Strengths of transitions between $0^{+}$ and $1^{+}$ states and their relationship to inelastic electron scattering form factors: Example of ${}^{24}{Mg}$

The strengths of transitions in

A = 24

between

J^{π} = 1^{+}

T = 1

states and the lowest

J^{π} = 0^{+}

states of

T = 0 and 2

are calculated from shell-model wave functions constructed in the full eight-particle

0 d_{\frac{5}{2}} - 1 s_{\frac{1}{2}} - 0 d_{\frac{3}{2}}

configuration space. The model Hamiltonian is an empirical interaction which yields a good accounting of the energies of intra-

sd

-shell states throughout the

A = 17 - 39

region. With these same wave functions the (

e, e^{'}

) form factors for the magnetic dipole excitation of

{}^{24}{Mg}

to its lowest five states of

J^{π} = 1^{+}

T = 1

are calculated in the plane-wave Born approximation. The predicted form factors and the associated predictions for

B (M 1)

and

B

(Gamow-Teller) are compared to existing experimental values.

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Strengths of transitions between0+and1+states and their relationship to inelastic electron scattering form factors: Example ofMg24