#### Abstract

The effect Δ${B}_{c}$ of the Coulomb interaction on the *Λ* separation energy ${B}_{\Lambda}$ of ${}_{\mathrm{\Lambda}}{}^{4}{}_{}{}^{}\mathrm{He}$ was obtained by variational calculations made for ${}_{\mathrm{\Lambda}}{}^{4}{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^{3}{}_{}{}^{}\mathrm{He}$. These calculations were made for several values of ${q}^{2}$ in the range 0≤${q}^{2}$≤9 where *qe* is the proton charge, i.e., the Coulomb repulsion was artificially boosted. For ${q}^{2}$≲3, the dependence on ${q}^{2}$ is linear, and interpolation to ${q}^{2}$=1 gives the physical values with improved accuracy: -Δ${B}_{c}$=0.05±0.02 and *0.025±0.015* MeV for the ground and excited state, respectively. This procedure also gives more accurate values for the differences between the proton and neutron radii of ${}_{}{}^{3}{}_{}{}^{}\mathrm{He}$. The corresponding differences of ${B}_{\Lambda}$ between ${}_{\mathrm{\Lambda}}{}^{4}{}_{}{}^{}\mathrm{He}$ and ${}_{\mathrm{\Lambda}}{}^{4}{}_{}{}^{}\mathrm{H}$, to be attributed to charge symmetry breaking effects, are then *0.40±0.06* and *0.27±0.06* MeV. From these values we obtain a phenomenological charge symmetry breaking potential which is effectively spin independent. An examination of meson-exchange charge symmetry breaking models shows that these are consistent with the phenomenological charge symmetry breaking potential for the triplet but not for the singlet case.

DOI: http://dx.doi.org/10.1103/PhysRevC.31.1400

- Received 27 August 1984
- Published in the issue dated April 1985

© 1985 The American Physical Society