Light Nuclear Systems Research Articles

Systematics of fusion of light nuclei

We have constructed the empirical formula for fusion barrier height (VB), fusion barrier position (RB), and inverted parabola (ħω) of light nuclei with atomic number in the range 2≤ZC≤10. This formula is obtained by studying the fusion barrier characteristics of 333 projectile target combinations. The values produced by the present formula are also compared with experiments. The present semi-empirical formula produces fusion barrier characteristics of light nuclei with the simple inputs of mass number (A) and atomic number (Z) of projectile targets. This semi-empirical formula can be utilized to calculate and interpret fusion barrier characteristics in light nuclear systems.

Towards a Bayesian evaluation technique for light nuclear systems

Towards a Bayesian evaluation technique for light nuclear systems

The 5α condensate state in 20Ne

The formed 4He (α) clusters consisting of two neutrons and two protons can be a building block in light nuclear systems. Intriguingly, these alpha clusters could potentially form alpha condensate states within the nuclear system. The Hoyle state at 7.65 MeV in 12C, which plays an essential role in stellar nucleosynthesis, is now considered to be a phase transition, namely the 3α Bose-Einstein condensate. Confirming the existence of Hoyle-analog states in Nα nuclei (N > 3) remains a major challenge. Here we show microscopic five-body calculations for the 20Ne nucleus. We find that one excited 0+ state has a distinct gas-like characteristic and represents the condensate state. Identifying the 5α condensate state is an important step in establishing the concept of α condensation in nuclear fermion systems.

Many-body expansion for light nuclear systems

We extend the many-body expansion (MBE), previously applied to hydrogen bonded and molecular systems, to the light nuclear systems $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$ by considering the nucleonic degrees of freedom as fundamental in the expansion. The analysis is based on the Pauli nucleonic dynamics (PND) model, a simple antisymmetrized dynamical code, inspired by the sophisticated constrained molecular dynamics (CoMD) model. The total energy of the $^{2}\mathrm{H}$ nucleus is calculated with this model at \ensuremath{-}2.312 MeV, which is within 4% of the experimental value of \ensuremath{-}2.225 MeV. The application of the MBE yields results for the three-body term in the $^{3}\mathrm{H}$ nucleus that is comparable with previous estimates, while it is reported for the first time for the nucleus of $^{3}\mathrm{He}$. The energies of $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$ that include the sum of the one- and two-body terms with the model are $\ensuremath{-}6.97\ifmmode\pm\else\textpm\fi{}0.21$ MeV and $\ensuremath{-}6.19\ifmmode\pm\else\textpm\fi{}0.21$ MeV and the three-body terms, estimated from the difference of the sum of the one- and two-body terms from the experimentally measured energies, are $\ensuremath{-}1.51\ifmmode\pm\else\textpm\fi{}0.21$ MeV and $\ensuremath{-}1.53\ifmmode\pm\else\textpm\fi{}0.21$ MeV, respectively. The MBE for the $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$ nuclei is qualitatively similar to the one previously reported for the water trimer: the two- and three-body terms are negative with the latter amounting to $\ensuremath{\sim}3%$ of the former. Additionally, the three-body terms correspond to about 16--23% of the total energy of the bound systems, a percentage that is also comparable to the one in the water trimer (17%). In this manner, the MBE analysis can be applied to light nuclear systems following the same protocol as the one that has been previously extensively used for hydrogen bonded molecular systems.

A novel R-matrix formalism for three-body channels

At low incident neutron energies nuclear reaction cross sections exhibit a distinct resonance structure which cannot properly be described by (semi-)microscopic models. Usually R-matrix theory is applied which provides a suffi ciently accurate but phenomenological description of the resonance region. However, standard R-matrix theory is only suited for two-particle channels. Three- and many-particle channels which may occur in light nuclear systems even at rather low incident energies are usually treated in an approximative or effective way. In this contribution a novel R-matrix formalism for three-body channels and its application to nuclear systems will be presented. It is a generalized and significantly modified form of a proposal by W. Glöckle based on the Faddeev equations.

A new R-matrix module for multi-channel calculations with GECCCOS

A versatile new R-matrix module for multi-channel reaction calculations was introduced into the code GECCCOS (GEneral Coupled-Channel COde System) which has been developed by the nuclear data group at TU-Wien to perform nuclear reaction calculations especially for light nuclear systems. It provides a tool for phenomenological R-matrix analyses of reaction data combined with calculations of a potential-based calculable R-matrix using the Lagrange-mesh technique. In addition it provides a platform for the development of non-standard extensions of R-matrix theory such as Reduced R-matrix analyses and the Hybrid R-matrix. A successful run of the code yields the complete S-matrix (collision matrix) as well as observables for unpolarized beams, angle-differential cross sections, excitation functions and, if existing, angle-integrated cross sections. Recently, extensions to polarization observables for spin-1/2 and spin-1 particles were implemented and tested. For phenomenological R-matrix analyses a separate module assembles calculated and available experimental values, automatically performs transformations with regard to reference frame and matching radii. Furthermore it allows to switch between incident channel and compound nucleus representation and provides the necessary feedback for the chi2 fitting process.

From correlations to universal behavior in few-nucleon systems

The deuteron, the only two-nucleon bound state, has a shallow character: its binding energy is strictly related to zero-energy parameters, the triplet scattering length 3anp and triplet effective range 3rnp. This fact places the deuteron inside the universal window, a region in which systems having a large value of the two- body scattering length are located. When the scattering length is large compared to the interaction range certain types of correlations can be observed. Increasing the number of nucleons these correlations are responsible for the particular spectrum of light nuclei as for example the lack of excited states in three- and four-nucleon systems. In this presentation some constraints imposed by the large values of the singlet and triplet scattering lengths in the spectrum of light nuclear systems are discussed.

Electric Quadrupole Moment of 7Li nucleus using Complex Generator Co-ordinate Technique

The electric quadrupole moment (EQM) of a nucleus is an important parameter used to determine the departure of the nucleus from its spherical shape. Besides the study of the nucleus, determination of the EQM value finds applications in solid state physics and in other areas such as chemical, medical and biological sciences. This paper focuses on a method developed for the calculation of nuclear structural properties of light nuclear systems which is used here to calculate the nuclear electric quadrupole moment for the ground state of 7lithium nucleus. In this approach the required anti-symmetrized nuclear wave function is constructed by using combination of shell model, cluster model, resonating group method, generator coordinate method, and the complex generator coordinate technique. The ground state of 7li nucleus is considered as a nuclear system consisting of one alpha cluster, one deuteron cluster and a neutron cluster. The wave function is written by taking internal spatial function, spin, and isospin functions where arguments of the internal function of clusters include the parameter coordinates and generator coordinates. The consideration of the parameters viz., total angular momentum, spin, and definite parity of the nucleus makes the approach inclusive. While the relative motion wave functions are taken into account between the alpha cluster and deuteron cluster and secondly between the alpha cluster and neutron cluster. The potential chosen in this approach is the Wood-Saxon potential which is somewhat between harmonic oscillator potential well and square well potential. By incorporating all the aforesaid inputs, a matrix of 7×7 order is constructed which leads to the calculation of EQM of 7lithium. The results compared with the available experimental and other theoretical data. The present value of EQM is found in good agreement with experimental data.

Bayesian analysis of nuclear polarizability corrections to the Lamb shift of muonic H-atoms and He-ions

The extraction of nuclear charge radii from spectroscopy experiments in muonic atoms is currently limited by the large uncertainties associated with the theoretical evaluation of the nuclear polarizability effects. To facilitate calculations, these polarizability corrections are conventionally expressed as an expansion in a dimensionless parameter η, which has been argued in previous literature to hold an approximate value of 0.33 in light-nuclear systems. In this work, we check this claim by doing a Bayesian analysis of the nuclear-polarizability corrections to the Lamb shift in μ 2H and μ 3H atoms and in μ 3He+ and μ 4He+ ions at various orders in the η-expansion. Our analysis supports the claim that η ≪ 1 in these systems and finds truncation uncertainties that are similar to the previous estimate, the only exception being the truncation uncertainties in the μ 3He+ ion, which are found to be larger.

Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei

Background: At the forefront of nuclear science, unstable nuclei are of special significance, in which the deformation and pairing correlations play an essential role in determining the nuclear structure. Under the mean field approach, the pairing and deformation effects have been uniformly considered within the deformed nonrelativistic Hartree-Fock-Bogoliubov model and the deformed relativistic Hartree-Bogoliubov (D-RHB) model. However, due to the limitation of the Hartree approach, an important ingredient of the nuclear force---the tensor force that contributes via the Fock diagram---is missing in the D-RHB model. Recently, the axially deformed relativistic Hartree-Fock (D-RHF) model was established for deformed nuclei, in which the $\ensuremath{\pi}$-pseudovector ($\ensuremath{\pi}$-PV) coupling can take into account the tensor force effects naturally. While limited by the BCS pairing, it cannot be safely applied to describe unstable nuclei.Purpose: The aim of this work is to develop the axially deformed relativistic Hartree-Fock-Bogoliubov (D-RHFB) model for the reliable description of a wide range of unstable nuclei, by utilizing the spherical Dirac Woods-Saxon (DWS) base.Method: Staring from the Lagrangian density that is based on the meson-propagated picture of nuclear force, the full Hamiltonian, that contains both mean field and pairing contributions, is derived by quantizing the Dirac spinor field in the Bogoliubov quasiparticle space, and the expectation with respect to the Bogoliubov ground state gives the full energy functional. As an extension of the D-RHF model, the degree of freedom associated with the $\ensuremath{\rho}$-tensor ($\ensuremath{\rho}\text{\ensuremath{-}}\mathrm{T}$) coupling is implemented, and incorporating with the Bogoliubov scheme the finite-range Gogny force D1S is utilized as the pairing force. Moreover, qualitative analyses on the nature of the $\ensuremath{\pi}$-PV and $\ensuremath{\rho}\text{\ensuremath{-}}\mathrm{T}$ couplings are presented to better understand their enhancements on the deformation effects.Results: Space convergence related to the spherical DWS base is confirmed for the D-RHFB model by taking light nucleus $^{24}\mathrm{Mg}$ and mid-heavy one $^{156}\mathrm{Sm}$ as candidates. Compared to light nuclei, extraordinarily more negative energy states are necessitated to keep the expansion completeness on the spherical DWS base for mid-heavy and heavy nuclei, due to the enhanced correlations between the expansion components with large $\ensuremath{\kappa}$ quantity, as indicated by the nature of the $\ensuremath{\pi}$-PV and $\ensuremath{\rho}\text{\ensuremath{-}}\mathrm{T}$ couplings. Furthermore, because of the enhanced deformation effects by the $\ensuremath{\pi}$-PV and $\ensuremath{\rho}\text{\ensuremath{-}}\mathrm{T}$ couplings, the RHF Lagrangian PKA1 presents a deeper bound ground state for $^{24}\mathrm{Mg}$ than the other selected Lagrangians, in addition to predicting a fairly deep bound local minimum with large oblate deformation.Conclusions: The axially deformed relativistic Hartree-Fock-Bogoliubov model has been established with confirmed convergence checks. The effects of the $\ensuremath{\pi}$-PV and $\ensuremath{\rho}\text{\ensuremath{-}}\mathrm{T}$ couplings, coupled with nuclear deformation, are analyzed in both light and mid-heavy nuclear systems, and are expected to be manifested in a wide range of unstable nuclei.

Experimental studies of clustering in light nuclei: 11,12,13,16C

Different, complementary, techniques are used to experimentally probe clustering aspects in several carbon isotopes: $$^{11,12,13,16}$$C. Our approaches involve breakup reactions with radioactive cocktail beams ($$^{16}$$C), compound nucleus reactions and resonant scattering at low energies ($$^{11,13}$$C), and direct reactions with the detection of in-flight resonance decay fragments ($$^{12}$$C). In this paper, we discuss results of our experimental campaign: in $$^{11}$$C, we unveil the existence of a new excited state, characterized by clustering nature, at an excitation energy of 9.36 MeV ($$5/2^-$$); the decay path of the Hoyle state in $$^{12}$$C (7.654 MeV, $$0^+$$) is investigated with unprecedented precision; we refine the spectroscopy of $$^{13}$$C above the $$\alpha $$-threshold supporting the possible appearance of the $$K^\pi ={3/2}^\pm $$ molecular bands, based on the $$\alpha + ^{9}$$Be structure, previously discussed in the literature; in $$^{16}$$C, we find evidence for $$^{6}$$He–$$^{10}$$Be decays. Our findings have an impact on the understanding of clustering phenomena in light nuclear systems.

Sequential binary decay of light nuclear systems: An assessment of statistical model codes

The sequential decay of excited nuclei is described as a succession of binary processes involving fragments in their ground, excited-bound and unbound states. Primary together with secondary decays lead to the final mass and charge distributions. Asymmetric mass splittings involving nucleon emission up to symmetric binary ones are treated within the Weisskopf evaporation formalism, in a unified manner. This procedure was imple- mented in the Monte-Carlo multi-step statistical model code MECO (Multisequential Evaporation COde). We study the evolution of the calculated final mass and charge distributions from 40Ar* as a function of the excitation energy, up to complete dissociation. Our results are compared with the predictions of statistical evaporation codes based on different assumptions for the compound nucleus decay.

Analysis of excited states in 13C and their cluster structure

An accurate understanding of the spectroscopy of 13C is key to understand clustering phenomena in light nuclear systems. In this nucleus, many theoretical models predict the existence of α-cluster configurations, stabilized by the presence of an extra neutron. Despite of its importance, the spectroscopy of13C is still affected by ambiguities, demanding for new data against which benchmarking the models. We improve the knowledge on the 13C level scheme by means of a comprehensive R-matrix analysis of several experimental data sets. Our new spectroscopic information contributes to solve existing ambiguities in 13C structure and will serve a valid benchmark for theoretical models attempting to describe clustering in neutron rich systems.

Lattice QCD input for nuclear structure and reactions

Explorations of the properties of light nuclear systems beyond their lowestlying spectra have begun with Lattice Quantum Chromodynamics. While progress has been made in the past year in pursuing calculations with physical quark masses, studies of the simplest nuclear matrix elements and nuclear reactions at heavier quark masses have been conducted, and several interesting results have been obtained. A community effort has been devoted to investigate the impact of such Quantum Chromodynamics input on the nuclear many-body calculations. Systems involving hyperons and their interactions have been the focus of intense investigations in the field, with new results and deeper insights emerging. While the validity of some of the previous multi-nucleon studies has been questioned during the past year, controversy remains as whether such concerns are relevant to a given result. In an effort to summarize the newest developments in the field, this talk will touch on most of these topics.

Constraining presaddle dissipation with fission cross sections of light nuclear systems

Nuclear fission is hindered by dissipation. Based on the stochastic Langevin model, we calculate the drop of fission cross section caused by friction with respect to its standard statistical-model value, ${\ensuremath{\sigma}}_{f}^{\mathrm{drop}}$, as a function of the presaddle friction strength ($\ensuremath{\beta}$) for fissioning nuclei $^{205}\mathrm{Bi}$, $^{215}\mathrm{Fr}$, $^{225}\mathrm{Pa}$, and $^{230}\mathrm{Np}$ at different angular momenta and excitation energies. It is found that with increasing the size of fissioning systems, the sensitivity of ${\ensuremath{\sigma}}_{f}^{\mathrm{drop}}$ to $\ensuremath{\beta}$ is reduced substantially, and it disappears for the $^{230}\mathrm{Np}$ system. Our findings suggest that on the experimental side, to more stringently constrain the presaddle dissipation strength by measuring fission excitation functions, it is optimal to yield those fissioning systems with a small size.

Standard model contribution to the electric dipole moment of the deuteron, 3H, and 3He nuclei

We calculate for the first time the electric dipole moment (EDM) of the deuteron, 3H, and 3He nuclei generated by the one-meson exchange CP-odd nuclear force in the standard model. The effective |ΔS| = 1 four-quark operators are matched to the |ΔS| = 1 standard model processes involving the CP phase of the Cabibbo-Kobayashi-Maskawa matrix at the electroweak scale and run down to the hadronic scale μ = 1 GeV according to the renormalization group evolution in the next-to-leading logarithmic order. At the hadronic scale, the hadron matrix elements are modeled in the factorization approach. We then obtain the one-meson (pion, eta meson, and kaon) exchange CP-odd nuclear force, which is the combination of the |ΔS| = 1 meson-baryon vertices which issue from the penguin operator and the hyperon-nucleon transition. From this CP-odd nuclear force, the nuclear EDM is calculated with the realistic Argonne v18 interaction and the CP-odd nuclear force using the Gaussian expansion method. It is found that the EDMs of light nuclear systems are of order O (10−31)e cm. We also estimate the standard model contribution to other hadronic CP violating observables such as the EDMs of 6Li, 9Be nuclei, and the atomic EDMs of 129Xe, 199Hg, 211Rn, and 225Ra generated through the nuclear Schiff moment. We then analyze the source of theoretical uncertainties and show some possible ways to overcome them.

Thermal Recovery of Plastic Deformation in Dissimilar Metal Weld

Stainless steel has been widely used in challenging environments typical to nuclear power plant structures, due its excellent corrosion resistance. Nickel filler metals containing high chromium concentration, including Alloy 82/182, are used for joining stainless steel to carbon steel components to achieve similar high resistance to stress corrosion cracking. However, the joint usually experience weld metal stress corrosion cracking (SCC), which affects the safety and structural integrity of light water nuclear reactor systems. A primary driving force for SCC is the high tensile residual stress in these welds. Due to large dimension of pressure vessel and limitations in the field, non-destructive residual stress measurement is difficult. As a result, finite element modeling has been the de facto method to evaluate the weld residual stresses. Recent studies on this subject from researchers worldwide report different residual stress value in the weldments [5]. The discrepancy is due to the fact that most of investigations ignore or underestimate the thermal recovery in the heat-affect zone or reheated region in the weld. In the current study, the effect of heat treatment on thermal recovery and microhardness is investigated for materials used in dissimilar metal joint. It is found that high equivalent plastic strains are predominately accumulated in the buttering layer, the root pass, and the heat affected zone, which experience multiple welding thermal cycles. The final cap passes, experiencing only one or two welding thermal cycles, exhibit less plastic strain accumulation. Moreover, the experimental residual plastic strains are compared with those predicted using an existing weld thermo-mechanical model with two different strain hardening rules. The importance of considering the dynamic strain hardening recovery due to high temperature exposure in welding is discussed for the accurate simulation of weld residual stresses and plastic strains. Finally, the experimental result reveals that the typical post-buttering heat treatment for residual stress relief may not be adequate to completely eliminate the residual plastic strains in the buttering layer.

Dynamics of light, intermediate, heavy and superheavy nuclear systems formed in heavy-ion collisions

The dynamical description of light, intermediate, heavy and superheavy nuclei formed in heavy-ion collisions is worked out using the dynamical cluster decay model (DCM), with reference to various effects such as deformation and orientation, temperature, angular momentum etc. Based on the quantum mechanical fragmentation theory (QMFT), DCM has been applied to understand the decay mechanism of a large number of nuclei formed in low-energy heavy-ion reactions. Various features related to the dynamics of competing decay modes of nuclear systems are explored by addressing the experimental data of a number of reactions in light, intermediate, heavy and superheavy mass regions. The DCM, being a non-statistical description for the decay of a compound nucleus, treats light particles (LPs) or equivalently evaporation residues (ERs), intermediate mass fragments (IMFs) and fission fragments on equal footing and hence, provides an alternative to the available statistical model approaches to address fusion–fission and related phenomena.

Strange Light Nuclei

Strange means 1) unusual or surprising, especially in a way that is difficult to explain or understand or 2) having strangeness degree of freedom. Light nuclear systems with strangeness, light hypernuclei, are perfect playground to study baryon force which would be a bridge between well established nuclear force in low energy region and QCD, the first principle of the strong interaction. Overview of study of light hypernuclei is given and recent experimental findings are reviewed.

Simplicity from Complexity

The emergence of clustering in light nuclear systems is explored using the deformed harmonic oscillator as a starting point. The experimental evidence for various geometrical arrangements of clusters in carbon-12 is discussed.