diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index e91a25a9e23e8..0dd452c53e3a4 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -115,6 +115,7 @@
 
 if TYPE_CHECKING:
     from pandas import MultiIndex, RangeIndex, Series
+    from pandas.core.indexes.datetimelike import DatetimeIndexOpsMixin
 
 
 __all__ = ["Index"]
@@ -2895,9 +2896,8 @@ def _union(self, other, sort):
 
     @final
     def _wrap_setop_result(self, other, result):
-        if isinstance(self, (ABCDatetimeIndex, ABCTimedeltaIndex)) and isinstance(
-            result, np.ndarray
-        ):
+        if needs_i8_conversion(self.dtype) and isinstance(result, np.ndarray):
+            self = cast("DatetimeIndexOpsMixin", self)
             result = type(self._data)._simple_new(result, dtype=self.dtype)
         elif is_categorical_dtype(self.dtype) and isinstance(result, np.ndarray):
             result = Categorical(result, dtype=self.dtype)
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index d1d6013f8e2ed..3fbb4364d112e 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -612,6 +612,13 @@ def insert(self, loc: int, item):
     # --------------------------------------------------------------------
     # Join/Set Methods
 
+    _inner_indexer = _join_i8_wrapper(libjoin.inner_join_indexer)
+    _outer_indexer = _join_i8_wrapper(libjoin.outer_join_indexer)
+    _left_indexer = _join_i8_wrapper(libjoin.left_join_indexer)
+    _left_indexer_unique = _join_i8_wrapper(
+        libjoin.left_join_indexer_unique, with_indexers=False
+    )
+
     def _get_join_freq(self, other):
         """
         Get the freq to attach to the result of a join operation.
@@ -832,13 +839,6 @@ def _union(self, other, sort):
     # Join Methods
     _join_precedence = 10
 
-    _inner_indexer = _join_i8_wrapper(libjoin.inner_join_indexer)
-    _outer_indexer = _join_i8_wrapper(libjoin.outer_join_indexer)
-    _left_indexer = _join_i8_wrapper(libjoin.left_join_indexer)
-    _left_indexer_unique = _join_i8_wrapper(
-        libjoin.left_join_indexer_unique, with_indexers=False
-    )
-
     def join(
         self, other, how: str = "left", level=None, return_indexers=False, sort=False
     ):
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index 2eda9f9ba41ac..879f2ddbcfcd1 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -31,12 +31,11 @@
 )
 import pandas.core.common as com
 import pandas.core.indexes.base as ibase
-from pandas.core.indexes.base import ensure_index, maybe_extract_name
+from pandas.core.indexes.base import maybe_extract_name
 from pandas.core.indexes.datetimelike import DatetimeIndexOpsMixin
 from pandas.core.indexes.datetimes import DatetimeIndex, Index
 from pandas.core.indexes.extension import inherit_names
 from pandas.core.indexes.numeric import Int64Index
-from pandas.core.ops import get_op_result_name
 
 _index_doc_kwargs = dict(ibase._index_doc_kwargs)
 _index_doc_kwargs.update({"target_klass": "PeriodIndex or list of Periods"})
@@ -580,32 +579,6 @@ def _get_string_slice(self, key: str):
         except KeyError as err:
             raise KeyError(key) from err
 
-    # ------------------------------------------------------------------------
-    # Set Operation Methods
-
-    def _setop(self, other, sort, opname: str):
-        """
-        Perform a set operation by dispatching to the Int64Index implementation.
-        """
-        self._validate_sort_keyword(sort)
-        self._assert_can_do_setop(other)
-        res_name = get_op_result_name(self, other)
-        other = ensure_index(other)
-
-        i8self = Int64Index._simple_new(self.asi8)
-        i8other = Int64Index._simple_new(other.asi8)
-        i8result = getattr(i8self, opname)(i8other, sort=sort)
-
-        parr = type(self._data)(np.asarray(i8result, dtype=np.int64), dtype=self.dtype)
-        result = type(self)._simple_new(parr, name=res_name)
-        return result
-
-    def _intersection(self, other, sort=False):
-        return self._setop(other, sort, opname="intersection")
-
-    def _union(self, other, sort):
-        return self._setop(other, sort, opname="_union")
-
     # ------------------------------------------------------------------------
 
     def memory_usage(self, deep: bool = False) -> int:
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index 21b5841a87ef9..fbc7f578d760e 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -685,14 +685,6 @@ def symmetric_difference(self, other, result_name=None, sort=None):
 
     # --------------------------------------------------------------------
 
-    @doc(Int64Index.join)
-    def join(self, other, how="left", level=None, return_indexers=False, sort=False):
-        if how == "outer" and self is not other:
-            # note: could return RangeIndex in more circumstances
-            return self._int64index.join(other, how, level, return_indexers, sort)
-
-        return super().join(other, how, level, return_indexers, sort)
-
     def _concat(self, indexes, name):
         """
         Overriding parent method for the case of all RangeIndex instances.
diff --git a/pandas/tests/indexes/period/test_join.py b/pandas/tests/indexes/period/test_join.py
index 56ca7a572c49c..e895bb81ea061 100644
--- a/pandas/tests/indexes/period/test_join.py
+++ b/pandas/tests/indexes/period/test_join.py
@@ -8,6 +8,14 @@
 
 
 class TestJoin:
+    def test_join_outer_indexer(self):
+        pi = period_range("1/1/2000", "1/20/2000", freq="D")
+
+        result = pi._outer_indexer(pi._values, pi._values)
+        tm.assert_numpy_array_equal(result[0], pi.asi8)
+        tm.assert_numpy_array_equal(result[1], np.arange(len(pi), dtype=np.int64))
+        tm.assert_numpy_array_equal(result[2], np.arange(len(pi), dtype=np.int64))
+
     def test_joins(self, join_type):
         index = period_range("1/1/2000", "1/20/2000", freq="D")