Scissors Modes and Spin Excitations in Light Nuclei IncludingΔN=2 Excitations: Behaviour of8Be and10Be

Abstract

Shell model calculations are performed for magnetic dipole excitations in 8 Be and 10 Be, first with a quadrupole quadrupole interaction (Q } Q) and then with a realistic interaction. The calculations are performed both in a 0p space and in a large space which includes all 2 | excitations. In the 0p with Q } Q we have an analytic expression for the energies of all states. In this limit we find that in 10 Be the L=1 S=0 scissors mode with isospin T=1 is degenerate with that of T=2. By projection from an intrinsic state we can obtain simple expressions for B(M1) to the scissors modes in 8 Be and 10 Be. We plot cumulative sums for energy-weighted isovector orbital transitions from J=0 + ground states to the 1 + excited states. These have the structure of a low-energy plateau and a steep rise to a high-energy plateau. The relative magnitudes of these plateaux are discussed. By comparing 8 Be and 10 Be we find that contrary to the behaviour in heavy deformed nuclei, B(M1) orbital is not proportional to B(E2). On the other hand, a sum rule which relates B(M1) to the difference (B(E2) isoscalar &B(E2) isovector ) succeeds in describing the difference in behaviours in the two nuclei. The results for Q } Q and the realistic interactions are compared, as are the results in the 0p space and the large (0p+2 |) space. The Wigner supermultiplet scheme is a very useful guide in analyzing the shell model results.

The isovector quadrupole-quadrupole interaction used in shell model calculations

“…2 and Table II. For B = 0 the T = 1 and T = 2 scissors are degenerate in energy [17,14], and there are four degenerate states in all for each T . As B is made negative two T = 1 states come down in energy and two come up.…”

Question of low-lying intruder states in8Beand neighboring nuclei

“…For x = 1, y = 1 one gets the best fit to the Bonn A matrix elements and this choice is used in this work. This has been discussed extensively in previous references [5,9,11].…”

“…Hence, besides the intruder state, we have the above two J = 0 + states as candidates for the experimental 0 + 2 state at 6.18 M eV . As noted in the previous work [5] if, in the 0p-shell model space we fit χ to get the energy of the lowest 2 + state in 10 Be to be at the experimental value of 3.368 M eV (18χ), then the two sets of triplets are at an excitation energy of 30χ which equals 5.61 M eV -not far from the experimental value. There is however a problem -in a 0p-space calculation with Q · Q, the lowest 2 + state is two-fold degenerate, corresponding to J = 2 + K = 0 and J = 2 + K = 2.…”

“…In recent works [5,6] the current authors and S. S. Sharma allowed up to 2hω excitations in 8 Be and in 10 Be, and indeed 2p− 2h intruder states were studied with some care in 10 Be. Using a simple quadrupole-quadrupole interaction −χQ • Q with χ=0.3615 M eV /f m 4 for 10 Be and hω = 45/A 1/3 − 25/A 2/3 .…”

The isospin-dependent quadrupole-quadrupole interaction used in shell model calculations – the effects of including ΔN = 2 excitations and a two-body spin-orbit interaction term

“…It was noted by Fayache, Sharma and Zamick [7] that the isovector scissors mode in 10 Be is at quite a high energy, E ≈ 22 MeV. One cannot obtain such a high energy for this state with an isospin-independent Q · Q interaction whose strength is chosen so that the 2 + 1 energy comes out correctly.…”