Searcharxiv⌕ Search

arXiv subjects

Larry Zamick

Publications and source records attributed to Larry Zamick.

At least 55 records · Page 3Linked to original sources
arXiv2015

Wave functions of the Q.Q interaction in terms of unitary 9-j coefficients

We obtain wave functions for 2 protons and 2 neutrons in the g_{9/2} shell expressed as column vectors with amplitudes D(J_{p},J_{n}). When we use a quadrupole-quadrupole interaction (Q.Q) we get, in many cases, a very strong overlap with wave functions given by a single set of unitary 9j coefficients --U9j= ((jj)^{2j} (jj^{J_{B}} \ (jj)^{J_{p}} (jj)^{J_{n}})^{I}. Here J_{B}=9 for even I T =0 states. For both even and odd T=1 states we take JB equal to 8 whilst for odd I, T=0 we take JB to be 7. We compare the Q.Q results with those of a more realistic interaction.

nucl-th↗
arXiv2014

Asymptotics of the 3j and 9j Coefficients

In this work we present the details of calculations we previously performed for the large j behavior of certain 3j and coefficients. We compare exact and asymptotic expressions.

nucl-th↗
arXiv2014

J=0, J=J_{max} and quadrupole pairing

We consider 2 neutrons and 2 protons in the g_{9/2} shell.Wave functions and energy levels are obtained for various interactions. The wave functions for states with total angular momentum I greater or equal to 10 are not affected by what the pairing interacton (J=0 T=1) is.Other parts of the interaction are therefore of increased importance.

nucl-th↗
arXiv2014

Magnetic g Factors With a Surface Delta Interaction

We examine the consequences of using a surface delta interaction to obtain the nuclear magnetic dipole g factors for 86Kr in a 2 proton hole model space. We find that the g factors of lowest the 2+ and 4+ states are equal to one, or more properly gl. The inclusion of a spin-orbit interaction is also discussed. Comparisons are made with large space calculations.

nucl-th↗
arXiv2014

More on Asymptotic behaviors of 9j Coefficients

Previouslywe noted in numerical calculations that a certain unitary ninej coefficient U9j =((jj)^{2j} (jj)^{2j} | (jj)^{2j} (jj) ^{(2j-2)})^{I} decreases with increasing j and for small I the decrease is of the form C j^{m} e^{-αj} . The exponential decay dominates. It is here shown that α= 4 ln(2) and m=3/2.

nucl-th↗
arXiv2013

The large j limit for certain 9-j symbols-power law behaviour

In a previous work certain unitary9-j symbols were shown to go asymptotically to zero in the large j limit. In this work we examine this inmore detail. We find an approximate power law for the behaviour of ccertain U9-j's in the large j limit and exponential decreased for others.

nucl-th↗
arXiv2013

Isobaric analog states in the f_{7/2} and g_{9/2} shells

Calculations are performed for energies of isobaric analog states with isospins T=2 and T=3 in regions where they have been found experimentally e.g. f-p shell, and regions where they have not yet been found e.g. g_{9/2} near Z=50,N=50. We consider two approaches--one using binding energy formulas and Coulomb energies contained therein and the other using shell model calculations. It is noted that some (but not all) calculations yield very low excitation energies for the J=0^{+} T=2 isobaric analog state in ^{96} Ag.

nucl-th↗
arXiv2013

Isobaric Analog State in ^{96} Ag

Preiviously, in a single j-shell calculation (j=g_{9/2}), we obtained the excitation energy of the T=2 J=0+ isobaric analog state in ^{96} Ag to be a bit below 1 MeV relative to the J=8+ T=1 ground state . We here use binding energy data and Coulomb energy estimates to obtain this same excitation energy and to see if the 2 approaches are consistent.

nucl-th↗
arXiv2012

Symmetries in the \bm{g_{9/2}} shell

We consider symmetries which arise when two-body interaction matrix elements with isopin T=0 are set equal to a constant in a single-j -shell calculation. The nucleus ^{96} Cd is used as an example.

nucl-th↗
arXiv2012

Streched Magnetic Moments

We note that for a system of 2 nucleons in a stretched case (J=J1+J2) the magnetic moment of the combined system is the sum of the magnetic moments of the 2 constituents. We compile other simple formulas.

nucl-th↗
arXiv2012

The (2j-1) rule with other interactions

We recently formulated a rule for isomeric states for a system of 4 nucleons with isospin T=1, namely that if the nucleons are in a single j shell then states with angular momenta J=2 and J=(2j-1) are either isomeric or ground states [ze12]. To show that this is a robust result, we here consider a new interaction from the literature that was used to discuss even-even and odd-even nuclei. We here apply it to an odd-odd nucleus.

nucl-th↗
arXiv2012

Single j-shell studies of cross-conjugate nuclei and isomerism

It is noted that in a calculation with 4 nucleons with isospin 1 in a single j shell (f_{7/2}, g_{9/2}, h_{11/2}) the state with median angular momentum J = (J_{max}+1)/2 lies very low in energy becoming either an isomeric state or a ground state. Also states with J = J_{max} are isomeric for the orbits g_{9/2} and h_{11/2}. Comparisons with experiment are made. A hybrid mixture of shell model and rotational model arguments are used to explain the (J_{max} +1)/2 rule.

nucl-th↗
arXiv2012

Symmetry energy and neutron-proton radii studies with a Wigner-Heisenberg monopole-monopole interaction

The symmetry energy in nuclei is studied using a monopole-monopole two boby interaction which has an isospin dependent term. A Hartree theory is developed for this interaction which has an oscillator shell model basis with corresponding shell structure. The role of shell structure on the symmetry energy is then studied. We also find that the strength of the Heisenberg interaction is very important for understanding the difference between proton and neutron radii and features associated with halo nuclei. PACS numbers: 21.10.Sf, 21.65Cd, 21.65Ef

nucl-th↗
arXiv2011

Partial Dynamical Symmetry in the f7/2 and g9/2 shell

We discuss partial dynamical symmetries which occur in single j shell calculations mostly for high spin states for systems of three or four particles (holes). The relevant nuclei are 43Ti,43Sc, 44Ti, 52Fe,53Fe, 53Co,96Cd,97Cd, and 97In.

nucl-th↗