Question: How does a person thank Hashem for giving him a child?
Answer: Rabbi Shlomo HaKohen, the rav of Vilna (Responsa Binyan Shlomo, vol. 1, pp. 68-70), argues that both parents should, in theory, recite specific biblical verses upon the birth of a child. (Today, uttering verses about korbanot serves as a substitute for offering them.)
The Torah (Leviticus 12:1-12:7) specifically states that a woman was required to bring a korban on the 41st day after the birth of a boy and the 81st day after the birth of a girl. The Talmud (Niddah 31b) explains that she must bring a korban to atone for swearing during labor (due to the intense pain) never to become pregnant again.
Nowadays, in the absence of a Beit HaMikdash, a woman should recite the biblical verses relating to her sacrificial obligation since she can’t offer a korban. (Saying verses relating to a korban is like actually bring that korban, say our Sages.) The father should also recite these verses because a husband is duty-bound to bring any korban his wife is required to bring (Nedarim 35).
Rabbi Shlomo HaKohen ultimately argues against a father reciting these verses for a variety of reasons. The main reason he offers is as follows: Bringing a korban used to involve laying out money. And since husbands were obligated upon marriage to assume all of their wives’ financial obligations vis-à-vis their sacrificial requirements, they were therefore responsible for their wives korbanos. The same cannot be said, though, regarding the recitation of biblical verses, which costs nothing.
In addition, only the mother needed the atonement that the korban offered. Rav HaKohen concludes that mothers of newborn children should recite the suitable biblical verses on either the 41st or 81st day following the birth of their child. Most women, however, are not accustomed to do so.
The Levush writes that a man whose wife gives birth to a girl (and certainly if she gives birth to a boy – see Machtzit Hashekel, Orach Chayim 282) gets an aliyah in shul before a man whose son is about to have a bris if his wife comes with him to shul. The Sefer Panim Me’irot (vol. 2:124) explains that we’re talking about a woman coming to shul for the first time after giving birth, having gained sufficient strength post-birth to do so.
Responsa B’Tzeil Ha’Chochma (vol. 6:78) states: “It is a custom from antiquity that a woman not depart her home after giving birth without first going to the synagogue as a remembrance of the sacrifice she brought post childbirth when our Temple existed.”
She also goes to synagogue so that her husband can say HaGomel (the blessing of thanksgiving one recites after surviving a dangerous situation) on her behalf (as per Berachot 54b).
The Magen Avraham (Orach Chayim 219:1) notes that Kavanat Ha’Ari questions why women themselves don’t recite this blessing (which can even be said without a minyan). He argues that women should, in fact, say this blessing before one or two men. The Magen Avraham suggests that we are lenient and allow the blessing to be said without a minyan because it is not obligatory.
I have personally seen some women say this blessing before other women or quietly on their side of the mechitzah with a minyan. I have never seen a woman recite the biblical verses that Rav HaKohen requires her to say. If anyone has, please contact me.