arXiv subjects
Publications and source records attributed to Castaly Fan.
We show 2 matrices that have identical eigenvalues but different eigenfunctions. This shows that in obtaining two body nuclear matrix elements empirically, it is not sufficient to consider only energy levels. Other quantities like transitions must also be included.
With shell model codes being able to encompassing larger and larger spaces we find that the percentage occupancy of the leading spaces becomes smaller and smaller. How can the shell model survive in such circumstances? We will not solve this puzzle here but rather will show examples where, with some explanations, the shell model holds fast. We will use nuclear moments as an example.
In 1967 Akito Arima spent a year as a visiting professor in the physics department of Rutgers University. In this work we pay tribute to him by discussing topics that we worked on that were directly influenced by his works or were closely related to his interests. These include nuclear Symmetries, magnetic and other moments, analytic expressions in the single $j$ shell model and schematic interactions.
We continue here to study simple matrix models of quantum mechanical Hamiltonians. The eigenvalues and eigenfunctions were associated energy levels and wave functions. Whereas previously we considered the weak coupling limits of our models, we here address the more difficult strong coupling limits. We find that the wave functions fall into 2 classes and we can assign a quantum number to distinguish them. Implications for transition rates are also discussed.
This is a brief technical note of analyzing the $\nu_\mu$ disappearance in SBN detector. We here provide a kind of method of plotting the histograms and the heat map plot. We will explore the properties via ROOT framework supported by CERN. The main language we used is C++.
We perform shell model calculations for $^{48}$Cr using GXPF1A and FPD6 interactions by varying single particle energies. We find a scaling behavior which leads to the finding that many different sets of interactions with vastly different single particle energies can give almost identical results for the yrast spectrum of $^{48}$Cr
We compare the effects of turning off and turning on the T=0 interaction on the spectra of 92Pd and 48Cr--both 8 particle systems. We find qualitative differences for the 2 nuclei.Turning the T=0 interaction off destroys the linearity in 92Pd but not in 48Cr. We also consider B(E2)'s and static quadruple moments.