arXiv subjects
Publications and source records attributed to I. Stetcu.
We discuss properties of the method based on time dependent superfluid local density approximation (TDSLDA) within an application to induced fission of 240Pu and surrounding nuclei. Various issues related to accuracy of time evolution and the determination of the properties of fission fragments are discussed.
Two major recent developments in theory and computational resources created the favorable conditions for achieving a microscopic description of nuclear fission almost eighty years after its discovery in 1939 by Hahn and Strassmann (1930). The first major development was in theory, the extension of the Time-Dependent Density Functional Theory (TDDFT) to superfluid fermion systems. The second development was in computing, the emergence of powerful enough supercomputers capable of solving the complex systems of equations describing the time evolution in three dimensions without any restrictions of hundreds of strongly interacting nucleons. Even though the available nuclear energy density functionals (NEDFs) are phenomenological still, their accuracy is improving steadily and the prospects of being able to perform calculations of the nuclear fission dynamics and to predict many properties of the fission fragments, otherwise not possible to extract from experiments, are within reach, all without making recourse anymore to uncontrollable assumptions and simplified phenomenological models.
We study the fission dynamics of 240Pu within an implementation of the Density Functional Theory (DFT) extended to superfluid systems and real-time dynamics. We demonstrate the critical role played by the pairing correlations. The evolution is found to be much slower than previously expected in this fully non-adiabatic treatment of nuclear dynamics, where there are no symmetry restrictions and all collective degrees of freedom (CDOF) are allowed to participate in the dynamics.
The emission of prompt fission $γ$ rays within a few nanoseconds to a few microseconds following the scission point is studied in the Hauser-Feshbach formalism applied to the deexcitation of primary excited fission fragments. Neutron and $γ$-ray evaporations from fully accelerated fission fragments are calculated in competition at each stage of the decay, and the role of isomers in the fission products, before $β$-decay, is analyzed. The time evolution of the average total $γ$-ray energy, average total $γ$-ray multiplicity, and fragment-specific $γ$-ray spectra, is presented in the case of neutron-induced fission reactions of $^{235}$U and $^{239}$Pu, as well as spontaneous fission of $^{252}$Cf. The production of specific isomeric states is calculated and compared to available experimental data. About 7% of all prompt fission $γ$ rays are predicted to be emitted between 10 nsec and 5 $μ$sec following fission, in the case of $^{235}$U and $^{239}$Pu $(n_{\rm th},f)$ reactions, and up to 3% in the case of $^{252}$Cf spontaneous fission. The cumulative average total $γ$-ray energy increases by 2 to 5% in the same time interval. Finally, those results are shown to be robust against significant changes in the model input parameters.
Within the framework of the unrestricted time-dependent density functional theory, we present for the first time an analysis of the relativistic Coulomb excitation of the heavy deformed open shell nucleus $^{238}$U. The approach is based on Superfluid Local Density Approximation (SLDA) formulated on a spatial lattice that can take into account coupling to the continuum, enabling self-consistent studies of superfluid dynamics of any nuclear shape. We have computed the energy deposited in the target nucleus as a function of the impact parameter, finding it to be significantly larger than the estimate using the Goldhaber-Teller model. The isovector giant dipole resonance, the dipole pygmy resonance and giant quadrupole modes were excited during the process. The one body dissipation of collective dipole modes is shown to lead a damping width $Γ_\downarrow \approx 0.4$ MeV and the number of pre-equilibrium neutrons emitted has been quantified.
Solutions to the nuclear many-body problem rely on effective interactions, and in general effective operators, to take into account effects not included in calculations. These include effects due to the truncation to finite model spaces where a numerical calculation is tractable, as well as physical terms not included in the description in the first place. In the no-core shell model (NCSM) framework, we discuss two approaches to the effective interactions based on (i) unitary transformations and (ii) effective field theory (EFT) principles. Starting from a given Hamiltonian, the unitary transformation approach is designed to take into account effects induced by the truncation to finite model spaces in which a numerical calculation is performed. This approach was widely applied to the description of nuclear properties of light nuclei; we review the theory and present representative results. In the EFT approach, a Hamiltonian is always constructed in a truncated model space according to the symmetries of the underlying theory, making use of power counting to limit the number of interactions included in the calculations. Hence, physical terms not explicitly included in the calculation are treated on the same footing with the truncation to a finite model space. In this approach, we review results for both nuclear and trapped atomic systems, for which the effective theories are formally similar, albeit describing different underlying physics. Finally, the application of the EFT method of constructing effective interactions to Gamow shell model is briefly discussed.
We describe systems of two and three nucleons trapped in a harmonic-oscillator potential with interactions from the pionless effective field theory up to next-to-leading order (NLO). We construct the two-nucleon interaction using two-nucleon scattering information. We calculate the trapped levels in the three-nucleon system with isospin $T=1/2$ and determine the three-nucleon force needed for stability of the triton. We extract neutron-deuteron phase shifts, and show that the quartet scattering length is in good agreement with experimental data.
A fully symmetry unrestricted Time-Dependent Density Functional Theory extended to include pairing correlations is used to calculate properties of the isovector giant dipole resonances of the deformed open-shell nuclei 172Yb (axially deformed), 188Os (triaxially deformed), and 238U (axially deformed), and to demonstrate good agreement with experimental data on nuclear photo-absorption cross-sections for two different Skyrme force parametrizations of the energy density functional: SkP and SLy4.
We set up the framework for the calculation of electric dipole moments (EDMs) of light nuclei using the systematic expansion provided by chiral effective field theory (EFT). We take into account parity (P) and time-reversal (T) violation which, at the quark-gluon level, originates from the QCD vacuum angle and dimension-six operators capturing physics beyond the Standard Model. We argue that EDMs of light nuclei can be expressed in terms of six low-energy constants that appear in the P- and T-violating nuclear potential and electric current. As examples, we calculate the EDMs of the deuteron, the triton, and 3He in leading order in the EFT expansion.
We study systems of few two-component fermions interacting via short-range interactions within a harmonic-oscillator trap. The dominant interactions, which are two-body, are organized according to the number of derivatives and defined in a two-body truncated model space made from a bound-state basis. Leading-order (LO) interactions are solved for exactly using the formalism of the No-Core Shell Model, whereas corrections are treated as many-body perturbations. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. We present results at unitarity for three- and four-fermion systems, which show excellent agreement with the exact solution (for the three-body problem) and results obtained by others methods (in the four-body case). We also present results for finite scattering lengths and non-zero range of the interaction, including (at positive scattering length) observation of a change in the structure of the three-body ground state and extraction of the atom-dimer scattering length.
We discuss the problem of two particles interacting via short-range interactions within a harmonic-oscillator trap. The interactions are organized according to their number of derivatives and defined in truncated model spaces made from a bound-state basis. Leading-order (LO) interactions are iterated to all orders, while corrections are treated in perturbation theory. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. In the large-model-space limit we regain results from a pseudopotential. Arbitrary scattering lengths are considered, as well as a generalization to include the non-vanishing range of the interaction.
One of the central open problems in nuclear physics is the construction of effective interactions suitable for many-body calculations. We discuss a recently developed approach to this problem, where one starts with an effective field theory containing only fermion fields and formulated directly in a no-core shell-model space. We present applications to light nuclei and to systems of a few atoms in a harmonic-oscillator trap. Future applications and extensions, as well as challenges, are also considered.
We construct effective two-body Hamiltonians and E2 operators for the p-shell by performing $16\hbarΩ$ ab initio no-core shell model (NCSM) calculations for A=5 and A=6 nuclei and explicitly projecting the many-body Hamiltonians and E2 operator onto the $0\hbarΩ$ space. We then separate the effective E2 operator into one-body and two-body contributions employing the two-body valence cluster approximation. We analyze the convergence of proton and neutron valence one-body contributions with increasing model space size and explore the role of valence two-body contributions. We show that the constructed effective E2 operator can be parametrized in terms of one-body effective charges giving a good estimate of the NCSM result for heavier p-shell nuclei.
The electric dipole polarizabilities of $^3$H, $^3$He, and $^4$He are calculated directly using the Schrödinger equation with the latest generation of two- and three-nucleon interactions. These polarizabilities are necessary in order to obtain accurate nuclear-polarization corrections for transitions involving S-waves in one- and two-electron atoms. Our results are compared to previous results, and it is shown that direct calculations of the electric polarizability of $^4$He using modern nuclear potentials are smaller than published values calculated using experimental photoabsorption data. The status of this topic is assessed in the context of precise measurements of transitions in one- and two-electron atoms.
We construct effective 2- and 3-body Hamiltonians for the p-shell by performing 12\hbarΩab initio no-core shell model (NCSM) calculations for A=6 and 7 nuclei and explicitly projecting the many-body Hamiltonians onto the 0\hbarΩspace. We then separate these effective Hamiltonians into 0-, 1- and 2-body contributions (also 3-body for A=7) and analyze the systematic behavior of these different parts as a function of the mass number A and size of the NCSM basis space. The role of effective 3- and higher-body interactions for A>6 is investigated and discussed.
A permanent electric dipole moment (EDM) of a physical system requires time-reversal (T) and parity (P) violation. Experimental programs are currently pushing the limits on EDMs in atoms, nuclei, and the neutron to regimes of fundamental theoretical interest. Here we calculate the magnitude of the PT-violating EDM of 3He and the expected sensitivity of such a measurement to the underlying PT-violating interactions. Assuming that the coupling constants are of comparable magnitude for pi-, rho-, and omega-exchanges, we find that the pion-exchange contribution dominates. Our results suggest that a measurement of the 3He EDM is complementary to the planned neutron and deuteron experiments, and could provide a powerful constraint for the theoretical models of the pion-nucleon PT-violating interaction.
We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and four two-component fermions in a harmonic trap. In the unitary limit, we find that three-particle results are within 10% of known semi-analytical values even in small model spaces. The method is very general, and can be readily extended to other regimes, more particles, different species (e.g., protons and neutrons in nuclear physics), or more-component fermions (as well as bosons). As an illustration, we present calculations of the lowest-energy three-fermion states away from the unitary limit and find a possible inversion of parity in the ground state in the limit of trap size large compared to the scattering length. Furthermore, we investigate the lowest positive-parity states for four fermions, although we are limited by the dimensions we can currently handle in this case.
We present a new approach to the construction of effective interactions suitable for many-body calculations by means of the no-core shell model (NCSM). We consider an effective field theory (EFT) with only nucleon fields directly in the NCSM model spaces. In leading order, we obtain the strengths of the three contact terms from the condition that in each model space the experimental ground-state energies of 2H, 3H and 4He be exactly reproduced. The first (0^+;0) excited state of 4He and the ground state of 6Li are then obtained by means of NCSM calculations in several spaces and frequencies. After we remove the harmonic-oscillator frequency dependence, we predict for 4He an energy level for the first (0^+;0) excited state in remarkable agreement with the experimental value. The corresponding 6Li binding energy is about 70% of the experimental value, consistent with the expansion parameter of the EFT.