arXiv subjects
Publications and source records attributed to Larry Zamick.
In this work we use matrix models to study the problem of strength distributions. This is motivated by noticing near exponential fall offs of strengths in calculated magnetic dipole excitations. We emphasize that the quality of the exponential fall offs depend on the parameters in our matrices, especially the relative size of the couplings to the unperturbed level separations. We also find a matrix for which all transitions vanish.
In this work we calculate the energies odd J$^{+}$ states in selectedeven-even nuclei-$^{44}$ Ti $^{52}$ Fe and $^{96}$Cd. Of particularinterest is the fact that in many cases the first T=0 and the first T=1 state are close in energy. Whether the lowest odd J state hasT=0 or T=1 is here considered.
In previous works we examined they systematics of magnetic dipole transitions in a single j shell. We here extend the study to large space calculations.We consider the nuclei $^{44}$ Ti, $^{46}$Ti and $^{48}$C. Of particular interest is the contributions to B(M1) of the spin and orbital parts of the magnetic dipole operator. Whereas usual scissors mode analyses have as an initial state the J=0+ ground state (of an even-even nucleus) we here start with the lowest J=1+ T=1 state. This enables us to reach many more states e.g. J=2,T=0,1, and 2 and thus getter a better picture of the collectivity of this state.
We perform shell model calculations using a quadrupole-quadrupole interaction (Q.Q).We show results in single j shell spaces and the full S-D shell . We show that one gets useful results with Q.Q in both spaces.. We emphasize the importance of the choice of single particle energies in order to obtain the results of Elliott using a Q.Q interaction without the momentum terms. We show a J(J+1) spectrum for a ground state band but with B(E2)'s different from the rotational model. We also show excited J(J-1), J((J-1) and J(J+3) spectra.We find spectra starting with J=0 which have both even J and odd J members.
In previous works we examined the spectra for systems of 2 protons and 2 neutrons, in a single j shell calculation, by obtaining matrix elements from experiment. More recently we considered schematic interactions in the same model space. We continue in this vein here. The present work and the former can be regarded as 2 bookends on a bookshelf.
If one examines two-body matrix elements from experiment one notices that not only J=0 T=1 lies low but also J=1T=0 and J=J_{max} =2j T=0. It is sometimes thought that one needs both T=1 and T=0 two-body matrix elements to get equally spaced spectra of even I states i.e. vibraitonal spectra. We here attempt to get equally spaced levels with only those that have T=1 (even J).As an example we perform single-j calculations (f_{7/2}) in ^{44} T and ^{46} Ti. We then shift gears and decide to play around with the input two particle matrix, elements (not worrying about experiment) to generate interesting spectra e.g. rotaional spectra with and then without T=0 two-body matrix element. Of special interest is a new partial dynamical symmetry found when the "123", the "1234" etc.,interactions are used.
By starting with a simple configurations of 2 neutrons in a single j shell we hare able to learn the effects of high lying configurations on physical properties such as nuclear magnetic g factors. Some counterintuitive results are found when both high lying spin orbit partners are allowed to admix with the basic configuration.
If we add one neutron to doubly magic ^{100}Sn, we can associate the low lying states in^{101} Sn with single particle states.The the J=5/2^{+} and J= 7/2^{+} states are identified as d_{5/2}and g_{7/2}states respectively...They are separated by an energy of 0.18 MeV.Unfortunately there is a disputeas to the ordering of these states.We examine how the 2 scenarios-- J=5/2^{+} ground state or J=7/2^{+}ground state-- affect spectra of higher Sn isotopes .
The strong interactions are charge independent. If we limit ourselves to the strong interactions, we have the isospin $T$ as a good quantum number. Here we consider the lack of level repulsion of states of different isospin and how this effect manifests in nearest neighbor spacing (NNS) histograms, which provide a visual and statistical context in which to study distributions of energy level spacings. In particular, we study nucleons in the f-p model space for the nucleus $^{44}$Ti. We also study the effect of the Coulomb interaction on the level spacing distribution.
Previously [1] it was shown that for a configuration of 2 protons and 2 neutrons in the g_{9/2}shell there is a certain degeneracy that occurs when the quadrupole-quadrupole interaction (Q.Q) is used to to obtain the wave functions.. We here show 3 other examples of such degenerate pairs, all, as before, involving T=0 and T=2 states. . More important we discuss an unusual peculiarity of the original example. Also we point out that degeneracies can be confusing and steps can be taken to remove them.
We report the discovery of a partial conservation law obeyed by a schematic Hamiltonian of two protons and two neutrons in a j shell. In our Hamiltonian the interaction matrix element of two nucleons with combined angular momentum J is linear in J for even J and constant for odd J. It turns out that in some stationary states the sum J_p + J_n of the angular momenta J_p and J_n of the proton and neutron pairs is conserved. The energies of these states are given by a linear function of J_p + J_n. The systematics of their occurrence is described and explained.
Using an attractive surface delta interaction we obtain wave functions for 2 neutrons (or neutron holes) in the model space of 2 orbits (l=4, j=7/2) and (l=2, j=5/2). If we take the single particle energies to be degenerate we find that the g factors for I=2, 4 and 6 are all the same -namely the orbital g factor of the single nucleon. For a free neutron this quantity zero all 2particle or 2 hole g factors are equal to zero as well.. Only the orbital part of the g -factors contribute - the spin part cancels out. We then consider the effects of introducing a single energy splititng between the 2 orbits. We speculate that g factors for all n can be obtained by a linear approximation.
There has been a great deal of attention to the low lying energy spectum in a nucleus becuse of the abundance of experimetal data. Likewise ,perhaps to a lesser extent but still significant the high end for a given configuratiion has been examined. Here ,using single j shell calculations as a guide we examine the middle part of the spectum resulting form single j shell calculations.Seniority arguments are used to partially explain the midshell behaviours even though in general seniority is not a good quantum number for mixed systems of neutrons and protons.
We note that in large space shell model calculaiotns and experiment one sometimes get results, the form of which also appear in smaller space calculations. On the other hand there are some results which demand the large space approach.
In a single j-shell calculation we consider the effects of several different interactions on the values of Gamow-Teller (B(GT)'s) and magnetic moments. The interactions used are MBZE, J=0 pairing, J_{max} pairing and half and half.
Wave functions arising form a pairing Hamiltonian E(0) i,e, one in which the interaction is only between J=0^{+}T=1 pairs, lead to magnetic dipole and Gamow-Teller transition rates that are much larger than those from an interaction E(J_{max}) in which a proton and a neutron couple to J=2j. With realistic interactions the results are in between the 2 extremes. In the course of this study we found that certain M1 and GT matrix elements vanish with E(0) . These are connected to seniority and reduced isospin isospin selection rules. We find the surprising result that The M1 strength to the single j scissors is larger for a J=0 T=1 pairing interaction than it is for Q.Q.
The scissors mode, a magnetic dipole excitation-mainly orbital is usually discussed in terms of a transition from a J=0^{+} ground state to a J=1^{+} excited state. This is understandable because it follows from the way the experiment is performed-e.g. inelastic electron scattering. Here however, we start with the excited 1^{+} state and consider all possible transitions to J=0,1 and 2 states.
Calculations of B(E2)'s and quadruplole moments in the g_{9/2 region below ^{100} Sn are hampered by the fact that the inclusion of the g_{7/2}configuration leads to model spaces that are too large to handle. We therefore examine lighter nuclei if the fp region where one can easily include all the orbitals, f,{}_{7/2}, p_{3/2}, p_{1/2}and f_{5/2} . We perform such calculations but then take a step back and exclude the f_{5/2} orbital. By comparing the 2 calculations we can hope to get insight into the importance of the missing spin-orbit partner in other regions.