Approach to Perturbative QCD Results in Transition Amplitudes of NucleonNegative-Parity Resonances

The scaling behaviors of the nucleon resonance transition amplitudes from perturbative QCD (PQCD) are utilized to parametrize the amplitudes of the first negative-parity nucleon resonance . Our analysis indicates that the constraints of the transition amplitude for the resonance at the limit by QCD sum rule calculations are not applicable at a moderate range of compared with the present available data if the contribution of is dominant in the limit.

SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach

We present Path Integral Monte Carlo C code for calculation of quantum mechanical transition amplitudes for 1Dmodels.The SPEEDUP C code is based on the use of higher-order short-time effective actions and implemented to themaximal order p=18 in the time of propagation(Monte Carlo time step),which substantially improves the convergence of discretized amplitudes to their exact continuum values.Symbolic derivation of higher-order effective actions is implemented in SPEEDUP Mathematica codes,using the recursive Schrodinger equation approach.In addition to the general 1D quantum theory,developed Mathematica codes are capable of calculating effective actions for specific models,for general 2D and 3D potentials,as well as for a general many-body theory in arbitrary number of spatial dimensions.

Pion-photon and kaon-photon transition distribution amplitudes in the Nambu–Jona-Lasinio model

The Nambu–Jona-Lasinio model is utilized to investigate the pion-and kaon-photon leading-twist transition distribution amplitudes using proper time regularization.Separately,the properties of the vector and axial vector pion-photon transition distribution amplitudes are examined,and the results meet the desired properties.Our study involves sum rule and polynomiality condition.The vector and axial vector pion-photon transition form factors that are present in theπ^(+)→γe^(+)νprocess are the first Mellin moments of the pion-photon transition distribution amplitudes.The vector transition form factor originates from the internal structure of hadrons,the axial current can be coupled to a pion,this pion is virtual,and its contribution will be present independently of the external hadrons.The kaon transition form factors are similar.The vector form factor's value at zero momentum transfer is determined by the axial anomaly,while this is not the case for the axial one.The vector and axial form factors,as well as the neutral pion vector form factor F_(πγγ)(t),are depicted.According to our findings,the pion axial transition form factor is harder than the vector transition form factor and harder than the electromagnetic form factor.We also discuss the link betweenπ−γandγ−πtransitions distribution amplitudes.

Single ionization of helium atoms by energetic fully stripped carbon ions

A four-body distorted wave approximation is presented for theoretical investigations of the single ionization of groundstate helium atoms by fully stripped carbon ions at impact energies of 2 MeV/amu and 100 MeV/amu. The nine-dimensional integrals for the partial quantum-mechanical transition amplitudes of the specified reaction are reduced to some analytical expressions or one-dimensional integrals over real variables. Fully differential cross sections（FDCSs） are calculated and compared with their experimental values as well as the results obtained from other theories. Despite the simplicity and quickness of the proposed quadrature, the comparison shows that the obtained results are in reasonable agreement with the experiment and are compatible with those of other complicated theories.

Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation

A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-invariant transition probability amplitudes is derived.

Spatial variations of terrain and their impacts on landscape patterns in the transition zone from mountains to plains—A case study of Qihe River Basin in the Taihang Mountains

Terrain plays a key role in landscape pattern formation, particularly in the transition zones from mountains to plains.Exploring the relationships between terrain characteristics and landscape types in terrain-complex areas can help reveal the mechanisms underlying the relationships. In this study, Qihe River Basin, situated in the transition zone from the Taihang Mountains to the North-China Plain, was selected as a case study area. First, the spatial variations in the relief amplitudes(i.e.,high-amplitude terrain undulations) were analyzed. Second, the effects of relief amplitudes on the landscape patterns were indepth investigated from the perspectives of both landscape types and landscape indices. Finally, a logistic regression model was employed to examine the relationships between the landscape patterns and the influencing factors(natural and human) at different relief amplitudes. The results show that with increasing relief amplitude, anthropogenic landscapes gradually give in to natral landscapes. Specifically, human factors normally dominate the gentle areas(e.g., flat areas) in influencing the distribution of landscape types, and natural factors normally dominate the highly-undulating areas(e.g., moderate relief areas). As for the intermediately undulating areas(i.e.,medium relief amplitudes), a combined influence of natural and human factors result in the highest varieties of landscape types. The results also show that in micro-relief areas and small relief areas where natural factors and human factors are more or less equally active,landscape types are affected by a combination of natural and human factors.The combination leads to a high fragmentation and a high diversity of landscape patterns. It seems that appropriate human interferences in these areas can be conducive to enhancing landscape diversity and that inappropriate human interferences can aggravate the problems of landscape fragmentation.