Coulomb breakup of $^{37}$Mg and its ground state structure

We calculate Coulomb breakup of the neutron rich nucleus $^{37}$Mg on a Pb target at the beam energy of 244 MeV/nucleon within the framework of a finite range distorted wave Born approximation theory that is extended to include the effects of projectile deformation. In this theory, the breakup amplitude involves the full wave function of the projectile ground state. Calculations have been carried out for the total one-neutron removal cross section $(\sigma_{-1n})$, the neutron-core relative energy spectrum, the parallel momentum distribution of the core fragment, the valence neutron angular, and energy-angular distributions. The calculated $\sigma_{-1n}$ has been compared with the recently measured data to put constraints on the spin parity, and the one-neutron separation energy ($S_n$) of the $^{37}$Mg ground state ($^{37}$Mg$_{gs}$). The dependence of $\sigma_{-1n}$ on the deformation of this state has also been investigated. While a spin parity assignment of $7/2^-$ for the $^{37}$Mg$_{gs}$ is ruled out by our study, neither of the $3/2^-$ and $1/2^+$ assignments can be clearly excluded. Using the spectroscopic factor of one for both the $3/2^-$ and $1/2^+$ configurations and ignoring the projectile deformation effects, the $S_n$ values of $0.35 \pm 0.06$ MeV and $0.50 \pm 0.07$ MeV, respectively, are extracted for the two configurations. However, the extracted $S_n$ is strongly dependent on the spectroscopic factor and the deformation effects of the respective configuration. The narrow parallel momentum distribution of the core fragment and the strong forward peaking of the valence neutron angular distribution suggest a one-neutron halo configuration in either of the $2p_{3/2}$ and $2s_{1/2}$ configurations of the $^{37}$Mg ground state.