Session PF: Nuclear Theory III

Relativistic time-dependent Fermion-mass renormalization using statistical regularization.

The time-dependent electromagnetically self-coupled Dirac equation is solved numerically by means of the staggered-leap-frog algorithm with reflecting boundary conditions. The stability region of the method versus the interaction strength and the spatial-grid size over time-step ratio is established. The expectation values of several dynamic operators are then evaluated as functions of time. These include the fermion and electromagnetic energies and the fermion dynamic mass. There is a characteristic, non-exponential, oscillatory dependence leading to asymptotic constants of these expectation values. In the case of the fermion mass this amounts to renormalization. The dependence of the expectation values on the spatial-grid size is evaluated in detail. Furthermore, the contribution of positive and negative energy states to the asymptotic values and the gauge fields is analyzed. Statistical regularization, employing a canonical ensemble whose temperature is the inverse of the grid size, is used to remove the grid-size and momentum-dependence and produce a finite result in the continuum limit.   

Effects of Chiral Two-Body Currents on Neutrinoless Double-Beta Decay Matrix Elements

Two-body currents in chiral effective field theory, including both one-pion-exchange and contact terms, are taken into account to correct the transition operator for neutrinoless double-beta decay. We compare the normal-ordering approximation with a more complete treatment of the many-body decay operator for the decay of $^{48}$Ca, $^{76}$Ge, and $^{82}$Se, in various nuclear-structure models. We discuss whether two-body currents quench neutrinoless decay as much as its two-neutrino counterpart.   

Adiabatically describing rare earths using microscopic deformations

Recent works showed that reactions on well-deformed nuclei in the rare-earth region are very well described by an adiabatic method. This assumes a spherical optical potential (OP) accounting for non-rotational degrees of freedom while the deformed configuration is described by couplings to states of the g.s. rotational band. This method has, apart from the global OP, only the deformation parameters as inputs, with no additional fit- ted variables. For this reason, it has only been applied to nuclei with well-measured deformations. With the new computational capabilities, microscopic large-scale calculations of deformation parameters within the HFB method based on the D1S Gogny force are available in the literature. We propose to use such microscopic deformations in our adi- abatic method, allowing us to reproduce the cross sections agreements observed in stable nuclei, and to reliably extend this description to nuclei far from stability, describing the whole rare-earth region. Since all cross sections, such as capture and charge exchange, strongly depend on the correct calculation of absorption from the incident channel (from direct reaction mechanisms), this approach significantly improves the accuracy of cross sections and transitions relevant to astrophysical studies.   

Moldauer's sum rule as a test of the consistency of transmission coefficients in Hauser Feshbach theory

For neutron induced reactions below 20 MeV incident energy, the Unresolved Resonance Region (URR) connects the fast neutron region with the Resolved Resonance Region (RRR). The URR is problematic since resonances are not resolvable experimentally yet the fluctuations in the neutron cross sections play a discernible and technologically important role -- the URR in a typical nucleus is in the 100 keV -- 2 MeV window where the typical fission spectrum peaks. The URR also represents the transition between R-matrix theory used to describe isolated resonances and Hauser-Feshbach theory which accurately describes the average cross sections. In practice, only average or systematic features of the resonances in the URR are known and are tabulated in evaluations in a nuclear data library such as ENDF/B-VII.1. Here we apply Moldauer's ``sum rule for resonance reactions'' to compute the effective transmission coefficients for reactions in the RRR and URR regions. We compare these to the transmission coefficients used in the fast region in the EMPIRE Hauser-Feshbach code, demonstrating the consistency (or lack thereof) between these different physical regimes. This work suggests a better approach to evaluating the URR average parameters using the results from the fast region modeling.   

Prospects for Brueckner-Hartree-Fock calculations in the Density Matrix Expansion approach

Recently, a microscopically based nuclear energy density functional was derived by applying the Density Matrix Expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory ($\chi$EFT) two- and three-nucleon interactions[1]. The Hartree-Fock approach cannot contain the full many-body correlations. Brueckner-Hartree-Fock (BHF) theory gives an improved definition of the one-body potential U by replacing the interaction by a reaction matrix G. The central result of modern renormalization theory is that a general RG decoupling generates an infinite series of counterterms consistent with the input interaction. Then we can apply the DME at Hartree-Fock level with long-range $\chi$EFT interactions and zero-range contact interactions to model BHF correlations. \\ \\[1]A. Dyhdalo, S.K. Bogner, R.J. Furnstahl. Phys. Rev. C \mathbf{95}, 054314(2017)   

A general ab initio framework for non-scalar observables in medium-mass nuclei

In the past decade, there has been a vast expansion of the applicability of so-called ab initio methods which describe nuclear structure by solving the many-body Schrödinger equation as accurately as possible, starting from realistic inter-nucleon interactions. While many of these methods have very successfully ventured into the medium-mass region, most have not yet been exploited to predict observables other than energies, such as transition strengths and moments. This talk will discuss new applications of the in-medium similarity renormalization group (IMSRG) to compute excited states and non-scalar observables for medium-mass closed- and open-shell nuclei. [arXiv:1705.05511, submitted to Phys. Rev. C]   

Covariant energy density functionals: parametric correlations and the propagation of statistical errors

Because of the complexity of nuclear many-body problem modern theoretical tools rely on some approximations in its solution. As a result, it becomes necessary to estimate theoretical uncertainties in the description of physical observables. This is especially important when one deals with the extrapolations beyond the known regions. There are two types of such uncertainties: systematic and statistical. Systematic theoretical uncertainties in the description of physical observables within the covariant density functional theory have been evaluated in [1]. Present work is focused on the evaluation of statistical uncertainties for major classes of covariant energy density functionals (CEDFs) and their propagation with particle number (towards extremes of nuclear landscape) and deformation. These uncertainties are evaluated for different classes of physical observables (ground state and single-particle properties [2], fission barriers [3]) and compared with systematic ones. Moreover, the correlations between the parameters of the CEDFs are evaluated with the goal to see to which degree they are independent. [1] S. E. Agbemava et al, Phys. Rev. C 89, 054320 (2014). [2] S. E. Agbemava and A. V. Afanasjev, submitted to Phys. Rev. C. [3] S. E. Agbemava et al, Phys. C 95, 054324 (2017)   

Hyperheavy nuclei in covariant density functional theory: the existence and stability

The limits of existence of finite nuclei is one of interesting questions of modern low-energy nuclear physics. A lot of theoretical efforts have been dedicated to the study of superheavy nuclei with $Z<126$ [1,2]. However, very little is known about existence and stability of hyperheavy nuclei with proton numbers $Z>126$. Almost all investigations of such nuclei consider only spherical shapes for the ground states [2]. However, the study of superheavy nuclei [2] indicates that such assumption leads in many cases to misinterpretation of the situation. Thus, we performed a systematic investigation of such nuclei for proton numbers from 122 up to 184 and from two-proton drip line up to two-neutron one within the axial relativistic Hartree-Bogoliubov theory [3]. The calculations are carried out in large deformation space extending from megadeformed oblate shapes via spherical ones up to scission configuration. The stability of such nuclei against fission (including triaxial and octupole shapes) and beta-decays have been investigated and the islands of their stability have been defined. [1] S.E. Agbemava et al, Phys. Rev. C 92, 054310 (2015). [2] M. Bender et al, Phys. Lett. B 515, 42 (2001). [3] A. Gyawali et al, in preparation.   

Expressions ForTotal Energy And Relativistic Kinetic Energy At Low Speeds In Special Relativity Must Include Rotational And Vibrational As Well As Linear Kinetic Energies

Einstein calculated the total energy at low speeds in the Special Theory of Relativity to be $E_{total}= m_0c^2 + 1/2m_0v^2.$ However, the total energy must include the rotational and vibrational kinetic energies as well as the linear kinetic energies. If $1/2I\omega^2$ is the expression for the rotational kinetic energy of mass and $1/2kx_0^2$ is the vibrational kinetic energy expression of a typical mass, the expression for the total energy of a mass at low speeds must be $E_{total}= m_0c^2 + 1/2m_0v^2 + 1/2I\omega^2 + 1/2kx_0^2.$ If this expression is correct, the relativistic kinetic energy of a mass. at low speeds must include the rotational and vibrational kinetic energies as well as the linear kinetic energies since according to Einstein $K=(m-m_0)c^2$ and therefore, $K= 1/2m_0v^2 + 1/2I\omega^2 + 1/2kx_0^2.$