We report on a search for electromagnetic and/or hadronic showers ( cascades ) induced by a diffuse flux of neutrinos with energies between 5 TeV and 300 TeV from extraterrestrial sources .
Cascades may be produced by matter interactions of all flavors of neutrinos , and contained cascades have better energy resolution and afford better background rejection than through-going \nu _ { \mu } -induced muons .
Data taken in 1997 with the AMANDA detector were searched for events with a high-energy cascade-like signature .
The observed events are consistent with expected backgrounds from atmospheric neutrinos and catastrophic energy losses from atmospheric muons .
Effective volumes for all flavors of neutrinos , which allow the calculation of limits for any neutrino flux model , are presented .
The limit on cascades from a diffuse flux of \nu _ { e } + \nu _ { \mu } + \nu _ { \tau } + \overline { \nu } _ { e } + \overline { \nu } _ { \mu } + \overline% { \nu } _ { \tau } is E ^ { 2 } \frac { d \Phi } { dE } < 9.8 \times 10 ^ { -6 } \mathrm { GeV cm ^ { -2 } s ^ { -1 } sr ^ { -1 } } , assuming a neutrino flavor flux ratio of 1:1:1 at the detector .
The limit on cascades from a diffuse flux of \nu _ { e } + \overline { \nu } _ { e } is E ^ { 2 } \frac { d \Phi } { dE } < 6.5 \times 10 ^ { -6 } \mathrm { GeV cm ^ { -2 } s ^ { -1 } sr ^ { -1 } } , independent of the assumed neutrino flavor flux ratio .