Nuclear structure of the closed subshell nucleus ${}^{90}\mathrm{Zr}$ studied with the ${(n,n}^{\prime }\gamma )$ reaction

States in ${}^{90}\mathrm{Zr}$ have been observed with the ${(n,n}^{\prime }\gamma )$ reaction using both spallation and monoenergetic accelerator-produced neutrons. A scheme comprised of 81 levels and 157 transitions was constructed concentrating on levels below 5.6 MeV in excitation energy. Spins have been determined by considering data from all experimental studies performed for ${}^{90}\mathrm{Zr}.$ Lifetimes have been deduced using the Doppler-shift attenuation method for many of the states, and transition rates have been obtained. A spherical shell-model interpretation in terms of particle-hole excitations assuming a ${}^{88}\mathrm{Sr}$ closed core is given. In some cases, enhancements in $B\left(M1\mathrm{}\right)\mathrm{}$ and $B\left(E2\mathrm{}\right)\mathrm{}$ values are observed that cannot be explained by assuming simple particle-hole excitations. Shell-model calculations using an extended $\mathrm{fpg}$-shell-model space reproduce the spectrum of excited states very well, and the gross features of the $B\left(M1\mathrm{}\right)\mathrm{}$ and $B\left(E2\mathrm{}\right)\mathrm{}$ transition rates. Transition rates for individual levels show discrepancies between calculations and experimental values.