Effects of the spin-orbit and tensor interactions on M1 excitations in light nuclei

Abstract

The effects of varying the spin-orbit and tensor components of a realistic interaction on M 1 excitation rates and B(E2) ′ s are studied on nuclei in the 0p and 1s − 0d shells. Not only the total M 1 but also the spin and orbital parts separately are studied. The single-particle energies are first calculated with the same interaction that is used between the valence nucleons. Later this stringent condition is relaxed somewhat and the 1s level is raised relative to 0d. For nuclei up to 28 Si, much better results i.e stronger B(M 1) rates are obtained by increasing the strength of the spin-orbit interaction relative to the free value. This is probably also true for 32 S, but 36 Ar presents some difficulties. The effects of weakening the tensor interaction are also studied. On a more subtle level, the optimum spin-orbit interaction in the lower half of the s − d shell, as far as M 1 excitations are concerned, is substantially larger than the difference E(J = 3/2 + )1 − E(J = 5/2 + )1 = 5.2 M eV in 17 O. A larger spin-orbit splitting is also needed to destroy the triaxiality in 22 N e. Also studied are how much M 1 orbital and spin strength lies in an observable region and how much is buried in the grass at higher energies. It is noted that for many nuclei the sum B(M 1) orbital + B(M 1)spin is very close to B(M 1) total , indicating that the summed cross terms are very small.In what follows we discuss present calculations for what we call B(M 1) physical , B(M 1) orbital and B(M 1) spin . In terms of a magnetic dipole operator, the B(M 1) is defined aswhere A = 3/4π protons (g lπ l i + g sπ s i ) + neutrons (g lν l i + g sν s i )

Allowed Gamow–Teller excitations from the ground state of 14N

“…In Table IV, we present the values of the coefficients C As mentioned in the introduction, it has been noted in the past [6,7,10,11] to a similar conclusion in their study of M1 excitation rates in the 0p and 1d − 0d shells [20]. It is useful to note here, as pointed out by Wong [21], that the tensor interaction in an open-shell acts to some extent like a spin-orbit interaction of the opposite sign of the basic spin-orbit interaction, so that these two types of adjustments to the N − N interaction are really equivalent for our purpose.…”

Possible explanation of the electron positron anomaly at 17 MeV in 8 Be transitions through a light pseudoscalar

“…If one of the two states in the lower 1p 3/2 level is lifted into the previously empty 1p 1/2 level it would form with its remaining partner in the 1p 3/2 level a J P = 1 + state which gives, together with the remaining J P = 0 + nucleons, a J P = 1 + state consistent with the quantum numbers of 8 Be * . Its excitation energy of 18.15 MeV is consistent with -following [12] perhaps slightly larger than -the expectations from nuclear spin-orbit splitting. During the transition from 8 Be * to 8 Be a photon or -as considered here -a pseudoscalar can be emitted emitted from a single nucleon falling from a 1p 1/2 state into the lower 1p 3/2 state.…”

Interference term between the spin and orbital contributions toM1transitions

“…We can also consider the summed strength to all calculated states. It was already noted in our previous work [1] that for some cases " B(M1) is very close to B(M1) σ + B(M1) l ". This would imply a cancellation of the summed interference terms.…”

“…In a previous work [1], the magnetic dipole transitions from the ground states to excited states of several nuclei in the s − d shell were calculated: 20 Ne, 22 Ne, 24 Mg, 28 Si, 32 S, and 36 Ar. The main focus of the work was on how the transition strengths were affected by the strengths of the spin-orbit and tensor interactions inside a nucleus, and near the end of the paper, it was briefly mentioned that a new topic would be of interest: "the cross-correlation between the spin and orbital parts of B(M1)".…”