Structure of the nearly degenerate61+and62+

Abstract

The 6

Effects ofT=0two body matrix elements onM1and Gamow-Teller transitions: Isospin decomposition

“…The reason for these degeneracies was explained in the first two references. [1,2] In a full fp calculation the even spin spectrum spread out a bit more -leaning slightly toward a rotational spectrum when the T=0 matrix elements were reintroduced (ie full FPD6 interaction) but only slightly. It thus appeared that keeping only the T=1 matrix elements led to a reasonable spectrum and the T=0 matrix elements were only needed for fine tuning.…”

“…[1,2] In this work we will focus on the transition rates. In the former work we used an FPD6 interaction to get the energy levels of 44 Ti, 46 Ti, and 48 Ti as well as a second interaction wherein the T=0 matrix elements were set to zero while the T=1 matrix elements we left unchanged.…”

Symmetries in theg9/2shell

“…Although many 6-j and 9-j relations were used in Refs. [2,3] to describe why these symmetries are partial, one simple argument is illuminating. If a given angular momentum can occur for, say, four g 9/2 neutron holes (T = 2), then there is a constraint on the T = 0 states with the same angular momentum-namely their wave functions have to be orthogonal to the T = 2 states.…”

“…In a previous work by these authors [3], the main emphasis was on the f 7/2 shell, although the equations were written in a general way so as to apply to any shell. In this work we elaborate on the work in Ref.…”

Zeros of 6-jsymbols: Atoms, nuclei, and bosons

“…Sometimes the vanishing 6-j's are part of a bigger picture. Robinson and Zamick [3] used this relationship along with some 'diagonal conditions' to demonstrate that for a system of two protons and one neutron in a single j shell a partial dynamical symmetry (PDS) occurred when one sets all two body matrix elements with T=0 to zero in a shell model calculation. It turns out that not only J but also J p and J n separately are good quantum numbers.…”