Weak Skyrmions and sphalerons

When the gauged non-linear -model is supplemented by a Skyrme term stable as well as unstable classical solutions exist: weak Skyrmions and sphalerons. Without the Skyrme term there remains only a sequence of sphalerons, which can be continued to finite Higgs masses. Here we investigate a model containing both, a finite Higgs mass and a Skyrme term. Stable weak Skyrmion solutions occur only above critical values of the Higgs mass and the Skyrme coupling constant.     

The Skyrme-TQRPA calculations of electron capture on hot nuclei in pre-supernova environment

We combine the thermal QRPA approach with the Skyrme energy density functional theory (Skyrme–TQRPA) for modelling the process of electron capture on nuclei in supernova environment. For a sample nucleus, ⁵⁶Fe, the Skyrme–TQRPA approach is applied to analyze thermal effects on the strength function of GT₊ transitions which dominate electron capture at E _e ≤ 30 MeV. Several Skyrme interactions are used in order to verify the sensitivity of the obtained results to the Skyrme force parameters. Finite-temperature cross sections are calculated and the results are comparedwith those of the other model calculations.     

Neutrino scattering rates in the presence of hyperons from a Skyrme model in the RPA approximation

The contribution of -hyperons to neutrino scattering rates is calculated in the random phase approximation in a model where the interaction is described by a Skyrme potential. Finite temperature and neutrino trapping are taken into account in view of applications to the deleptonization stage of protoneutron star cooling. The hyperons can remove the problem of ferromagnetic instability common to (nearly) all Skyrme parametrizations of the nucleon-nucleon interaction. As a consequence, there is not any longer a pole at the transition in the neutrino-baryon cross-section. However there still remains an enhancement in this region. In the absence of ferromagnetism the mean free path in np matter is reduced compared to its value in np matter as a consequence of the presence of this additional degree of freedom. At high density the results are very sensitive to the choice of the - interaction.     

The Interaction Energy of Well-Separated Skyrme Solitons

We prove that the asymptotic field of a Skyrme soliton of any degree has a non-trivial multipole expansion. It follows that every Skyrme soliton has a well-defined leading multipole moment. We derive an expression for the linear interaction energy of well-separated Skyrme solitons in terms of their leading multipole moments. This expression can always be made negative by suitable rotations of one of the Skyrme solitons in space and iso-space. We show that the linear interaction energy dominates for large separation if the orders of the Skyrme solitons multipole moments differ by at most two. In that case there are therefore always attractive forces between the Skyrme solitons.     

Constant-cutoff approach toSU(3)-symmetry breaking for strange dibaryon states

We suggest a quantum stabilization method for theSU(2)-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB = 1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then show that the approach toSU(3)-symmetry breaking for strange dibaryon states proposed by Kopeliovichet al. can be simplified by omitting the Skyrme stabilizing term and using the constant-cutoff stabilization method. We derive the results for spectra of some strange and nonstrange dibaryon states and obtain the numerical results for the absolute masses of these states, in reasonable agreement with the values obtained, using the complete Skyrme model, by Kopeliovichet al.     

Neutron stars in a Skyrme model with hyperons

Available Skyrme parametrizations with hyperons are examined from the point of view of their suitability for applications to neutron stars. It is shown that the hyperons can attenuate or even remove the problem of ferromagnetic instability common to (nearly) all Skyrme parametrizations of the nucleon-nucleon interaction. At high density the results are very sensitive to the choice of the interaction. The selected parameter sets are then used to obtain the resulting properties of both cold neutron stars and hot protoneutron stars. The general features known from other models are recovered.     

Solitons on Tori and Soliton Crystals

Necessary conditions for a soliton on a torus \({M = \mathbb{R}^m/\Lambda}\) to be a soliton crystal, that is, a spatially periodic array of topological solitons in stable equilibrium, are derived. The stress tensor of the soliton must be L ² orthogonal to \({\mathbb{E}}\) , the space of parallel symmetric bilinear forms on TM, and, further, a certain symmetric bilinear form on \({\mathbb{E}}\) , called the hessian, must be positive. It is shown that, for baby Skyrme models, the first condition actually implies the second. It is also shown that, for any choice of period lattice Λ, there is a baby Skyrme model which supports a soliton crystal of periodicity Λ. For the three-dimensional Skyrme model, it is shown that any soliton solution on a cubic lattice which satisfies a virial constraint and is equivariant with respect to (a subgroup of) the lattice symmetries automatically satisfies both tests. This verifies, in particular, that the celebrated Skyrme crystal of Castillejo et  al., and Kugler and Shtrikman, passes both tests.     

An SO(3) Gauged Skryme Model on R3

A proof of the existence of a spherically symmetric, finite energy solution of the variational equations of an SO(3) gauged Skyrme model on ³ is presented.     

Half-lives of rp-process waiting point nuclei

We give results of microscopic calculations for the half-lives of various proton-rich nuclei in the mass region A = 60-90, which are involved in the astrophysical rp-process, and which are needed as input parameters of numerical simulations in Nuclear Astrophysics. The microscopic formalism consists of a deformed QRPA approach that involves a self-consistent quasiparticle deformed Skyrme Hartree-Fock basis and residual spin-isospin separable forces in both the particle-hole and particle-particle channels. The strength of the particle-hole residual interaction is chosen to be consistent with the Skyrme effective force and mean-field basis, while that of the particle-particle is globally fixed to = 0.07 MeV after a judicious choice from comparison to experimental half-lives. We study and discuss the sensitivity of the half-lives to deformation and residual interactions.     

Constant-Cutoff Approach to Axially Symmetric Dibaryons

We suggest a quantum stabilization method forthe SU(2) -model, based on the constant-cutofflimit of the cutoff quantization method developed byBalakrishna et al., which avoids the difficulties with the usual soliton boundary conditions pointedout by Iwasaki and Ohyama. We investigate the baryonnumber B = 1 sector of the model and show that after thecollective coordinate quantization it admits a stable soliton solution which depends on asingle dimensional arbitrary constant. We then study thedibaryon configurations in this approach, using thegeneralized axially symmetric ansatz to determine the soliton background. Thus we calculate therotational contributions to the masses of the axiallysymmetric dibaryons and show that they are inqualitative agreement with the results obtained usingthe complete Skyrme model. We conclude also that,as in the case of the complete Skyrme model, the lowestallowed S = –2 state has the quantum numbers ofthe H-particle. We find that in the present approach, similarly to the case of the complete Skyrmemodel, this particle is bound, even though the neglectedvacuum effects might contribute to the unbinding of theH-particle.     

Anharmonic corrections in constant-cutoff soliton model

We suggest a quantum stabilization method for theSU(2) -model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB=1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then derive the results for anharmonic corrections to the hyperon energy in the bound-state approach to theSU(3)-soliton model for the hyperons, withSU(3)-symmetry breaking. Thus we show that the anharmonic corrections give, as in the case of the complete Skyrme model, negative contributions to the hyperon energies and that they are of the same order of magnitude as those obtained using the complete Skyrme model for bound heavy-flavor two-meson systems in the case of cascade hyperons.     

Approximately straight kink theories

A precise meaning is given to the idea of a kink theory approximating a vectoror vector-bundle-valued theory. It is shown that vector theories taking values in a vector bundle with groupSO(n- s,s;), acting naturally, do not approximate any kink theory. It is further shown that, where a kink theory is approximated by a vector bundle theory, the field equations in the vector theory can give rise to field equations in the kink theory. The theory of Skyrme and the sine-Gordon theory are of this form. An example is given of a nonlinear modification of electromagnetism having solitonlike solutions.     

Equation of state and symmetry energy within the stability valley

We apply the direct variational method to derive the equation of state for finite nuclei within the stability valley. The extended Thomas-Fermi approximation for the energy functional with Skyrme forces is used. Applying the leptodermous expansion for the profile nucleon densities, we have studied the neutron coat and the isospin symmetry energy for neutron-rich nuclei. Using the equation of state for the pressure, we derive the region of spinodal instability of finite nuclei and its dependence on the mass number, the asymmetry parameter and the Skyrme force parameters. We suggest the procedure of derivation of the isospin symmetry energy from the analysis of the isospin shift of the chemical potential = - beyond the beta-stability line. We show that both the structure of the neutron coat and the position of the drip line depend significantly on the Skyrme force parameters.     

Supercurrent coupling in the Faddeev–Skyrme model

Motivated by the sigma model limit of multicomponent Ginzburg–Landau theory, a version of the Faddeev–Skyrme model is considered in which the scalar field is coupled dynamically to a one-form field called the supercurrent. This coupled model is investigated in the general setting where physical space M$M$ is an oriented Riemannian manifold and the target space N$N$ is a Kähler manifold, and its properties are compared with the usual, uncoupled Faddeev–Skyrme model. In the case N=S²$N=S^2$, it is shown that supercurrent coupling destroys the familiar topological lower energy bound of Vakulenko and Kapitanski when M=R³$M={\mathbb{R}}^3$, and the less familiar linear bound when M$M$ is a compact 3-manifold. Nonetheless, local energy minimizers may still exist. The first variation formula is derived and used to construct three families of static solutions of the model, all on compact domains. In particular, a coupled version of the unit charge hopfion on a three-sphere of arbitrary radius is found. The second variation formula is derived, and used to analyze the stability of some of these solutions. In particular, it is shown that, in contrast to the uncoupled model, the coupled unit hopfion on the three-sphere of radius R$R$ is unstable   for all R$R$. This gives an explicit, exact example of supercurrent coupling destabilizing a stable solution of the usual Faddeev–Skyrme model, and casts doubt on the conjecture of Babaev, Faddeev and Niemi that knot solitons should exist in the low energy regime of two-component superconductors.     

Compression properties of finite nuclei in a semi-classical relativistic approach

Skyrme type potentials are known to lead — in the framework of the scaling model — to a finite-nucleus incompressibility valueK _A where the volume coefficientK _v equals roughly the negative surface coefficient K_s. This is found for Skyrme interactions with K_v between 200 and 360 MeV. In a semi-classical relativistic approach on the basis of the — model (linear as well as non-linear) using in addition local density approximations, we findK _s to depend in particular on the surface energy coefficienta _s , and not so much on the value ofK _v . For a realistic value of a_s, both the linear and the non-linear — model (with NL1 parameter set) yield a ratio ¦K _s K _v ¦ of approximately 1. We discuss implications of this finding with a particular view on recent empirical results onK _v andK _s .Dedicated to Prof. Dr. H. J. Mang on the occasion of his 60th birthday     

Radiative heat transfer analysis in pure water heater used for semiconductor processing

A simplified one-dimensional model is presented to analyze the non-gray radiative transfer in pure water heater used in the rinsing processes within semiconductor production lines, and the ray-tracing method is extended to simulate the radiative heat transfer. To examine the accuracy of the simplified model, the distribution of radiation absorption is determined by the ray-tracing method based the simplified model and compared with the data obtained by three-dimensional non-gray model in combination with Monte Carlo method in reference, and the effects of the water thickness on the radiation absorption are analyzed. The results show that the simplified model has a good accuracy in solving the radiation absorption in the pure water heater. The radiation absorption increases with the water thickness, but when the water thickness is greater than , the radiation absorption increases very slowly with the water thickness.     

Flavored exotic multibaryons and hypernuclei in topological soliton models

The energies of baryon states with positive strangeness, or anticharm (antibeauty), are estimated in the chiral soliton approach, in the “rigid oscillator” version of the bound-state soliton model proposed by Klebanov and Westerberg. Positive strangeness states can appear as relatively narrow nuclear levels (Θ-hypernuclei), and the states with heavy antiflavors can be bound with respect to strong interactions in the original Skyrme variant of the model (SK4 variant). The binding energies of antiflavored states are also estimated in the variant of the model with a sixth-order term in chiral derivatives added to the Lagrangian to stabilize solitons (SK6 variant). This variant is less attractive, and nuclear states with anticharm and antibeauty can be unstable relative to strong interactions. The chances of obtaining bound hypernuclei with heavy antiflavors increase within the “nuclear variant” of the model with a rescaled model parameter (the Skyrme constant e or e′ decreased by a out 30%), which is expected to be valid for baryon numbers greater than B ～ 10. The rational map approximation is used to describe multiskyrmions with a baryon number of up to about 30 and to calculate the quantities necessary for their quantization (moments of inertia, sigma term, etc.).