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Probability distribution for the ratio ($r$) of consecutive level spacings ofthe eigenvalues of a Poisson (generating regular spectra) spectrum and that ofa GOE random matrix ensemble are given recently. Going beyond these, for theensemble generated by the Hamiltonian $H_\lambda = (H_0+\lambdaV)/\sqrt{1+\lambda^2}$ interpolating Poisson ($\lambda=0$) and GOE ($\lambda\rightarrow \infty$) we have analyzed the transition curves for $\langler\rangle$ and $\langle \tilde{r}\rangle$ as $\lambda$ changes from $0$ to$\infty$; $\tilde{r} = min(r,1/r)$. Here, $V$ is a GOE ensemble of realsymmetric $d \times d$ matrices and $H_0$ is a diagonal matrix with a Gaussiandistribution (with mean equal to zero) for the diagonal matrix elements;spectral variance generated by $H_0$ is assumed to be same as the one generatedby $V$. Varying $d$ from 300 to 1000, it is shown that the transition parameteris $\Lambda \sim \lambda^2\,d$, i.e. the $\langle r\rangle$ vs $\lambda$(similarly for $\langle \tilde{r}\rangle$ vs $\lambda$) curves for different$d$'s merge to a single curve when this is considered as a function of$\Lambda$. Numerically, it is also found that this transition curve generates amapping to a $3 \times 3$ Poisson to GOE random matrix ensemble. Example forPoisson to GOE transition from a one dimensional interacting spin-1/2 chain ispresented.

Poisson to GOE transition in the distribution of the ratio of consecutive level spacings