Momentum distribution in heavy deformed nuclei: Role of effective mass

The impact of nuclear deformation and effective mass $m^{*}∕m$ on the momentum distributions (MD) of occupied proton states in ${}^{238}\mathrm{U}$ is investigated in the self-consistent Skyrme-Hartree-Fock (SHF) scheme with parameterizations SkT6, $\mathrm{Sk}{\mathrm{M}}^{*}$, SLy6, and SkI3 as well as with the phenomenological Woods-Saxon (WS) shell model. The deformation effect turns out to be significant in the low-momentum domain of $K^{\pi }=1∕2^{\pm }$ states (mainly of those lying near the Fermi surface) and negligible for other states. The most remarkable result is that all Skyrme parameterizations (with essentially different $m^{*}∕m$) and the WS potential give very similar MD. This means that the value of effective mass, although crucial for single-nucleon spectra, is not important for the spatial shape of the wave functions and thus for the MD. For the description of MD at $0⩽k⩽300\mathrm{MeV}∕c$, one may use any single-particle scheme fitted properly to the global ground state properties.

Figure 1

WS and SHF proton single-particle spectra in ${}^{238}\mathrm{U}$ at zero deformation (spherical limit). The levels of the positive and negative parity are depicted by solid and dotted lines, respectively. As a guide for the eyes, identical levels are connected by dashed lines. The chemical potentials are indicated by dotted lines with crosses.

Figure 2

Momentum distributions for occupied proton states in ${}^{238}\mathrm{U}$ calculated with $\mathrm{Sk}{\mathrm{M}}^{*}$ in the spherical limit (solid line) and at the equilibrium deformations (dashed line). The spherical ancestors are indicated for every state.

Figure 3

Proton momentum distributions in ${}^{238}\mathrm{U}$ calculated with WS (solid line) and Skyrme potentials SkT6 (dashed line), $\mathrm{Sk}{\mathrm{M}}^{*}$ (dashed-double-dotted line), SLy6 (dotted line), and SkI3 (dashed-dotted line).