A person who prays without a Minyan does not have the opportunity to hear the Chazan's declaration of "Barechu Et Hashem Ha'mevorach" or to respond "Baruch Hashem Ha'mevorach Le'olam Va'ed." Is there something else that he can recite instead, so that he can receive some credit as if he heard and responded to Barechu?
The Ben Ish Chai (Rabbi Yosef Chayim of Baghdad, 1833-1909) advises a person in this situation to recite in place of Barechu the Midrashic passage in which Rabbi Akiva describes how an angel named Yisrael declares Barechu in the heavens, and all the other angels respond with "Baruch Hashem Ha'mevorach…" This passage can be recited in place of Barechu when one prays privately.
At which point in the service may one recite this passage?
Chacham Ovadia Yosef addresses this question in his work Halichot Olam (vol. 1, p. 81), focusing on the issue of whether this passage may be recited immediately following Yishtabach, at the point where Barechu is recited in the synagogue. In between Yishtabach and the Beracha of "Yotzer Or," it is permissible to speak in matters involving a Mitzva. Thus, for example, Chacham Eliyahu Chamoui of Aram Soba ruled that one may answer "Baruch Hu U'varuch Shemo" at this point of the service. Similarly, from Rosh Hashanah through Yom Kippur we recite the chapter of Tehillim, "Shir Ha'ma'alot Mi'ma'amakim" at this point. Instinctively, then, we might conclude that one may recite at this point the Midrashic passage in place of Barechu, as well. Chacham Ovadia concludes, however, that this passage should not be recited after Barechu. In his opinion, when one recites this passage, he may not utter God's Name in the phrase, "Barechu Et Hashem Ha'mevorach." Since Barechu may be recited only in the presence of a Minyan, one who recites this Midrashic passage must use the word "Hashem" in place of God's Name. Hence, the recitation of this passage amounts to much less than Barechu itself, and therefore Chacham Ovadia rules that it may not be recited after Yishtabach.
Instead, a person who prays privately should recite this passage before Aleinu, where, in the presence of a Minyan, a second Barechu would be recited.
Summary: One who prays privately, and thus cannot hear or respond to Barechu, can recite in place of Barechu before Aleinu the Midrashic passage that tells of the angels' recitation of Barechu in the heavens. When reciting this passage, one must say the word "Hashem" rather than the actual Name of God.
