Theoretical study of atomic and molecular gases and their reactions in the upper atmosphere Summary report, 1 May - 31 Oct. 1965
Wave functions and total energy of energy states of diatomic molecules - Hartree-Fock calculation
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Wave functions and total energy of energy states of diatomic molecules - Hartree-Fock calculation
Hartree-Fock calculation method as zero-order approximation for determining atomic and molecular second-order properties
Quasi-fission occurs in fully damped heavy-ion collisions following a significant mass transfer between the fragments, without formation of a compound nucleus. As in fission, quasi-fission is expected to be affected by quantum effects leading to asymmetric mass splits. Quantum shells stabilising fission fragments with octupole shapes have been invoked as a factor determining the distribution of nucleons between the fragments at scission, explaining the fact that the centroid of the heavy fragment charge distribution is found around Z = 54 protons in fission and quasi-fission of actinides. These shell effects are studied in microscopic studies of quasi-fission. In particular, time-dependent Hartree-Fock (TDHF) calculations have been performed for reactions forming actinides.
The nuclear rates for reactions involving 12 C and 16 O are key to computing the energy release and nucleosynthesis evolution of massive stars during their advanced burning phases. Ultimately, these burning rates shape the stellar structure and evolution and influence the nature of the compact objects produced at the end of the stellar life. We explore the implications of new nuclear reaction rates from both experimental and theoretical studies for 12 C(α, γ) 16 O, 12 C+ 12 C, 12 C+ 16 O, and 16 O+ 16 O reactions for massive stars. Our goal is to investigate how the chemical structure and nucleosynthesis evolve from the He-exhaustion stage to the O-burning phase and how these processes influence the ultimate stellar fate. We computed rotating and non-rotating models for stars of different masses at solar metallicity. We used the stellar evolution code GENEC, which includes a large network of nuclear reactions and isotopes involved in advanced phases, as well as updated rates for 12 C(α,γ) 16 O. For the three fusion reactions involving 12 C and 16 O, we considered new rates following a data-driven fusion suppression scenario (hereafter HIN(RES)) and new theoretical rates obtained with time-dependent Hartree-Fock (TDHF) calculations. The updated 12 C(α, γ) 16 O rates mainly impact the chemical structure evolution changing the 12 C/ 16 O ratio at He-exhaustion and have little effect on the CO core mass. This variation in the 12 C/ 16 O ratio is in some cases critical for predicting the final fate of the model, which is very sensitive to 12 C abundance, and in particular the 20 M ⊙ remnant may change from a black hole to a neutron star. The He-burning (C-burning) lifetime is also decreased (increased) by about −2% (+15%). The combined new rates for 12 C+ 12 C and 16 O+ 16 O fusion reactions according to the HIN(RES) model lead to shorter C- and O-burning lifetimes by ≈ − 10%, and −50%, respectively, and shift the ignition conditions to higher temperatures and densities. In contrast, the theoretical TDHF rates primarily affect C-burning, increasing its duration by about 30% and lowering the ignition temperature. These changes modify the chemical structure of the core, the size and duration of C-burning shells, and hence their compactness. They also impact the central and shell nucleosynthesis (by ±1 dex and by factors of ±2–10, respectively), while 12 C+ 16 O reaction rates variations remain the least important.
In deep-inelastic collisions of heavy nuclei, reaction products with a wide range of mass and charge are produced. Such collisions been considered as a possible way to produce superheavy nuclei, as an alternative to fusion reactions. To provide reliable theoretical predictions, it is desired to develop microscopic approaches that correctly and accurately describe nucleon transfer processes in dissipative collisions of heavy nuclei. The purpose of the present work is (1) to investigate the mechanism of nucleon transfers in dissipative collisions of two heavy nuclei, and (2) to explore possible pathways to produce neutron-rich heavy nuclei, through detailed theoretical analyses of fluctuations and correlations in nucleon transfers in 208 Pb + 208 Pb reactions. Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are performed for the collisions of 208 Pb + 208 Pb at 𝐸 c.m. = 832, 936, and 1040 MeV, using the Skyrme SLy4d energy density functional. To calculate fluctuations and correlations in nucleon transfers, we employ the stochastic mean-field (SMF) theory, and the results are compared with another theoretical framework currently available, the time-dependent random phase approximation (TDRPA). Primary and secondary production cross sections are calculated with the SMF theory combined with a statistical model, GEMINI ++ . Using information of nucleon flow across a neck of colliding nuclei in TDHF calculations, we solve quantal diffusion equations for fluctuations and correlations in nucleon transfers based on the SMF theory. From the SMF calculations, we obtain the time evolution of diffusion coefficients as well as fluctuations and correlations in nucleon transfers for a range of initial orbital angular momenta. We compare the results of the SMF calculations with those of TDRPA, showing that TDRPA tends to predict substantially larger fluctuations and correlations in strongly damped collisions of heavy nuclei, which exhibit complex initial angular momentum dependence, while the SMF results provide almost constant (stable) values. Using the obtained fluctuations and correlations, we calculate primary and secondary production cross sections for the 208 Pb + 208 Pb collisions. From the results, we find that both lighter and heavier reaction products as compared to 208 Pb are produced for a wide region in the 𝑁−𝑍 plane as primary products, thanks to the quantal diffusion mechanism in the dissipative collisions. However, we show that cross sections for production of heavy nuclei with 𝑍 ≳ 90 or 𝑁 ≳ 135 are washed out due to secondary particle evaporation and/or fission processes. On the other hand, we find that there remain sizable cross sections for production of neutron-rich nuclei along 𝑁 = 126 with 𝑍< 82, even after secondary disintegration processes. We demonstrate that the secondary production cross sections depend weakly on incident energies, but lower (higher) energy is slightly preferred for production of nuclei with smaller (larger) atomic numbers as compared to 𝑍 = 82. Here, based on the microscopic SMF calculations, it has been shown that deep-inelastic collisions of heavy nuclei, such as 208 Pb + 208 Pb examined in this study, can be a promising means to produce neutron-rich heavy nuclei along 𝑁=126. Discrepancies between the SMF and TDRPA approaches are left unsolved for future investigations.
Twisted bilayer graphene (TBG) has emerged as a paradigmatic platform for exploring the interplay between strong interactions in a multi-band system with nearly flat bands, while offering unprecedented control over the filling fraction of electron/hole carriers. Despite much theoretical work, developing a comprehensive ab initio model for this system has proven challenging due to the inherent trade-off between accurately describing the band structure and incorporating the interactions within the Hamiltonian. Here, we constructed an extended multi-orbital Hubbard model, and performed Hartree-Fock (HF) calculations to explore its phase diagram across commensurate fillings. We found several nearly-degenerate insulating states at charge neutrality, all of which exhibit orbital orders. We also observed that most of the Hartree–Fock ground states exhibit a generalized valley Hund’s-like rule, resulting in valley polarization. Importantly, we show that the incorporation of the intra-valley and inter-valley exchange interactions is crucial to properly stabilize the ordered symmetry-broken states. In agreement with experiments, we find significant particle-hole asymmetry, which underscores the importance of using particle-hole asymmetric models.
Formulation of hartree-fock approximation for final states of atomic oxygen photoionization
Random-phase approximation of dielectric response for resonant and scattering states, describing optical absorption associated with hydrogenic excitons
Gauge invariance of Hartree-Fock approximation in presence of nonlocal potentials
Theoretical photodetachment cross section for negative atomic oxygen ion
Coupled Hartree-Fock approximation for calculating frequency-dependent refractive index of helium gas
Perturbation expansions for ground state function of helium atom, using Hartree or Hartree-Fock model Hamiltonian, based on Weiss-Martin variation-perturbation calculation
The neutron radiative capture reaction 17 O (𝑛,𝛾) 18 O plays a pivotal role in both nuclear structure studies and astrophysical nucleosynthesis, particularly in the formation of elements during hydrostatic and explosive stellar environments. We calculated the 17 O (𝑛,𝛾) 18 O cross section within the Skyrme Hartree-Fock potential model and analyzed electric dipole 𝐸1 transitions to both positive- and negative-parity states below the α-decay threshold in 18 O. Our cross sections are significantly different from the data available in commonly used libraries. We further investigate the impact of the new calculated cross section on weak 𝑟-process nucleosynthesis using large-scale reaction network calculations across a wide range of electron fractions and entropies. Our results show that the 17 O (𝑛,𝛾) 18 O reaction rate significantly influences the production of first 𝑟-process peak elements, such as strontium, under specific astrophysical conditions. This study highlights the importance of accurate nuclear data for light isotopes in modeling heavy-element synthesis and provides updated reaction rates for future nucleosynthesis simulations.
Accurate modeling of the absorption of tens-of-MeV $ν_e$ on $^{40}$Ar is needed to enable measurements of astrophysical neutrinos using large liquid argon time projection chamber (LArTPC) detectors, such as those planned for the Deep Underground Neutrino Experiment (DUNE). We revisit the MARLEY neutrino interaction model used in present estimates of DUNE sensitivity to supernova and solar neutrino signals. Multiple theoretical refinements are pursued, especially in the unbound continuum region of nuclear excitation energy. Inclusive charged-current neutrino-argon cross sections are calculated using a hybrid strategy. Nuclear transitions to unbound states are treated using a Hartree-Fock Continuum Random Phase Approximation (HF-CRPA) model, including forbidden contributions. Allowed transitions to low-lying discrete levels are also included using indirect measurements and approximate corrections for the momentum transfer dependence. Exclusive predictions are obtained by coupling these calculations with a statistical nuclear de-excitation model. The impact on observables of interest for DUNE and similar experiments is examined in terms of both total and differential cross sections. Our refined calculations predict a lower allowed portion of the cross section relative to the prior MARLEY model. At neutrino energies appreciably below 100 MeV, the inclusion of forbidden transitions does not fully compensate for the loss of allowed strength. For a representative neutrino burst from a galactic core-collapse supernova, our results suggest that MARLEY 1.2.0 overestimates the event yield in a DUNE-like detector by approximately 20%. However, because this overestimation is more severe at backwards angles, use of the charged-current $ν_e$-$^{40}$Ar reaction for supernova pointing may be more feasible than previously expected.
Results are reported for quantum-mechanical studies of the ions HSiO(+) and HOSi(+). The equilibrium geometries, rotation constants, and relative stabilities of these ions are determined using the matrix Hartree-Fock model with a basis set of Slater exponential functions. Optimum bond lengths are calculated, and an empirical correction to the computed bond lengths is introduced. The isomer HOSi(+) is found to be more stable than HSiO(+). A frequency of 35.77 GHz is obtained for the J = 1-0 transition of HOSi(+) by assuming that the vibration-rotation interaction constants for this isomer are the same as those for HCP.
We present a detailed comparison of fusion in 16 O + 40,48 Ca within a fully microscopic time-dependent Hartree-Fock framework over sub-, near-, and above-barrier energies. While 16 O + 40 Ca fusion cross sections are reproduced within the available experimental energy range, calculations for the neutron-rich 16 O + 48 Ca system systematically overestimate the measured near-barrier cross sections. The discrepancy persists across the tested energy density functionals, indicating that it is not tied to a particular parametrization. Analysis of the dynamical interaction potentials reveals an outward shift and softening of the barrier region at the lowest collision energies. These results are then compared to a frozen density description where the barrier modifications are absent and the predicted cross sections are brought closer to experiment. Here, this demonstrates that the observed discrepancy is closely linked to dynamical surface rearrangement and isovector effects, and highlights the sensitivity of low-energy fusion to both the structure and dynamics of neutron-rich nuclei. This suggests that limitations in the isovector sector of conventional Skyrme EDFs in describing the structure of 48 Ca, as highlighted by CREX, are also manifested in the fusion dynamics of the 16 O + 48 Ca system.
We present a variant of the approximate second order coupled-cluster method (CC2) with a two-parameter size-consistent Brillouin–Wigner (BW-s) partitioning instead of a Møller–Plesset (MP) partitioning for the unperturbed Hamiltonian, which we refer to as BWs-CC2. The computational complexity of this model scales identically to CC2 with molecular size. Conventional CC2 and its regularized BWs-CC2 variants, as well as conventional MP2 and two of its regularized BW-s2 variants, were assessed on a 535 element database spanning thermochemistry, non-covalent interactions, barrier heights, and isomerization energies. To ensure a well-defined model chemistry, the assessment was performed using internally stable spin-polarized Hartree–Fock (HF) orbitals in the finite aug-cc-pVQZ basis without counterpoise corrections. As a result of using stable orbitals, contrary to conventional wisdom, we find that CC2 substantially outperforms MP2 on molecules with significantly spin contaminated reference orbitals without a significant increase in error on systems with a spin-pure reference, showing the value of its single substitutions. While no single choice of regularization parameters can be optimal for all datasets, we find that BWs-CC2 generally outperforms both CC2 and BW-s2 with a single judicious parameter choice. Additional tests on dipole moments and bond lengths of diatomics provide further support for the utility of this choice. Furthermore, the main outliers and poorest performing cases are associated with large amounts of spin-contamination in the HF reference, which is indicative of systems with either strong correlation or extensive artificial symmetry breaking. Overall, these findings argue that the perception of the quality of the CC2 ground state should be reevaluated and that it can be further improved upon by the soundly based BWs-CC2 variant with the recommended parameter choice.
We devise a deterministic quantum algorithm to produce antisymmetric states of single-particle orbitals in the first quantization mapping. Unlike sorting-based antisymmetrization algorithms, which require ordered input states and high Clifford-gate overhead, our approach initializes the state of each particle independently. For a system of $η$ particles and $N$ single-particle states, our algorithm prepares antisymmetrized states of non-trivial localized (e.g., Hartree-Fock) orbitals using $O(η^2\sqrt{N})$ $T$-gates, outperforming alternative algorithms when $η ≲ \sqrt{N}$. To achieve such scaling, we require $O(\sqrt{N})$ dirty ancilla qubits for intermediate calculations. Knowledge of the single-particle states to be antisymmetrized can be leveraged to further improve the efficiency of the circuit, and a measurement-based variant reduces gate cost by roughly a factor of two. We show example circuits for two- and three-particle systems and discuss the generalization to an arbitrary number of particles. For a specific three-particle example, we decompose the circuit into Clifford $+T$ gates and study the impact of noise on the prepared state.