We investigate hydrogen electron capture in the ocean of neutron stars accreting at rates 10 ^ { -10 } \lesssim \dot { M } \lesssim 10 ^ { -8 } M _ { \odot } { yr ^ { -1 } } .
These stars burn the accreted hydrogen and helium unstably in the upper atmosphere ( \rho \lesssim 10 ^ { 6 } { g cm ^ { -3 } } ) and accumulate material which usually contains some small amounts of hydrogen ( mass fractions are typically X _ { r } \approx 0.1 - 0.2 ) mixed in with the heavier iron group ashes .
The subsequent evolution of this matter is determined by compression towards higher densities until electron capture on the hydrogen occurs .
We construct steady-state models of the electron captures and the subsequent neutron recombinations onto the heavy nuclei .
The density discontinuity from these captures gives rise to a new g-mode ( much like a surface wave ) , which has a lowest order ( l = 1 ) frequency of \approx 35 { Hz } ( X _ { r } / 0.1 ) ^ { 1 / 2 } on a slowly rotating ( f _ { s } \ll 30 { Hz } ) star .
We also discuss , for the first time , a new set of non-radial g-modes unique to these high accretion rate neutron stars .
These modes are “ trapped ” in the finite thickness layer where the electron captures are occurring .
The lowest order mode frequencies are in the 1 - 10 { Hz } range for a few radial nodes on a slowly rotating star .
Though the majority of the mode energy resides in the electron capture transition layer , the eigenmode propagates to higher altitudes above the layer and can thus be potentially observable and excited by the nuclear burning or other mechanisms .
We also show that the density jump splits the ocean ’ s thermal modes into two distinct sets , which have most of their energy either above or below the discontinuity .
We conclude by discussing how the dispersion relations for these modes are modified for a rapidly rotating ( f _ { s } \gg 30 { Hz } ) neutron star .
Whether any of these modes are observable depends on the damping mechanism and the ability to excite them , issues we will address in a future paper .