Nuclear Physics Models Research Articles

Modelling Hadronic Matter

Hadron physics stands somewhere in the diffuse intersection between nuclear and particle physics and relies largely on the use of models. Historically, around 1930, the first nuclear physics models known as the liquid drop model and the semi-empirical mass formula established the grounds for the study of nuclei properties and nuclear structure. These two models are parameter dependent. Nowadays, around 500 hundred non-relativistic (Skyrme-type) and relativistic models are available in the literature and largely used and the vast majority are parameter dependent models. In this review I discuss some of the shortcomings of using non-relativistic models and the advantages of using relativistic ones when applying them to describe hadronic matter. I also show possible applications of relativistic models to physical situations that cover part of the QCD phase diagram: I mention how the description of compact objects can be done, how heavy-ion collisions can be investigated and particle fractions obtained and show the relation between liquid-gas phase transitions and the pasta phase.

Continuity of generalized wave maps on the sphere

We consider a generalization of wave maps based on the Adkins-Nappi model of nuclear physics. In particular, we show that solutions to this equation remain continuous at the origin, which is a first step towards establishing a regularity theory for this equation.

MCNPX simulations of the silicon carbide semiconductor detector response to fast neutrons from D–T nuclear reaction

Silicon Carbide (SiC) has been long recognized as a suitable semiconductor material for use in nuclear radiation detectors of high-energy charged particles, gamma rays, X-rays and neutrons. The nuclear interactions occurring in the semiconductor are complex and can be quantified using a Monte Carlo-based computer code. In this work, the MCNPX (Monte Carlo N-Particle eXtended) code was employed to support detector design and analysis. MCNPX is widely used to simulate interaction of radiation with matter and supports the transport of 34 particle types including heavy ions in broad energy ranges. The code also supports complex 3D geometries and both nuclear data tables and physics models. In our model, monoenergetic neutrons from D–T nuclear reaction were assumed as a source of fast neutrons. Their energy varied between 16 and 18.2 MeV, according to the accelerating voltage of the deuterons participating in D–T reaction. First, the simulations were used to calculate the optimum thickness of the reactive film composed of High Density PolyEthylene (HDPE), which converts neutral particles to charged particles and thusly enhancing detection efficiency. The dependency of the optimal thickness of the HDPE layer on the energy of the incident neutrons has been shown for the inspected energy range. Further, from the energy deposited by secondary charged particles and recoiled ions, the detector response was modeled and the effect of the conversion layer on detector response was demonstrated. The results from the simulations were compared with experimental data obtained for a detector covered by a 600 and 1300 [Formula: see text]m thick conversion layer. Some limitations of the simulations using MCNPX code are also discussed.

Connexions for the nuclear geometrical collective model

The Bohr–Mottelson–Frankfurt model of nuclear rotations and quadrupole vibrations is a foundational model in nuclear structure physics. The model, also called the geometrical collective model or simply GCM(3), has two hidden mathematical structures, one group theoretic and the other differential geometric. Although the group structure has been understood for some time, the geometric structure is a new feature that this paper investigates in some detail. Using the de Rham Laplacian for the kinetic energy extends significantly the physical scope of the GCM(3) model. This Laplacian contains a ‘magnetic’ term due to the connexion between base manifold rotational and fibre vortex degrees of freedom. When the connexion specializes to irrotational flow, the Laplacian reduces to the Bohr–Mottelson kinetic energy operator.

Critical fermion density for restoring spontaneously broken symmetry

We show how the phenomenon of spontaneous symmetry breakdown is affected by the presence of a sea of fermions in the system. When its density exceeds a critical value, the broken symmetry can be restored. We calculate the critical value and discuss the consequences for three different physical systems: First, for the Standard Model (SM) of particle physics, where the spontaneous symmetry breakdown leads to nonzero masses of intermediate gauge bosons and fermions. The symmetry restoration will greatly enhance various processes with dramatic consequences for the early universe. Second, for the Gell-Mann–Lévy [Formula: see text]-model of nuclear physics, where the symmetry breakdown gives rise to the nucleon and meson masses. The symmetry restoration may have important consequences for formation or collapse of stellar cores. Third, for the superconductive phase of condensed-matter, where the BCS condensate at low-temperature may be destroyed by a too large electron density.

Measurement of the EMC effect in the deuteron

We have determined the structure function ratio $R^d_{\rm EMC}=F_2^d/(F_2^n+F_2^p)$ from recently published $F_2^n/F_2^d$ data taken by the BONuS experiment using CLAS at Jefferson Lab. This ratio deviates from unity, with a slope $dR_{\rm EMC}^{d}/dx= -0.10\pm 0.05$ in the range of Bjorken $x$ from 0.35 to 0.7, for invariant mass $W>1.4$ GeV and $Q^2>1$ GeV$^2$. The observed EMC effect for these kinematics is consistent with conventional nuclear physics models that include off-shell corrections, as well as with empirical analyses that find the EMC effect proportional to the probability of short-range nucleon-nucleon correlations.

Nuclear Structure and Setting Constraints on the r-process?

One of the open questions in all of physics today has to do with the site of the r-process. There are uncertainties associated with the astrophysics, the observations, and the physics of nuclei far from stability. This paper uses existing nuclear physics models and their implied properties for nuclei far from stability to determine the nuclei that have the greatest impact on a given astrophysical scenario. The properties considered are nuclear masses, beta- decay rates, and neutron capture rates individually as well as in a correlated way to identify the most important nuclei in a given r-process trajectory. The ultimate goal is to set some constraints on potential sites of the r-process based on the nuclear properties.

The Ultraviolet Cutoff and Water Temperature Dependence of the Sonoluminescence Bubble Spectrum

In this paper, we calculate the emitted light spectrum from the sonoluminescence effect by considering that the vibration modes have a quantized energy like the nuclear energy levels in the collective model in nuclear physics. In this model we characterized the excited mode by the quantum angular momentum, so that the energy of the excited vibration modes comes from the surface vibration parameters of the bubble. We related these parameters to the surface tension of water. We assume that the vibration modes of the bubble with angular momentum J are excited by the acoustic wave and have a probability of excitation proportional to the acoustic wave frequency and angular momentum of the modes. So by using this assumption we tried to explain some characters of the sonoluminescence spectrum.

Exactly solvable pairing models in nuclear and mesoscopic physics

The exact solution of the BCS pairing Hamiltonian dates back to the work of Richardson in 1963. Little attention was paid to this exactly solvable model for almost 40 years. However, at the beginning of the 21th century, there was a burst of work focusing on its applications in different areas of quantum physics. In this contribution we introduce the generalized integrable Richardson-Gaudin models, and discuss a recent application of the hyperbolic model to heavy nuclei.

A Class of -Dimensional Dirac Operators with a Variable Mass

A class of d-dimensional Dirac operators with a variable mass is introduced (), which includes, as a special case, the 3-dimensional Dirac operator describing the chiral quark soliton model in nuclear physics, and some aspects of it are investigated.

On the regularity of the 2+1 dimensional equivariant Skyrme model

One of the most interesting open problems concerning the Skyrme model of nuclear physics is the regularity of its solutions. In this article, we study2+12+1dimensional equivariant Skyrme maps, for which we prove, using the method of multipliers, that the energy does not concentrate. This is one of the important steps towards a global regularity theory.

Three Different Approaches to the Same Interaction: The Yukawa Model in Nuclear Physics

After a brief discussion of the meaning of the potential in quantum mechanics, we examine the results of the Yukawa model (scalar meson exchange) for the nucleon-nucleon interaction in three different dynamical frameworks: the non-relativistic dynamics of the Schrodinger equation, the relativistic quantum mechanics of the Bethe-Salpeter and Light-Front equations and the lattice solution of the Quantum Field Theory, obtained in the quenched approximation.

Branching exponential flights: travelled lengths and collision statistics

The evolution of several physical and biological systems, ranging from neutron transport in multiplying media to epidemics or population dynamics, can be described in terms of branching exponential flights, a stochastic process which couples a Galton–Watson birth–death mechanism with random spatial displacements. Within this context, one is often called to assess the length ℓV that the process travels in a given region V of the phase space, or the number of visits nV to this same region. In this paper, we address this issue by resorting to the Feynman–Kac formalism, which allows characterizing the full distribution of ℓV and nV and in particular deriving explicit moment formulas. Some other significant physical observables associated to ℓV and nV, such as the survival probability, are discussed as well, and results are illustrated by revisiting the classical example of the rod model in nuclear reactor physics.

Validation of nuclear models used in space radiation shielding applications

A program of verification and validation has been undertaken to assess the applicability of models to space radiation shielding applications and to track progress as these models are developed over time. In this work, simple validation metrics applicable to testing both model accuracy and consistency with experimental data are developed. The developed metrics treat experimental measurement uncertainty as an interval and are therefore applicable to cases in which epistemic uncertainty dominates the experimental data. To demonstrate the applicability of the metrics, nuclear physics models used by NASA for space radiation shielding applications are compared to an experimental database consisting of over 3600 experimental cross sections. A cumulative uncertainty metric is applied to the question of overall model accuracy, while a metric based on the median uncertainty is used to analyze the models from the perspective of model development by examining subsets of the model parameter space.

A FINITE NUCLEON EXTENDED VOLUME MODEL FOR NUCLEAR MATTER

We investigate the effects of a finite volume extension for nucleons immersed in nuclear matter. We wish in this way to explore the role played by this non-vanishing (but fixed) volume in shaping nuclear matter properties, in contrast with other models of nuclear physics in which nucleons are treated as point-like particles. We introduce a model characterized by an exclusion volume à la Van der Waals, as well as an effective non-relativistic approximation to model meson-exchange interactions between nucleons. The model is consistent with experimental values of saturation density and binding energy of nuclear matter in the domain of typical densities for neutron stars.

Population Characteristics for Spin and Excitation Energy of Fragments in Thermal Neutron Induced Fission

The characterisation of fragments from nuclear fission in terms of excitation energy and spin population is still a debated subject. We show that data on excitation energy, kinetic energy and spin of the fragments in thermal neutron induced fission of the actinides can be consistently described by the statistical model in nuclear physics. We present an empirical relationship which allows calculating the temperature of fission products at the scission point. From the temperature we derive the distribution functions for excitation, kinetic energy and fragment spin. We compare the results from the statistical model with experimental data from the LOHENGRIN spectrometer at the Institut Laue-Langevin in Grenoble/France.

Proton elastic scattering differential cross-sections for 12C

Carbon depth profiling presents a strong analytical challenge for all the major ion beam analysis (IBA) techniques, with elastic backscattering spectroscopy (EBS) being widely implemented. In the past, the 12C(p,p) 12C reaction has been successfully evaluated for proton beam energies up to 4.5 MeV. Currently, an attempt is being made to extend this evaluation to higher energies, namely up to E p,lab = 7 MeV. There is a certain lack of available and/or coherent datasets in literature for these relatively high proton beam energies at backward angles, suitable for IBA. Moreover, the few existing datasets are in certain cases discrepant. Thus, in the present work, the differential cross-section of proton elastic scattering on carbon were measured between 140°and 170°, in steps of 10°, for the proton beam energy range between 2.7 and 7 MeV. The experimental results obtained, along with data from literature, were evaluated applying nuclear physics models. The evaluated results were benchmarked using a thick, mirror polished glassy carbon target at different beam energies and detector angles.

Statistical validation of HZETRN as a function of vertical cutoff rigidity using ISS measurements

Measurements taken in Low Earth Orbit (LEO) onboard the International Space Station (ISS) and transit vehicles have been extensively used to validate radiation transport models. Primarily, such comparisons were done by integrating measured data over mission or trajectory segments so that individual comparisons to model results could be made. This approach has yielded considerable information but is limited in its ability to rigorously quantify and differentiate specific model errors or uncertainties. Further, as exploration moves beyond LEO and measured data become sparse, the uncertainty estimates derived from these validation cases will no longer be applicable. Recent improvements in the underlying numerical methods used in HZETRN have resulted in significant decreases in code run time. Therefore, the large number of comparisons required to express error as a function of a physical quantity, like cutoff rigidity, are now possible. Validation can be looked at in detail over any portion of a flight trajectory (e.g. minute by minute) such that a statistically significant number of comparisons can be made. This more rigorous approach to code validation will allow the errors caused by uncertainties in the geometry models, environmental models, and nuclear physics models to be differentiated and quantified. It will also give much better guidance for future model development. More importantly, it will allow a quantitative means of extrapolating uncertainties in LEO to free space. In this work, measured data taken onboard the ISS during solar maximum are compared to results obtained with the particle transport code HZETRN. Comparisons are made at a large number (∼77,000) of discrete time intervals, allowing error estimates to be given as a function of cutoff rigidity. It is shown that HZETRN systematically underestimates exposure quantities at high cutoff rigidity. The errors are likely associated with increased angular variation in the geomagnetic field near the equator, the lack of pion production in HZETRN, and errors in high energy nuclear physics models, and will be the focus of future work.

OLTARIS: On-line tool for the assessment of radiation in space

OLTARIS (On-Line Tool for the Assessment of Radiation In Space) is a space radiation analysis tool available on the World Wide Web. It can be used to study the effects of space radiation for various spacecraft and mission scenarios involving humans and electronics. The transport is based on the HZETRN transport code and the input nuclear physics model is NUCFRG. This paper describes the tools behind the web interface and the types of inputs required to obtain results. Typical inputs are mission parameters and slab definitions or vehicle thickness distributions. Radiation environments can be chosen by the user. This paper describes these inputs as well as the output response functions including dose, dose equivalent, whole body effective dose equivalent, LET spectra and detector response models.

Exact nuclear data uncertainty propagation for fusion neutronics calculations

Recently, we have presented an exact method (now called “Total Monte Carlo”) to propagate uncertainties of fundamental nuclear physics experiments, models and parameters to different types of criticality-safety benchmarks. We now show that such exact uncertainty calculations are directly relevant to the optimal and safe design of fusion reactors by applying this methodology to a series of fusion shielding benchmarks, namely those connected to the Oktavian, Fusion Neutronics Source and LLNL Pulsed Sphere experiments. Uncertainties on neutron and gamma leakage fluxes for 13 shielding benchmarks are obtained, in the mass range from natMg to natW. Uncertainties for cross-sections, angular distributions, single- and double-differential emission spectra, and gamma-ray production cross-sections are considered in this uncertainty propagation scheme.