Isospin Effects in the Giant Dipole Resonance of ${}^{42}{Ca}$

The giant dipole resonance (GDR) of

{}^{42}{Ca}

was investigated through the

{}^{41}K (p, γ_{0}) {}^{42}{Ca}

reaction. The gross structure indicates two peaks at 17.4 ± 0.1 MeV (

Γ = 3.3 \pm 0.5

MeV) and 20.4 ± 0.1 MeV (

Γ = 4.4 \pm 0.1

MeV) which contain 13 and 87%, respectively, of the

E 1

strength in the (

γ, p_{0}

) channel. From a comparison of structure and excitation energies of the GDR in

{}^{40}{Ca}

and

{}^{42}{Ca}

, the two peaks can be identified with the

T = 1

(at 17.4 MeV) and the

T = 2

(at 20.4 MeV) isospin components of the GDR. This energy separation gives an effective symmetry potential of

V = 63

MeV in agreement with the general predictions and observation in other nuclei. However, identification of the peaks with the

K = 0

and

K = 1

dipole oscillations in the deformed

{}^{42}{Ca}

ground state is not ruled out. A shell-model calculation of the dipole states in

{}^{42}{Ca}

with good isospin was done by diagonalizing large matrices and using the Kuo-Brown

G

matrix elements. This gives a concentration of

T = 1

strength at 17.1 MeV and

T = 2

strength at 19.6 MeV, in good agreement with the experimental results, and supports the isospin identification of the two components.

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Isospin Effects in the Giant Dipole Resonance ofCa42