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Evaporated $\alpha$-spectra have been measured in coincidence with low energydiscrete $\gamma$-rays from residual nucleus $^{68}$Zn populated in thereaction $^{64}$Ni($^9$Be,$\alpha$n)$^{68}$Zn at $E(^9$Be) = 30 MeV producing$^{73}$Ge compound nucleus. Low energy $\gamma$-gated $\alpha$-particlespectra, for the first time, have been used to extract the nuclear leveldensity (NLD) for the intermediate $^{69}$Zn nucleus in the excitation energyrange of E $\approx$ 5-20 MeV. The slope of NLD as a function of excitationenergy for $^{69}$Zn matches nicely with the slope determined from RIPLestimates for NLD at low energies and the NLD from neutron resonance data.Extracted inverse NLD parameter (k = A/$\widetilde{a}$) has been used todetermine the nuclear level density parameter value $a$ at neutron separationenergy $S_n$ for $^{69}$Zn. Total cross-section of $^{68}$Zn(n,$\gamma$)capture reaction as a function of neutron energy is then estimated employingthe derived $a(S_n)$ in the reaction code TALYS. It is found that the estimatedneutron capture cross-section agrees well with the available experimental datawithout any normalization. The present result indicates that experimentallyderived nuclear level density parameter can constrain the statistical modeldescription of astrophysical capture cross-section and optimize theuncertainties associated with the astrophysical reaction rate

Nuclear level density of $^{69}$Zn from gamma gated particle spectrum and its implication on $^{68}$Zn(n, $\gamma$)$^{69}$Zn capture cross-section