Searcharxiv⌕ Search

arXiv subjects

Larry Zamick

Publications and source records attributed to Larry Zamick.

At least 19 recordsLinked to original sources
arXiv2026

Spectroscopy of 211,213,215Pb isotopes and seniority properties

We first consider lead isotopes with valence neutrons in the g9/2shell. We especially compare 211Pb (n=3), 213Pb (n=5) and 215Pb (n=7), 213Pb being at mid-shell. Motivated by the fact the J = 21/2+ and J =3/2+ states are pure seniority v=3 states for both n=3 and n=5, we compare the energy splitting E(J=21/2+)-E(J=3/2+) for various interactions. We then discuss the position of the lowest J=3/2+ state in both n=3 and n=5, although, this state has not been found experimentally. Calculations with configurations beyond g9/2 are also considered. We next address the fact that the J=21/2+ state is isomeric for both n=3 and n=5.

nucl-th↗
arXiv2023

The Sturdiness of the Shell Model: Informal Review

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.

nucl-th↗
arXiv2023

Systematic shell-model study for structure and isomeric states in $^{200-210}$Po isotopes

We report systematic large-scale shell-model calculation for Po isotopes with $A=$ 200 to 210. We have performed calculations using KHH7B interaction in the model space $Z$ = 58-114 and $N$ = 100-164 around doubly-magic $^{208}$Pb. We allow valence neutrons to occupy in the $1f_{5/2}$, $2p_{3/2}$, $2p_{1/2}$, and $0i_{13/2}$ orbitals, while two valence protons beyond $Z=82$ are occupied in $0h_{9/2}$, $1f_{7/2}$ and $0i_{13/2}$ orbitals. The calculated energies and electromagnetic properties are compared with the available experimental data and predicted where experimental data are not available. We have also reported shell-model results for different isomeric states of these nuclei.

nucl-th↗
arXiv2022

The Nuclear g9/2 Shell -Comparison of our work with an old B.H. Flowers Paper

In an old paper [ 1] B.H. Flowers discussed calculations for odd A nuclei in the g9/2 shell. He finds when he varies the parameters of a certain interaction that the lowest energy state is always a seniority v=1 state with angular momentum J=9/2+. However experiments show about half the states have J=9/2+ lower and the other ones have J=7/2+ lower. More recently we considered selected nuclei between Z=40 and Z=50. For lower odd N Zr isotopes we find J=7/2+ comes below J=9/2+ while for odd Z isotones near Z=50 the opposite is true i.e. J=9/2+ comes below J= 7/2+.We justify using different interactions in the 2 regions by considering nuclear deformation near the Z=40 region. A plea to find missing energy levels is made.

nucl-th↗
arXiv2022

Back and Forth with Akito Arima

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.

nucl-th↗
arXiv2021

Minimal Theory of Isomerism -Q.Q and Other Interactions

We perform shell model calculations using a quadrupole-quadrupole interaction (Q.Q) in single a j shell space. We show that this one-parameter interaction is a good predictor of where nuclear isomerism occurs and where it does not occur. The limitations of this interaction are also discussed. We then include other interactions e.g. in the f_{7/2} shell those obtained from the (local) spectrum of a 2 particle system and then from a 2 hole system. In the g_{9/2}where there is insufficient empirical data from the 2 hole system and so various empirical interactions are used.

nucl-th↗
arXiv2021

Matrix Model: Emergence of a Quantum Number in the Strong Coupling Regime

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.

nucl-th↗
arXiv2020

Wave Functions of Pentadiagonal Matrices in the Weak Coupling Limit

We consider a pentadiagonal matrix which will be described in the text. We demonstrate practical methods for obtaining weak coupling expressions for the lowest eigenvector in terms of the parameters in the matrix, v and w. It is found that the expressions simplify if the wave function coefficients are put in the denominator.

physics.gen-ph↗
arXiv2020

The Q.Q Interaction and Variation of Single Particle Energies

In this work we make further studies of the quadrupole quadrupole interaction used in shell model calculations.Whereas in a previous work we adjusted the single particle energies so as to obtain the rotatonal spectrum of the Elliott model, we here vary the single particle energies and see the various spectral shapes that evolve.

nucl-th↗
arXiv2020

Distribution of Magnetic Dipole Strength -Binning

In previous works we examined the systematics of magnetic dipole transitions in a single j shell. We here extend the study to large space calculations. We consider Ti and Cr isotopes.. In this work we focus on the B(M1) strength as a function of excitation of energy. The initial state is the lowest J= state. T=1 state in a specified nucleus. The final states are J=0 T=2 , all in one plot, and J=2 T=2 in another. The initial figures have points all over the map although there is a suggestion of an exponential trend. To reduce clutter we perform binning operations in which the summed strength in a given energy interval is represented by a single point. The new binning curves show more clearly the exponential fall of B(M1)'s with energy.

nucl-th↗
arXiv2020

Calculated Inter-band B(E2)'s in the p-f Shell

Whereas previous works for B(E2)'s in the even-even Ti isotopes focused on yrast transitions we here also consider inter-band transitions to a second group i.e. states like 1_{1} , 2_{2}, 3_{1} , 4_{2} , 5_{1}e.t.c.. We focus on variations from one even-even Ti isotope to the next. We make a qualitative comparison with similar transitions in a heavier deformed nucleus.

nucl-th↗
arXiv2019

Shell Model Symmetries-Honoring Franco Iachello

We discuss L=0 vs L=2 couplings, symmetries of the pairing interaction for neutrons and protons, and the J_{max} interaction. We show that certain schematic interactions yield exponentially decreasing transition strengths.We compare shell model calculations of B(E2)'s and quadrupole moments in the p-f shell with collective model results.

nucl-th↗
arXiv2019

Cascade Calculations with Schematic Interactions

In previous works we considered schematic Hamiltonians represented by simplified matrices. We defined 2 transition operators and calculated transition strengths from the ground state to all exited states. In many cases the strengths decreased nearly exponentially with excitation energy. Now we do the reverse We start with the highest energy state and calculate the cascade of transitions until the ground states is reached. On a log plot we show the average transition strength as a function of the number of energy intervals that were crossed. We give an analytic proof of exponential behavior for transition strength in the weak coupling limit for the T2 transition operator.

nucl-th↗
arXiv2019

Relation between exponential behavior and energy denominators -- Weak Coupling Limit

We show some interesting properties of tridiagonal and pentadiagonal matrices in the weak coupling limits. In the former case of this limit the ground state wave function amplitudes are identical to the Taylor expansion coefficients of the exponential function e$^{(-v/E)}$. With regards to transition rates a dip in the pentadiagonal case which is not present in the tridiagonal case is explained. An intimate connection between energy denominators and exponential behavior is demonstrated.

quant-ph↗
arXiv2018

Matrix Model of Strength Distribution: Extension and Phase Transition

In this work we extend a previous study of matrix models of strength distributions. We still retain the nearest neighbor coupling mode but we extend the values the coupling parameter v. We consider extremes, from very smal v to very large v. We first use the same transiiton operator as before \textless{}n T(n+1)\textgreater{} =constat(=1). For this case we get an exponential decreasefor small v but we get a phase transition beyond v=10. In that case we get an even-odd effect-separate exponentials for even n and for odd n. We now also consider also the dipole choice--where \textless{}nT(n+1)\textgreater{} = $\sqrt{(n+1)}$ .

nucl-th↗