Precise Tests of Ab-initio Calculations of Light Nuclei and Charge Symmetry Breaking in A=10 $^{10}$B

Electromagnetic transition matrix elements have provided stringent tests of modern ab-initio calculations using realistic nuclear forces. Precise measurements of the B(E2:2$\rightarrow$0) transition rates in $\mathrm{^{10}B}$e and $\mathrm{^{10}}$C have been compared to recent Variational and Greens Function Monte Carlo calculations and the formulation of the 3-body forces [1,2]. They revealed that these electric transitions are almost purely isoscalar in character, corresponding to tumbling of the di-alpha core. Precise measurements of the analogous transition in $\mathrm{^{10}B}$ provide additional constraints for a possible isotensor contribution. The relevant state in $\mathrm{^{10}B}$, at E$_x$ = 5.164 MeV, is particle unbound. Therefore, precise measurements of both the particle decay branch and the gamma branch are needed to extract the electric transition rate. We report on a new study of the $\alpha$-particle branch by studying the $^{10}$B(p,p$'$)$^{10}$B* reaction in inverse kinematics with the HELIOS spectrometer at Argonne National Laboratory. [1] E.A. McCutchan et al., Phys.Rev.Lett. 103, 192501 (2009). [2] E.A. McCutchan et al., Phys.Rev. C 86 014312 (2012).