How degeneracies can obscure interesting physics

We show how degeneracies, accidental or otherwise, can obscure some interesting physics. We further show how one can get around this problem

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

Topics in Nuclear Structure

We consider work performed over the last decade on single-j-shell studies. We will discuss four topics.Comment: 6 pages, two columns. Celebration of Prof. Raduta's 70th anniversar

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.Comment: arXiv admin note: text overlap with arXiv:1107.406

More on Odd-J Pairing in Nuclei

We point out a simplicity that arises when we use an interaction in which only an energy with odd J is non-zero. The emphasis is on J=J_{\text{max}} and in particular J=9^{+} in the g_{9/2} shell. It is noted that high overlaps can be deceptive. In many cases a single set of unitary 9-j coefficients gives either an exact or a surprisingly good approximation to the wave function of a non-degenerate state. The many degeneracies that occur in these calculations are discussed and explained. As a counterpoint, we compare the results with an interaction in which both the J=0 and J=J_{\text{max}} two-body matrix elements are equal (and attractive). Comparisons with a more realistic interaction are also made.Comment: arXiv admin note: substantial text overlap with arXiv:1210.385

Alternate derivation of the Ginocchio--Haxton relation [(2j-3)/6]

We have found an alternate way of deriving the Ginocchio-Haxton relation [(2j-3)/6], where the square brackets mean the largest integer that is less than or equal to what is inside them. Our derivation involves the calculation of the number of states with total angular momentum J=j for 3 identical particles (e.g., neutrons) in a j-shell.Comment: Abstract submitted for the APR05 Meeting of The American Physical Societ

Shell model test of quadrupole properties predicted by the rotational formula--the degenerate SDI interaction and non-degenerate FPD6

In the rotational model for a K=0 band in an even-even nucleus, there is a single parameter--Q_0, the intrinsic quadrupole moment. All B(E2)'s in the band and all static quadrupole moments are expressed in terms of this one parameter. In shell-model calculations, this does not have to be the case. In this work, we consider ground-state bands in {44}Ti, {46}Ti, {48}Ti, {48}Cr, and {50}Cr. We have two models. First, we use a Surface Delta Interaction with degenerate single-particle energies (SDI-deg). We compare this with results of a shell-model calculation using the standard interaction FPD6 and include the single-particle energy splitting. Neither model yields a perfect rotational I(I+1) spectrum, although the SDI-deg model comes somewhat closer. Overall, the simple rotational formula for B(E2)'s and static quadrupole moments hangs together very nicely.Comment: 17 pages, 6 figures. 1 more reference adde

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

Degeneracies with the Q.Q interaction in a single j shell

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

Odd- J Pairing in Nuclei

We point out a simplicity that arises when we use an interaction in which only an energy with odd J is non-zero. The emphasis is on J= J_{max} and in particular J=9+ in the g_{9/2} shell. It is noted that high overlaps can be deceptive. In many cases a single set of U9-j coefficients gives either an exact or a very good approximation to the wave function of a yrast state