Gemara

45b (Mishnah): If a Kohen married a woman forbidden to him, he is Pasul until he vows not to benefit from her.

46a (Beraisa): He vows, does the Avodah, and divorces her after finishing the Avodah.

Question: Perhaps he will go to a Chacham to permit his vow!

Answer #1: Our Tana holds that one must be Mefaret (tell all details of) a vow before a Chacham may permit it.

Question: This is like the opinion that one must be Mefaret a vow. According to the opinion that one need not be Mefaret, how can we answer?

Answer #2: He must vow Al Da'as Rabim (according to the will of many people).

(Ameimar): A vow Al Da'as Rabim cannot be permitted for Reshus, but it can be permitted for a Mitzvah.

Question: If a Kohen (habitually) becomes Tamei Mes, it suffices for him merely to accept not to do so again. If a Kohen married a forbidden woman, why must he vow?

Answer: There is less temptation to become Tamei, so we are not concerned lest he not honor his acceptance.

Gitin 35b (Rav Nachman): If one seeks to permit a vow (through Beis Din), he need not be Mefaret.

If he needed to, sometimes he would omit a detail, and the Heter (permission) would be Pasul, since Beis Din permits only what they hear!

(Rav Papa): He must be Mefaret.

We are concerned lest he seeks to permit a vow in order to transgress!

Erchin 23a (Mishnah - R. Eliezer): If Reuven was Makdish property Meshu'abad to pay his wife's Kesuvah, when he divorces her, he must vow not to benefit from her (lest he schemes to remarry her after she collects from Hekdesh);

R. Yehoshua says, he need not vow.

Suggestion: They argue about a Neder b'Rabim (made in front of many people). R. Yehoshua holds that it can be permitted, so it is useless to force the husband to vow.

Rishonim

Rambam (Hilchos Bi'as Makdish 6:9): If a Kohen married women forbidden to him, he may not serve until Beis Din makes him vow Al Da'as Rabim that he will not sin more. He serves, descends and divorces. If he served before vowing, even though he is married b'Isur, he did not profane the Avodah.

Perush ha'Mishnayos (Bechoros 45b): A mere acceptance does not suffice for one who married a forbidden woman, for his lust compels him. He must vow Al Da'as Rabim, which can be permitted only for a Mitzvah. He cannot permit the vow, for we hold that one must be Mefaret, and the Chacham will ask about the vow.

Question (Maharit 1:142): If so, Al Da'as Rabim does not help for the opinion that does not require detailing the vow! It seems that the Rambam rules like the Amora who does not require detailing the vow. This refers to normal vows permitted through regret or a Pesach (a reason why the vow was a mistake). All require detailing a vow Al Da'as Rabim, so the Chacham can judge if the Mitzvah he wants to do overrides fulfilling the vow. Perhaps the original Perush ha'Mishnayos connoted so, and the intent was distorted in the translation to Hebrew. However, why would the Rambam rule unlike Rav Papa, who is Basra, and the Yerushalmi? All Meforshim rule like them. The Mishnah Torah is not explicit. In Hilchos Shevu'os (6:5) the Rambam connotes that one must be Mefaret and give his reason for regret. Also, if the Rambam rules like Rav Nachman, he should require a widow to vow Al Da'as Rabim, like the Gemara was forced to say for Rav Nachman! In Hilchos Ishus (6:11), the Rambam does not mention Al Da'as Rabim.

Answer #1 (Maharit): Rather, the Rambam requires detailing the vow, but not the reason he vowed. A widow vows to forbid Peros if she already received her Kesuvah. A Kohen merely vows benefit from his wife. The Rambam learned from Erchin 23a. There, we are concerned lest one permit a vow b'Rabim. Tosfos (23a DH Mar) explained that one must detail only the text of the vow, but not why he vowed. In Bechoros, we say that there is no concern according to the opinion that one must be Mefaret (detail) the vow in order to permit it. I.e. the Mishnah (which says that he vows and serves) is not difficult for him. The other opinion must say that we make him vow Al Da'as Rabim. Based on this conclusion, also the one who requires detailing a vow need not say that one must give the reason for it, like we say in Erchin. All say that he vows Al Da'as Rabim. If not, he could tell the Chacham 'I forbade benefit from my wife', and he would permit him. The Rambam does not obligate a widow to vow Al Da'as Rabim. Since she must detail the text of the vow, 'Peros are Asur if I benefited from my Kesuvah', a Chacham would not permit it.

Answer #2 (Pri Chodosh (Mayim Chayim, on Gitin 34b, cited by R. Akiva Eiger OC 128:40)): The Rambam rules that one need not detail the vow. It suffices to say what he swore about. This is why he requires a Kohen to vow Al Da'as Rabim. The Gemara asked that we should be concerned lest a widow vow and ask a Chacham to permit it, and answered that one must detail the vow. The Rambam does not rely on this answer. We hold that one who vowed benefit from Ploni may permit it only in front of Ploni. Therefore, we are not concerned lest a Chacham permit her not in front of the orphans. However, we cannot answer like this for the Shulchan Aruch, which requires detailing also the reason for the vow! Also, what is his source to require vowing after divorcing her? In Bechoros 46a, the Gemara said that we are more stringent about marrying Pasul women than Tum'ah, because there is a greater Yetzer for women. Therefore, even after divorce he must vow.

Rosh (Gitin 4:10): The Halachah follows Rav Papa, who obligates detailing, for he is Basra.

Rashba (Teshuvah 7:21): If a Kohen married a divorcee, we do not treat him with Kedushah, even to read first in the Torah. Even if he divorced her or she died, he is Pasul until he vows Al Da'as Rabim not to benefit from women forbidden to him, like it says in Bechoros.

Rivash (94): If a Kohen does not conduct with Kedushas Kehunah, e.g. he marries a Pasul woman, he forfeits the Kedushah. Chachamim did not refrain from cursing Kohanim of the greatest lineage who acted improperly (Menachos 53b, Yoma 71b). All the more so this applies nowadays, when Kohanim cannot prove their lineage.

Poskim

Shulchan Aruch (OC 128:40): If a Kohen married a divorcee, he may not Duchan (give Birkas Kohanim), and we do not treat him with Kedushah, even to read first in the Torah. Even if he divorced her or she died, he is Pasul until he vows Al Da'as Rabim not to benefit from women forbidden to him.

Beis Yosef (DH Tanan): Regarding Birkas Kohanim, the Poskim did not mention the Pesulim of marrying forbidden women or becoming Tamei. Perhaps this is because if one served before vowing or accepting, he did not profane the Avodah. If so, he may Duchan l'Chatchilah. Regarding one who is drunk, the Rambam said that whenever one is exempt for entering the Mikdash, he may Duchan. He also says that a Kohen who murdered or served idolatry may Duchan. However, Mahari Avuhav forbids a Kohen married to a divorcee to Duchan or receive an Aliyah as long as he rebels. In Siman 135, he learns from the Mishnah of a Kohen married to a divorcee that he or one who (intentionally) becomes Tamei may not Duchan until he vows or accepts. Also the Rashba is stringent. Since the Poskim did not explicitly permit, we follow Mar Shmuel Kohen and the Rashba, who explicitly forbid.

Question (Birkas ha'Zevach (Sof Menachos; this is not found in Asifas Zekenim)): A Kohen who married a woman b'Isur may serve immediately after vowing not to benefit from her. The opinion that one need not be Mefaret obligates him to vow Al Da'as Rabim, lest a Chacham permit it. The Shulchan Aruch (YD 228:14) obligates detailing the vow. Why must a Kohen who married b'Isur vow Al Da'as Rabim?

Answer #1 (Magen Avraham 58): Amora'im argue about whether one must detail the vow. The Gemara did not say whom the Halachah follows. The Rambam and Rashba are concerned lest a Kohen go to a Chacham who holds that one need not detail the vow.

Eshel Avraham: Why do the Rambam and Bartenura obligate the Kohen to vow Al Da'as Rabim? They rule that one must be Mefaret the vow! The Maharit said that one must be Mefaret, but he need not give the reason. However, he still needs his first reason to explain Perush ha'Mishnayos. Perhaps a Kohen will sincerely believe that he permits for the sake of a Mitzvah, i.e. not to divorce his wife. Therefore, he explained that one must detail the vow. Indeed, if one permits improperly (i.e. intentionally - PF), it is not permitted. Tosfos did not ask about one who already divorced his wife, for no one would think that it is a Mitzvah to permit it to enable remarrying her. It seems that the Mechaber disagrees. He requires a vow Al Da'as Rabim even if she died. Tosfos holds that such concern does not apply in such a case. This is good for the Rambam. However, the Rashba and Shulchan Aruch hold that one must detail the reason. Therefore, the Magen Avraham explains that we are concerned lest he go to a Chacham who holds like Tosfos, that one need not give the reason.

Answer #2 (Magen Avraham): Tosfos (Erchin 23a DH Mar) says that the opinion that obligates detailing the vow requires only saying all the words, but he need not say why he vowed. The Rashba and Shulchan Aruch hold that one must say why he vowed, but they are concerned lest a Chacham who holds like Tosfos hear the vow 'I will not marry a divorcee' without hearing the reason or knowing that he is a Kohen. One who hears that a widow vowed 'Peros are forbidden to me if I benefit from my Kesuvah' will not permit it.

Question: Tosfos said that no one will permit a Kohen, for he must vow 'I will not benefit from my forbidden wife!' If we are concerned for a Chacham who holds like Tosfos, we should force a Kohen to vow this text, and not require Al Da'as Rabim!

Answer (Machatzis ha'Shekel): One could do so. Since we must change the vow, the Rambam and Rashba gave a solution that the Gemara mentioned.

Magen Avraham (59): Keneses ha'Gedolah says that the Re'em says that even if he vowed not to benefit from her from now, even if he cannot divorce her due to Ones, even mortal Ones, he may not Duchan and he does not read first from the Torah until he divorces her. This is difficult, for the Gemara says that he vows, serves, descends and divorces!

Kaf ha'Chayim (239): The Magen Avraham did not see the Re'em. The Re'em forbids only when he will not be able to divorce her immediately.

Mishnah Berurah (147): He is disqualified only due to Aveiros that Kohanim are commanded about more than Yisre'elim. Since he profanes the extra Kedushah of Kohanim, mid'Rabanan he is Pasul until he vows Al Da'as Rabim.

Mishnah Berurah (149): Also, he must divorce his forbidden wife. The Shulchan Aruch did not mention this because he discusses the case in which he already divorced her or she died. If he wants to delay divorcing her for a period of time after vowing, he does not Duchan or read first from the Torah.