp$-process peak condition are predicted to be reduced as compared with the terrestrial case, especially for $^{64}$Ge and $^{68}$Se.

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arXiv2023

Nuclear $β$ spectrum from projected shell model (I): allowed one-to-one transition

Nuclear $β$ spectrum and the corresponding (anti-)neutrino spectrum play important roles in many aspects of nuclear astrophysics, particle physics, nuclear industry and nuclear data. In this work we propose a projected shell model (PSM) to calculate the level energies as well as the reduced one-body transition density (ROBTD) by the Pfaffian algorithm for nuclear $β$ decays. The calculated level energies and ROBTD are inputed to the Beta Spectrum Generator (BSG) code to study the high precision $β$ spectrum of allowed one-to-one transitions. When experimental level energies are adopted, the calculated $β$ spectrum by ROBTD of the PSM deviates from the one by the extreme simple particle evaluation of the BSG by up to $10\%$, reflecting the importance of nuclear many-body correlations. When calculated level energies are adopted, the calculated $β$ spectrum shows sensitive dependence on the reliability of calculated level energies. The developed method for ROBTD by the PSM will also be useful for study of the first-forbidden transitions, the isovector spin monopole resonance etc. in a straightforward way.

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arXiv2022

An effective and efficient algorithm for the Wigner rotation matrix at high angular momenta

The Wigner rotation matrix ($d$-function), which appears as a part of the angular-momentum-projection operator, plays a crucial role in modern nuclear-structure models. However, it is a long-standing problem that its numerical evaluation suffers from serious errors and instability, which hinders precise calculations for nuclear high-spin states. Recently, Tajima [Phys. Rev. C 91, 014320 (2015)] has made a significant step toward solving the problem by suggesting the high-precision Fourier method, which however relies on formula-manipulation softwares. In this paper we propose an effective and efficient algorithm for the Wigner $d$ function based on the Jacobi polynomials. We compare our method with the conventional Wigner method and the Tajima Fourier method through some testing calculations, and demonstrate that our algorithm can always give stable results with similar high-precision as the Fourier method, and in some cases (for special sets of $j, m, k$ and $θ$) ours are even more accurate. Moreover, our method is self-contained and less memory consuming. A related testing code and subroutines are provided as Supplemental Material in the present paper.

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arXiv2021

Description of $^{93}$Nb stellar electron-capture rates by the Projected Shell Model

Capture of electrons by nuclei is an important process in stellar environments where excited nuclear states are thermally populated. However, accurate treatment for excited configurations in electron capture (EC) rates has been an unsolved problem for medium-heavy and heavy nuclei. In this work, we take the $^{93}$Nb $\rightarrow$ $^{93}$Zr EC rates as the example to introduce the Projected-Shell-Model (PSM) in which excited configurations are explicitly included as multi-quasiparticle states. Applying the prevalent assumption that the parent nucleus always stays in its ground state in stellar conditions, we critically compare the obtained PSM results with the recently-measured Gamow-Teller transition data, and with the previous calculations by the conventional shell model and the quasiparticle random-phase approximation. We discuss important ingredients that are required in theoretical models used for stellar EC calculations, and demonstrate effects of the explicit inclusion of excited nuclear states in EC rate calculations, especially when both electron density and environment temperature are high.

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arXiv2021

A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations

We present a Pfaffian formula to calculate matrix elements of three-body operators in symmetry-restoration beyond-mean-field methods, including the case of multiple quasi-particle configurations. Detailed derivation based on [Mizusaki et al., Phys. Lett. B 715, 219 (2012)] and [Hu et al., Phys. Lett. B 734, 162 (2014)] is provided, and potential applications in generator coordinate method with chiral interactions, as well as in study of nuclear matrix elements in neutrinoless double beta decay are discussed.

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arXiv2021

Urca Cooling in Neutron Star Crusts and Oceans: Effects of Nuclear Excitations

The excited-state structure of atomic nuclei can modify nuclear processes in stellar environments. In this work, we study the influence of nuclear excitations on Urca cooling (repeated back-and-forth beta decay and electron capture in a pair of nuclear isotopes) in the crust and ocean of neutron stars. We provide for the first time an expression for Urca process neutrino luminosity which accounts for excited states of both members of an Urca pair. We use our new formula with state-of-the-art nuclear structure inputs to compute neutrino luminosities of candidate Urca cooling pairs. Our nuclear inputs consist of the latest experimental data supplemented with calculations using the projected shell model. We show that, in contrast with previous results that only consider the ground states of both nuclei in the pair, our calculated neutrino luminosities for different Urca pairs vary sensitively with the environment temperature and can be radically different from those obtained in the one transition approximation.

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