RMAN-03002, RMAN-06403, ORA-01034, ORA-27101: shared memory realm does not exist

using target database control file instead of recovery catalog

RMAN-00571: ===========================================================
RMAN-00569: =============== ERROR MESSAGE STACK FOLLOWS ===============
RMAN-00571: ===========================================================
RMAN-03002: failure of allocate command at 01/04/2012 13:25:07
RMAN-06403: could not obtain a fully authorized session
ORA-01034: ORACLE not available
ORA-27101: shared memory realm does not exist

Check your database is running or down by

$ps -ef | grep pmon

sekiazubck05.rman06> ps -ef | grep pmon
oracle 352464           1 0     Jun 16 - 42:56 ora_pmon_dbname
oracle 688150 962658 0 18:17:10 pts/0 0:00 grep pmon

it shows like this, your db is running. otherwise check your instance