M1 transitions and the validity of SU(4) symmetry in light nuclei

doi:10.1016/0375-9474(72)90022-X

Nuclear Physics A

Volume 185, Issue 2, 1 May 1972, Pages 413-432

https://doi.org/10.1016/0375-9474(72)90022-X Get rights and content

Abstract

A sum rule for M1 transitions is derived and is found to be saturated with low11ing states in ⁶Li and ¹⁰B. This is consistent with a very small amount of supermultiplet impurity present in the ground state. For self-conjugate 4N and conjugate 4N ± 1 nuclei, using experimental data on ΔT = 1 M1 transitions from the ground to excited states, we are able to estimate the super-multiplet impurity present in the ground state. It is found that the amount of supermultiplet impurity reaches a maximum at the middle of the shell and decreases to zero at the beginning and at the end of the shell. Under the assumption that the giant magnetic dipole resonance dominates the sum rules we find a relation which predicts the excitation energy of the T = 0, J^π = 1⁺ state in ¹²C to be 12 MeV as compared with the experimental value of 12.71 MeV.

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We investigate the Coulomb dissociation of $^{8}$ B on a $^{208}$ Pb target at the beam energy of 250 MeV/nucleon, employing the cross sections for the radiative capture reaction $^{7}$ Be(p,γ) $^{8}$ B calculated within the Shell Model Embedded in the Continuum (SMEC) approach. In contrast to the situation at lower beam energies, the Coulomb breakup cross sections are found to be sensitive to the M1 transitions. Comparisons of SMEC and single-particle potential model predictions show that the Coulomb breakup cross sections at these high energies are sensitive to the structure model of $^{8}$ B. Comparison with the preliminary data on the angle integrated spectra reported recently by the GSI group shows that the theory is able to reproduce the absolute magnitude as well as the shape of this data well. The contributions of the E2 component strongly depends on the range of the angles of the p– $^{7} Be$ center of mass with respect to the beam direction, included in the angular integrations of the double differential cross section. If integrations are done over the angular range of 0°–1.87°, the E2 multipolarity contributes up to 25 % to the cross sections even for the relative energies of [p– $^{7} Be$ ] below 0.25 MeV. However, these contributions are reduced by an order of magnitude at lower relative energies if the maximum of the angle integration is ∼ 1°.
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SU(6) ⊗ SU(4) tensor decomposition of effective interactions in the 2s-1d shell has been carried out to examine the relative importance of the various irreducible tensors in many-particle spaces. For this purpose norms of the irreducible tensors are evaluated in many-particle spaces. Variation of the expectation value of the square of the irreducible tensor parts with excitation energy has also been examined using the polynomial expansion method. A new measure of symmetry breaking that is theoretically more sound is derived which includes in its definition partial width as well as internal width. This is used to study SU(4) symmetry mixing in nuclei.
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Nuclear Physics A

Abstract

References (22)

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Phys. Rev.

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Rev. Mod. Phys.

Phys. Rev.

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Phil. Mag.

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Nucl. Phys.

Cited by (13)

Structure effects on the Coulomb dissociation of <sup>8</sup>B at relativistic energies

Study of the <sup>7</sup>Be(p, γ)<sup>8</sup>B and <sup>7</sup>Li(n, γ)<sup>8</sup>Li capture reactions using the shell model embedded in the continuum

Effect of ground-state correlation on the total Gamow-Teller strength of doubly LS closed shell nuclei

Unitary group decomposition of hamiltonian operators. II. SU (4) irreducible tensors, norms and their energy variation and symmetry breaking

The persistence of supermultiplet selection rules in nuclear weak and electromagnetic transitions

Mass measurements on stable nuclides in the rare-earth region with the Penning-trap mass spectrometer TRIGA-TRAP